Raman spectroscopy of biomedical polyethylenes

Accepted Manuscript Review article Raman spectroscopy of biomedical polyethylenes Giuseppe Pezzotti PII: DOI: Reference:

S1742-7061(17)30177-0 http://dx.doi.org/10.1016/j.actbio.2017.03.015 ACTBIO 4783

To appear in:

Acta Biomaterialia

Received Date: Revised Date: Accepted Date:

15 September 2016 1 March 2017 9 March 2017

Please cite this article as: Pezzotti, G., Raman spectroscopy of biomedical polyethylenes, Acta Biomaterialia (2017), doi: http://dx.doi.org/10.1016/j.actbio.2017.03.015

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Raman spectroscopy of biomedical polyethylenes Giuseppe Pezzotti1,2,3,4* 1 Ceramic Physics Laboratory, Kyoto Institute of Technology, Sakyo-ku, Matsugasaki, 606-8585 Kyoto, Japan 2 Department of Orthopedic Surgery, Tokyo Medical University, 6-7-1 Nishi-Shinjuku, Shinjuku-ku, 160-0023 Tokyo, Japan 3 The Center for Advanced Medical Engineering and Informatics, Osaka University, Yamadaoka, Suita, 565-0871 Osaka, Japan 4 Department of Molecular Cell Physiology, Graduate School of Medical Science, Kyoto Prefectural University of Medicine Kamigyo-ku, 465 Kajii-cho, Kawaramachi dori 602-0841 Kyoto, Japan

*Corresponding author: [email protected]; Tel. & Fax: 81-75-724-7568.

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Abstract With the development of three-dimensional Raman algorithms for local mapping of oxidation and plastic strain, and the ability to resolve molecular orientation patterns with microscopic spatial resolution, there is an opportunity to re-examine many of the foundations on which our understanding of biomedical grade ultra-high molecular weight polyethylenes (UHMWPEs) are based. By implementing polarized Raman spectroscopy into an automatized tool with an improved precision in nondestructively resolving Euler angles, oxidation levels, and microscopic strain, we become capable to make accurate and traceable measurements of the in vitro and in vivo tribological responses of a variety of commercially available UHMWPE bearings for artificial hip and knee joints. In this paper, we first review the foundations and the main algorithms for Raman analyses of oxidation and strain of biomedical polyethylene. Then, we critically re-examine a large body of Raman data previously collected on different polyethylene joint components after in vitro testing or in vivo service, in order to shed new light on an area of particular importance to joint orthopedics: the microscopic nature of UHMWPE surface degradation in the human body. A complex scenario of physical chemistry appears from the Raman analyses, which highlights the importance of molecular-scale phenomena besides mere microstructural changes. The availability of the Raman microscopic probe for visualizing oxidation patterns unveiled striking findings related to the chemical contribution to wear degradation: chain-breaking and subsequent formation of carboxylic acid sites preferentially occur in correspondence of third-phase regions, and they are triggered by emission of dehydroxylated oxygen from ceramic oxide counterparts. These findings profoundly differ from more popular (and simplistic) notions of mechanistic tribology adopted in analyzing joint simulator data. Keywords: Raman spectroscopy; artificial joints; polyethylenes; in vitro testing; in vivo service

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1. Introduction A large number of investigators have focused their research on analyzing in vitro tested or explanted joint components by a variety of different experimental techniques, with the commitment to conceive new data-driven strategies and rigorous evaluations of surface and sub-surface degradation phenomena.[1-5] Soft polyethylene sliding counterparts have so far appeared as the weakest link in the chain of artificial joint functionality, which has intrinsically hindered the extension of artificial joint lifetime to several decades. Yet, with several successive generations of joint biomaterials showing yet insufficient progress in lifetime elongation to cover the needs of increasingly younger patients, it is felt that new criteria are needed in material design, and improved analytical probes should be searched for characterizing the complex phenomena dominating the tribological behavior of biomedical polyethylenes at the molecular scale. If lifetime elongations up to several decades must be challenged in artificial joint materials, we must develop quantitative methods to move forward and probe beyond today’s “mechanistic” models of joint tribology, merely based on kinematics similarity. Only following a more nuanced model of physical chemistry that could better align with the complex nature of the human joints’ environment, we can succeed in further advancing the realization of long-lasting artificial hip and knee joints. Foundations thus need to shift from a mechanistic/phenomenological approach of macroscopic wear measurements (i.e., the one prevailing nowadays) toward a more comprehensive (and interactive) view including notions of solid-state chemistry, crystallography, and micromechanics, which better fit the microscopic events taking place at the bearing surface and beneath it in the severe environment of human joints. As practiced today, in vitro evaluations in joint simulators establish a criterion of “equivalency” to in vivo conditions according to the number of cycles to which the joint components are exposed. [6] Specifications about gait kinematics and lubrication conditions have thoroughly been standardized, wear rate as a function of the number of cycles being their main output. However, no emphasis has yet been placed on chemical, crystallographic, and micromechanical factors, which are key in frequently observed discrepancies between in vitro and in vivo performances. It is implicitly assumed that the in vivo lifetime is the consequence of a cyclic progression of tribological bits that can be rationalized, simulated, and repeated. However, the clinical experience has long shown that the joint performance is often unpredictable and multifaceted since triggered by strongly non-linear events of chemical and crystallographic nature. Unfortunately, in vitro simulations conspicuously fail in addressing such events. Nowadays, principles of materials selection and characterization are locked into the outputs of such rigidly standardized procedures, and the forced simplicity of the adopted models often misleads researchers to overlook the complex dynamics of the joint tribolayer. One of the main aims of this review paper has been that of comparing polyethylene surfaces after in vivo service in the human body with those undergoing an “equivalent” number of cycles in the hip simulator. The comparison shows that an upgraded approach is needed in evaluating biomaterials for joint arthroplasty. This author believes that in vitro standards for tribological tests should 3

be complemented with and, subsequently, improved in view of an analytical screening at the molecular level. Such an improved approach will not only give deeper insights into surface degradation phenomena, but also validates the “equivalency” criterion adopted for the simulator testing procedure through a comparison with in vivo exposed samples. Nevertheless, having said that, how could such a molecular-level screening be efficiently accomplished? The practice of Raman spectroscopy in biomaterials’ science has undergone substantial advancements over the past two decades,[7] yet even its most committed theorists and practitioners - myself among them - have often failed to extract from it quantitative and directly applicable notions. As in the case of any other analytical method, the more the probing procedure embraces multiple variables of different nature, the clearer the probe limitations become. Such a complexity indeed applies to artificial joint components that operate in the human body. However, Raman spectroscopy can be quite effective in characterizing biomaterials for artificial joints. It is particularly suitable for UHMWPE components, whose chemical, crystallographic, and mechanical evolution in service is crucial to the lifetime of the joint implants. However, resulting from fine interplays and overlaps of multiple reciprocally dependent factors, in vivo tribological loading of joint biomaterials might lead to counterintuitive spectroscopic outputs. UHMWPE acetabular liners in hip joints or tibial plates in knee joints can be mated either to metallic or to ceramic components. Either the case, artificial joints employing various tribological combinations are classified as “hard on soft” implants. The main consequence of articulating soft polyethylene against a hard counterpart is surface wear, liberating wear debris. Osteolysis (a detrimental consequence of wear debris) is the major cause for a significantly reduced lifetime in artificial joint implants.[8, 9] Despite progresses in material manufacturing, the UHMWPE components have long been considered the “weak link” of the chain in joint arthroplasty.[10] Accordingly, manufacturers have aggressively pursued through the years minimization in the release of wear debris. In particular, radiation cross-linking has been successful in minimizing wear debris and in prolonging the lifetime of joint implants in terms of aseptic loosening. Although there is still a lot of unpredictability in the damage observed in implants, there is a strong correlation between wear rate, time in vivo and aseptic loosening due to polyethylene debris in conventional UHMWPE. The purpose of this article is to review and implement further protocols and quantitative algorithms of polarized/confocal Raman spectroscopy in support to advanced microstructural characterizations of UHMWPE components. It is believed that Raman spectroscopy could provide a unique tool for quality control of the biomedical polyethylene components released on the market, which will ultimately lead to a better performance in vivo. It will be shown that this vibrational method has great potential in elucidating microstructural details of chemical, crystallographic, and micromechanical nature, whose interplay is yet conspicuously unknown and left aside in current standardizations. The challenge here is to bring the theory of the Raman effect applied to biomedical polyethylenes to quantitative and statistical algorithms capable to extract crystallographic, oxidative, and micromechanical information at the molecular level from the Raman spectrum of polyethylene. After experimental details being giv4

en in the following Section 2, the first part of the paper (i.e., the five sub-sections of Section 3) will lay the theoretical foundations of the Raman emission from polyethylene, with details of the Raman probe morphology and response functions in a polyethylene medium being set apart in the dedicated Appendix A. Based on these developments, we then proceed to the clarification of crystal orientation, oxidative modifications, and mechanical strain of UHMWPE structures at the molecular scale. In this review, extensive comparisons are carried out between Raman data and data collected at the same locations by the well-established Fourier Transform Infrared Spectroscopy (FT-IR) method as a function of depth away from the sliding surface. The importance of adjusting probe differences and validating the Raman approach through a comparison with FT-IR resides in the possibility of using Raman in fully nondestructive evaluations, whereas FT-IR in transmission mode mandatorily requires sample slicing and manipulation. Given the high transparency of polyethylene to visible light, in depth analyses could then be carried out down to depths of several millimeters in a fully non-destructive way. We also offer in Section 4 a description of the salient properties of commercial UHMWPE components of hip and knee joints. This latter section describes the in vitro and in vivo performances of UHMWPE joint components manufactured by different makers and belonging to successive generations. The subsequent Section 5 reviews and evaluate some recently launched innovative ideas to improve the wear performance of biomedical polyethylenes for artificial joint components. Sub-sections 3.1 and 3.5 contain somewhat cumbersome theoretical descriptions, which serve for rigorously justifying a number of algorithms applied in the applicative Section 4. The author considers such theoretical expansions a fundamental step in lifting the characterizations of biomedical UHMWPEs to a long-missing quantitative level. However, care was taken in enabling the not interested Readers to skip the details of those theoretical sections and yet to be able to follow the contents of the applicative sections. 2. Experimental procedures The Raman equipment used throughout our studies is a typical instrument developed in the late 1990s (T-64000, Horiba/Jobin-Yvon, Kyoto, Japan), although now much more empowered as compared to those early devices by means of the attached software packages, including a remarkable capacity in data storage, spectral fitting, and analytical manipulations. All the Raman spectroscopic experiments showed in this review paper were carried out at room temperature in backscattering configuration. A triple monochromator was equipped with a multichannel liquid-nitrogen-cooled CCD camera, a confocal pinhole and polarization filters. A quite high level of laser straylight rejection, as compared to standard notch filter configurations, represents another key feature of the used equipment. Moreover, the use of the triple additive monochromator configuration made it possible to achieve a quite high spectral resolution (better than 0.15 cm-1) and, thus, to accurately detect the position of Raman bands and to clearly discern their separation. The equipment included a set of holographic diffraction gratings 600 gr/mm, 1800 gr/mm, and 2400 gr/mm and the dispersion at a 5

wavelength of 600 nm with the lattice 1800 gr/mm in subtraction mode was 0.64 nm/mm, while in addition mode 0.21 nm/mm. This intrinsically high spectral resolution could be further improved by systematically collecting, together with each Raman signal emitted by the sample, a signal from a neon lamp suitably selected in the spectral region of interest. This latter signal, external to the sample, served as an internal calibration source against local fluctuations of the spectrometer apparatus (i.e., due to room temperature or electrical noise). In some cases, the employed Raman device was also used with a single-type monochromator configuration. This latter configuration enabled enhancing measurement speed (i.e., especially useful in the collection of large Raman maps), and signal intensity in weakly scattering samples. Single monochromator measurements were suitable when the output of the spectroscopic assessments was limited to Raman intensity measurements, and especially during collections of maps at high spatial resolution in polarized/confocal configurations. The excitation source used in the present experiments was a 488 nm blue line of an Ar-ion laser (Stabilite 2017, Spectra-Physics, Mountain View, CA, US) or a 532-nm Nd:YVO4 diode-pumped solid-state laser (SOC JUNO, Showa Optronics Co. Ltd., Tokyo, Japan). An objective lens with magnification x100 and with a numerical aperture NA=0.7 was used throughout the Raman experiments to focus the laser beam at (or below) the sample free surface, as well as to successively collect the scattered Raman light. Raman experiments were always conducted in a confocal probe configuration, with the pinhole aperture of the optical circuit set to 0.1 mm. Typical measurement conditions by means of a confocal x100 objective lens required a higher laser power of 100 mW applied for 5 s through two or three successive (cumulative) acquisitions. On the other hand, the maximum laser power focused on the sample area was in the order of 20~35 mW for all the investigated materials, which enabled us to minimize sample modifications arising from laser irradiation and, in particular, to preserve the pristine crystallographic structure of the samples owing to a controlled local heating up of the laser irradiated zone. A goniometric jig served to collect Raman bands at a fixed spatial location with rotating the sample under polarized light in the selected configuration. Polarized Raman measurements were made by acquiring spectra with either parallel or cross polarization with respect to the inherent polarization of the excitation laser. Polarized spectra could be obtained by inserting a polarizer (i.e., a polarization filter) in the beam path of the diffracted light between the sample and the spectrometer, thus allowing the selected configuration. On the other hand, polarization of the laser beam was kept in its normal state without further manipulations. During polarized light acquisitions, a half-wave plate was employed to compensate for the polarization dependence of the monochromator. Spatially resolved maps were collected using a motorized automatically (computer-) driven stage with the spatial resolution of 10-4 mm. Spectral Raman lines were analyzed using a commercially available software package (LabSpec 4.02, Horiba/Jobin-Yvon, Kyoto, Japan). Spectral fitting was performed according to Voigtian (i.e., mixed Gaussian/Lorentzian) functions after systematically subtracting a linear baseline. Except for spectral fitting, all the computational procedures shown throughout this review were carried out with the aid of commercially 6

available computational software (MATHEMATICA 7.0, Wolfram Research, Inc., Champaign, IL, US). For comparisons of the oxidative state, oxidation profiles of UHMWPE were also determined on microtomed sections by using FT-IR as a function of depth away from the sliding surface. FT-IR microscopic analyses were carried out using the imaging system Spotlight 200 (Perkin Elmer, Waltham, Massachusetts, USA). FT-IR spectra of polyethylene were acquired at aperture size of 200×200 µm2. An oxidation index (OI) was calculated according to ASTM 2102 as the ratio of the area under the carbonyl peak at around 1720 cm-1 to the area under the C-H absorption peak centered around 1370 cm-1.[11] For stoichiometric comparisons, the surface of some or the investigated UHMWPE samples was also studied by means of X-ray photoemission spectroscopy (XPS). In these assessments, we used a photoelectron spectrometer (JPS-9010 MC; JEOL Ltd., Tokyo, Japan) with an X-ray source of monochromatic MgKα (output 10 kV, 10 mA). The surface of the samples was cleaned up by Ar+ sputtering in the pre-chamber, while the measurements were conducted in the vacuum chamber at around 2×10-7 Pa, upon setting the analyzer pass energy to 10 eV and the voltage step size to 0.1 eV. The X-ray angle of incidence and the takeoff angle were 34° and 90°, respectively. Regarding the investigated samples, their specifications are given in each specific sub-section. All the retrievals investigated were either analyzed within few days from explantation or stored in vacuum seals and refrigerated, so to minimize oxidative alterations on shelves post-surgery. 3. Theoretical foundations and working algorithms 3.1 Raman emissions from different polyethylene mesostructures The interpretation of the Raman spectrum of polyethylene requires, as in the case of inorganic crystals, the knowledge of the structure of the elementary molecule. The structure of UHMWPE consists of very long chains of CH2 groups (i.e., (-CH2-)n ), which one could foresee, in first approximation, of infinite length. How-ever, the order in which such multitude of long chains assemble in the polymeric structure is key in Raman emission. UHMWPE chains may exist in two main configurations, crystalline and amorphous, in addition to an intermediate structure referred to as the “third phase” (Fig. 1(a)).[12-14] The amorphous structure can be represented with a sort of random coil with several gauche bonds, while the “third” phase consists of an assembly of chains mainly of the trans conformation, but yet lacking the regular packing of the crystalline phase (Fig. 1(a)). The intermediate phase is non-crystalline but represents the continuation of crystallized macromolecules across the crystal/amorphous phase boundaries. In these peculiar areas, amorphous portions of macromolecules possess a lower mobility as a consequence of the constraint imposed by the neighboring crystalline structures. Accordingly, this intermediate phase has also been referred to as the “rigid amorphous fraction” as counterposed to the unconstrained amorphous phase, which is usually addressed as the “mobile amorphous fraction”.[12] In a crystalline structure, the chains are found in a planar zigzag configuration (Fig. 1(b)), 7

while in an amorphous structure the chain configuration is essentially random and only restricted by the conservation of bond angles and distances (Fig. 1(c)). Figure 1(c) also shows that chains in the amorphous regions can be bridged to each other through the so-called crosslinking bonds, which are simply C-C molecular connections between neighboring polyethylene chains. Accordingly, an extensive presence of crosslinking produces a complex (and partially strained) three-dimensional network in the material, making stiffer the polyethylene structure, as the constituent chains more difficultly separate under stress (cf. red segments representing crosslinking bonds in the illustrative draft of Fig. 1(c)). The crosslinking phenomenon is tightly related to the important issues of aging and oxidation in polyethylene structures, which will be discussed in more details later in this section. On the other hand, the amorphous configuration is supposed to be completely disordered, but it might become partially aligned when the sample is stretched. According to the concurrent existence of intermediate structures between perfectly aligned and fully disordered ones, the Raman spectrum of polyethylene should be the superposition of spectra from three different types of chain configuration. However, the Raman spectrum emitted from a completely amorphous region should obey no selection rules, while selection rules should rigorously be observed by the highly symmetric chain arrangements of the crystalline regions and survive, although partly violated, in regions of third phase. Crystalline regions in polyethylene are assembled according to precise geometrical characteristics (0.255 × 0.494 × 0.741 nm3; cf. Fig. 1(b)), and the essential features of the Raman spectrum of polyethylene can be derived from pure molecular symmetry considerations, thus by simply considering one isolated molecule. Actually, a morphological translation of the model to the case of the full unit cell can only have the effect of splitting the frequencies of the isolated molecule, but such split can be assumed to only occur by a small (negligible) amount. However, depending on symmetry characteristics, a possible alteration of some selection rules might also take place. In a polyethylene structure, the repeating unit in a single infinitely long chain basically consists of two CH2 groups. This elementary unit is shown in Fig. 2(a), while Fig. 2(b) represents a cross section of the skeletal structure of the orthorhombic polymorph of the polyethylene crystal. In the former figure, the symmetry elements in the repeating unit are shown, which can be listed as follows: (i) a translation along the chain, which is the identity, E; (ii) a mirror plane in the plane of carbon chain, σh; (iii) mirror planes in the planes of the methylene groups, σv; (iv) twofold axes bisecting the methylene groups, C2 ; (v) twofold axes bisecting the C-C bonds and perpendicular to σh, referred to as
 ; (vi) centers of inversion at the midpoints of the C-C bonds, i ; (vii) a twofold screw axis, denoted by
̅ , lying along the chain axis; (viii) a glide plane, referred to as  , containing the chain axis, and perpendicular to σv and σh; and, (ix) a pure translation,  , along the chain axis. The symmetry operations that apply to the linear structure of polyethylene are also schematically drawn in Fig. 2(a). The multiplication table for the factor group, Vh (line), is given in Table I, which was obtained by applying line-group operations on a single repeating unit. Any operation, which had the effect of completely translating a repeating unit into the next, was taken 8

as an identity. It could easily be shown from the multiplication table that the factor group for polyethylene is isomorphous with point group V ≡  . The set of symmetry elements { ,
̅ ,  } actually defines a factor group, in terms of which the spectroscopic behavior of polyethylene can be analyzed in a similar way as usually done for inorganic crystals.[15, 16] Among the possible Brillouin zones for the orthorhombic structure, the one appropriate for the polyethylene structure is the base centered one depicted in inset to Fig. 2(a). The group-theory analysis implies that only those vibrational modes in which all polyethylene unit cells move in phase can become infrared or Raman active. The factor group for a single polyethylene chain was found to be isomorphous with the point group D2h, and the character table for this point group is given in Table II. Shown in this table, as derived from the factor group analysis, are the number of normal modes and the selection rules in both infrared and Raman spectra under each symmetry species. The normal modes were classified into “skeletal” C-C vibrations, “external hydrogen” vibrations of CH2, and “internal hydrogen” vibrations of CH2. These modes are explicitly shown in Fig. 2(c). The number of normal modes, n i, under any given symmetry species is also shown as they diversify into pure translations, T, translatory type vibrations, T’, rotatory type vibrations, R’, (which includes a pure rotation Rx) and internal vibrations, n’. Among the 3 × 6-4=14 normal modes of the repeating unit of polyethylene, there are 5 infrared active fundamental frequencies, 8 Raman active fundamental frequencies, and one frequency inactive in both infrared and Raman spectra. Note also that the frequencies that are active in the infrared are actually inactive in the Raman spectrum, and vice versa. In other words, the so-called mutual exclusion rule holds for the polyethylene structure. Carrying the factor-group notions one step further, one can also deduce the approximate physical nature of the vibrational modes from the symmetry properties of the various species (i.e., by reviewing the vibrational modes of small molecules, as depicted in Fig. 2(c)). It becomes then evident that the relative amplitudes of motion of the various atoms are not determinable from symmetry considerations alone, but depend upon the particular masses and on the intramolecular force field. The normal modes of the component CH2 groups are, however, well known, and so also the relative phase of the motion in neighboring.[17, 18] The vibrational modes can, therefore, be very closely approximated by the above procedure. The derivation of the normal modes of the chain from those of the component CH2 groups leads to a natural classification of the physical nature of the chain modes in terms of the corresponding group modes. This classification, also listed in inset to Fig. 2(c), is now the one more generally adopted by researchers working in the field of Raman spectroscopy of polymers. The space group for orthorhombic polyethylene is the Pnam- , with two chains passing through each unit cell.[19] The factor-group operations of this space group are the identity, three two-fold screw axes, two glide planes, one mirror plane, and a center of inversion (as already shown in Fig. 2(a)). The factor group is thus isomorphous with Vh. Among the factor-group operations, the mirror plane, a screw axis, the center of inversion and identity leave invariant the axis of gravity of any

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chain. These operations constitute the factor group isomorphous with C2h. On the other hand, the site sub-group, which leaves any given wavenumber vector invariant, is found to be isomorphous with C2. The character table for the orthorhombic structure of crystalline polyethylene is given in Table III, together with the number of normal modes, and the selection rules. According to Table III, 36 frequency branches can be found for the orthorhombic crystal of polyethylene, which can be classified as: (i) three acoustic translational modes, (ii) three translational lattice modes, (iii) two rotational lattice modes; and, (iv) twenty eight internal vibrational modes. The irreducible representation at the Γ point of the base centered orthorhombic Brillouin zone (cf. Fig. 2(a)) thus becomes:[20, 21]

Γ = 3 + 2 + 2 + 

(1)

If one focuses with the fundamental modes of an infinitely long chain of CH2 groups, the finite length and the branched nature of the polyethylene chains are neglected. Both of these features might account for the presence of CH3 groups, which can also contribute appreciably to the observed spectrum. Since the CH3 groups are essentially randomly located in structure, their fundamental frequencies are likely to lack sharp selection rules. However, one could expect to find in the spectrum frequencies assignable to the stretching, bending, wagging, and rocking modes of the hydrogen atoms in the CH3 group. Moreover, from crystalline areas, skeletal vibrations can also be found, in which CH2 groups move as a unit along the three directions of a Cartesian frame fixed to the orthorhombic structure. Figure 3 shows and Table IV summarizes the main features of the polarized Raman spectrum of a highly oriented polyethylene fiber in the frequency interval 1000~1500 cm-1. Band labeling was made according to Eq. (1) and considering the band assignments shown by previous investigators.[18, 22-27] The in-plane-rotation Euler angle, ψ, (in inset to Fig. 3) was taken with reference to the long axis of the fiber and the angular dependence of the Raman intensities will be discussed in detail in a successive sub-section. A close-form mathematical analysis of the Raman spectrum of polyethylene becomes feasible when it is limited to take into account the eigendisplacements with their tensor axes coincident with the axes of the structural units, namely only the modes with Ag and B1g symmetry, while neglecting the B2g or B3g modes. Polymer spectroscopists are used to divide the Raman spectrum of polyethylene in the range between 950 and 1600 cm-1 into three main regions (cf. also Fig. 3): Region I, which is dominated by the C-C stretching vibrational mode and localized in the interval 9501150 cm-1; Region II, mainly represented by the twisting vibrations of the unit -CH2-, located at around 1305 cm-1; and Region III, which is characteristic of the -CH2bending mode between 1350 and 1500 cm-1. The in-phase skeletal stretching vibration of the C-C bonds in the extended polyethylene molecule emits at 1130 cm-l, and represents the symmetry properties of both Ag and Blg species. Interestingly, this frequency approximately coincides with that theoretically calculated for the normal-mode frequency of a single chain,[28] and is also 10

consistent with the C-C skeletal vibrations of n-paraffins. In this latter case, the frequency of C-C stretching vibration for molecules having one or two gauche bonds was the same as that of the fully extended molecule.[26, 29] Therefore, the intensity of the 1130 cm-l band can be considered to be associated with all-trans C-C bonds, independent of whether these bonds are located in the crystalline or in the amorphous phase. The 1080 cm-l band (labeled as A* in Fig. 3) can be assigned to stretching of the C-C skeleton in different kinds of gauche structure,[26, 29, 30] i.e., primarily from the amorphous part of the polymer and from the folds between adjacent planar zigzag sequences in the crystalline phase. In principle, therefore, it contains crystallographic information about the amorphous phase.[31] However, in the majority of biomedical polyethylene samples, the intensity of this band is too low for accurate morphological analyses, due to their high crystallinity. The band at 1170 cm-l possesses the Ag+B1g symmetry and results from the rocking displacements of the CH2. As in the case of the 1130 cm-l feature, this band mainly arises from the crystalline part of the polymeric structure. However, trans C-C bonds are also expected to emit from the amorphous phase, although in a rather weak way, and to contribute the scattered intensity at this frequency. An early study[31] has used this band to calculate the orientation of the crystalline part of samples of low-density polyethylene, since it is clearly visible for certain polarizations, but it is almost completely extinguished in others. The origin of the bands due to the CH2 bending modes of polyethylene around 1450 cm-l is even more ambiguous because of the possibility of Fermi resonance between the Raman active CH2 bending modes and the first overtones, as well as the possible combinations of the infrared active CH2 rocking modes.[22, 27] Nevertheless, it has been shown that orthorhombic polyethylene, which contains two structural units per unit cell, undergoes factor group splitting of the CH2 mode, and as a result, two Raman components are seen at 1418 and 1440 cm-1.[32] The 1418 cm-l band is well separated from any other component of this spectral region and, recently, it has been successfully used to determine online at the manufacturing site the crystallinity polyethylene fibers.[33] According to the hypothesis of coexistence for melted and solid (or “third”) amorphous phases,[13, 14] two broad bands were assigned to these phases at 1460 and 1440 cm-l, respectively. Emissions from these two distinct phases are thus different from that of the orthorhombic crystalline phase at 1418 cm-l. With the broad band at 1080 cm-1 being associated with the presence of an amorphous phase, the band at 1414 cm-1 being instead solely characteristic of the orthorhombic phase (i.e., the almost totality of the crystalline phase), and the band at 1293 cm-1 being representative of the overall degree of crystallinity of the UWMWPE structure,[34-39] the fractions of amorphous (αa) and crystalline (αc) phases can be calculated from the Raman spectrum, according to the following equations:[36]  = !.#$( , = 

 

&'()(* )

(2)

(*

&'( )(*

(3)

11

where I is the integral intensity of each individual Raman band identified by the subscript (i.e., after spectral deconvolution). Note also that the sum (αa+αc) might locally be <1, because of the presence of the “third” phase. Accordingly, the fraction of this intermediate phase, αt, can be expressed as follows: - = 1 − (, +  )

(4)

As already mentioned, the Raman band located at around 1414 cm-1 is specifically characteristic of an orthorhombic crystalline phase, among other possible crystalline polymorphs. Thus, this feature of the Raman spectrum makes it possible to quantitatively analyze the volume fraction of orthorhombic phase, αo, according to the following equation: 0 = !.2(

11

&'( )(* )

(5)

Equations (2)~(5) constitute the basis of the Raman spectroscopic method for characterizing the partially crystalline structures of the UHMWPE. 3.2 Raman selection rules to probe crystal orientation in polyethylene The intrinsic symmetry of the orthorhombic polyethylene molecule dictates the relative intensity of its Raman bands as a function of three Euler angles in space (cf. variations of the Raman intensities of the polyethylene fiber in Fig. 3 as a function of inplane rotation angle, ψ). The three Euler angles define the orientation of the principal axes of the crystal structure with respect to a (reference) laboratory’s Cartesian frame. This relationship is of a tensorial nature and represents the foundation for quantitative Raman crystallographic assessments. The inherent properties of a phonon with respect to Raman scattering are described by a second-rank Raman tensor, ℜ, namely a quantity that is represented by a 3x3 matrix of Raman tensor elements (RTE).[40, 41] The tensor, ℜ, is related to an expansion of the polarizability tensor in powers of the scalar amplitude of the vibrational displacement of the lattice (to first order). Therefore, the polarizability tensor described in the classical quantum mechanics theory and the Raman tensors used in this review are simply related through a direct proportionality relationship. Upon exploiting the symmetry properties of the phonons, one can deduce the number of independent components among the nine components of the second-rank Raman tensor. In the case of the orthorhombic crystal, the number of independent components is six, given by the symmetry of the structure. The Raman tensor formalism is based on the simple concept that different phonon branches in a crystal will correspond to different symmetries of vibration and will, thus, be conditional on irreducible representations of the space group of the studied crystal lattice. The selection rules for Raman-active phonons can be determined by standard methods of group theory, while the intensities of Raman-scattered radiations can be rationalized according to the directions of polar12

ized incoming/scattered monochromatic light with respect to the principal axes of the investigated crystal.[40, 41] In other words, an experimental collection of polarized Raman spectra from known crystallographic planes might serve as a means for providing physical insight into the actual symmetry properties of phonon branches or, vice versa, the knowledge of the selection rules for the investigated crystal can be applied to quantitative assessments of unknown crystallographic directions. Based on our previous studies,[42, 43] a quantitative determination of the RTE constants for orthorhombic polymorph of polyethylene is given hereafter. Polarized Raman experiments can be defined according to the so-called Porto formalism,[44] namely by means of two distinct systems of Cartesian axes associated with the incoming and scattered radiation, and described by a total of four rotational indexes. The formalism, expressed as i(kl)j, refers to incident light propagated along the i direction with its electric vector in the k direction, and Raman scattered light collected along the j direction with the analyzer so placed that it passes light with the electric vector aligned along the l direction. In other words, the symbols outside and inside the brackets refer to the directions of light propagation and of the electric vector, respectively. The relative intensities of a given Raman mode can then be described, as follows: 4 ∝ 6789 ℜ8: 7, 6



(6)

where I is the scattered Raman intensity, ℜ8: is the second-rank Raman tensor of the orthorhombic structure; and ein and esc are the unit polarization vectors of the electric field for incident and scattered light, respectively. In all the experiments described in the remainder of this review, the polarization of the incident light was fixed (i.e., parallel to the y-axis), while both parallel and cross polarizations were applied to the (Raman) scattered light in a backscattered geometry. Such configurations correspond to Porto notations: ;(<<);̅ and (=<);̅ , respectively (cf. Fig. 4(a) for our choice of Cartesian axes and Euler angles for the vibrational modes generated in the orthorhombic structure of a highly aligned polyethylene fiber). The configurations expressed as ;(<<);̅ and ;(=<);̅ will be henceforth simply denoted as “parallel” and “cross” polarized configurations, respectively. The unit polarization vectors can then be explicitly expressed in Cartesian coordinates: 789 (=, <, ;) = (0

0 1 ∥ (=, B (=, ), @ A @ 7 <, ;) = , 7 <, ;) = 1 0 1 0A , , 0 0

(7)

where the superscripts, // and ┴ , refer to parallel and cross configurations, respectively. Equation (6) shows that the intensity of the Raman scattering inherits the symmetry of the crystal structure through the morphology of the second-rank Raman tenG DEF , sor. Taking now into account the matrix of Euler angles, ΦDEF , and its inverse, Φ which enable one to transform the Cartesian system of coordinates associated to the 13

crystallographic frame into that of the laboratory frame, the back-scattered intensity of any Raman band can be expressed as: ℜ8:

(D,E,F)

(H,I,J) G

= ΦDEF ℜ8:

ΦDEF

(8)

where the transformation matrix of Euler angles and its inverse are given as: ΦDEF = cos N cos O cos P − sin O sin P @− sin O sin P − cos N cos O sin P sin N cos O

cos N sin O cos P + cos O sin P cos O sin P − cos N sin O sin P sin N sin O

− sin N cos P sin N sin P A (9) cos N

cos N cos O cos P − sin O sin P − sin O cos P − cos N cos O sin P sin N cos O G DEF = @cos N sin O cos P + cos O sin P cos O cos P − cos N sin O sin P sin N sin O A (10) Φ − sin N cos P sin N sin P cos N

With 0 ≤ θ ≤ π, 0 ≤ φ ≤ 2π, and 0 ≤ P ≤ 2π. Euler angles (N, O, P), the Cartesian coordinates of the crystal system, (X, Y, Z)≡ (Xcry, Ycry, Zcry), and laboratory system coordinates, (x, y, z) ≡ (xlab, ylab, zlab), as defined for the orthorhombic structure of polyethylene, are shown in Fig. 4(a). Substituting for Eqs. (8)~(10) in Eq. (6), and introducing the Raman tensor, ℜ8: XYZ (H

,IXYZ ,JXYZ )

, pertaining to the investigated crystal struc-

ture, it is possible to obtain a series of independent periodic equations in the three Euler angles, which represent an expansion of the so-called Raman selection rules and fully describe the angular dependences in space of the intensity of the Raman modes for any given crystal structure. Orthorhombic polyethylene (single-crystal) lamellae possess a thickness that ranges from 5 to 25 nm and the lateral dimensions from 1 to 50 µ m. The multi-scale structure of UHMWPE is shown in Fig. 4(b) together with our choice of Euler angles for the RTE analysis using a polyethylene fiber. As seen from the figure, the planar zigzag carbon chains of the polyethylene molecules are parallel to the crystallographic caxis in the orthorhombic unit cell of the crystal, which in turn is perpendicular to the long axis of the crystalline lamellae. The strict regularity of molecular packing in polyethylene lamellae forms a “crystal” in the most conventional sense. A confirmation of such assertion has been provided by electron diffraction experiments, which have indicated how molecular chains are always nearly perpendicular to the flat surfaces of the lamellae,[45, 46] with one more detailed investigation[47] showing that the molecular chains could incline up to 30o with lamellar faces in some particular case. The fact that the molecular chains should essentially be perpendicular to the lamellar surfaces implies that the long chain molecules must be folded back and forth many times on a plane perpendicular to the rhombus (lozenge in technical terms)[48] surface of the lamellae (cf. Figs. 1(a) and 4(b)), because more than 90% of the molecules are many times longer than the lamella thickness.[45] Polyethylene fibers usually possess the orthorhombic structure, although the degree of crystallinity might vary according to the adopted spinning conditions.[49] During 14

stretching of the melt, lamellar polyethylene crystals nucleate and grow epitaxially on fibril nuclei generated by the tensile straining and orientation of the melt. If the stress is low, the lamellar crystals are prone to twist, as they grow outward from the fibril nucleus.[50] On the other hand, crystallization at higher stress levels is associated with negligible twist of the crystalline lamellae. In our Raman calibrations, the investigated sample was a monofilament of a commercially available ultrahigh molecular weight polyethylene fiber (manufactured by Ningbo Dancheng Advanced Materials Co. Ltd.; Zhejiang, China) with crystallinity as high as 99.8%, according to Eq. (2). Accordingly, we neglected the effect of the amorphous fraction on the Raman spectrum and considered the highly aligned fiber structure as a “single-crystal” sample. The Raman tensors for an orthorhombic structure belonging to the space group Pnam are given as:[41] ℜ[\

^ = ]0 0

0 0 0 _ 0] , ℜa\ = ]b 0 ` 0

b 0 0

0 0 0 0] , ℜa&\ = ]0 0 7 0 0

0 0 0 7 0] , ℜa(\ = ]0 0 c] (11) 0 c 0 0

where a, b, c, d, e and f are six independent RTE constants. However, since we are mainly concerned here with the Ag and B3g vibrational modes, the Raman tensor elements of interest in our analyses will be a, b, c, and d=f. The dependence of both Ag and B3g modes on the Euler angles locating the c-axis of the orthorhombic structure in space can be expressed in the laboratory system of Cartesian coordinates, xyz, (cf. draft in Fig. 4(a)). The resulting Raman intensities for Ag, B2g, and B3g modes can be expressed as periodic functions of the Raman tensor elements and of three Euler angles in space, as follows: (i) Ag mode: 4[∥\ = Ψ ∥ef sin N sin P + g(sin O cos P + cos N cos O cos P) + h(cos O cos P − cos N sin O sin P) i + H∥

(12)

4[B\ = Ψ B k−  (g − h ) cos N sin 2O cos 2P + sin P cos P (g sin O + h cos O − 



f sin N) − cos  N sin P cos P (g cos  O + h sin O)l + H B

(13)

(ii) B1g mode: 4a∥\ =

Ψ∥ e−2m(sin O cos P + cos N cos O sin P) × (cos O cos P − cos N sin O sin P)i + H∥ (14) 4aB\ =

ΨB em(cos N cos 2O cos 2P − 2cos O cos P sin O sin P − 2 cos  N cos O cos P sin O sin P)i + H B 15

(15)

(iii) B2g mode: 4a∥&\ = Ψ∥ e−27 sin N sin P (sin O cos P + cos N cos O sin P)i + H ∥

4aB&\ = ΨB eo sin N (sin O cos P − sin O sin P + cos N cos O sin 2P)i + H B (iv) B3g mode: 4a∥(\ = Ψ∥ e2p sin N sin P (cos O cos P − cos N sin O sin P)i + H ∥

4aB(\ = ΨB ep sin N (cos N sin O sin 2P − cos O cos 2P)i + H B

(16)

(17)

(18) (19)

where Ψ ∥,B and H ∥,B are instrumental constants related to the configuration of the optical circuit in the Raman device. One could also retrieve four working equations to describe the intensities of the observed Raman bands from mixed modes, as follows: 4[∥\ )a\ = Ψ∥ , ef sin N sin P + g(sin O cos P + cos N cos O sin P) + h(cos O cos P − cos N sin O sin P) i + (1 − , ) ∗ e−2m(sin O cos P + cos N cos O sin P)(cos O cos P − cos N sin O sin P)i + H ∥ (20) 4a∥&\ )a(\ = Ψ∥ re−so sin N sin P (sin O cos P + cos N cos O sin P)i +  esp sin N sin P (cos O cos P − cos N sin O sin P)i t + H ∥ 

(21)

4[B\ )a\ = ΨB , k−  (g − h) cos N sin 2O cos 2P + sin P cos P (g sin O + 



h cos  O − f sin N) − cos  N sin P cos P (g cos  O + h sin O)l + (1 − , ) ∗ em(cos N cos 2O cos 2P − 2cos O cos P sin O sin P − 2 cos  N cos O cos P sin O sin P)i + H B (22)

4aB&\ )a(\ = ΨB reo sin N (sin O cos  P − sin O sin P + cos N cos O sin 2P)i +  ep sin N (cos N sin O sin 2P − cos O cos 2P)i t + H B (23) 

In the case of a highly crystalline fiber (showing mainly the Ag and B3g modes) with molecular structure almost fully aligned along its long axis, the four Eqs. (20)~(23) can be greatly simplified. Accordingly, one can set periodic dependences only in terms of in-plane rotation angle, ψ, in the a-plane of the orthorhombic cell (i.e., according to different polarization geometries), as follows: 4[∥\ = Ψ ∥|h cos  P + f sin P| + H∥

(24)

4a∥(\ = Ψ∥ |2p sin P cos P| + H ∥

(25)

4[B\ = Ψ B |(h − f) sin P cos P| + H B

(26) 16

4aB(\ = ΨB |p(cos  P − sin P)| +H B

(27)

Note that Eqs. (24)~(27) are only valid for highly aligned structures (e.g., the ultrahigh molecular weight polyethylene fiber investigated in these experiments), while Eqs. (20)~(23) are valid also for partly amorphous polyethylene structures. In the case of highly aligned fibers, the contribution of the B1g and B2g modes is lost (and, with it, also the possibility to assess the RTE e by using the model fiber sample). Using the fiber sample, Eqs. (24)~(27) were applied as trial functions to fit experimental plots of relative intensity for the 1170 and 1296 cm-1 bands as a function of in-plane rotation angle, ψ. Fitting of experimental plots obtained in parallel and cross polarization configurations to those periodic functions allowed the determination of a set of values for five RTE of the orthorhombic structure of polyethylene (i.e., a, b, c, and d=f). These values are intrinsic to the orthorhombic cell of polyethylene; thus, their knowledge represent fundamental information for the assessment of Euler angles in UHMWPE structures with unknown crystallographic patterns. The previously shown Figs. 3(a) and (b) give the Raman spectra collected on the polyethylene fiber sample as a function of rotation angle, ψ, in parallel and cross polarization geometry, respectively. As seen in the spectra collected at different in-plane angles, a clear variation in the relative intensity of the 1170 cm-1 and 1296 cm-1 bands could be found with rotating the polarized probe on the side surface of the polyethylene fiber. The experimentally recorded dependence of the relative Raman intensities indeed revealed periodic functions (as shown in Figs. 5(a)~(d) for both parallel and cross polarizations) that could be fitted to a high degree of precision to the trial functions theoretically set in Eqs. (24)~(27) for the selected polarized configurations. The results of a least-square fitting to the experimental data are also represented in Figs. 5(a)~(d) as full lines. Upon applying the angular rotation analysis at a fixed location with n different ψ angles in the interval, 0 ≤ P ≤ 2π, one obtains a system of 4n independent equations. From a computational viewpoint, it should be noted that applying Eqs. (24)~(27) to the fiber structure involves a total of five unknown parameters, including four Raman tensor elements (i.e., a, b, c, and d=f), and one unknown Euler angle, φ. Moreover, by considering that four instrumental constants (Ψ ∥,B and H ∥,B ) are also involved with the calculation, a total of 9 unknown parameters must be determined. One should thus select a number of different angular configurations, n, which suffices to obtain a number of independent equations >9. In the experiments described here, n=18 measurements were made in the interval, 0 ≤ P ≤ 2π, as shown in Figs. 5(a)~(d). A least-square fitting procedure led to the determination of values, a=0.260 ± 0.002, b=0.202 ± 0.001, c=-0.898 ± 0.004, and f=-0.664 ± 0.002, for the four RTE constants. Note that such tensor elements are parameters generally valid for the studied crystal structure, while the other parameters obtained by fitting vary with measurement location and adopted optical circuit. From the practical side, the availability of the fiber sample enabled us to experimentally calibrate from Raman spectral intensities a set of five RTE values that represent intrinsic properties of the orthorhombic structure of polyethylene. The knowledge of such intrinsic parameters great17

ly reduces the number of unknown parameters to be assessed in setting general equations when attempting to unfold unknown patterns of local molecular orientation in polyethylene components (i.e., as shown in the applicative part of this review). 3.3 An indirect Raman algorithm to probe oxidation in polyethylene The extent of overall oxidation of polyethylene components, and specifically certain oxidation index profiles present in orthopedic implant components made of UHMWPE, represent a fundamental issue in modern biomaterials science. Oxidation occurring to UHMWPE components when embedded in biological environment has long been shown to degrade both mechanical properties and wear resistance of the polymer and, thus, to adversely affect the in vivo lifetime of orthopedic devices.[51] Oxidation causes “aging” of the polymeric component, this term specifically referring to a change (usually a degradation) of the material structure and properties over time. Oxidative degradation is triggered when an atom or a group of atoms in the polyethylene chain gain at least one unpaired electron. Such defective sites are also referred to as “free radicals”. In the presence of free radicals, molecules of oxygen present in the tribolayer selectively bond to sites possessing electron-unbalanced characteristics.[52] With progressing the state of oxidation, the material becomes increasingly brittle and thus prone to wear at higher rates. a) FT-IR assessments of polyethylene oxidation Standard measurements of the amount of oxidation in ultra-high molecular weight polyethylene are made through the definition of a specific parameter referred to as the oxidation index (OI).[53] By definition, this parameter is computed from the ratio between the area subtended by the infrared absorption bands of polyethylene located in the spectral interval 1650~1850 cm-1 and the area of the absorption bands located in the interval 1330~1396 cm-1 (i.e., emissions related to C-H bending). The measurement of oxidation state in the polymer is made it possible by the fact that the intensity (area) of the carbonyl stretching absorptions (C=O) centered at around 1720 cm-1 is directly related to the amount of chemically bound oxygen present in the material. Note that the C=O double bond, which is cumulatively monitored by the infrared activity around 1720 cm-1, is present in different types of oxidation products (Fig. 6). Depending upon the details of the molecular structure around the C=O bond, the infrared frequency is slightly altered, and the emission splits into several sub-bands (cf. infrared spectral frequencies vs. oxidation sites in Fig. 6). The C=O bond stretching of simple ketones, aldehydes, and carboxylic acids absorb at 1718, 1720, and 1711 cm-1, respectively. On the other hand, esters absorbs at higher frequencies ~1730-1740 cm-1, while conjugation of C=O with a C=C (vinyl) group lowers the stretching frequency to ~1680 cm-1. Unlike esters and simple or conjugated ketones, aldehydes and carboxylic acids are located at the terminal locations of alkane chains. The ratio of the cumulative area subtended by the infrared emission in the neighborhood of the 1720 cm-1 to that under the standard band centered at around 1370 cm-1 is thus a direct measure of the overall oxidation event. Note that the infrared absorption method gives the investigator a unique means to compare the relative extent of carbonyl oxidation present in various polyethylene samples, although it is generally recognized that it 18

could be hard to distinguish between different oxidative species in the spectrum and, accordingly, to estimate the importance of each of them as a contributor to the degradation of the material characteristics. One main issue in practical infrared spectroscopy assessments is related to the efficiency of its emission. In the infrared spectral interval where the bands of interest manifest, the collection of back-scattered spectra is usually quite inefficient, and spectroscopic measurements must be performed in transmission geometry. The main consequence of such measurement set-up is the need to obtain a thin slice out of the pristine sample in order to reach a suitable spectral quality. The consequence of the slicing procedure is twofold. First, the pristine sample is heavily manipulated in order to thin it down, with the factual risk that the original microstructure and oxidation state are altered. Then, the thinning procedure is destructive to the sample; thus, it does not allow deterministic non-destructive sampling, but only a statistic control of the samples from the production line. This means that modern technological developments in biomaterials quality control mandatorily call for the development of a fully noncontact and non-destructive characterization method in back-scattering geometry. b) Raman assessments of polyethylene oxidation Raman spectroscopy has also been proposed as a direct means for investigating the oxidation degree of ultra-high molecular weight polyethylene. Chenery[54] identified the marker bands directly related to oxidation products at 870 cm-1 (peroxy), 935 cm-1 (epoxy), 1151 cm-1 (alcohol), 1770 cm-1 (peroxy acid) and 1794 cm-1 (acyl peroxy). Unfortunately, direct Raman spectroscopic assessments based on the above bands have proved unable to detect at the relatively low levels of polyethylene oxidation,[55, 56] which typically represent the initial levels from which biomedical devices degrade toward a shortened lifetime in vivo. Accordingly, using the above-mentioned Raman bands does not actually represent a viable approach to non-destructive oxidation analyses and quality control. An alternative Raman method, although indirect, has been proposed and validated by means of control infrared spectroscopy characterizations on a series of ultra-high molecular weight polyethylene sample.[39] This indirect method is based on the circumstance that oxidation mainly takes place in the amorphous (either rigid or mobile fractions) matrix of the polymer, especially due to the presence of excessive (and unstable) crosslinking sites. Such strained and unstable sites spontaneously break off over time leaving free radicals available for oxygen to join the amorphous structure. [57-59] The phenomenological consequence of such process is an increased crystallization ratio, mainly in the morphology of the orthorhombic polymorph. Note that the crystalline portion of UHMWPE is extremely compact and it is unlikely that an external molecule could penetrate its tiny (0.45 nm) interstices. On the other hand, the amorphous phase encompasses continuous free volume among its flexible polymeric chains, which might allow relatively large (and flexible) molecules (e.g., fatty acids, cholesterol, triglycerides, etc.) to diffuse. These species, once diffused in the UHMWPE structure, scavenge hydrogens from the polymeric chains and create new free radicals in them. According to the above descriptions, one can usually find a clear correlation between the oxidation index and the increased fraction of orthorhombic phase present in the 19

polymer. The validity of a general relationship between OI and αc for ultra-high molecular weight polyethylene can be thus demonstrated, as shown in the following:[39] ln w4 =  tan( , +  ) − 2

(28)

where the numerical coefficients A1, A2, A3, and A4 depend on material processing and, in general, on the initial microstructural assembly. Equation (28) can be used to semiquantitatively estimate the degree of oxidation of the material, and it is particularly useful because it enables the determination of OI from the same (standard) spectral records used for analyzing the microstructural fractions of polyethylene. As shown in detail later in this sub-section, the main shortcoming in practically using Eq. (28) for oxidation assessments is that the coefficients of the equation are microstructuredependent and must be determined through case-by-case calibrations, including, for example, cycles of accelerated hydrothermal aging in an autoclave. Moreover, a “standard” microstructural condition should initially be established for each type of sample investigated (e.g., biomedical polyethylene brands) in order to evaluate its drift toward an oxidized state. Note also that Eq. (28) is quite sensitive to low oxidation levels, but it gives overestimated values for heavy oxidation states (OI>5) and when strong plastic deformations or mechanical friction contribute the crystallization process. This latter circumstance might specifically hinder the use of the indirect Raman method for the analysis of oxidation states at the surface of retrievals, in which frictional processes have presumably played a non-negligible role upon crystallization. Nevertheless, an environmentally induced increase in crystallization, whatever the environment involved with it, always represents a sign of chemical instability. Thus, monitoring crystallinity alterations provides a suitable evaluation parameter for quality control of biomedical polyethylene samples before implantation. Regarding the characterization of as-manufactured samples from different makers, once “standard” crystallization data are collected for specific brands of orthopedic implants, it might result relatively easy to deterministically (i.e., in each individual component) check defective parts while monitoring the degree of aging already occurred upon manufacturing or “on shelves”, before the component is actually implanted in patients. c) Validation of Raman assessments of oxidation through FT-IR experiments The above Raman approach is henceforth validated in direct comparison with FT-IR assessments and applied to assess the oxidation behavior of different types of UHMWPEs from commercially available joint implants. Some of the studied samples are now out of the market but were selected for the sake of comparison between different generations of implants. Accelerated aging tests and concurrent assessments by FT-IR were conducted by the standardized method (as specified later), which includes the preliminary extraction by solvent hexane before spectroscopic testing. Raman spectroscopic assessments were successively performed. Seven different types of UHMWPE, henceforth referred to as Sample 1~7, were tested. These materials were produced using resins GUR 4150, GUR 1020, or GUR 1050, and significantly differed in terms of manufacturing procedures. The first analyzed material, Sample 1, was the old generation HGP-II UHMWPE (non-irradiated PE) produced by Zimmer 20

for hip joints, implanted during the 1980s and through the 1990s, and now out of production. This type of liner was not highly cross-linked but sterilized by γ-ray in air with (nominally) 25 kGy. Sample 2 was the more recent brand Longevity, also produced by Zimmer, which belonged to the first generation of highly cross-linked (HXL) polyethylenes. In this material, compression molded sheets were electronbeam irradiated in air with a nominal dose of 100 kGy and subsequently remelted at 150°C for 6 hours. After being machined into liners and barrier packaged, Sample 2 was sterilized by gas plasma. Sample 3 was a second-generation HXL and vitamin E infused UHMWPE ((E1 ® by Biomet) by Biomet in 2009. This liner was machined from isostatically compression molded rods, irradiated with a 100 kGy dose of γ-ray, annealed for 24 hours at 130°C in order to homogenizing infusion of vitamin E before the final step of sterilization with γ-ray in inert atmosphere (25-40 kGy dose in argon). Samples 4 and 5 were both manufactured by Teijin/Nakashima Medical and were blended with vitamin E before consolidation of the resin by direct compression molding. While Sample 4 was a conventional PE machined and sterilized with ethylene oxide (EtO), Sample 5 was cross-linked by γ-ray with a nominal dose of 300 kGy and then annealed for 72 hours at 110°C. Samples 6 and 7 were both HXL materials commercialized by the same implant maker (Stryker Orthopedics, Inc., Mahwah, NJ, USA). Sample 6 belonged to a former generation of hip-joint polyethylene (Crossfire®), manufactured from GUR 1050 extruded rods, which were γ-irradiated in a single step with a nominal dose of 75 kGy, and subsequently annealed at 130oC for 8 hours. Further exposure to γ-irradiation for sterilization purpose was made with a nominal dose of 30 kGy in nitrogen atmosphere. This sample will be simply referred to as “single-step annealed” UHMWPE, henceforth. Sample 7 is the newest hip liner generation (X3®) manufactured from GUR 1020 compression-molded sheets. In this latter case, annealing at 130 oC followed γ-irradiation at a nominal dose of 30 kGy. The same irradiation/annealing procedure was sequentially repeated for three times (i.e., for a cumulative radiation dose of 90 kGy). This latter sample will be referred to as “three-step annealed” UHMWPE, henceforth. Specifications for Samples 6 and 7 are explicitly reported in Table V. Note that Sample 4 is only used to produce tibial inserts for artificial knee joints, while all the other samples under investigation were or are employed in acetabular liner components. The (average) initial crystallinity fractions, αc, of Samples 1~7 through their thickness were 0.40, 0.44, 0.45, 0.46, 0.45, 0.58, and 0.62, respectively. Three new liners for each material were cut through their thickness to obtain parts of semispherical segments from the bottom of the cups. Sections of 200-µm thicknesses were then microtomed as shown in Fig. 7(a). For each material, three slices from different cups were cut (Fig. 7(b)) and analyzed immediately after slicing by FT-IR and Raman spectroscopies in order to characterize the microstructure and the oxidative condition of the as-received liners. Regarding the remaining slices, accelerated aging testing procedures were performed according to the standards ASTM F2003-02 (reapproved in 2008),[60] according to which preliminary conditioning step consisted of irradiating the specimens with γ-ray (25 kGy average dose) and maintaining them at 23°C for 28 days. Slices for each irradiated material were placed in an oxygen bomb 21

at 70°C under 5 atm of pure oxygen for 3, 14 and 28 days (three slices for each aging time). For comparison, also three non-irradiated slices per each material were aged in the oxygen bomb for 28 days. All the specimens were analyzed by FT-IR and Raman spectroscopy within 5 days after the completion of the test. Oxidation profiles were determined by FT-IR on the UHMWPE microtomed cross sections as a function of depth from the sliding surface. OI values were calculated according to ASTM 2102 as described above.[11] In order to obtain reliable OI profiles, an experimental routine with five line-scans from the sliding surface toward the back surface of the liner with 200 µm steps (cf. blue square areas in Fig. 7(c)). For each oxidative condition and type of sample, OI profiles were averaged over three slices for each of three different cups. The OI at each location on the cross section was calculated as the average of 15 measurements. The Raman investigation at fixed locations on the same oxidized thin sections was specifically designed to ensure that the same volume monitored by FT-IR could be statistically probed by the Raman probe. Size adjustments of the two different probes were necessary in order to find a correct correlation between OI and the crystalline phase contents. For the interested Readers, quantitative specifications of the Raman probe size are explicitly given in Appendix A. Briefly for the present purposes, the FT-IR probe has an in-plane spatial resolution of 200×200 µm2 and the IR beam probes the whole thickness of the slice since it works in transmission. On the other hand, the Raman probe is confined in tens of microns around the focal plane (cf. small purple circles in Fig. 7(b)). The configuration of the Raman probe adopted throughout the analysis of the oxidized sections corresponded to a 100× objective and a pinhole diameter fixed at Φ=1 mm, giving an in-depth probe size of ~60 µm but filtered through a Gaussian-Lorentzian dependence on sample depth.[39] Figure 7(c) schematically describes the mapping procedure for the RS experiments in comparison to the FT-IR sampling routine. As seen, three Raman spectra (small purple circles) were collected within each IR probe spot (large blue squares). Moreover, given the limited depth of the Raman probe, maps had to be collected in confocal configuration at three different depths in order to cover the entire volume of the slice, while the IR probe covered at once each squared area in transmission (cf. the Raman purple cones and the IR blue squared in the lower right protocol of Fig. 7(b)). Individual Raman spectra were typically collected in 5 s in non-polarized probe configuration. The recorded spectra were averaged over three successive measurements at each selected location. Figure 8(a) shows the phenomenological correlations between αc and OI, which were obtained upon plotting FT-IR and Raman data from each individual slice of Samples 1~7. For each material investigated, points with similar OI (i.e., setting a variation of  ), 0.01 as significant) were grouped and for each group an average oxidation index (w4 crystallinity (α {| ), and its standard deviation (σ) were calculated. In each plot of Fig.  values, while 8(a), the shown y-axis values of OI represents the above computed w4 the corresponding (x-axis) crystallinity fractions, αc, were calculated as the sum of the average value and its standard deviation (α {| + σ). The choice of the highest statistically meaningful crystallinity value from Raman data within each group of a given OI 22

was motivated by the need to associate OI to the most severe microstructural variation induced by oxidation. Functions relating crystallinity to OI could be obtained by fitting the experimental data to Eq. (28).[39] According to the partial-least-square fitting method, the following Eqs.(29)~(35) could be obtained for Samples 1~7, respectively: ln w4 = 0.55 tan(6.95, − 4.31) − 0.17

(29)

ln w4 = 0.48 tan(6.32, − 4.34) − 0.01

(30)

ln w4 = 0.45 tan(6.49, − 4.55) − 0.66

(32)

ln w4 = 0.35 tan(6.02, − 4.29) − 0.20

(31)

ln w4 = 2.06 tan(1.50, − 0.95) − 0.61

ln w4 = 0.18 tan(15.08, − 8.14) − 0.34 ln w4 = 0.21 tan(4.04, − 0.68) − 0.04

(33) (34) (35)

with standard errors of the regression, S=0.046, 0.066, 0.038, 0.047, 0.004, 0.082, and 0.048 for Eqs. (29)-(35), respectively. The plots in Fig. 8(b) represent the oxidationinduced recrystallization rates,dα, ⁄bw4, which were calculated as the derivatives of Eqs. (29)-(33). A transient regime of fast recrystallization rate during the initial phase of oxidation (i.e., up to OI ≈ 0.1) was approximately the same for 5 the 7 materials (Samples 1~5) investigated. After such initial behavior, however, Samples 1 and 4 clearly showed higher rates than Samples 2, 3 and 5, which all showed similar gradients of recrystallization induced by oxidation. Interestingly, the highly cross-linked materials Samples 2, 3 and 5 experienced almost identical profiles of recrystallization rate, characterized by a steep decrease until reaching a plateau at relatively low levels of oxidation (i.e., OI ≈ 0.15). The patterns found for Samples 6 and 7 were instead quite different from those of the other samples. In both materials, the initial transient regime of recrystallization started from very low values of crystallization rates, which reached minima at around OI=0.1. Then, similar to Samples 1 and 4, a gradual increase toward higher rates of recrystallization was noticed. Actually, Sample 6 showed the slowest recrystallization rate for OI < 0.5, but also the fastest one among all the investigated materials at OI > 0.5. On the other hand, the new generation Sample 7 recrystallized at a slowest rate as compared to Samples 1~5 in the initial stage of oxidation (i.e., up to OI~0.4), but started to experience lower recrystallization rates as compared to Sample 6 for OI > 0.55. In other words, the microstructural designs of Samples 6 and 7 were quite successful in keeping the crystallization rate of the material to quite low values at the initial stage of environmental exposure, and thus in the earliest implantation lifetime. Note, however, that Sample 6 was the material that showed the steepest dependence of OI on the degree of crystallinity over the wide interval αc> 0.45 (cf. Fig. 8(a)), which testifies instability in the polymer structure. Such a weak point has been corrected by the maker with achieving a quite high initial 23

crystallinity with the introduction of the three-step irradiated and annealed Sample 7. This latter sample possessed a tailored microstructure that was by far more than the single-step irradiated/annealed material belonging to the previous generation. A number of previous studies have demonstrated that oxidation in polyethylene is followed by recrystallization,[38, 57, 61, 62] as a consequence of chain scission, subsequent increase of molecular mobility, and chain reorganization into more stable crystalline domains of lower energy. The observed crystallization upon oxidation might be accompanied by a reduction of both third and amorphous phase. According to the results showed in Fig. 8(a), the exponential equations used to fit the OI values as a function of the αc for Samples 2 and 3 yields similar parameters. On the other hand, the evolution of crystallinity during oxidation in the remaining materials differed more markedly. Differences in the retrieved OI(αc) functions could be attributed both to different (initial) crystallinity and crosslink concentration. As a matter of fact, as long as the oxidation proceeds, the three highly irradiated polyethylenes (Samples 2, 3 and 5) experienced the lowest recrystallization rates due to their high crosslink density, which act like a constraint and impede the reptation of the polyethylene chains after scission (cf. Fig. 8(a) in the range of high oxidation). In addition, the molecular weight distribution, which is different between the studied samples, may also impact both crystallinity values and oxidation kinetics in the materials. In Sample 1 the crystallinity of the pristine sample was the lowest among the 7 investigated materials, suggesting that the higher the amount of amorphous phase, the higher the mobility of the chains and, subsequently, the higher the recrystallization rate, especially starting from relatively high levels of oxidation (i.e., OI > 0.4). On the other hand, Sample 4 showed high recrystallization rate despite its initial crystallinity fraction being relatively high. This experimental evidence may suggest that the chain mobility was enhanced by the presence of vitamin E, which was reported to act like a plasticizing agent that improves the wear and fatigue resistance of UHMWPE.[63, 64] The amount of recrystallization occurring immediately after the initial chain scissioning (i.e., in the range 0 < OI < 0.1) grew quite fast in all the investigated materials, the small differences in terms of recrystallization rate being negligible also considering the standard errors of the regression, S (cf. above-reported values). However, the behaviors of Samples 1 and 4 clearly separate from those of Samples 2, 3 and 5 at OI > 0.4, which reveals the main limitation of the Raman method, namely, the necessity of an ad hoc preliminary calibration to assess the recrystallization rate as affected by the peculiar microstructure of the polyethylene under investigation. This might make it difficult to analyze retrievals from early generation UHMWPE materials, for which pristine samples are not anymore fabricated. However, unlike FT-IR, the Raman assessment basically reads a crystallization process and, thus, has the advantage to be independent of absorbed species containing carbonyl groups. Since the calibration curves, given by Eqs. (29)~(35) were obtained after extracting any adsorbed carbonyl groups by hexane, they can also be used on retrieval samples. d) Microstructural mechanism linking recrystallization to oxidation Specifically regarding the mechanism at the molecular scale, the draft in Fig. 6 shows that the interaction between oxygen and polymeric chains is a complex phenomenon. 24

However, a simplified view of it can be given by mainly considering the formation of the hydroperoxide and the carboxylic acid groups, namely those oxidative units located at the terminal locations of alkane chains. The former groups are responsible for the high mobility of free radicals in the amorphous phase, while the latter ones involve chain scission. On the other hand, peroxy radicals can quickly propagate the oxidative patterns, because they suck hydrogens from the neighborhood. On the other hand, carboxylic acid groups fully saturate the tetravalent carbon and, making it a terminal unit of the chain, chop off the polymeric chains. Since oxidation-induced chain chop off is the phenomenon precursor to recrystallization, increased patterns of crystallization mean occurrence of oxidation and vice versa. Note also that a structure with lowered molecular weight undergoes recrystallization more easily than the pristine high-molecular-weight structure. Figure 9 schematically shows the mechanism that links oxidation to crystallization. The attack by oxygen to the polyethylene structure mainly occurs in amorphous regions, where free radicals are easily formed and oxygen finds faster diffusion (Fig. 9(a)). Free radicals and oxygen then recombine to form the above-mentioned two types of oxidation byproducts, namely hydroperoxide and carboxylic acid with formation of one new free radical in the neighborhood and one chain scissioned, respectively [65]. In the draft of Fig. 9(b), blue arrows locate hydroperoxide groups (with a broken line linking the newly formed free radical and hydroxyl), while red arrows identify carboxylic acid groups (with a broken line replacing the scissioned C-C bond). It should be noted that long chains in the amorphous structure of polyethylene are significantly strained and their scission into shorter units greatly facilitates the formation of newly crystallized units, as schematically shown in Fig. 9(c) (newly crystallized areas located by broken-line squares). The above-described cascade of phenomena at the molecular scale results in either thickening the original crystals or in newly creating (small) recrystallized domains in the amorphous matrix. Highly strained regions would presumably suffer the highest number of chain scissions events and develop an enhanced crystallinity. Note, however, that a validation of the above concepts in vivo is yet lacking. The Raman findings refer to adhesive/abrasive wear and its related surface damages and should be distinguished from delamination damage, which is a much more detrimental phenomenon, related to oxidation via the weakening of the material’s mechanical properties. Moreover, the effect of proteins and lipids yet shows unclear aspects. In an early study by Eyerer et al. [66], it was suggested that the wear amount of UHMWPE liners was accelerated in vivo by the presence of synovial fluid. More recently, Sawae et al. [67] compared the oxidation rate reached UHMWPE pins in laboratory wear (pin-ondisk and multidirectional sliding pin-on-plate) tests vs. alumina ceramics conducted in bovine serum with that conducted in phosphate buffered saline solution. Accelerated oxidation of UHMWPE was found for the former condition. Interestingly, besides higher amounts of oxygen, XPS analyses revealed the presence of nitrogen and sulfur in the worn UHMWPE surface. Sawae and Murakami [68] later reported about the results of UHMWPE pins on 316 stainless steel disks tests. These researchers found a wear rate almost ten times greater for UHMWPE pins tested in diluted bovine serum as compared to those tested in saline solution. The combination of lipids and serum 25

proteins, especially gamma globulin in synovia was indicated as the main factor in triggering in vivo wear degradation in UHMWPE. Specifically regarding the molecular modifications at the surface of UHMWPE liners, Fourier transform infrared attenuated total internal reflection (FTIR-ATR) techniques is a quite useful technique to clarify the specific item of protein and lipid adsorption to biomaterial surfaces. Exploiting spectrometers with high wavelength precision, this method allows for the subtraction of water, a strong infrared absorber, from the spectra of the adsorbed proteins [69]. Kinetics of protein adsorption, changes in protein secondary structure, and orientation upon adsorption to surfaces can also be obtained by FTIR-ATR, which could highly improve the analyses of UHMWPE retrievals. Costa et al. [70] elegantly demonstrated the application of FTIR-ATR to retrieved UHMWPE hip liners. Despite differences in sterilization procedures, all retrieved UHMWPE components revealed adsorption of species to their bearing surfaces, which mainly consisted of synovial liquid protein components. Additional species, such as cholesterol, fatty esters of cholesterol and squalene, which also originated from the synovial liquid, were found to diffuse into the sample bulk. Among the important conclusions of the Costa’s study, it was that wear tests using bovine serum as a lubricant agent could be unable to give realistic results, because the testing time is too short to include the occurrence of diffusion-related changes of the material properties. To avoid fundamental aspects of chemistry being missed, the standard nowadays requires soaking into bovine serum the UHMWPE components for about one month before simulation test. Based on Raman spectroscopy evidences, we shall discuss in the forthcoming Section 4.1 the insufficiency of hip simulator tests in assessing the wear response of UHMWPE bearing surfaces in vivo, according to the detection of microscopic crystallographic patterns. It is hoped that our new Raman findings will similarly help to improve the simulation standards in terms of contact micromechanics. Through the years, different makers have selected different strategies to tailor the polyethylene microstructure and to achieve improved performances. However, our data clearly show that no perfect polyethylene material so far exists, and a compromise in material performance must be accepted depending on which specific aspect of structural instability needs to (or is preferred) be mandatorily corrected. In conclusion, the above investigation of seven different polyethylenes used in total joint arthroplasty was designed to validate an indirect algorithm for measuring oxidation in biomedical polyethylenes by Raman spectroscopy. The exponential character of the function used for non-linear regression analysis proved to generally represent the oxidation-induced recrystallization phenomenon in different types of polyethylene, although the recrystallization rate of polyethylene was found to be dependent on crosslink density and initial crystallinity. Nevertheless, based on the newly developed phenomenological Eqs. (29)~(35) for different UHMWPE commercial brands, thousands of liners daily made of the same material during manufacturing could be quickly, quantitatively, and non-destructively scrutinized for quality control before implantation in patients.[71-73] Note, finally, that the presence of thermal treatments in the manufacturing processes of these materials is known to affect the microstructure of UHMWPE together with 26

cross-linking and crystallization processes. As the studied materials are manufactured very differently, Raman spectroscopy is shown here particularly suitable for providing more detailed and quantitative insights into the effects of manufacturing differences. Such microstructural details could serve future researches and developments of biomedical polyethylenes more efficiently than the analytical techniques presently in use in this field. 3.4 A Raman algorithm to probe plastic strain in polyethylene In highly crystalline and molecularly aligned polyethylene structures (e.g., fibers), it is possible to apply the same basic principles that rationalize the stress dependence of Raman band frequencies on stress for inorganic single-crystals.[74] Such stress dependence is represented by a linear relationship between stress and the frequency shift of a given Raman band, which holds up to GPa levels of applied stress. Conversely, additional efforts are required to bring such findings to usefulness in practical applications in polymers whose structure is comprehensive of partly amorphous regions. Regarding basic vibrational assessments of highly crystalline and aligned polyethylene structures, Tashiro et al.[75] monitored the Raman spectra of fibers with different draw ratio under tensile stress with respect to the skeletal stretching bands, namely, the C-C symmetric stretching mode at 1131 cm-1 and the C-C antisymmetric stretching mode at 1064 cm-1. Although Tashiro and co-workers considered those bands as single-mode bands, we have shown in Section 3.2 that these bands instead represent mixed modes Ag+B1g and B2g+B3g, respectively (cf. also polarized spectra in Fig. 3). A linear tendency to low-frequency shifts was clearly observed up to ~0.9 GPa of applied uniaxial tensile stress, with no detectable band broadening and no appreciable difference among samples drawn at different ratios. Within an experimental error <5%, the frequency shift rate was retrieved as -6.0 and -4.5 cm-1/GPa for the 1131 and the 1064 cm-1 bands, respectively. The drawn ratio, defined as the ratio of the crosssectional area of the undrawn material to that of the drawn material, is directly related to the degree of crystallinity and of orientation of the crystallites in the polymeric structure, the higher the drawn ratio the higher both fiber crystallinity and crystallite degree of orientation. Therefore, the finding of a unique value for the frequency-shift rate of the polyethylene bands, independent of drawn ratio, should be rigorously valid as both crystallinity and degree of alignment tend to unity in the spun fibers (i.e., with the polyethylene fiber becoming a “pseudo-single-crystal” sample, independent of draw ratio). In the case of a polyethylene chain (Fig. 10(a)) that belongs to a highly crystalline fiber (Fig. 10(b)), the main part of strain energy is covered by the intramolecular C-C stretching and the C-C-C deformation of the skeletal chains. On the other hand the energy associated with vectors of intermolecular interactions is negligibly small. It follows that, under tensile stress conditions, large frequency shifts might occur for intramolecular C-C stretching bending modes associated with C-C-C skeletal units, while shifts associated with the intermolecular modes can be neglected. In an orthorhombic polyethylene structure, the zigzag angle of the chains is, at equilibrium, inclined by α=41 o about the b-axis of the fiber.[76] A tensile stress, σ, induced by a 27

force, F, along the chain axis increases the zigzag angle, α+dα, and the C-C bond length, R+dR, which pile up into a macroscopic elongation of the fiber, L+dL, (cf. Fig. 10(a)). Under linearly elastic conditions, a series of proportionality relationships applies, which ends in a proportional shift toward lower Raman frequencies, dν , with increasing stress, σ, for the C-C stretching and C-C-C bending modes († ∝ σ ∝ d‡ (or dα ∝ d‰)). The negative sign in front of the frequency shifts of the above Raman bands arises from lowered Raman frequencies in response to positive (tensile) stresses. Tensile stress calibrations of Raman frequency dependence for bulk biomedical polyethylene were performed by Kyomoto et al.,[77] with emphasis placed on the effect of cross-linking. In situ Raman assessments allowed the concurrent determination of crystallinity variations, while crystallite orientation was monitored by high-resolution microscopy experiments after the end of tensile tests. This comprehensive approach not only tested the proportionality relationship σ ∝ d‰ in bulk polyethylene, but also enabled a clarification of its microstructural evolution under stress. Bulk polyethylene specimens for tensile testing were machined from a compression-molded UHMWPE (GUR1050 resin) bar stock, while cross-linked polyethylene specimens were machined from a compression-molded UHMWPE bar stock, which was irradiated by gamma rays with 25 to 100 kGy in N2 gas and then annealed at 110oC in N2 gas. A tensile loading jig was used for in situ spectroscopic assessments in the Raman device, with the applied strain being monitored by a micrometer screw. Tensile tests were performed in situ in the Raman spectroscope, while pulling in tension a dog-bonetype sample 41.6 × 3.1 × 1.2 mm3 in length, width, and thickness, respectively. The tensile experiments were quasi-static, and Raman spectra were measured after mechanical relaxation in order to avoid underestimation of the applied strain. Regarding Raman assessments of a bulk polyethylene structure under stress, the main finding in the study by Kyomoto et al.[77] was that no linear relationship could be found between applied tensile stress and Raman frequency of the skeletal C-C chain. While this is a direct consequence of the composite structure of the polymer (i.e., as explained later), a new and interesting feature could be found with monitoring the full width at half maximum (FWHM) of selected Raman bands as a function of uniaxial strain. Such a relationship was of a linear nature in polyethylene bulk materials within a detectable range of strain (i.e., up to several strain units), and could be expressed, as follows: Δ†‹Œ = ∏ 

(36)

whereΔ†‹Œ is the variation in full width at half maximum of a given Raman band, ε is the average strain piled up in the sample (e.g., during a tensile calibration in this case, but also applicable to compressive uniaxial strain, as shown later in this subsection), and А is a proportionality coefficient. A careful screening of the stress dependence of all Raman bands of polyethylene revealed that bulk samples of both conventional and cross-linked polyethylene did not show any Raman band obeying a 28

proportionality relation between tensile stress and Raman spectral shift. However, the width of some selected band obeyed a linear relationship with strain. The coefficient А for the 1127 cm-1 Raman band (symmetric C-C stretching) was equal to 0.42 ± 0.01 × 10 -2 cm-1/% elongation and 0.48 ± 0.01 × 10 -2 cm-1/% elongation for conventional bulk polyethylene and cross-linked polyethylene, respectively. These calibration lines were straight to a degree of accuracy, their correlation coefficients being 0.990 and 0.968, respectively. A comparison between the microstructures of the pristine and the residually (tensile) strained bulk sample of conventional polyethylene (elongation 0%, 40%, and at break, respectively) revealed a progressive alignment of the crystalline lamellae parallel to the deformation direction. The degree of crystallinity before loading in conventional and cross-linked polyethylene was 0.31 and 0.37, respectively. In the former sample, it first increased up to 0.36 between 0 and 50% elongation, and then decreased to 0.17 between 50% and break. On the other hand, the degree of crystallinity of cross-linked polyethylene decreased from 0.37 to 0.15 with increasing elongation. Since the fractions of amorphous phase were almost unchanged in both samples with increasing elongation, the fraction of third phase was the one mainly varying under tensile strain. Thus, the decrease in crystallinity is accompanied by the formation of the third phase, which still preserves the longitudinal structure of the crystalline phase but has lost its transversal order.[34, 78] The surface of ultra-high molecular weight polyethylene used in biomedical application undergoes large plastic strain deformation of compressive nature.[79] Edidin et al.[80] suggested that the mechanical loading conditions at the bearing surface of acetabular liner components might be precursor to the development of a plasticityinduced damage layer. This concept has been introduced to explain the near-surface orientation of crystalline lamellae and the consequent increase in crystallinity observed in wear-tested acetabular liners. Cross-linking reduces plastic deformation but also inhibits chain mobility and reorientation, thus causing a decrease in the material capacity of plastically deforming besides decelerating wear.[81, 82] The possibility of measuring local values of residual strain from the variation in FWHM of selected Raman bands can be very useful in assessing the performance of clinically used UHMWPE. From a polymer physics viewpoint, band broadening arises from the dispersion of detected functional group vibration, which increases with increasing elongation. The Raman spectrum thus reflects the structural morphology of polyethylene as well as the degree of orientation of its constituent crystallites. Raman spectroscopic experiments on bulk polyethylene under compressive stresses are of crucial importance in the field of artificial joint devices. Having different makers developed different recipes through the years for manufacturing polyethylene liners (i.e., including different starting resins, forming procedures, irradiation methods and doses, and thermal cycles), the mechanical response of the commercially available liners might greatly differ. Specifically regarding joint arthroplasty, the main stress field is of a compressive origin, and the plastic deformation associated with it is usually referred to as “creep deformation” or simply “creep”. While some creep is unavoidable in the joints, if it reaches relatively high displacements, a phenomenon referred to as “joint migration” might occur and the sliding counterparts couple with the wrong geometry. 29

As far as creep deformation issues in acetabular liners are concerned, clinical and retrieval studies have clarified that femoral head migration can be clearly observed on X-ray radiographs as a consequence of the polyethylene liner (creep) deformation. The migration rate is relatively high in the initial post-operative period, but such rate reduces significantly in the subsequent years. Dai et al.[83] reported linear migrations of 40% of the total penetration at a 10-year follow-up after two postoperative years. Femoral head migration after a mean evaluation time of 3~4 months represented 56% of the 2-year total, indicating the significance of creep during the initial postoperative period. Clinical (and hip simulator) studies of cross-linked polyethylene liners by Wroblewski et al.[84] also revealed high rates of penetration over the first 18 months (or 1.5 million cycles), followed by significantly lower deformation rates. Several additional reports showed consistent results, according to which, after an initial migration of 0.2~0.4 mm, the subsequent penetration rate became rather small.[85-88] One could indeed regard femoral-head migration as a “natural” event of strain-energy minimization. In fact, creep of the liner would increase joint contact area and decrease contact pressure, thus playing a role in the reduced penetration rate over time. However, with such a significant amount of the early dimensional changes potentially attributed to creep, it is imperative to more accurately rationalize migration data, to link them to wear rates, and to understand the effects of both design parameters and polyethylene microstructures on combined creep and wear of acetabular cups. Raman studies of microstructural modifications induced by plastic compressive strain in polyethylene biomaterials are thus key in providing physical insight into the role of biomaterial microstructure on the deformation behavior. As an example of Raman characterization of the plastic deformation behavior of biomedical polyethylenes under compressive stress, we compare here two UHMWPE liners manufactured by Stryker Orthopedics, which differed for their manufacturing procedures (cf. specifications for both materials in Table V). These two materials have been described in detail in the previous sub-section (where they were referred to as Samples 6 and 7). In the context of this sub-section, we shall refer the investigated samples to as “single-step annealed” and “three-step annealed” UHMWPE. Structural modifications induced by plastic deformation were studied using uniaxial relaxation tests in a compressive geometry, which were applied to samples cut from acetabular cups as received from the maker. The samples were subjected to a sudden compressive strain of a predetermined magnitude, which was kept constant for 24 h in order to allow the full occurrence of stress relaxation within the polymer microstructure. The uniaxial strain field was then released and the sample allowed recovering its anelastic strain for additional 24 h, so that only plastic strain remained stored in the microstructure. The residual (plastic) strain was measured along the axis of the applied uniaxial load by means of a micrometer caliper, and the deformed samples analyzed by Raman spectroscopy. The residual strain in different materials was assumed to be ε=0 and a constant (uniaxial) strain magnitude (i.e., henceforth referred to as true strain before recovery, εi) was increasingly applied at subsequent steps up to a level εi~32%. Figure 11(a) shows plots of true strain after recovery, εf, as a function of externally (or initially) applied strain, εi, for both the investigated materials. The εf =εf(εi) plots ob30

tained for both materials were linear in nature and their comparison revealed a distinct difference in slope (in inset), which was higher for single-step as compared to the three-step annealed sample. In other words, for the same applied constant strain, εi, the latter material revealed a higher capacity of recovery as well as of relaxation, thus incorporating a lower amount of plastic strain, εf, and residual stress. Note that no change in crystalline phase fraction could be noted in both samples upon plastic deformation (Fig. 11(b)). This experimental finding can be interpreted as a clear proof for a higher resistance to permanent deformation of the three-step annealed microstructure as compared to that of the single-step annealed one. In Fig. 12(a), experimental results are shown of Raman bandwidth (FWHM) as retrieved from unpolarized Raman spectra at different values of residual compressive strain, εf, after strain recovery. The 1130 cm-1 band of the orthorhombic polyethylene structure was narrower in spectra collected from the three-step annealed sample as compared to the single-step annealed one, due to the higher crystallinity of the former material (61.7% vs. 58%).[89, 90] The lower molecular weight of the starting resin of three-step annealed sample (GUR1020) as compared to that of the single-step annealed one (GUR1050) obviously had also a role in the formation of the recorded spectroscopic difference.[91] For better distinguishing the repercussions of external strain on microstructural rearrangement from the initial effects of the manufacturing procedures, the trends of band broadening observed in both types of material can be replaced with the bandwidth variation, ∆FWHM , with respect to the initial bandwidth value, in the as-received undeformed state. Accordingly, curves εf=εf (∆FWHM) relating the plastic strain after recovery to spectroscopic features could be obtained, as shown in Fig. 12(b). Least-square fitting of the experimental data in Fig. 12(b) leads to two phenomenological equations of a common cubic nature, as follows: ’ = 18.05Δ†‹Œ − 21.04Δ†‹Œ + 24.76Δ†‹Œ ’ = 13.11Δ†‹Œ − 7.77Δ†‹Œ + 24.28Δ†‹Œ 

(37) (38)

in which ∆FWHM is expressed in units of cm-1. Equations (37) and (38) refer to threestep and one-step annealed samples, respectively. The plots in Fig. 12(b) show that, under the same level of applied strain, εf >5%, the Raman spectrum of the former material undergoes a relatively higher broadening than that of the latter one. Based on the plots of Figs. 11 and 12, one can attempt to rationalize the origin of the microstructural modifications induced by uniaxial compression in bulk polyethylene and, ultimately, to discriminate the differences related to the particular processing that the polymer underwent to. Spectroscopic studies of deformation in highly crystalline and textured polymers usually show the occurrence of both Raman band shift and bandwidth broadening, as a consequence of stretching of oriented molecules in both crystalline and amorphous regions.[75, 92, 93] Unlike those studies, in the present experiment on bulk polyethylene, the observed broadening of the 1130 cm-1 band was accompanied by a conspicuous statistical invariance in Raman peak position. As previously shown in this sub-section, spectral shifts of Raman bands under strain are ex31

pected to occur toward opposite directions for applied (uniaxial) strain magnitudes of tensile and compressive nature. The Raman band is also expected to only broaden (without shifting), when both types of deformation events (i.e., tensile and compressive) occur with the same statistical relevance at different locations within the probe volume. A three-stage model could be invoked to explain the sequence of microstructural modifications induced by uniaxial compressive load on the polymeric structure. The sigmoidal shape of the experimental curves in Fig. 12(a), which can be fitted to three distinct linear segments with different slopes, indeed suggests the existence of three stages in the overall deformation process. According to general notions in the field of deformation of bulk polymers,[48, 94] the inelastic response of semicrystalline UHMWPE can be considered to begin with the main deformation process occurring within the amorphous regions of the polymeric structure, immediately followed by the activation of plastic deformation into the crystalline lamellae, predominantly via crystallographic slip mechanisms. Figure 13(a) shows a schematic representing the microstructure of undeformed polyethylene, in which the preferential orientation of lamellar axes is broadly perpendicular to the bearing surface of the liners for both single-step and sequentially irradiated UHMWPE samples, in agreement with a previous study by Bellare and Cohen.[95] According to that study, both ramextruded rods and compression-molded sheets of UHMWPE presented crystallographic texture in the polymer microstructures. The preferential orientation of molecular chains is a consequence of crystallization of the oriented polyethylene melt under a perpendicular compressive stress. In the amorphous phase surrounding the crystalline orthorhombic lamellae, due to the high molecular weight of polyethylene and to the high irradiation dose applied, the concentration of tie molecules, entanglements and crosslinks is high and affects the response of the microstructure to the applied external load. During the first stage of deformation (i.e., up to ≈ 2% plastic strain, labeled as Stage I in Fig. 12(a)), the molecular chains present in the amorphous phase are those that mainly undergo deformation. However, the important characteristic since the initial stage of deformation is that the strain locally stored at the molecular level is not necessarily compressive in nature, due to the high concentration of entanglements and crosslinks throughout the disordered (amorphous) phase (cf. Fig. 13(b)). However, at this initial stage, rotation of crystalline lamellae is barely activated by the external compressive load. An increasing presence of strain gradients in the amorphous fraction of the materials explains the incipient occurrence of band broadening (Stage II in Fig. 12(a)). During this stage of secondary deformation (i.e., in the range 2≤ ε’ ≤11%; cf. Fig. 12(a)), both materials showed the most remarkable variation in ∆FWHM. Significant band broadening, due to over stressed tie molecules, entanglements and crosslinks between crystalline and amorphous regions, arose from steeper strain gradients of both tensile and compressive nature (Fig. 13(b)). At this stage, crystalline lamellae might undergo significant rotation, with a larger population of crystallites experiencing preferential orientation and aligning along a plane parallel to the sample surface. The rotation of lamellae should be massively activated by the previously mentioned exacerbation of tensile and compressive strain gradients in the amorphous phase, while also a mechanism of structural re-arrangement of intra32

lamellar sliding concurrently takes place on the crystalline side of the structure.[96] A confirmation about the rotational activity of the orthorhombic lamellae under compressively strained conditions can be obtained by monitoring the out-of-plane (tilting) inclination angle, θp, at different level of plastic strain (cf. the presence of three different stages also in Fig. 14(a)). As shown in the explanatory drafts of Fig. 13, one should expect that the inclination of the lamellae tends to become perpendicular to the loading direction as plastic strain proceeds, according to a rate determined by the mobility of the polymeric chains in the microstructure. The angular inclination, θp, can be monitored by polarized Raman experiments of in-plane rotation as those described in Section 3.2 (i.e., by using Eqs. (20)~(23) as fitting functions with the knowledge of the Raman tensor elements of polyethylene also listed in Section 3.2). By comparing plots of residual strain as a function of variations in tilt angle of the lamellae, εf(∆θp), the secondary stage of deformation occurring in the two different polyethylene structures can be found to affect the tilt angle more pronouncedly in the three-step annealed sample than in the single-step annealed one (cf. Fig. 14(b)). This finding suggests a higher concentration of crosslinks in the amorphous phase of the former material, although the cumulative dose of irradiation was the same for both samples. Indeed, as proved by Bartczak[97] and Boontongkong et al.,[98] when subjected to the same strain magnitude in a range of relatively low deformations, highly entangled and/or highly cross-linked polyethylene structures achieve a higher degree of crystallographic orientation as compared to less cross-linked and/or less entangled structures. In other words, if the concentration of crosslinking is very high, the molecular chains in the amorphous region might quickly become fully stretched to their maximum limit, even at relatively low strain magnitudes. Such microstructural circumstance in turn triggers a faster reorientation of the crystalline lamellae according to the mechanism shown in Figs. 13(b) and (c). In the last (third) stage of compressive deformation (i.e., true strains in the interval, 11≤ ε’ ≤13%), the observed variations of bandwidth and molecular orientation became milder than those in the second deformation stage (cf. similarly milder slopes in Figs. 12(a) and 14(a), respectively). Such a mitigation of the process of molecular rearrangement concurs with the saturation of the rotation process, with a large population of molecular chains now experiencing preferential orientation at maximized tilt angle variations, ∆θp. Further plastic flow among crystalline lamellae is hindered by the onset of strain hardening correlated to the presence of crosslinks. Above this stage, only chain slip within individual crystallites can be expected to become active as an intrinsic deformation mechanism. Crystalline slip occurs along the [001] direction of the orthorhombic structure (i.e., which corresponds to slip along the most closely packed crystallographic plane).[96] In other words, strain hardening becomes the preponderant effect and should also be responsible for the milder band broadening experienced by both materials in Fig. 12(a) at ε’ ≥11%. Note, however, that such high levels of plastic strain are not expected to occur under the mere effect of creep deformation in acetabular cups. On the other hand, the severe damage induced by abrasive/adhesive wear might locally produce extreme elongations in the lamellae, with the microstructure developing a texture similar to that of a 33

single crystal (fibrillar structure).[98] At these extreme levels of deformation, the effect of strain hardening induced by crosslinking should also be maximized. At the compressive strain levels experienced by the two investigated materials during the present characterization of plastic deformation, one could detect only to a lower extent the above-mentioned difference in strain hardening effect. Nevertheless, it is clarified that sequentially irradiated UHMWPE, despite being produced from a lower molecular weight resin (i.e., with an expectedly lower initial concentration of molecular entanglements), showed a higher resistance to plastic deformation, a larger recovering capacity, and underwent to a faster molecular orientation at the initial deformation stage (i.e., up to 11% compressive plastic strain) as compared to single-step irradiated polyethylene. Such properties, which should also involve an earlier strain hardening effect at higher strain levels, are representative of an improvement in deformation behavior as a consequence of the sequentially applied irradiation/annealing manufacturing procedure. As a conclusive statement to this sub-section on plastic deformation of biomedical polyethylene, it could be stated that, as far as compressive strain fields are concerned, phenomenological correlations enable non-destructively assessments of residual compressive strain in biomedical polyethylene by Raman spectroscopy. Such phenomenological relationships differ for UHMWPE materials with different manufacturing histories. Polarized Raman spectroscopy can also be applied to retrieve variations in tilt angle occurring upon loading and representing the main microstructural rearrangement occurring during creep deformation. In conclusion, Raman spectroscopic calibrations of plastic strain in biomedical polyethylenes play a key role in quantitatively locating UHMWPE microstructures more resistant to plastic deformation than others. 3.5 Molecular populations in polyethylene structures When the structure of the material of interest is partly disordered, as in the case of UHMWPE, and the disorder lies on a scale smaller than the probe size, the quantitative application of a spectroscopic method necessarily requires a statistical approach. The parameters of interest in the analysis of biomedical UHMWPEs, including molecular orientation, oxidation gradients, and strain, generally experience a degree of disorder on a scale smaller than the size of the Raman probe. For example, crystallographic disorder in UHMWPE is represented by a loss of periodicity on the lattice scale, but it concurrently accompanies with the appearance of different periodicities of crystallographic domains on a mesoscopic scale (i.e., an intermediate one between individual molecules and the probe size). Without a repeating lattice or in a lack of uniform periodicity for domain structures within the probe, one cannot feasibly define the polymeric structure in terms of atomic or crystal coordinates. Instead, a statistical definition of an orientational distribution function for a set of vectors (or tensors) should be made, which can relate, via rotations, to the local geometry of mesoscopic domain structures. One way the studied system could be characterized on a statistical basis resides in selecting a function, henceforth simply referred to as orientation distribution function (ODF), capable to establish a meaningful correlation with the orientation trend inside the probe volume. While the definition of ODF might seem an 34

enormously difficult task, we shall show in the remainder of this section that the large numbers of constraint which govern the geometry of real domain structures make it possible to derive a finely approximate structure from accessible bits of polarized Raman information. Nowadays, the ODF approach represents a fundamentally important modus operandi in computational analyses.[99] The availability of an analytical form for ODF, which can describe a distribution of crystal orientations, has long represented a fundamental tool in the field of texture analysis (i.e., not only limited to Raman spectroscopy,[42, 100] but also including X-ray diffraction,[98] nuclear magnetic resonance,[101] and fluorescence polarization[102]), although it is yet conspicuously unexplored in the field of biomaterials. Historically, the ODF approach dates back to Müller,[103, 104] who first realized that, if the spatial distribution of plane normals from an X-ray experiment can graphically be represented on the surface of a sphere, their mathematical description should be given in terms of spherical harmonics. However, no conceptual connection was made at that time between the proposed expansion into harmonics and the orientation functions previously defined by Hermans for connecting birefringence results obtained with polymeric chain orientations.[105, 106] Since then, various direct methods for the calculation and representation of an ODF have been suggested.[107-109] Among them, the prevailing mathematical treatment relies on a series expansion over the generalized spherical harmonics, as introduced into the field of texture analysis more than 40 years ago independently, but concurrently, by Bunge[110] and Roe.[111] The formalism and related conventions followed by Bunge in his seminal contributions to the field of texture analysis notably include the description of an orientation by Euler angles, and the consequent series expansion of the ODF as a linear combination of generalized spherical harmonics.[112] It should also be noted that the use of Euler angles as a parameterization of rotations is not necessarily ideal since the existence of certain singular orientations that do not correspond to a unique set of Euler angles.[113] These orientations have been reported to give rise to singularities in the formulas used to determine the result of sequential rotations.[114-116] While these limitations have no relevance in the present analyses of domain structures in UHMWPE, it is definitely true that the description of domain textures in the orientation space might result notably more complex when the Euler-angle parameterization is adopted[117] than for some of the alternatives.[118-121] Our choice here of the Euler angle formalism is essentially based on the fact that it permits the deterministic construction of a domainorientation space that is substantially simpler to visualize and interpret. Particularly relevant to the work presented here is the use of rotation operators, as they were first put forward by McBrierthy to facilitate the interpretation of polymer properties from different experimental techniques.[122] The rotation operators described by McBrierthy are basically spherical tensors, also referred to as Wigner functions, which constitute a three-dimensional rotation group.[123, 124] Jen et al.[125] first reported about the promising application of such rotation operators in Raman spectroscopic studies of symmetry in liquid crystals. Successively, van Gurp gave a general approach based on rotation operators and ODF for polymeric materials, thus showing the full potential of this approach in partially oriented structures.[126] 35

As previously described in Section 3.2, from the relative intensity of selected Raman bands and with the knowledge of the full set of Raman tensor elements for a given crystallographic structure, it is possible to quantitatively assess crystal orientation in the three-dimensional space. In other words, we have proved that, when dealing with a crystallographically homogeneous sample, Raman spectroscopy can locate and map orientation patterns. The same formalism and analytical approach can be applied to partly textured structures, although this will unavoidably lead to the determination of average values of Euler angles for the investigated texture. Such average values conspicuously lack statistical meaning and, thus, the depth necessary to analyze the inherent structure of domain textures. For a statistical approach to describe the distribution of domains in the three-dimensional space in terms of three Euler angles, computational algorithms based on local ODF determination can be set so that the fractional distribution of Euler angles within the Raman probe is correctly described on a statistical base. The starting point for this treatment is to set the probability of finding in the Raman probe domain textures with individual orientation comprised between angles (, •, –) and ( + b, • + b•, – + b–) , as follows: —œš! —›š! —™š! p(, •, –) sin • mm•m– = 1 ˜

˜

˜

(39)

where p(, •, – ) is the ODF and (, •, – ) is an arbitrary system of Euler angles in space. It can be assumed, according to Eq. (39), that the ODF is a normalized and positive distribution function, while a further assumption, which suits the present analyses, is that, according to internal symmetry, the studied samples only possess one preferential axis of orientation. This latter assumption allows one accounting for the dependence on only one angle. The ODF is then built as a series of spherical (complex) functions (i.e., the Wigner functions), 9 (, •, –), as follows: (ž)

(ž) (ž) ž ž p(, •, –) = ∑¡ žš! ∑š ž ∑9š ž ^9 9 (, •, – )

(40)

Depending on the value of L, the Wigner functions constitute a complete set of (2L+1)2 orthogonal functions. The indices m and n may assume values between –L and +L. A complete overview of the various properties of rotation matrices can be found in the textbook written by Gray and Gubbins.[127] The property of orthogonality of the Wigner functions can be expressed as: —œš! —›š! —™š! 9 (, •, –) &&9& sin • mm•m– = ž ˜

˜

˜

(ž )

¢˜&

(ž )

 )

£žž& £&& £9& 9& (41)

where the upper bar stands for the complex conjugate, and with £ being the Kronecker operator in its usual form. It is possible to demonstrate that the coefficients, ^9 , in Eq. (40) are equal to the average of the Wigner function, as follows: (ž)

36

^9 = (ž)

ž) ¢˜ &

(ž) 〈 9 (, •, –)〉

(42)

where the average of the Wigner function is given by: (ž) (ž) 〈 9 (, •, – )〉 = —œš! —›š! —™š! 9 (, •, –)p(, •, – ) sin • mm•m– ˜

˜

˜

(43)

The ODF in terms of Wigner functions thus displays in a compact form: ž ž p(, •, –) = ∑¡ žš! ∑š ž ∑9š ž

ž) ¢˜&

(ž) (ž) 〈 9 (, •, –)〉 9 (, •, –)

(44)

The explicit form of the Wigner functions is given by:[124] 9 (, •, –) = eexp(−©ª)im9 (•)eexp (−©«–)i (ž)

(ž)

(45)

where the small Wigner functions, m9 (• ), are functions of the angle, β, only: (ž)

› ž)9  :

(ž) m9 (•) = ∑¡ :š! ¬: (­, ®, ¯) °cos ± 

›  9):

°−sin ± 

(46)

where: ¬: (­, ®, ¯) =

( )² ³(ž))!(ž)9)!(ž 9)!(ž )! (ž  :)!(ž)9 :)!(:) 9)!:!

(47)

In the case of polarized Raman scattering, inelastic collision occurs of a photon and a molecule with an energy loss (or gain) of the scattered light that corresponds to the energy jump associated with a rotational or vibrational transition in the molecule. According to Eq. (44) and making use of the fact that the scalar product of two spherical tensors introduces the complex conjugate of one of the two,[124, 128] Eq. (6) can be rewritten as: 

4 ∝ 〈|78 ℜµ¶ 7 | 〉 = 〈°∑ž, 7 (ž,) ℜµ¶ ± 〉 = 

·ž,¸

ž ( 〈°∑ž9 7 (ž,) 9 , •, –)ℜ,¹E ± 〉 = ·ž,9¸

(ž,9) (ž 9 ) ž ž ( ∑ž9 ∑žº º9º 7 (ž,) 7 ·ž , ¸ 〈 9 , •, – )  º 9º (, •, – )〉 ℜ,¹E ℜ,¹E º

º

º

º º

(48)

where L,L’=0,1,2, and m, n, m’, n’ range from –L to +L and from –L’ to +L’; the subscripts “lab” and “cry” refer to the Raman tensor being expressed in the laboratory žº ž ( and crystal lattice frames, respectively. The product, 〈 9 , •, –)  º 9º (, •, – )〉 , can then be expressed as a single rotation according to the Clebsch-Gordan series:[124]

37

¾šž)ž ¾ ž ž ( » » » » 〈 9 〉(49) , •, –)  º 9º (, •, – )〉 = ∑¾šž žº
(­­ ¼; ®® )
(­­ ¼; ¯¯ ) 〈 ) º ,9)9» º

º

where the constants, C, refer to the so-called Clebsch-Gordan coefficients (tabulated in Table VI).[129] In most cases, L and L’ will only be 0 and 2 (symmetric tensors), which means that the Raman experiments will yield second- and fourth-rank order ž ( parameters. Coefficients for constructing higher order Wigner functions, 9 , •, –), (ž,9) are given in Table VII.[114] Once 7 are known from the experimental setup and ℜ,¹E from the crystal structure (cf. Eq. (11)), Eq. (48) can be solved with the aid of ·ž,¸

Eq. (49). With assuming no azimuthal dependence and thus a uniaxial orientation system, the angle, α, can be disregarded in the ODF treatment. Furthermore, when cylindrical geometry exists within each individual domain, the dependence on, γ, cancels out, and the system is categorized as an axially symmetric one. We then could imagine the simplified function, f(β), having the form of cos •. This function reaches its maximum value when β=0, with most of the domains lying with their c-axis aligned along the preferential orientation axis. Perpendicular to such axis, at β=π/2, cos  • = 0 and there is no domain with this orientation. In order to normalize and incorporate a measure of order, a parameter, P, (i.e., the “order parameter”) which determines the width of the ODF, must be introduced. This parameter also determines the width of the ODF: c(• ) = (1 − ¿ + 3¿ cos  •)  

(50)

which is always positive when − 1À2 ≤ ¿ ≤ 1. If the system is fully isotropic, P=0

and the distribution is independent of β. On the other hand, when P=1, the maximum degree of order is achieved. Addition of higher order terms (i.e., cos 2 •, cos •, etc.) refines the structure of the ODF, the sharper the ODF the more terms are needed. Normalization of the expansion of cosine functions leads to a series expansion of Legendre polynomials (i.e., with all polynomials integrated over β=0 but the 0th rank, which equals 1): c(• ) = ∑¡ 8š! ^8 ¿8 (cos •)

(51)

¿8 (cos •) = Á 8! Â(|ÃÄ ›)Á (cos • − 1)8

(52)

where ¿8 (cos •) are the Legendre polynomials, defined as: 

ÂÁ

Note that this approach is consistent with the general formulation of Wigner functions, as given above. From the explicit form of the Wigner functions (Eqs. (45)-(47)), it follows that they reduce to the Legendre polynomials for the case, m=n=0: (ž) !! (, •, –) = ¿ž (cos •)

(53)

38

According to Eq. (52), one can find: ¿! (cos •) = 1 ¿ (cos •) =

¿2 (`Åƕ ) =

(54)

 |ÃÄ& ›  

(55)

(Ç ,0 1 › ! ,0 & ›)) ¢



(56)

We then can again invoke the orthogonality property of the Legendre polynomials in order to calculate their average values, < ¿8 (cos •) > , finding the followings: —! ¿8 (`Åƕ) ¿: (`Åƕ )Æʯ•b• = (:)) £8: ˜



(57)

with £8: being the Kronecker operator in its usual form. The average expression for the Legendre polynomials is given by: ËÌ¿ Ë(`Åƕ)Í = —˜ ¿ (`Åƕ) ∑¡ ^ ¿ (`Åƕ )Æʯ•b• = : 8š! 8 8 ! 8

 ^£ (:)) : 8:

(58)

From a comparison with Eq. (51), the ODF now becomes: c(• ) = ∑¡ 8š!

8) Ë 

Ì¿: Ë(`Åƕ)Í¿8 (`Åƕ)

(59)

which also represents the structure of Eq. (44) in its simplified form (i.e., under the above assumptions of uniaxial system with cylindrical geometry.[100, 130-132] The coefficients, < ¿8 (cos •) >, are also referred to as the “order parameters” of the Legendre polynomials. As already mentioned above, polarized Raman scattering yield only the two parameters, < ¿ (cos •) > and < ¿2 (cos •) >. The order parameters in Eq. (59) give an indication of the degree of orientational order in the domain texture. The parameter, < ¿ (cos •) >, assumes the value 0 when the domain orientation is fully random, while values 1 and -0.5 are experienced when a perfect orientation parallel and perpendicular to a preferential orientation axis is reached, respectively. The orientation parameter, < ¿ (cos •) >, is the primary parameter in judging about the alignment of domain textures. However, the information provided by this parameter might result incomplete in some particular cases. For example, < ¿ (cos •) > might be incapable of distinguishing between perfect order and perfect disorder, since < ¿ (cos •) >=0 holds for both a fully isotropic distribution and a perfect alignment at an angle β = ¢!! Ï Ç2#

(i.e., in that case cos  • = 1/3 , from which, <

¿ (cos •) >=0; cf. Eq. (55)). In such limit cases, higher order parameters are needed to make the distinctions, which are, however, related to < ¿ (cos •) >. For example, it is possible to demonstrate that the two parameters < ¿ (cos •) > and < ¿2 (cos •) > are bound within the following limits: 39

Ñ

ËÒ¿ Ë(`Åƕ)Ó ≥ 2

e35ËÒ¿ Ë(`Åƕ)Ó − 10ËÒ¿ Ë(`Åƕ)Ó − 7i Ë ËÒ¿ Ë(`Åƕ)Ó ≤  e5ËÒ¿ Ë(`Åƕ)Ó + 7i 2  

¢



(60)

In the remainder of this review paper, we will mainly refer to the parameter, < ¿ (cos •) >, for statistically assessing domain orientation textures, although also showing the related < ¿2 (cos •) > parameter. In practice, only a limited number of order parameters can be experimentally determined. In order to complete the knowledge of the ODF, one can set its morphology as the “widest possible”, which means the smoothest possible ODF that contains the least possible information. From a physical point of view, this means that the information entropy is maximized.[133135] The information entropy, S, is expressed as: ˜ ˜ ˜ Ô = −Õ —œš! —›š! —™š! c(, •, –) lnecË(, •, –)iËbb•b–

(61)

where K is a constant. If now we maximize the information entropy with the following restrictions and with using the Lagrange’s method of multipliers (with the number of multipliers, 랝9 , being less than the number of order parameters): —œš! —›š! —™š! c(, •, –) bb•b– = 1 ˜

˜

˜

˜ ˜ ˜ (ž) (ž) ×Ë 9 ØË —œš! —›š! —™š! 9 (, •, –)c(, •, –) bb•b–

(62) (63)

then, it follows that the ODF can be expressed as: ž ž c(, •, –) = 7=Ùe− ∑¡ µ9 λ9 9 (, •, –)i

(64)

where A is a constant. In the simple case of only two order parameters, < ¿ (cos •) > and < ¿2 (cos •) >, for a uniaxial system with cylindrical geometry, Eqs. (63) and (64) reduce to: ËÒ¿ Ë(`Åƕ)Ó = —˜ —˜ —˜ ¿(`Åƕ) Æʯ•bb•b– œš! ›š! ™š! ËÒ¿ Ë(`Åƕ)Ó = —˜ —˜ —˜ ¿ (`Åƕ) Æʯ•bb•b– 2 œš! ›š! ™š! 2 c(•) = 7=Ùr−eλ ¿ (`Åƕ) + λ2 ¿2 (`Åƕ)it

(65) (66) (67)

Figure 15 shows our choices of Cartesian systems, in which the following axes are defined: a Cartesian system, (xlab, ylab, zlab), integer to the laboratory frame, a Cartesian system, (Xcry, Ycry, Zcry), integer to the domain orientation axes (i.e., with taking 40

(109)

the Z cry -axis parallel to the c-axis of the orthorhombic structure), and an additional Cartesian system, (xp, yp, zp), locating the axes of preferential orientation of the crystal texture within the polarized Raman probe. As far as different sets of Euler angles are concerned (cf. Fig. 15), the set of angles (θ,φ,ψ) locates the orientation in space of an arbitrary domain (i.e., located by the Cartesian coordinate system (Xcry, Ycry, Zcry)) with respect to the Cartesian system (xlab, ylab, zlab)). Within the polarized Raman probe, the set of angles (α,β,γ) instead describes the rotations in space of the Cartesian frame integer to the crystal orientation axes, (Xcry, Ycry, Zcry), with respect to the axes of preferential orientation of the domain structure, (xp, yp, zp). In addition, the set of Euler angles describing the rotations of the preferential orientation axes, (xp, yp, zp), of the molecular domains with respect to the laboratory frame, (xlab, ylab, zlab), are labeled as (θp,φp,ψp). According to the above notations, the three Euler angles (θ,φ,ψ) describing the orientation of any arbitrary domain in space with respect to the laboratory Cartesian system, (xlab, ylab, zlab), can be expressed as functions of α, β, γ, θp, φp, and ψp by considering a double matrix rotation for the Euler angles, as follows: `ÅÆN`ÅÆO`ÅÆP − ÆʯOÆʯP `ÅÆOÆʯP + `ÅÆN`ÅÆPÆʯO Ô = @−`ÅÆN`ÅÆOÆʯP − `ÅÆPÆʯO `ÅÆO`ÅÆP − `ÅÆNÆʯOÆʯP ÆʯN`ÅÆO ÆʯNÆʯO

`ÅÆNÛ `ÅÆOÛ `ÅÆPÛ − ÆʯOÛ ÆʯPÛ  = Ú−`ÅÆNÛ`ÅÆOÛ ÆʯPÛ − `ÅÆPÛ ÆʯOÛ ÆʯNÛ `ÅÆOÛ

(69)

`ÅÆ`Åƕ`ÅƖ − Æʯ–Æʯ Ý = @−`Åƕ`ÅƖÆʯ − `ÅÆÆʯ– Æʯ•`ÅƖ

−ÆʯN`ÅÆP ÆʯNÆʯP A `ÅÆN

`ÅÆOÛ ÆʯPÛ + `ÅÆNÛ `ÅÆPÛ ÆʯOÛ `ÅÆOÛ `ÅÆPÛ − `ÅÆNÛ ÆʯOÛ ÆʯPÛ ÆʯNÛ ÆʯOÛ

`ÅƖÆʯ + `Åƕ`ÅÆÆʯ– `ÅƖ`ÅÆ − `ÅƕÆʯ–Æʯ Æʯ•Æʯ–

(68)

−ÆʯNÛ `ÅÆPÛ ÆʯNÛÆʯPÛ Ü `ÅÆNÛ

−Æʯ•`ÅÆ Æʯ•Æʯ A `Åƕ

(70)

where S=sij (i, j=1, 2, 3) represents the rotations of (Xcry, Ycry, Zcry) with respect to (xlab, ylab, zlab); M=mij (i, j=1, 2, 3) the rotations of (xp, yp, zp) with respect to (xlab, ylab, zlab), and N=nij (i, j=1, 2, 3) the rotations of (Xcry, Ycry, Zcry) with respect to (xp, yp, zp) (cf. Fig. 15). The matrix product T=MN=tij (i, j=1, 2, 3) is equal to S, thus equating the elements s33=t33 and s23=t23, two Euler angles can be expressed as θ = θ(α, β, θÛ, φÛ , ψÛ ) and ψ = ψ(α, β, θÛ , φÛ , ψÛ ), as follows: N = `ÅÆ ß`Åƕ`ÅÆNÛ − cos· + OÛ ¸ Æʯ•ÆʯNÛ à

(71)

P = Æʯ  Ñß`ÅÆ`ÅÆPÛ Æʯ•ÆʯOÛ + ÆʯPÛ ·`ÅƕÆʯNÛ − `ÅÆNÛ ÆʯÆʯ•ÆʯOÛ ¸ +

`ÅÆOÛ × Æʯ•(`ÅÆPÛ Æʯ − `ÅÆ`ÅÆNÛ ÆʯPÛ )à



&

á ß,0›,0âã  |ÃÄ·œ)äã ¸89›89âã à

å

(72)

Upon considering φ as a constant equal to φp in our calculations, namely neglecting any torsional rotations of an orthorhombic cell around its c-axis, a working equation 41

that includes both Raman selection rules and domain distribution patterns can be set, as follows: —îì —íì —ëì ç (â,ä,é)’(›)89›ÂœÂ›Â™ B,∥ 4 &ê ê &ê æ,0¶ (N, O, P) = &ê

ê

&ê

è,∥

—îì —íì —ëì ’(›)89›ÂœÂ›Â™

(73)

B,∥ with 4 æ,0¶ (N, O, P) being the observed (i.e., crystallographically averaged) polarized

Raman intensity of a given vibrational mode, k, and the polarized Raman intensity, 4æB,∥ (N, O, P), being given by the selection rules shown in Eqs. (20)~(23). In a computational process for cases only including the dependence on the polar angle, β, experimental Raman intensities collected upon rotation of the probe volume enable to set Eq. (73) (i.e., after substituting for the variables θ and ψ from Eqs. (71) and (72)) at each of the n selected in-plane rotation angles, ψ, thus obtaining a system of n independent equations that can be numerically solved by means of an iterative routine. Note that the number n of selected ψ angles, and thus the number of independent equations, should exceed the number of unknown parameters (i.e., in this case, five unknown parameters: θp, φp, ψp, λ2, and λ4, after calibration of the instrumental constants). Given the possibly high number of variables involved in the integration, and the large number of collected points in a textured structure, the computation might become quite time consuming. In the interval, 0 ≤ ψ ≤ π/2, it is possible to collect a relatively large number, n, of relative intensity values at each investigated location, which might largely exceeded the number of unknown parameters. From any five independent equations, one can then obtain the unknown parameters, θp, φp, ψp, λ2, and λ4, according to a best fitting procedure, while using the remaining equations for a confirmation of the obtained values. Calculations of Lagrange multipliers according to the aforementioned fitting procedure then enable one determining the three characteristic (unknown) parameters, A, < ¿ (cos •) >, and < ¿2 (cos •) >, by solving the system of three additional equations (Eqs. (39), (65), and (66)). In the applications of the ODF formalism shown in the forthcoming applicative section, the calculated values of ψp and θp represent the in-plane rotation and the out-of plane tilt angles with respect to the sample surface, respectively. These angles, thus, directly represent the microscopic domain structure of UHMWPE or its microstructural modifications, as induced by a plastic strain field applied along an unknown Cartesian direction. In particular, in-plane angular displacements, which can be distinguished through monitoring variations of the in plane angle, ψp, are related to displacements of molecular domains induced by frictional forces at the surface of the sample. 4. Evaluating the performance of biomedical polyethylenes 4.1 In vitro vs. in vivo molecular patterns at the surface of hip liners The theoretical findings developed in the initial part of this review can now be applied to practical purposes in the analysis of new, simulator-tested, and retrieved polyethylene components. The Raman selection rules have made it available to us the angular 42

dependences of the polarized Raman intensity for the Ag, B1g, B2g, and B3g modes, which can serve to determine unknown crystallographic orientation patterns as they develop in vivo and in vitro at UHMWPE bearing surfaces of acetabular cups. Moreover, the ODF formalism (as given in Section 3.6) implemented the Raman selection rules for the orthorhombic structure of polyethylene and provided a path toward statistically probing the molecular orientation of orthorhombic lamellae. In this applicative sub-section, a quantitative examination is given of the molecular orientation patterns developed on the surface of four in vivo exposed UHMWPE acetabular cups. Comparisons are made with the pre-existing patterns in an unused cup and with the patterns developed upon standard cycles in the hip joint simulator. The main goal of these experiments is to reveal the surface distribution of orientation angles of in vivo worn UHMWPE surfaces and to compare them to those from pristine samples and samples tested in vitro. Concurrently, also variations in crystallinity for main wear zones vs. non-wear zones are screened in the same set of samples and exactly at the same probed locations. Crystallographic texture analysis is one of the three fundamental issues that Raman spectroscopy can tackle in biomedical polyethylene, the other two being the assessments of oxidation index and residual (plastic) strain (shown in later sub-sections). Here, we challenge the fundamental tenet of the criterion of “equivalency” between in vitro evaluations in joint simulators and the actual in vivo conditions. Such criterion is based on the kinematic correspondence with gait motion and on the assumption that damage similarly accumulates in vitro and in vivo as a function of the sliding cycles to which the joint components are exposed. The present Raman analysis questions the principle of equivalency and attempts to unfold the role of chemical and crystallographic effects at the bearing surfaces of hip joints at the molecular scale. Nowadays, the most widely applied type of prosthesis in total hip arthroplasty consists of a femoral head made of a metal alloy (e.g., CoCr) sliding against an ultra-high molecular weight polyethylene acetabular cup. The UHMWPE acetabular undertakes the multiple roles of body-weight bearing, low-friction sliding surface, and impact absorber. However, the UHMWPE bearings might undergo extensive creep and wear damages with the concurrent formation of polyethylene debris, which in turn trigger the risk of osteolysis.[136, 137] The clinical experience has long been prodigal of phenomenological evidences for the in vivo degradation of polyethylene joint components.[138-140] However, many aspects of the combination of chemical, crystallographic, and mechanical factors leading to UHMWPE surface degradation yet remain obscure. More importantly, it is not clear whether the in vitro testing in hip simulator could actually reproduce at the microscopic scale the in vivo frictional interaction between the joint sliding surfaces. In an attempt to clarify the origin of implant degradation and to propose methods for elongating their lifetime, a number of Raman studies have been carried out, which focused on assessing phenomena of chemical and structural degradation (e.g., oxidation and degree of crystallinity) in polyethylene structures.[51, 54, 141-143] Such Raman studies have provided precious contributions to advance our knowledge of degradation processes in biomedical polyethylene grades. However, a long way re43

mains to go until the development of a rigorous and quantitative knowledge will become available. Screening at the molecular level the concurrent progression of crystallization and crystallographic alignment of the polyethylene lamellae is a step forward. At least as important as the macroscopic (phenomenological) screening of the tribological performance of UHMWPE components, building up a microscopic “view” of the material behavior is crucial for future developments. Orthorhombic lamellae in pristine UHMWPE components might be randomly oriented within the amorphous matrix or lie along preferential directions as a consequence of the manufacturing process. However, the orientation of crystalline lamellae is sensitive to mechanical and frictional loading.[144-146] The lamellae will naturally tend to preferentially orient themselves on the surface of the UHMWPE acetabular cup during in vivo loading. This molecular re-arrangement reflects both primary and secondary motions generated at the contact surface in artificial hip joints, thus representing a key microscopic circumstance, precursor to the formation of wear debris throughout the loading history. In the remainder of this sub-section, mapping of the in-plane local Euler angle, ψ , is selected to quantitatively describe the orientation patterns generated upon frictional sliding at the surface of acetabular cups retrieved after different periods of in vivo exposure (i.e., ranging between ~2 and 12 y) in comparison with unused and in vitro tested acetabular cups of the same type. Four different acetabular cups were investigated, which were all retrieved from leftside hip joints in the respective patient bodies at Tokyo Medical University. These acetabular cups will also be referred to as short-term (2.4 y and 2.8 y) and long-term (10.3 y and 12.2 y) retrievals, respectively. The short-term retrieved (23 x 32 mm) acetabular components were both made of highly cross-linked polyethylene, manufactured from 1900H bar stock by isostatic compression molding (with no addition of calcium stearate) (ArCom®, Biomet Japan Inc., Tokyo, Japan) and sterilized by gamma-ray irradiation with a dose of 33 kGy. One cup belonged to a 61-y-old male patient for which the cause of revision was infection with a follow-up period of 2.4 y, while the other cup belonged to a 53-y-old female patient for which the cause of revision was infection dislocation with a follow-up period of 2.8 y. On the other hand, two long-term retrievals were made from GUR4150 bar stock by Ram extraction molding (calcium stearate was added in these cases) and sterilized with a dose of gamma-ray radiations ranging between 25 to 37 kGy. One cup (manufactured by Zimmer Inc., Tokyo, Japan) belonged to 47-y-old male patient, while the other cup (ArCom®, Biomet Japan Inc., Tokyo, Japan) belonged to a 60-y-old female patient. Both cups were retrieved due to aseptic loosening and the follow-up period was 10.4 y and 12.2 y, respectively. All acetabular retrievals operated against commercial CoCr heads 32 mm in diameter, and were cleaned before storage and analysis. For comparison, unused acetabular cups were investigated, which were from the same manufacturers and possessed the same manufacturing characteristics of the short-term retrieval described above. Location of the main wear zone on both short-term and long-term retrievals could be pursued in a relatively easy way by the naked eye, owing to a slight difference in surface roughness (and, thus, in sample translucency) as compared 44

to the non-wear zone. Comparisons were also carried out with in vitro tested UHMWPE components of the same type coupled with the same type of CoCr femoral heads. Hip-simulator wear experiments were performed according to the standardized procedure ASTM F1714-96. The UHMWPE components, which showed no detectable oxidation level before testing (OI<0.02), were presoaked in bovine serum for 1 month prior testing. The hip simulation study was performed using an Shore Western 12-station hip simulator (Monrovia, CA) at a rate of 1 Hz. Tests were first carried out to a total of 5 x 106 cycles of simulated gait under clean conditions in new born calf serum diluted 2:1 with distilled water (protein concentration after dilution: 19 g/l). Then, bone cement powder was added to a final concentration of 10 g/l and abrasive test ran for additional 2 x 10 6 cycles. Test kinematics followed a Paul hip curve for the load profile with 23o bi-axial oscillation and a 2.4 kN maximum load. Raman spectral mapping was performed in both parallel and cross polarization geometries on areas typically 100×100 µm2 in dimension (i.e., with a sampling of 5 µ m step for a total of 21×21 = 441 points). Mapping was repeated at 5 random locations of each selected zone for each individual acetabular liner (i.e., ≈ 105 µ m2 per each investigated cup). The obtained maps of relative Raman intensity were then converted into maps (and histograms) of average molecular orientation according to the quantitative knowledge of the Raman tensor elements. Maps (and histograms) of degree of crystallinity (i.e., volume fractions of the orthorhombic phase) were also prepared at the same locations (according to Eq. (5)). ODF were also computed and the full set of Raman data compared with unused acetabular liners and liners tested in hip simulator. Four working equations for the general structure of UHMWPE were selected, involving both crystalline and amorphous phases, as directly obtained from the theoretical treatment given in Section 3.2. They describe the relative intensities of the observed Raman bands, as functions of Euler angles (defined as shown in Fig. 15): 4[∥\ )a\ = Ψ∥ × r, e`Æʯ NÆʯ P + ^ (ÆʯO`ÅÆP + `ÅÆN`ÅÆOÆʯP) + _(`ÅÆO`ÅÆP − `ÅÆNÆʯOÆʯP) i + (1 − , ) ∗ e−Æb(ÆʯO`ÅÆP − `ÅÆNÆʯOÆʯP)i t + Η ∥ (74) 4a∥&\ )a(\ =

Ψ∥ × ð re−27ÆʯNÆʯP(ÆʯO`ÅÆP + `ÅÆN`ÅÆOÆʯP)i + e2cÆʯNÆʯP(`ÅÆO`ÅÆP −  

`ÅÆNÆʯOÆʯP)i tñ + Η ∥

(75)

4[B\ )a\ = ΨB × ð, k−  (^ − _)`ÅÆNÆʯ2O`ÅÆ2P + ÆʯP`ÅÆP × (^Æʯ O + _`ÅÆ  O − 



`Æʯ N) − `ÅÆ  NÆʯP`ÅÆP(^`ÅÆ  O + _Æʯ  O)l + (1 − , ) ∗ eb(`ÅÆN`ÅÆ2O`ÅÆ2P −

2`ÅÆO`ÅÆPÆʯOÆʯP − 2`ÅÆ  N`ÅÆO`ÅÆPÆʯOÆʯP)i ò + Η B

45

(76)

4aB&\ )a(\ = ΨB × ð re7Æʯ(ÆʯO`ÅÆ  P − ÆʯOÆʯ P + `ÅÆN`ÅÆOÆʯ2P)i + 

ecÆʯN(`ÅÆNÆʯOÆʯ2P − `ÅÆO`ÅÆ2P)itñ + Η B

(77)

where the full set of Raman tensor element values, intrinsic to the orthorhombic structure of polyethylene, has previously been determined experimentally (cf. Section 3.2). The statistical orientation of a population of polyethylene molecule embedded in the three-dimensional Raman probe can be expressed in terms of Wigner functions, as reduced to Legendre polynomials according to symmetry considerations (cf. Section 3.6). For doing so, an additional set of Euler’s angles (α,β,γ) is needed, whose spatial position is relative to a right-handed macroscopic system of Cartesian axes (xyz)lab (cf. Fig. 15). In our choice here, the angle, γ, indicates the degree of anticlockwise rotation (i.e., about the yp axis) of the orthorhombic structure in the probe volume. The analytical formulation of the probability of finding a set of UHMWPE molecules with orientation between angles (α,β,γ) and (α+dα,β+dβ,γ+dγ) then represents the definition of the orientation distribution function, f(α,β,γ)≥ 0 (cf. Eq. (39)). When dealing with an in plane aligned molecular pattern, which is indeed the purpose here, one could rule out in first approximation azimuthal dependences and assume that the orientation distribution function is only dependent on the polar angle, β. This involves that a uniaxial symmetry is assumed with respect to the ylab axis (cf. Fig. 15). The resulting orientation distribution function can then be expressed through the “order parameters” in Eqs. (55) and (56) to be experimentally determined. In the present case, it is convenient to newly define the angle, ^¯• β, = arctan ( ó(^¯ + 1)) , which is comprised between the ylab axis and the projection of the axis yp (i.e., indicated as Ycry in Fig. 15) onto the plane (yz)lab, it folô lows that θ = − β, . Thus, the system of equations (74)~(77) can now be rewritten,

as follows:



∥,(B) 4[\ )a\ (N, O, P)

=

∥,(B) 4a&\ )a(\ (N, O, P)

ëì&ê îì&ê íìê ∥,(è)

—ëì —îì —íì õ\ ö÷ (›º ,ä,é)’(›)89›ÂœÂ›Â™ \

=

ëì&ê îì&ê íìê

—ëì —îì —íì ’(›)89›ÂœÂ›Â™

ëì&ê îì&ê íìê ∥,(è)

—ëì —îì —íì ÷&\ ö÷(\ (› º ,ä,é)’(›)89›ÂœÂ›Â™ ëì&ê îì&ê íìê

—ëì —îì —íì ’(›)89›ÂœÂ›Â™

(78)

(79)

with Raman intensities in the integrals given for the general case by Eqs. (74)~(77). Note that using the equality sign in Eqs. (78) and (79) involve the knowledge of two instrumental constants (i.e., one additive and the other multiplicative to the angular dependences in Eqs. (74)~(77)). Such instrumental constants in turn depend on the optical setup of the spectrometer. The ODF is then given as:

46

c(• ) = 7=Ùß−·λ ¿(`Åƕ ) + λ2 ¿2 (`Åƕ )¸à

(80)

where A is a constant and the parameters λi(i=2,4) are the Lagrange multipliers used in the definition of the principle of maximum information entropy reported by Jaynes.[133] The three parameters A, λ2, and λ4, can be determined by solving the system of three equations given by Eq. (67) and the two following equations, which describe the average values of the Legendre polynomials: ËÒ¿ Ë(`Åƕ)Ó = —™š˜ —œš˜ —›š˜ ¿(`Åƕ)c(• ) Æʯ•bb•b– ™š!

œš!

›š!

(81)

™š!

œš!

›š!

(82)

ËÒ¿2 Ë(`Åƕ)Ó = —™š˜ —œš˜ —›š˜ ¿2 (`Åƕ)c(• ) Æʯ•bb•b–

The order parameter < ¿ (`Åƕ) >, referred to as the Hermans’ orientation parameter, assumes the value 0 when the orientation of the orthorhombic lamellae is fully random, while values 1 and -0.5 represent a perfect orientation along and perpendicular to a given (preferential) axis, respectively. For the present purpose, the Hermans’ orientation parameter is sufficient for exhaustively describing the alignment of UHMWPE orthorhombic lamellae. The additional order parameter displayed in the Legendre polynomial, < ¿2(`Åƕ) >, also contributes to describe the degree of orientation of the structure. However, the contribution of this latter parameter is less meaningful and straightforward than that of < ¿ (`Åƕ) >.[100] According to the above-described Raman polarization algorithms, near-surface molecular orientation maps were collected in the four studied UHMWPE acetabular retrievals both in main wear and non-wear zones. For comparison, maps were also collected at similar locations in an unused UHMWPE acetabular cup. The fraction of orthorhombic phase was evaluated at each location of the maps according to Eq. (5). On the other hand, a computer program was also set up to calculate the mean molecular orientation of the orthorhombic cell in the Raman probe at each location of the maps and its distribution function. Angular in-plane rotation was performed at each location to retrieve both orientation angles and distribution functions according to Eqs. (74)~(77), (78), and (79). In Section 3.2, we have determined (i.e., a, b, c, and f) 4 of the 6 Raman tensor elements of orthorhombic polyethylene. The collection of polarized spectra upon full in-plane rotation enables to obtain a large number of working equations, which suffice to retrieve three unknown Euler angles, (θ,φ,ψ), two order parameters (< ¿ (`Åƕ) > and < ¿2 (`Åƕ) >), three constants A, λ2, and λ4, and four instrumental constants (H//, ΗB , Ψ//, and Ψ B ). Moreover, besides confirming the values of the Raman tensor elements previously found on the fiber sample (as previously described in Section 3.2), we newly retrieved values of -0.403 and -0.849 for the missing d and e elements, respectively. Figures 16(a)~(e) show typical maps (100 x 100 µ m2, in dimension) of in-plane molecular orientation patterns as collected in both wear and non-wear zones. Maps from the same zones were also collected for crystallinity fractions, as shown in Figs. 17(a)~(e). In both the above figures, maps in (a), (b), (c), (d), and (e) refer to the un47

used cup, and to cups retrieved after 2.4, 2.8, 10.3, and 12.2 y, respectively. Regarding the in-plane molecular orientation represented by the maps of Figs. 16(a)~(e), an orientation of the orthorhombic c-axis along the line ψ=0 corresponds to the blue broken line separating the anterior-superior (A-S) zone of the cup from its posteriorinferior (P-I) zone. Positive angles are then counted anti-clockwise (cf. Fig. 16). The full red line, perpendicular to the ψ=0 axis, represents the direction of the gait motion. Figures 18(a)~(j) display histograms of molecular orientation angle, ψ, and crystallinity, αc, which are representative of the full set of statistical data collected on five 100 x 100 µ m2 maps per each different zone (i.e., A-I zone in (a)~(e); P-S zone in (f)~(j)) of each cup. Regarding the statistical population of oriented molecules at liner surfaces, average ODF were obtained by best fitting in-plane rotation dependencies of selected Raman bands to Eqs. (78) and (79). Average results of Raman rotation experiments are given in Figs. 19(a) and (b) for the Ag+B1g (parallel) and B2g+B3g (cross) modes in the nonwear zone (NWZ) and main wear zone (MWZ) of both a long-term retrieval (cf. maps in Figs. 16(d) and 17(d)) and a short-term retrieval (cf. maps in Figs. 16(c) and 17(c)). For comparison, the functions retrieved for a highly crystalline/aligned fiber sample and for an unused cup are also shown as an upper and lower boundary for the degree of orientation of the UHMWPE structure, respectively. The ODF obtained for those same samples are given in Fig. 19(c) together with a draft showing in inset the relationship between polyethylene chain, the systems of Cartesian axes and Euler angles. All the parameters characterizing the orientation distribution functions are explicitly listed in Table VIII. The plots in Fig. 19(c) are representative of about 2200 spectra over a total area of ≈105 µm2 per each zone of the investigated cup. The degree of alignment can be clearly visualized by the narrow peak centered at β=0, the higher the peak the higher the degree of alignment. Results confirm that the probability of finding UHMWPE lamellae oriented along the direction of gait motion in the hip joint was the highest in the MWZ of the cup sample exposed for long time in vivo, although such a degree of orientation was far from reaching the quite high value found for the UHMWPE fiber along its long axis. On the other hand, some increase in the degree of alignment was visible upon exposure in vivo even in the conspicuous lack of mechanical load (i.e., in the NWZ), as compared with the unused cup (i.e., < ¿ (`Åƕ) >=0.58 vs. 0.40). The salient features revealed by a comparison among maps and histograms in Figs. 16~19 can be listed as follows: (i) The statistical trend for the degree of crystallinity in the unused cup was uniformly represented (i.e., over the entire surface of the cup) by a relatively broad distribution, whose mean value was ~54%. However, as a general trend, all crystallinity histograms of the in vivo exposed cups appeared to be broadened over a much wider interval of αc values. As a result, the mean values were only slightly shifted towards higher fractions. Irrespective of exposure time in vivo and of whether they belonged to main wear or non-wear zones, the αc histograms collected on the bearing surface of

48

the UHMWPE cups appeared significantly altered by in vivo implantation with the formation of “hot spots” of crystallinity reaching values as high as 80~85 %. (ii) The unused cup showed a weak pattern of molecular alignment on its surface, with a quite low value of Herman’s parameter, < ¿ (`Åƕ) >=0.40 (cf. histogram in Fig. 18(a) and Table VIII). (iii) Unlike the unused cup, the distribution of the in-plane molecular orientation angle, ψ , on the surfaces of the retrievals was always bimodal. In other words, the exposure in vivo appeared to introduce a new population of oriented orthorhombic lamellae sharply clustered at orientation angles around 30o. This new angular population grew at the expenses of the originally homogeneous angular population oriented at around 68 o as observed in the unused cup. The strongly bimodal character of the angular distribution was a common feature to all maps collected on retrievals as can be easily perceived by the conspicuous absence of grey zones (i.e., the predominance of black and white regions) in the related maps. (iv) Black regions in the maps of angle, ψ, represent the original orientation of the orthorhombic cell on the cup surface after manufacturing. While the distribution of white regions appeared to be at random locations on the analyzed surfaces, the molecular alignment within those zones conspicuously differed from the direction of the main sliding displacement (gait motion) at the contact surface between femoral head and acetabular cup (cf. displacement and c-axis orientation directions in Fig. 16) during gait. This is an important feature, which suggests that also secondary motions (e.g., torsions) play a key role on surface molecular alignment. Analyses of local orientation distribution in NWZ showed that the black regions maintained quite low values of the Hermans’ parameter (i.e., in the narrow range 0.4 ≤< ¿(`Åƕ) >≤ 0.47 ), as in the case of the unexposed material. The low degree of alignment in NWZs could also be confirmed by comparing the angular dependences of Raman intensity in these zones with those in the unused cup. Interestingly, as far as the MWZs were concerned, black regions in the ψ maps often corresponded to highly crystallized regions, while no such relationship could be observed in the NWZs; despite they also showed some increase in degree of crystallinity as compared to the unused cup. In the MWZs, the angular dependences of Raman intensity were more pronounced (cf. white areas in the ψ maps) and could locally reach < ¿ (`Åƕ) > values as high as 0.90. (v) No clear trends for an increase in both crystallinity and Hermans’ parameter as a function of in vivo exposure time could be obtained in this study. In particular, the long-term retrieval in Figs. 16(e) and 17(e) showed significantly lower degrees of crystallinity and molecular alignment as compared with the other long-term retrieval in Figs. 16(d) and 17(d). The values were comparable with those of the short-term exposed cups. While a lack of statistics hampers any final conclusion regarding the relationship between the degree of crystallinity/alignment and in vivo exposure time, we speculate here that the presumed lower activity of a 60 y old female patient vs. that of a 49 y old male patient could be, for an otherwise same type and size of implant, the reason for the observed microstructural differences.

49

Despite such a lack in statistics, the experimental data clearly suggest that the observed variation of structural patterns in the MWZ, namely both the fractional increase of orthorhombic lamellae population and their clustering around an orientation different from the direction of gait motion in the hip joint, visualizes the occurrence of wear damage on the UHMWPE bearing surface. In other words, the highly crystallized/aligned zones (i.e., the “hot spots” observed in the αc maps) formed as a result of prolonged and repetitive sliding motion of the femoral head along the direction of gait motion and are likely to detach from the surface, thus becoming wear debris (in agreement with a phenomenological description given in previous literature).[147] Note that the fractional increase in the orthorhombic lamellae population and their clustering around an orientation different from the principal direction of normal gait in the hip joint may aid in the visualization of wear damage on the UHMWPE surface. Data obtained by shifting the focal plane of the confocal probe along the subsurface of the acetabular cups (i.e., with steps of 1 µm) revealed detectable spectral variations (i.e., toward the original structure of the unexposed material) starting from a sub-surface depth, z0=5~8 µm, while the full restoration of the original structure occurred starting from depths at around 20 µm. Figures 20(a), (b), and (c) show a scanning electron micrograph, a crystallinity map, and a molecular orientation map, respectively, which were collected in the same area of the main wear zone of the UHMWPE liner retrieved after 10.3 y in vivo (cf. the complete maps in Figs. 16(d) and 17(d)). A comparison among the three maps reveals that lumpy areas seen in the electron micrograph corresponded to almost fully crystalline molecular assemblies, while the smooth molecular profiles represented amorphous structures. Figure 20(d) shows a schematic draft of the cross section of UHMWPE liner in the neighborhood of the sliding surface in the main wear zone. As the crystallinity of a polymer is related to the tertiary structure of the polymer chains, the observed patterns substantiate shortly sectioned crystalline chain assemblies in the lumps, together with flatly deformed and aligned chains in the smooth enclaves. Moreover, the evidences obtained here are in line with general notions of polymer tribology.[148] The so-called “smooth molecular profile” polymers, such as UHMWPE, produce, once tribological sliding has commenced, highly oriented and weakly adherent layers at their surfaces. Briscoe and Stolarski first demonstrated the basic idea that, under the combined action of linear and rotational sliding, shear gradients would produce reoriented interfacial zones.[148] Linear sliding produces oriented interfaces with low friction and high wear, while the superimposed rotation disrupts the natural orientation process and create the observed surface lumps. Wang et al.[149] have revisited this problem in the context of the wear of UHMWPE in artificial joints. They provided persuasive evidence that rotation (i.e., torsional microdisplacements) disrupts highly oriented molecular assembly. From a general perspective, the microstructural analysis performed by polarized Raman spectroscopy confirmed and quantified that the degree of alignment of the orthorhombic structure on the surface of in vivo exposed UHMWPE acetabular cups depends on loading history, namely on the patient’s patterns of activity. The findings also suggest that the Hermans’ parameter should be regarded as a measure of both 50

cumulative wear history and effective lifetime in acetabular cups exposed in vivo. When applied to a fully quantitative level, polarized Raman spectroscopy provides a powerful non-contact tool for the characterization of surface orientation patterns in acetabular liners made of UHMWPE. The Raman selection rules and the experimental calibration of the full set of elements for the Raman tensor for the orthorhombic structure of UHMWPE represent a unique body of physical information and properties, which can either be applied with the purpose of quality control on freshly manufactured UHMWPE acetabular cups or serve in retrieval analyses to experimentally verify the liner performance and to rationalize its in vivo lifetime. Based on the insight obtained from the Raman analysis of UHMWPE retrievals, we proceed next to a comparison at the molecular scale between in vivo exposed and in vitro tested components. The literature dealing with hip simulators has been quite successful in establishing phenomenological correlations between run-in and steady-state wear periods, and the differences between standards.[150, 151] However, the physical and chemical aspects of frictional heating and wear mechanisms at the molecular level have so far been almost ignored. From a kinematics point of view, it should be observed that a number of patient activities would offer potential for implant impingement and subluxation maneuvers quite unpredictably in the activities of daily life. Depending on implant orientations and patient activities, the femoral head may alternate between subluxing and impinging on the rim of the acetabular liner. Moreover, micro-displacements of torsional nature overlap the main articular swing. These situations are difficult to replicate in vitro and can hardly become the object of standardization. However, the question of how hip bearings should be studied in the laboratory, so that the tests are relevant to surface degradation, cannot simply be confined to kinematics issues. Unfolding the key-factors behind the performance of UHMWPE in artificial joints and establishing a sound criterion of “equivalency” between in vivo and in vitro mandatorily requires rationalizing also the chemical and crystallographic aspects of the tribological interaction. Let’s thus test the response at the molecular level of the surface of UHMWPE liners under standard hip-simulator conditions and compare them with in vivo tested liners. Figure 21 shows crystallographic orientation patterns (Figs. 21(a) and (b)) and crystallinity fractions (Figs. 21(c) and (d)) evaluated from Raman spectroscopic maps collected in the MWZ and NWZ (cf. labels) of hip-simulator tested UHMWPE liners of the same type as the unused and retrieval liners in Figs. 16(a)~(c) and 17(a)~(c). Upon comparing Figs. 21(a) and (b) with Figs. 16(a)~(c), it clearly appears that the surface of the liners tested in hip simulator for 5 M cycles under standard conditions preserved the random patterns of the unused liner. This trend was independent of the presence of abrasive cement particles in the additional 2 M cycles. Similar considerations applied to the patterns of crystallinity (cf. Figs. 21(c) and (d) with Figs. 17(a)~(c)). The absence of molecular orientation and crystallinity patterns, as found in the retrievals, at the surface of the in vitro tested liners might be due to different lubrication conditions in vivo and in vitro. While the hip-simulator test is designed to make the couple sliding under hydrodynamic lubrication conditions, the observed molecular 51

patterns suggest that in vivo sliding takes place under boundary lubrication conditions. Under these latter conditions, which are likely due to a paucity of synovial fluid in the implanted joint, the UHMWPE bearing surface is subjected to a more severe shearing stress field and undergoes faster and more severe damages. If the principle of “equivalency” states that 1 M cycles in hip simulator are roughly comparable with 1 y in vivo, data in Figs. 16, 17, and 21 show that an exposure in vivo of 2.4 y seriously damages the UHMWPE surface where simulating cycles lasting more than twice the number of in vivo cycles leave the surface as flawless as the pristine one. Figure 22 gives speculative views of in vivo (boundary lubrication conditions) vs. in vitro (hydrodynamic lubrication conditions). Based on the Raman analyses shown in Fig. 20, in vivo frictional sliding at CoCr asperities has the effect to pull and align the amorphous chains, while creating lumps of less compliant crystalline lamellae. On the other hand, the presence of compacted solid protein layer (with possible entanglements between protein chains; cf. Fig. 22)[152, 153] conspicuously impedes the CoCr surface asperities to damage the UHMWPE bearing surface, the frictional forces mainly leading to denaturation/cleavage, and to the formation of collagen peptides. It should also be noted that hip simulator studies are often performed at 1~2 Hz whereas gait is at approximately 0.3 Hz. Moreover, there are many discrepancies between laboratories on how much they dilute bovine serum and if bovine serum is in fact equivalent to synovial fluid at all. However, the rule of thumb in any engineering design is to create standards according to the most severe cases, in order to keep the design on the safety side. Hip-simulator standards seem to represent an exception to such a general criterion, as the lubrication regime has been set to minimize the tribological burden to the sliding couples.[154-156] In summary, our Raman spectroscopic analyses at the molecular level showed that there are likely discrepancies in the lubrication regime under which simulator testing is performed in vitro and those of implants in vivo. This suggests that while hip simulator testing in its current form might be useful in comparatively characterizing the wear resistance of bearing couples, lubrication and testing conditions that better simulate in vivo conditions (through incorporated spectroscopic analyses as those described here) should be explored. In substance, the in vitro standard tests should be re-designed according to the most severe lubrication conditions in order to check which couple better performs under the most realistic scenario. 4.2 Molecular scale alignment and residual strain in knee tibial plates This sub-section is dedicated to the Raman quantitative assessments of molecular rearrangement and residual strain in polyethylene tibial inserts used in total knee arthroplasty (TKA). As done in the previous sub-section for hip components, the rearrangement propensity of molecular chains under strain in polyethylene tibial inserts can be expressed in terms of Euler angular displacements in space and orientation distribution functions. In showing the application of the Raman method, unused polyethylene tibial inserts belonging to different implant generations (i.e., an older generation of ethylene oxide (EtO)-sterilized and a new type made of γ-irradiated polyethylene materials) are first evaluated and compared. The obtained quantitative information is then applied to analyze four tibial inserts (from the same makers of the unused sam52

ples) retrieved after short to medium term in vivo exposures (7 mo ~ 5 y 8 mo) and cleaned before storage and analysis. With their higher cross-linking density, γirradiated samples are expected to show better strain-recovery capability and, thus, to experience lower texturing under compressive strain as compared to EtO-sterilized samples. In knee polyethylene components, the formation of molecular patterns and the accumulation of plastic strain during service include significant out-of-plane molecular rotations. Under compressive stress, the crystalline lamellae of the polyethylene structure tend to align onto planes increasingly parallel to the sample surface, until full saturation of the angular displacements is reached. It should be noted that the magnitude of the forces operating in a tibial plate are comparable to those developed in hip liners. However, the external cyclic load applied to the tibial plate is distributed over a more limited area than in the case of hip, thus generating levels of stress that could easily exceed the polymer yield strength.[157, 158] The motion in the knee joint is mainly linear rolling/sliding. But, rotation and medial-lateral sliding introduce cross-shear into the knee components.[159] The high stress magnitudes involved might greatly enhance crystalline texture, which in turn play a crucial role in both wear resistance and strength properties. It is well known that manufacturing procedures of polyethylene components can be tailored to obtain different microstructural characteristics.[160] Samples produced by extrusion and by compression molding have been extensively studied and their microstructural features related to different patterns of plastic deformation during manufacturing. Both ram-extruded rod stock and compression-molded sheets of UHMWPE are used in joint replacement prostheses. These different procedures induce different peculiar crystallographic textures in the polymer structure, although the extent of such a texture formation is mild as compared to that taking place in vivo under regimes of large plastic deformation. During deformation, a preferential orientation of the c-axis of the orthorhombic structure takes place along the plastic flow direction with the lamellae rotating away from the loading direction. Concurrently, a tendency of the orthorhombic a-axis to orient toward the loading direction was also reported.[161, 162] Building upon the theoretical treatments of molecular orientation and plastic strain assessments, polarized Raman microprobe spectroscopy quantitatively unfolds the microstructural modifications induced by plastic deformation in tibial inserts retrievals. In comparison with the respective unused samples as received from the makers, on which preliminary calibrations were performed, the plastic strain stored in the material can be correlated with the out-of-plane variation of the tilt angle in the polyethylene chains and the variation of the statistical ODF parameters. Retrieved knee joints produced by different manufacturers and sterilized by different methods then became quantitatively comparable with respect to their strain response in vivo. The structural modifications induced in vivo by plastic deformation could be visualized and linked to the manufacturing procedures. A total number of seven UHMWPE tibial inserts were characterized: three in the asreceived state from the makers and four retrieved after TKA revision surgery. Among the four retrieved UHMWPE tibial inserts, two inserts were manufactured by Japan Medical Materials (JMM, Osaka Japan) and sterilized by ethylene oxide gas (hence53

forth referred to as samples A and B), while the remaining two, referred to as samples C and D, were commercially distributed by Stryker K.K. (Tokyo, Japan) and Smith and Nephew Orthopedics (Tokyo, Japan), respectively. The tibial insert Sample C was vacuum/N2 flush packaged, and then γ-irradiated with 33 kGy. Insert Sample D was only sterilized with EtO. Insert Sample A belonged to a 73-year-old female patient for which the cause of revision was aseptic loosening with a follow-up period of 5 years and 8 months. Insert Sample B belonged to a 77-year-old female patient. The cause of revision in this latter case was also aseptic loosening, but it occurred after a slightly shorter follow-up period of 4 years 7 months. Samples C and D were retrieved from female patients whose ages were 83 and 81 y old, respectively. In the former case, the cause of revision was aseptic loosening after an implantation period of 4 years, while for the latter the cause was malpositioning after a follow-up of only 7 months. All patients were >70 y old, with similar body mass index (BMI), and showed limited activity, although all of them were normally ambulating. Table IX gives a summary of the investigated cases, including manufacturing characteristics and clinical data. The three unused tibial plates were of the same types as the retrieved ones, one from each manufacturer. All three types of tibial plate were machined from compression-molded sheets. For simplicity’s sake, the as-received samples were labeled with the same letters as the retrieved plates. Raman assessments were randomly performed at 20 locations, as selected in the MWZ and NWZ of each retrieval. In order to minimize the in-depth convolution of the Raman information, a confocal pinhole 100 µ m in diameter was employed. The probe size of the Raman assessments was 2.2 and 6.4 µ m in plane and in depth, respectively (cf. probe calibrations in Appendix A). Unlike EtO sterilization, γ-irradiation generates cross-linking (especially in the amorphous phase), which significantly affects the macroscopic strain behavior of the UHMWPE structure. The differences in plastic deformation behavior of the two differently sterilized (as-received) samples became evident when, stepwisely loading them in compression and allowing recovery for 24 h, polarized Raman spectra were systematically collected. The compressed surfaces were analyzed with placing the sample in a rotation jig and collecting polarized Raman spectra at different in-plane (azimuthal) angles, ψ. The overall analytical procedure, including spectral acquisitions and fitting procedures, was the same as that described in the previous subsection for hip liner analyses. In this way, we monitored the alteration of the polyethylene microstructures from their as-received state (i.e., at residual strain assumed to be ε=0) up to ε=12% of uniaxial compressive true strain. Noticeably, no appreciable difference could be found between the behaviors of the two studied EtO-sterilized materials produced by different makers. Accordingly, the strain calibration results are henceforth discussed as EtO-sterilized vs. γ-irradiated samples. The outputs of the Raman spectroscopic assessments are summarized in Figs. 23 and 24. Figures 23(a) and (b) summarize data for the (plastic) strain dependence of the out-of-plane tilting angle, θp, and the Hermans’ parameter, < ¿(`Åƕ) >, respectively, as computed from least-square fitting analyses of in-plane rotation experiments (cf. procedure in 54

Section 4.1). As seen, a comparison between the plots for EtO-sterilized and γirradiated samples revealed clear differences in the plastic strain response of the two types of pristine materials, the largest variance being observed at regimes of high strain (>3% and >8% for θp and < ¿ (`Åƕ) >, respectively). In Fig. 24(a), the observed trends of molecular rearrangement in both types of sample are expressed according to phenomenological curves, ε=ε(∆θp), where ∆θ p represents the variation of out-of-plane tilt angle with respect to the original orientation direction in the virgin (unstrained) sample. The plots in Fig. 24(a) show clear difference for EtO- and γirradiated materials. A procedure of least-square fitting led to two equations of a common cubic nature, as follows:  = 71.96ΔNÛ − 302.72ΔNÛ + 546ΔNÛ

 = 119.47ΔNÛ − 643.82ΔNÛ + 1293.28ΔNÛ

(83) (84)

(with angular variations expressed in radians) for the EtO- and γ-irradiated samples, respectively. The correlation factor R2 obtained for the fitting of the experimental curves to cubic polynomials was 0.993 and 0.987 for Eqs. (83) and (84), respectively. The above equations link the residual strain stored into the sample to a Ramanmeasurable microstructural parameter (i.e., ∆θp), and can be used to quantitatively discuss the amount of residual strain stored in tibial inserts during in vivo exposure. The ODF curves obtained at different levels of strain for the EtO- and γ-irradiated samples are reported in Figs. 24(b) and (c), respectively. As a general rule, an increase in applied strain led to a larger population of molecular chains experiencing preferential orientation, as shown by the increasingly pronounced maximum in the ODF. However, such a trend was more pronounced in the EtO-sterilized sample as compared to the γ-irradiated one. The salient notions that can be extracted from the plots in Figs. 23 and 24 can be summarized, as follows: (i) In the bulk sample, the molecular chains were initially aligned along a direction nearly perpendicular (θp ~π/12) to the sample surface in a similar way for both types of sample, although with an invariably low statistical frequency ( < ¿ (`Åƕ ) > ~0.25). (ii) The tilt angle, θp, which locates the direction of the long axis of the molecular chains, gradually increased up to θp ~π/5 (with a slope similar for both types of material) under application of compressive strain. (iii) Unlike the γ-irradiated sample, which showed a comparatively low statistical degree of molecular alignment (i.e., 0.25 ≤< ¿ (`Åƕ) >≤ 0.40) over the entire interval of investigated strain, the EtO-sterilized sample showed an abrupt increase in Hermans’ parameter (i.e., up to < ¿ (`Åƕ ) > ~0.70), starting from a threshold value of strain at around 7.5 %. As far as the above point (i) is concerned, the finding is in good agreement with a study by Bellare and Cohen[95] on compression-molded sheets and follows the same 55

trends discussed in Section 3.4. Namely, a similar angular population for EtOsterilized and γ-irradiated samples in their as-received state, which conceivably arises from both samples being manufactured from rods obtained by the same extrusion process. It is also reasonable that uniaxial strain tends to align the molecular chains in a direction parallel to the surface, i.e., perpendicular to the direction of the applied compressive load. Galeski et al.[96] showed that, at the initial stage of deformation, the main mechanism of structural rearrangement consisted of interlamellar sliding, while chain slip within individual crystallites became active only at a subsequent stage, when the molecular chains in the lamellae became prone to slip along the [001] direction of their orthorhombic structure (i.e., corresponding to a slip along the most closely packed crystallographic plane). At higher deformation levels, the lamellae were significantly elongated and a decrease in thickness was also observed. This latter structural modification was due to the movement of chains, which were forced to align along the direction of plastic flow with the microstructure becoming similar to a single crystal. According to the trends of θp angles in Fig. 23, the onset strain for lamellae mobility was about 3~4% for EtO-sterilized UHMWPE, while in γ-irradiated polyethylene such a strain threshold became about twice higher. This observation, together with the different trends of ODF (cf. Figs. 24(b) and (c)) between γ-irradiated and EtO-sterilized samples, confirms that highly cross-linked polyethylene samples achieve lower crystallographic orientation as compared to less crosslinked samples for the same level of externally applied strain.[97, 98] The initial deformation, accommodated by the amorphous regions below the yield stress, results in macromolecules getting extended and “locked” prior to activation of slip systems in the lamellar regions. If the polyethylene is crosslinked, then it gets fully stretched to its maximum limit at lower strains. Thus, macromolecular re-orientation is faster (i.e., recovery is more efficient) in highly crosslinked polyethylene. Shifting now the focus of the discussion on the molecular orientation in retrievals, local variations of in-plane angle, ψp cannot be neglected due to the dynamic (frictional) character of the in vivo loading conditions. Accordingly, the computational analysis of Raman intensities upon in-plane sample rotation was applied upon considering the concurrent variations of two Euler angles, θp andψp. Moreover, in analyzing retrieved tibial inserts, we took advantage of the two phenomenological Eqs. (83) and (84) in order to quantify the amount of compressive residual strain stored in the retrieved polyethylene plates. The results of polarized Raman analysis of four retrievals (i.e., as listed in Table IX) are summarized in Fig. 25 in terms of in-plane and out-of-plane Euler angles (i.e., θp and ψp, describing the preferentially oriented long axis of the molecular chains), while Fig. 26 gives the residual strain, ε, stored in both MWZ and NWZ of the investigated retrievals. Data in Fig. 25 indicate that the θ p and ψp values collected at a depth of 100 µm in the NWZs were all very close to the respective values observed in the unused plates (i.e., ψp ~π/5 and θp ~π/12; cf. also data in degrees given in figure insets), independent of sterilization process. The common manufacturing process of compressionmolded sheets mainly dictates such orientation angles for the crystalline lamellae. In other words, the microstructures in the NWZs looked very much the same as those of 56

the as-received samples, independent of exposure time in vivo and sterilization process. On the other hand, in the MWZs of the retrieved tibial plates, the angles of molecular orientation, θp and ψp, showed appreciable variations as compared to the asreceived samples in correspondence of locations at which the highest compressive and frictional loads were applied. In the three EtO-sterilized samples, the tilt angle, θp, was found to commonly lie in a narrow interval at around π/8, despite the quite different exposure times in vivo (which was significantly shorter for Sample D as compared to Samples A and B). The tilt angular rearrangement, ∆θp~π/22, recorded for these three samples corresponded, according to Eqs. (83) and (84), to surface strains comprised within a narrow range, ε= 5.0~5.5 % (cf. Fig. 26). This finding seems to confirm that the most significant amount of plastic deformation in polyethylene components occurred during the first year of implantation, as previously reported by other authors.[163, 164] It should be noted that the load–displacement curves obtained by Edidin et al.[164] showed a higher strain hardening for GUR 1050 as compared to GUR 1020. Accordingly, the lower amount of residual plastic strain in Sample D compared to Samples A and B might be partly due to a difference in the type of starting resin. Some residual strain seems also to accumulate in the NWZ, despite the conspicuously load-free conditions of such a part of the knee joint upon normal walking activity. Note that the conspicuous absence of wear in the non-wear zone during in vivo service does not necessarily mean absence of static load, which is the main cause of creep and out-of-plane molecular alignment. However, the calculated amount of residual strain was quite low and within the experimental scatter. On the other hand, the γ-irradiated Sample C, despite its comparatively long-term exposure in vivo, experienced a quite low tilt angle variation for a similar amount of plastic strain (i.e., ∆θp~π/40 and ε~6%; cf. Figs. 25 and 26). This observation confirms a higher strain hardening of the γ-irradiated sample as compared to the EtO-sterilized samples, which was also observed upon static loading experiments. Unlike the relatively straightforward outputs of the Raman analysis regarding the effect of compressive load on the surface of tibial insert retrievals, the analysis of inplane molecular displacements appears more complex and difficult to rationalize. Sample A, for example, although being implanted for a period of time 13 months longer than Sample B, showed less in-plane alignment along the direction of primary motion or the principal direction of sliding (i.e., ψ=π; cf. Fig. 25). With longer periods of exposure time in vivo, the long axis of the polyethylene molecules tends to align on the plate surface along the direction of primary motion. Such a molecular alignment process is similar to that discussed in hip liners in the previous section, and it has been reported to produce a reduction in wear resistance on the sample surface.[165] However, such a mobility process should strongly depend on both the level of activity and body weight of the patient. Unlike ψp angular displacements, clear differences could be found between ODFs calculated in the main wear zone and in the non-wear zone of each sample (Fig. 27) for Samples A, B, C and D, respectively). The plots in Fig. 27 were obtained from the average ODF parameters for each investigated area, while the Hermans’ parameters associated with each f(β) distribution curve are explicitly shown 57

in the inset to each plot. It should be noted that, although a preferential orientation of polyethylene chains was also observed in NWZ, the distribution of molecular directions in these zones was always quite broad. On the other hand, by comparing the ODFs in the main wear zone of EtO- sterilized samples (i.e., Samples A, B and D) with that of the γ-sterilized one (Sample C), a significant difference could be found, thus confirming that γ-sterilized UHMWPEs possessed a more “rigid” microstructure and, thus, was less prone to enhancements in the degree of texture associated with the occurrence of plastic deformation in vivo. In order to clarify the profile of molecular re-arrangement, the dependence on the indepth z-axis of the two preferential angles of the molecular chains, θp and ψp, for asreceived (pristine) and retrieved (average) tibial inserts was measured (Fig. 28). In Fig. 28(a), both orientation axes and rotation angles in the artificial knee joint are defined (in inset, cf. also the relationship between molecular chains and orthorhombic lamellae). Figure 28(b) shows the in-depth statistical frequency of the out-of-plane preferential orientation (angle, θp) for the γ-irradiated pristine sample, as expressed in terms of Hermans’ parameter, < ¿(`Åƕ) >. The plots in Figs. 28(c) and (d) give the in-depth dependences of the average preferential angles of the molecular chains, θp and ψp, respectively, for the retrievals in comparison with the pristine. These data give a comprehensive view of the in-depth polymer structure and confirm that γirradiated polyethylenes are more resistant to molecular texturing as compared to EtO-sterilized samples for similar levels of externally applied strain. In conclusion, polarized Raman spectroscopy was quantitatively applied to assess molecular rearrangements in terms of in-plane rotation and out-of-plane tilting Euler angles in polyethylene tibial inserts. Variations in the orientation of molecular chains directly relate to the residual strain and to the plastic flow that takes place during in vivo service. Variations in out-of-plane, θp, and in-plane, ψp, Euler angles, of the preferential orientation of the long axis of polyethylene chains obeyed compressive and frictional forces, respectively. ODFs expressed in quantitative terms the crystallographic textures developed upon in vivo service of retrieved components. Our Raman findings imply the possibility to further maximize the wear performance of biomedical polyethylene components by controlling the crystalline texture as the outcome of different technological regimes for surface machining during manufacturing. 4.3. Differentiating creep and wear degradation in hip joints Wear of polyethylene acetabular cups in patients who obtained total hip arthroplasty is routinely deduced from the penetration of the femoral head into the acetabular liner as observed in the radiographs.[166] However, the linear penetration measured in this way represents the cumulative contribution to thickness reduction of two distinct components: wear and creep. The erroneous attribution to wear of the entire penetration displacement of the head inside the cup might lead to misinterpretation of the tribological performance of the acetabular liner. Raman spectroscopy allows quantitatively differentiating the two different components of thickness reduction in retrievals, thus giving a correct estimate of the tribological performance of the studied implant. In this investigation, we employ Raman spectroscopy to evaluate the wear and creep 58

performances of a series of acetabular cups of the same type, which underwent different clinical histories. Creep and wear both represent degradation mechanisms in UHMWPE acetabular liners, which ultimately lead to significant reductions of joint lifetime in the human body.[55, 167-170] Creep refers to a permanent deformation that occurs under the effect of body weight and does not recover after load release, while wear involves both delamination and progressive peel-off of surface polyethylene flakes, which result in the formation of highly reactive debris. Oxidation, which will be discussed in detail in the next section, plays a detrimental role in triggering wear, since oxidized molecules might delaminate faster due to local damage of the polymeric network (cf. mechanism previously discussed in Section 4.1 and depicted in Fig. 20).[55] Moreover, the role of polymer molecular orientation and wear direction has also been visualized after in vivo exposure, and the performance of the acetabular cups was shown to be highly dependent on the direction of shear.[147] It should also be considered that the two degradation mechanisms of creep and wear might negatively interact, since a permanent deformation of the original bearing surface of the liner leads to femoral head migration and enhanced friction. Unlike wear, creep is not accompanied by irreversible mass loss from the material, but involves packing and adjustment of polyethylene molecules under compression. Despite their different physical origin, both these two main degradation mechanisms appear as a reduction in cup thickness, whose total extent is routinely measured in vivo by X-ray radiographs and by caliper on retrievals after explantation. Aimed at improving wear and deformation resistance, different methods of irradiation for UHMWPE have been developed and dose amounts investigated.[171-173] However, in examining the vast available literature, one might come across several aspects of the functional response of biomedical polyethylenes in vivo and in vitro that are somewhat contradictory to each other.[174-178] In their hip simulator studies, Dowson and Jobbins[177] have indicated that creep can account for an appreciable portion of the total penetration in 22 mm cups within the first few million cycles. However, a method for assessing the actual fraction of displacement due to creep in acetabular cups exposed in vivo is still lacking and the need of an improved evaluation of the performance of various polyethylene grades employed in hip arthroplasty calls for a better understanding of the relationships between molecular structure and mechanical properties. We scrutinized using the Raman microprobe 7 short and 4 middle term hip-liner retrievals of remelted polyethylene all of the same type (Longevity®; manufactured by Zimmer, Warsaw, Indiana, US) as listed in Table X. The retrievals were cleaned before storage and analysis. According to the experimental procedure based on bandbroadening assessments described in Section 3.4, unused samples made of Longevity® polyethylene were analyzed to obtain a phenomenological correlation between compressive residual strain after recovery and broadening of the Raman band located at 1130 cm-1 (symmetric stretching vibration of C-C bond). Figure 29 shows the obtained correlation between the percentage of compressive strain measured after 24 h recovery and the experimental band broadening, which, as previously shown, was 59

measured as the variation of FWHM. A cubic regression model was used to calculate the best-fitting curve and found to obey the following equation:  = −0.107 + 40.67ΔFWHM − 101.7Δ†‹Œ + 131.0Δ†‹Œ 

(85)

where the strain, ε, is in %. The confidence level of the fitting was 95 %, while the standard error of the regression (S) and the coefficient of correlation (R2) were 0.25% and 0.996, respectively. Once compressive (plastic) strain becomes locally measurable by Raman spectroscopy, in-depth Raman scanning can be used to evaluate thickness reductions due to creep. A reduction in thickness, ∆tc, due to creep can be calculated from experimental residual strain profiles along the in-depth abscissa, z, according to the following equation: Δ, = —! e (;) − ! (;)i b; ≅ ∑9:šߏ̅: (;) − ̅! (;)àΔ; -

(86)

where n is the number of data points collected at increasing depths along the liner thickness, t is the thickness of the cup in the main wear zone, ̅: is the average strain value measured in the probe at each location, ̅!: is the average strain value measured in the unused cup depending on the position along the thickness, and ∆z is the indepth size of the confocal probe. With knowledge of Δ, data in comparison with the overall displacements, Δ, which is directly measurable by caliper on the retrieval (in comparison with the thickness of the pristine sample), the creep contribution to the overall thickness reduction of the liner can simply be obtained as: Đ = Δ − Δ,

(87)

In Fig. 30(a), a draft is given of the protocol followed to characterize the 11 polyethylene liner retrievals. Each sample was cut into two halves, the cross section polished, and Raman line scans performed at 9 selected locations including MWZs and NWZs. In Figs. 30(b) and (c), pictures are shown of a sectioned retrieval and of its polished cross section, respectively. Figure 31 shows the results of creep, wear, and total reductions in thickness of the UHMWPE liner, as obtained for the 7 short-term retrievals according to Eqs. (85)~(87). For each liner, the data were plotted in polar coordinates according to experimental data collected at the above-mentioned 9 angular locations where the thickness was measured. The profiles were obtained by B-spline interpolation of the experimental points. The polynomial fitting equation used to assess the percentage of creep deformation incorporated an error of 0.5% (i.e., 2S, 95% confidence level). Note that reductions in thickness due to wear, as obtained by subtracting creep displacements from the total penetration, might give in some cases negative values in the order of few tens of microns. Negative values (corresponding to increases in thickness) are physically meaningless and simply arise from measurement errors integrated over the entire thickness. As a matter of fact, an error of 0.5 % in strain assessment integrated over the maximum thickness of 15.4 mm gives a maximum error 60

of 77 µm, while for the 6.3 mm cups the maximum error can be estimated at 31.5 µm. Wear in the short-term cups was always negligible and the creep contribution was considered to equal the total change in thickness of the liner. It is clear that samples of Cases 1 and 2 incorporated the lowest residual strain among short-term retrievals, mainly localized between locations L3 and L6, while cups with follow-up longer than 6 months (Cases 6 and 7) showed peaks of penetration higher than 100 µm, as well as detectable deformation also near the rim, presumably due to stem impingement. The highest deformation near the rim (L1 and L9) was detected in the sample of Case 7, which had the longest follow-up and a high abduction angle (47°; cf. Fig. 31 and Table X). A high abduction angle indeed favors the impingement of the neck of the stem against the rim. In Case 5, the main amount of deformation was instead localized around the top of the cup (L5), in agreement with a low abduction angle (30°). Similar to Fig. 31, the results of 4 middle-term retrievals are reported in the polar plots of Fig. 32. The onset of wear clearly appeared in all the examined middle-term liners, manly localized between locations L3 and L6, with the exception of liner Case 9, in which the reduction of thickness was lower in magnitude but widespread between L1 and L6. This different trend was probably due to the relatively low abduction angle (40°). Sample No. 8 was characterized by the highest creep and in it wear damage was sharply localized at L4, as expected by the abduction angle of 45°. Interestingly, the patient of the latter retrieval had the highest body mass index (BMI) among the four (BMI=33; cf. Table X) and suffered dislocation, which might explain the considerable magnitude of residual strain calculated also in locations that are not supposed to be loaded during gait motion. Moreover, all the middle-term retrievals showed significant creep deformation in both locations near the rim. Creep- and wear-related thickness reductions that occurred in vivo in the main wear zones are plotted for the full series of retrievals as a function of implantation time in Fig. 33. The plots clearly show that the consumption in thickness due to wear is negligible during the beddingin period, as compared to the thickness reduction due to creep. A linear regression analysis of these data enables one to calculate the femoral head migration rates experienced by the patient during both bedding-in and steady state follow-up periods. The total rates are also listed according to data of total thickness reduction, sum of creep and wear displacements. These results are reported in Table XI, which also includes the respective Pearson’s product moment correlation index (r), namely the measure of how well the shown data are related to the hypothesized trends. Overall, the creep deformation in the examined seven short-term retrievals was the predominant phenomenon and constantly increasing with implantation time. As a matter of fact, the short-term retrieval with implantation time close to 1 year (Case 7) showed a creep deformation, which was comparable to those found in middle-term retrievals, confirming earlier clinical data showing how, after the initial bedding-in period, the head penetration rate due to plastic deformation of the liner lowers.[178180] A closer examination of data in Fig. 33 and Table XI actually strengthens this argument. Wear rate at the steady state is 0.020 mm/y, which is negligibly low. The amount of plastic deformation experienced after bedding-in period is 0.010 mm/y, with a scattered distribution of the 4 middle-term data. Note that the rate consistently 61

drops down as compared to the 0.189 mm/y rate experienced during bedding-in period. Sample No. 8 possessed the highest peak of creep deformation among the four examined retrievals despite being the retrieval with the shortest implantation time. On the other hand, the liner in Case 9 experienced a creep deformation comparable to the 8-month retrieval Case 7. Interestingly, retrievals Cases 8 and 11, which showed the highest peaks of worn thickness, were both coupled with CoCr femoral head, while the other two middle-term retrievals (Cases 9 and 10) articulated against zirconia femoral heads. Considering the regression lines of the overall data, wear and creep rates were equal (0.026 mm/y). The total penetration rates were 0.189 mm/y, 0.027 mm/y and 0.046 mm/y for the bedding-in, steady-wear, and overall periods, respectively. These latter data can be compared with previously published clinical studies on remelted polyethylene.[178-180] However, all the methods used in those previous studies were not capable of discriminating between the amount of femoral head penetration due to wear damage or creep; but, they only relied on the consideration that during the initial bedding-in period the thickness variation should only be related to plastic deformation, while during the successive period of implantation the penetration should fully be associated to wear (i.e., steady-state wear). Manning et al.[180] reported results of retrievals at maximal 44-month follow-up, which were obtained by radiographies and showed an overall penetration rate of 0.018 mm/y, with a peak of 0.4 mm/y registered after 6 months, and a steady-state wear estimated to be 0.07 mm/y. Also Geller et al.[178] presented a clinical study of Longevity® retrievals based on radiographic evaluations of femoral head penetration for 36 and 40-mm heads in 71 patients. The median femoral head penetration during the first postoperative year was 0.24 mm, due to creep (bedding-in period), while up to 3 years periods of implantation the median steady wear rate dropped down to 0.06 mm/y. In a different study, the same authors used radiostereometric analysis to measure the femoral head penetration in retrievals of 28 and 36-mm head size, reporting the highest penetration rate during the first year of implantation of 0.055 mm/y, but during the second and third year there was no significant variation of head penetration indicating no occurrence of wear damage.[181] In some cases, published studies have given contradictory results, the observed discrepancies possibly arising from neglecting the dual contributions of wear and creep in femoral head migration analyses. It should also be noted that in-vitro wear simulations conducted on Longevity® liners showed much lower wear rates than those measured after explantation,[179] suggesting that in vitro hip simulation conspicuously fails in reproducing the degradation phenomena of polyethylene liners in vivo. In conclusion, the Raman spectroscopic method described here provided new information at the molecular scale, which enabled the obtainment of quantitative information yet unavailable from previously established analyses (e.g., radio-stereometry). Similar to radio-stereometry, we can obtain the volume reduction of the liner, but we can also distinguish between the volume actually worn out and that induced by creep, namely by an increase in local density of the UHMWPE structure. Figure 34 shows a graphical analysis of Case 8 with a quantification of the volume reductions due to wear and creep (a) and a cross section profile (b). Scanning the liner retrievals with a confocal Raman probe possesses a potential to become a routine 62

procedure in rationalizing the separate effects of creep and wear in UHMWPE bearings. The advanced spectroscopic method described here clearly shows the possibility to rationalize clinical studies on retrievals, finally conciliating the responses of UHMWPE in vitro and in vivo. 4.4 Oxidation and the effects of infused vitamin E in hip liners In 2010, Muratoglu et al. published an enlightening analysis of explanted UHMWPE acetabular liners.[182] As received from the maker, these liners were irradiated at 100 kGy and re-melted to fully annihilate residual free radicals (Longevity®, Zimmer, Warsaw, IN, USA). However, the surprising outcome of this study was that, after in vivo exposure, chemical changes resulted in increased free radical formation, a loss of crosslinking, and oxidation. Even after their explantation, the liners continued to oxidize. These findings seemed to contradict the widely held belief that the fraction of free radicals is negligible in a re-melted liner.[182] Indeed, the presence of free radicals in the highly cross-linked and re-melted UHMWPE liners was conspicuously eliminated at the manufacturing stage, such assertion being supported by oxidation analyses on long-term shelf-stored liners in air and by real-time aging in aqueous environments at homeostatic temperatures.[182, 183] However, a different mechanism was responsible for the observed in vivo and ex vivo degradation. Accordingly, a chemical rather than mechanical origin was postulated for the observed free-radical formation and ensuing oxidation.[62] First, it was reasoned that the number of loading cycles in vivo would have been too limited to explain oxidation as a loading fatiguerelated phenomenon, and then hypothesized that lipids (e.g., squalene) absorbed from the synovial fluid were the source of the free radicals and ensuing oxidation. It is known that UHMWPE absorbs lipids from synovial fluid in vivo,[70] and that lipids start to oxidize as soon as they come into contact with oxygen molecules either in vivo or ex vivo (e.g., on the shelf in presence of air after removal from the patient in the case of the report by Muratoglu et al.[182]). In support of this hypothesis, it was observed that even very short durations (e.g., 2 months) of in vivo exposure led to high levels of oxidation after long-term ex vivo storage.[182] The unsaturated C=C bonds in the lipid molecules (e.g., cholesterol, hexadecanoic and octadecanoic esters of cholesterol-like cholesteryl stearate, squalene, or other unsaturated precursors in cholesterol synthesis)[184] tend to react with the saturated polyethylene molecules and initiate degradation of the host polymer (Fig. 35(a)). Note that peroxidation of squalene can be initiated by a number of different chemical species, such as metal ions, reactive oxygen species, or hydroxyl free radicals present in the human body.[185] Formation of peroxy free radicals in the lipid molecules occurs because of their reaction with oxygen, which in turn leads to the formation of hydroperoxides by abstracting hydrogen atoms from the surrounding polyethylene chains (Fig. 35(b)). This attack by lipids forms new free radicals in polyethylene, preferentially in its amorphous phase, and their high mobility in the amorphous phase quickly propagates oxidation. In turn, oxidation results in a significant increase in crystallinity, chain scission (Fig. 35(c)), formation of a lower molecular weight polyethylene, and recrystallization, as previously explained in Section 3.3 (cf. also Figs. 8 and 9). Our analyses of retrieved irra63

diated and re-melted liners partially confirmed the findings of Muratoglu et al.[182]183 Figures 36(a) and (b) are graphs of the FT-IR-measured OI parameter for the same set of 11 Longevity® liners (7 short-term and 4 medium-term retrievals) discussed in the previous sub-section (cf. Table X). Note that the analyzed liners belonged to the same type of implant investigated by Muratoglu et al.[182] Elapsed shelf-time before completing the analyses with maximum and average OI values for the main-wear and nonwear zones are also provided below each plot. OI values were found clearly higher in the middle term in vivo exposed retrievals than in the short term exposed ones, but they were erratic with respect to on-shelf exposure. The overall picture for the data shown in Fig. 36 suggests that free radicals are actually formed in the UHMWPE structure during in vivo exposure. Their formation is cumulative and more pronounced in the MWZ. Free radicals readily turn into oxidation sites as soon as oxygen becomes available. Whether or not oxygen availability occurs during or after implantation is a matter of speculation, although it is conceivable to expect a hypoxic environment in joint articulation. Note that our spectroscopic analyses fully support the findings by Muratoglu et al.[182] However, unlike their interpretation, the dependence of the OI on exposure time was not erratic. Our experimental results indicated that the OI was primarily determined by in vivo implantation time, although we cannot rule out contributions from shelf time. As an example, the in-depth oxidation profiles, OI, recorded in the medium-term in vivo-exposed liner Case 8 (4.1 y and a post-explantation shelf period of 4.2 y), are shown in Fig. 37. With the oxidation index, OI, plotted as a function of the in-depth abscissa, z, along the liner thickness at various locations in the main-wear and nonwear zones, these data clearly show that high levels of oxidation (i.e., up to OI = 6) can be found in irradiated and re-melted liners. Moreover, data collected in the MWZ showed a pronounced sub-surface peak of oxidation (at around z = 600 µm) when compared to the NWZ (cf. locations L3, L4, and L5 with locations L7 and L9 in Fig. 37). This difference demonstrates that in vivo loading actually exacerbates free radical formation. Figure 38 compares in-depth profiles of oxidation index, OI, from FT-IR spectra (a) and crystallinity profiles, αc, from Raman spectra (b), as obtained at the same location L5 (cf. Fig. 37) of the retrieval Case 8. OI profiles collected on the retrieval are compared in Fig. 38(a) with profiles similarly collected on samples obtained from the same type of liner: as-received, subjected to 28 days shelf-aging at 23oC after 25 kGy γ-ray irradiation, and subjected to oxygen-bomb (5 atm) aging at 70oC after 25 kGy γ-irradiation and 28 days aging on shelves. As expected for a remelted liner, the as-received sample showed a quite low amount of oxidized species (OI equal to 0 in the majority of locations along the in-depth profile and a maximum of 0.01). The oxidative degradation of the sample clearly increased upon γ-ray irradiation and on-shelves aging, and showed some further oxidation upon in-vitro aging in oxygen. However, the OI values were yet well below the unity value and remained homogeneous along the thickness of the liner. The in vitro data clearly contrasted with the in vivo profile, for which a pronounced OI peak could be observed at around 1 mm in depth from the sliding surface of the bearing. The maximum OI magnitude was as high as 5.2. The αc profiles in Fig. 38(b), obtained by Raman spectroscopy on 64

the same sample slices tested by FT-IR (cf. protocol shown in Fig. 7), showed striking similarities with OI profiles, thus confirming also for the retrieval the phenomenological correlation already discussed in Section 3.3 (cf. Eq. (30)). Important conclusions can be drawn from the comparison between in vivo and in vitro oxidation experiments, as follows: (i) The absence of gradients in the OI profiles upon in vitro oxidation strongly suggests that the distribution of free radicals generated upon manufacturing and by the preliminary step of γ-irradiation was uniform (i.e., no gradients of residual free radicals existed along the thickness of the virgin liners). (ii) Experimental evidence was obtained, which indicates how the formation of free radicals is favored by mechanical load on the acetabular liner. Mechanical stress promotes both lipid diffusion and the rupture of the C–C bonds, especially underneath the surface where the highest contact stress is predicted by the Hertzian equation (i.e., localized at ~1mm in depth in the investigated retrieval). (iii) Given the above item (ii), it is clear that standardized aging tests in vitro are insufficient to predict oxidative degradation in vivo, because they neglect the coupling of chemical and mechanical effects during service. The pioneering findings by Muratoglu et al.[182], which motivated the present research, are of fundamental importance in future developments of joint arthroplasty not only because they revealed a previously overlooked mechanism for free radical formation in UHMWPE (which greatly decreases its oxidative stability), but also because they triggered a new line of research into antioxidant vitamin E doped UHMWPE liners.[186-188] Infusion of vitamin E into UHMWPE liners is performed to counteract the unwanted reactions of the formed free radicals. Vitamin E’s anti-oxidant property arises from the presence of an alcoholic hydroxyl group attached to the so-called chroman ring of its structure (Fig. 39(a)). The alcoholic hydroxyl has a tendency to give away its hydrogen and become a stabilized phenoxy radical. The free hydrogen quickly annihilates one free radical in the UHMWPE, according to the so-called “peroxyl radical trapping” mechanism (Fig. 39(b)). Such self-sacrificial attitude toward free radical formation contributes to preserve UHMWPE from oxidation. Hereafter, we shall test in vitro the efficacy of vitamin E as an anti-oxidant in a commercially available UHMWPE in which vitamin E has been infused from the bearing surface of the liner. Three different UHMWPE samples are compared, which were described in detail in Sections 3.3 and 3.4; namely, the brand Longevity®, a re-melted UHMWPE produced by Zimmer; the newest liner generation UHMWPE named X3TM, manufactured by Stryker Orthopedics; and the second-generation highly cross-linked and vitamin E infused UHMWPE, referred to as E1 ® and manufactured by Biomet. Figures 40 and 41 are plots of the in vitro tested degree of oxidation (by FT-IR) as a function of the normalized in-depth abscissa, z/t, where t is the thickness of the liner. The pristine samples were treated in different ways prior to FT-IR measurements, including accel65

erated aging (100% O2, under 5 kPa, at 70oC, for 28 days) (Fig. 40(a)), γ-irradiation (25 kGy) followed by accelerated aging (same as above) (Fig. 40(b)), and accelerated aging (same as above) after remaining immersed for 4 h in squalene (95% solution, Wako Pure Chemicals Industries, Ltd., Osaka, Japan) at elevated temperature (100oC in a convection oven) to induce diffusion of lipids in the microstructure before accelerated aging (Fig. 41). At the completion of the procedure of lipid diffusion, all samples were cooled down to room temperature in their respective lipid solution and remnants of the solution were carefully removed from the surface of the samples. All samples (with and without diffused lipids) underwent accelerated aging with preliminary conditioning step consisted of irradiating the specimens with a 25 kGy dose of γray and maintaining them at 23oC for 28 days. An oxygen bomb was used to age the specimens at 70 oC in pure oxygen (5 atm) for 14 days. All the specimens were then analyzed by micro-Raman spectroscopy within 10 days after the completion of the test. The spectroscopic data in Figs. 40 and 41 clearly show that an in vitro hydrothermal treatment following γ-irradiation or soaking in squalene leads to oxidation of vitamin E infused UHMWPE liners, although to a significantly lesser extent than both remelted (Longevity®) and three-step annealed liners (X3TM). Improved in vivo oxidation behavior for short-term retrievals of vitamin E-infused liners has already been reported.[189, 190] However, our own in vitro data show that the propensity for oxidation of UHMWPE in the presence of lipids is attenuated but not completely suppressed by vitamin E. Moreover, the present tests were performed in absence of mechanical stress, which we have seen to play a fundamental role in enhancing oxidation in retrievals (cf. Figs. 37 and 38). In light of its oxidative propensity, the amount of oxygen within the joint environment becomes a key issue. In other words, any source of oxygen in the tribolayer should be eliminated. This presents an interesting series of questions: Do oxide ceramic bearings release oxygen during service? If so, where does the oxygen go within the tribolayer? There is obviously no direct toxicity involved with the release of oxygen; but this does not mean there are no long-term negative consequences for joint function.[191] UHMWPE’s strong intrinsic affinity for oxygen is triggered by the unavoidable presence of free radicals in its structure. Consequently, bearing surfaces prone to release oxygen can hardly be considered “polyethylene friendly.” It is believed that these important findings will also prompt new research in the ceramic field as well and this topic will be further discussed in the forthcoming Section 5.2. In conclusion, given the propensity for all UHMWPE liners to oxidize in the longterm in vivo service, it is critical to minimize all sources of oxygen within the tribolayer of an otherwise anaerobic human joint. Note again that this is a direct consequence of the fundamental findings by Muratoglu et al.[182] Accordingly, judging the oxidative stability of UHMWPE liners based solely on the concentration of preexisting free radicals needs to be reconsidered. Our findings on the oxidation state of retrievals also suggest that in vitro testing standards should incorporate the effect of mechanical stress in order to realistically represent the propensity to oxidize of UHMWPE liners. 66

4.5 Deformation behavior of vitamin E infused vs. blended hip liners Antioxidant vitamin E ( α -tocopherol) dopant can be incorporated into the UHMWPE microstructure by two alternative methods in the manufacturing procedure: (i) blending vitamin E before consolidation and radiation crosslinking; and, (ii) infusing vitamin E via a homogenizing heat treatment after radiation crosslinking. Our in vitro studies, as reported in the previous sub-section, have shown that vitamin E successfully contributed to retain oxidation at low levels in UHMWPE hip liners after accelerated aging tests combined with lipid absorption. Our data are in agreement with published literatures for both vitamin-E blended and infused liners.[192-194] However, the effects of different procedures to add vitamin E on the crystalline morphology of UHMWPE and its impact on the resistance to plastic (compressive) strain need further elucidations in order to complement the positive chemical effect found for oxidation stability. This task is the object of this last sub-section of experimental evaluation of commercially available UHMWPEs. Vitamin E-blended UHMWPE was first developed and clinically introduced in hip arthroplasty in 2013 in Japan,[195] while Vitamin E-diffused UHMWPE was first developed and clinically introduced in THA in 2007 in the USA.[187] Building upon the substantial body of evidences provided in Section 4.3 on deformation-induced molecular reorientation and phase transitions in polyethylene, the role of vitamin E on the deformation behavior was scrutinized at the molecular scale through quantitative structural measurements by confocal/polarized Raman spectroscopy. Three different UHMWPE components were compared: (i) a vitamin E infused liner, referred to as E1® and manufactured by Biomet (the same studied in the previous sub-section; referred to as VEI, henceforth); (ii) a vitamin E blended from resin highly crosslinked through electron-beam irradiation (10 MeV) with a total dose of 300 kGy in vacuum (BLEND-E® commercialized by Nakashima Medical Co., Ltd., Okayama, Japan; referred to as VEB, henceforth); and, (iii) a vitamin E free liner prepared in exactly the same way (e.g. consolidation, radiation dose, thermal treatment and machining), but without vitamin E blending into the starting UHMWPE resins (referred to as VEF, henceforth). This latter sample was not available in the market and was manufactured for the only purpose of comparison. All samples were manufactured from resin GUR 1050. Figure 42(a) shows a comparison between the manufacturing steps of the VEI and VEB liners (3 samples were tested for each type) together with their photographs (in (b) and (c), respectively). The VEF sample was the same as the VEB one, except for vitamin E blending. The experiments described in this sub-section were specifically designed to detect the effect of vitamin infusion or blending on the microstructural alterations taking place upon compressive deformation at room temperature. The liners of different types were all of 28 mm in inner diameter and 7.5 mm thickness. Uniaxial compression was applied using an alumina ceramic femoral head (BIOLOX®forte; manufactured by CeramTec AG, Germany) at room temperature (24 ± 2 °C) with the strain rate of 1 x 10-3 s-1. As previously described for knee samples, the applied strain was kept constant for 24 h in order to allow for stress-relaxation phenomena to fully occur within the microstructure. The strain field was then released 67

and the sample allowed recovering elastic and anelastic strain for an additional 24 h, so that only plastic strain remained stored within the studied microstructure. Repeating the above procedure on three samples for each liner group average microstructural values were collected at the pre-determined magnitude of residual (plastic) strain, εf, of 10%. Such a strain value represents a quite severe plastic deformation and thus a worst-case from a clinical perspective. The residual strain value was measured by means of a thickness gauge. Static uniaxially compression is considered here as a representative test of the intrinsic deformation properties of the studied materials and the main responsible for the phase structure and molecular texturing developed upon in vivo service. Figures 43, 44, and 45 are plots of the in-depth profiles of crystalline, amorphous, and third (intermediate) phase fractions, respectively, as detected in VEI, VEB, and VEF samples. In each plot, data are given before and after a compressive straining of 10% (in (a) and (b), respectively). In all the investigated samples, the observed phase profiles were markedly non-linear with initially high gradients along the sub-surface until reaching nearly constant values in the depth of the samples. In all the virgin samples, the crystalline phase fraction, αc, increased with increasing in-depth abscissa, z. On the other hand, the third-phase fraction, αt, showed a decreasing pattern toward the bulk, independent of sample type. Regarding the amorphous fraction, αa, only the VEI sample showed a monotonic decrease from the surface along the sub-surface, while both VEB and VEF actually showed maxima of αa at around 5 and 20 µm in the sample depth. The trends for the third-phase fraction, αt, in the virgin samples were most dissimilar at the very surface of the liners, with the VEF sample showing the highest amount at ~39%, followed by the VEB and VEI samples at ~23 and 6%, respectively. On the other hand, the highest degree of surface crystallinity was reached by the VEI sample at ~43% vs. a common value of ~35% for both the VEB and VEF samples. A saturated degree of crystallinity in the bulk (at ~100 µm) was similar at ~53% for VEI and VEB, while it was ~60% and did not reach any saturated value in the VEF sample. Note also that, in the as-received state of the bulk region, the VEF liner showed a ~6% higher αc than the VEB liner, despite having incorporated exactly the same irradiation dose and being subjected to the same post-irradiation annealing conditions. In substance, the virgin VEI sample was the one with the highest degree of crystallinity in the first 40 µm of depth and with the highest content of amorphous phase over the all investigated thickness (at the expenses of a very low or null third-phase fraction). The major fractional differences observed among the three types of liner in their asreceived state (cf. Figs. 43(a), 44(a), and 45(a)) can be rationalized as follows: (i)

(ii)

Blending vitamin E before molding, cross-linking irradiation, and subsequent annealing clearly altered the structure of UHMWPE (cf. VEB vs. VEI), despite the raw resin being the same (cf. Fig. 42(a)). The ~20% lower crystallinity at the surface of the VEB liners as compared with the VEI ones testifies a different response to surface machining, which is again a consequence of the initial presence of vitamin E. This suggests a role of vitamin E as a “plasticizing agent”, which enhances mo68

(iii)

(iv)

(v)

(vi)

lecular mobility and chain reorientation under the surface machining procedure. Leaving aside the marked difference at the very surface of the liners (as discussed in the above item (ii)), the VEB and VEI liners showed similar αa values at few micrometers below the free surface. However, the significant difference in αa observed for the saturated levels beyond a sub-surface depth of 35 µ m (~30%) should mainly be attributed to the different molding (isostatic vs. direct compression) and irradiation procedures (γ-rays vs. electron beam), rather than to behavioral alterations related to the presence of vitamin E. In the case of the bulk VEB liner structure, for a similar crystallinity fraction as compared to the VEI structure, a ~12% lower amorphous fraction was detected. Such difference was compensated by a substantial increase in third phase in the bulk region, which could also be attributed to an enhancement in chain mobility in the presence of vitamin E before molding. The near-surface VEF structure showed the highest fraction of αt among all the studied liners. Such a high fraction was also accompanied by a substantially low amount of amorphous phase, while the crystallinity was conspicuously the same as that of the VEB structure (and lower than the VEI one). This suggests that the method of cross-linking the sample plays the main role in the formation of the crystalline phase. Moreover, the “plasticizing” presence of vitamin E during final surface machining (exactly the same for VEB and VEF samples) affected the formation of a plasticityinduced surface layer by allowing maintaining a higherαa in the VEB than in the VEF sample. The clear difference in bulk crystallinity between the VEF and VEB samples suggests that the annealing-induced crystallization mechanism was restricted and topologically hindered by the presence of vitamin E within the VEB polyethylene microstructure, with a larger amount of phase being kept in the amorphous state as compared to in the VEF sample.

Looking now at the effect of a 10% applied compressive strain on different UHMWPE structures (cf. Figs. 43(b), 44(b), and 45(b)), it can be noted as a general issue that all the investigated UHMWPE samples underwent clear microstructural changes upon straining. The variations in third-phase contents were the less pronounced in the VEI samples with a 30% increase only in the first few micrometers nearby the sample surface. Such an increase was, however, of negligible amount in the overall phase structure of the VEI sample, given its very small content of third phase. Dramatic structural variations were noticed in comparing the behavior of VEB and VEF in the presence of strain with respect to their third-phase contents, with the former structure reaching the initial αt (high) content of the latter and, vice versa, VEF lowering its αt content to the same initial level of the VEB liner. The upper insets in part (b) of Figs. 44 and 45 help visualizing the strain-induced structural modifications. The significant increase of αt in the VEB structure upon straining mainly occurred at 69

the expenses of the amorphous phase fraction, which dramatically dropped down by more than 40% in the near-surface zone, while the profile of crystalline fraction remained conspicuously unchanged (<0.5%) down to the bulk of the sample. The distinctively different features observed upon straining the VEI and VEB samples, with their different decreases in amorphous structure, ∆αa, and increases in near-surface third phase, ∆αt, nearby the free surface, can be comparatively observed in the upper insets to Fig. 44(b) and 45(b), respectively. In summary, the interpretation of the observed effects of compressive strain on the studied UHMWPE phase structures could be rationalized, as follows: (i)

(ii)

Phase transitions in crystalline and non-crystalline phase, i.e. amorphous and intermediate (third) phase, were found to be part of a structural reconstruction process after plastic deformation in the samples. The VEB UHMWPE structure exhibited a more pronounced molecular mobility as compared to VEI, but crystallinity changes were totally inhibited by the presence of vitamin E during deformation. As a result, a significant occurrence of amorphous-to-intermediate phase transition mainly occurred. The VEF liner showed a significant strain-induced recrystallization throughout all of the analyzed depths, to be compared with the negligible recrystallization of the VEB liner, which was not statistically significant at most depths. The amount of recrystallization at the surface of the VEF samples after uniaxial compression was 21.8 ± 0.7%. These results suggest that the addition of vitamin E induced earlier activation of compression deformation modes in crystalline and non-crystalline phases (e.g., chain slip, interlamellar shear and rotation) due to an increase in polyethylene chain mobility.

Figure 46(a) shows plots of true strain after recovery, εf, as a function of externally applied (or initial) strain, εi, for VEI and VEB liners. In both liners, a linear dependence between εf and εi was found, but the slopes of the fitting lines were clearly different. The slope of the VEB liner was steeper (εf /εi =0.51) as compared to VEI (εf /εi =0.42), which suggests that the microstructure of the VEI liner was more resistant to plastic deformation as compared to that of the VEB liner. As a matter of fact, for the same applied constant strain, εi, the VEI material showed a higher capacity of recovery, thus incorporating a lower amount of residual plastic strain, εf, despite possessing a higher fraction of amorphous phase. The observed strain-recovery behaviors can be explained by considering the balance between phase composition and crosslink density in the UHMWPE structure. Subject to loading, the crystalline regions represent the most rigid phase in the polyethylene microstructure, while the amorphous regions are most easily compressed and distorted. The character of the third phase could be assumed as possessing a slightly stiffer mechanical response as compared to the amorphous phase.[196] Thus, a balanced microstructural “blend” of the above three phases can lead to strength, ductility, and toughness characteristics suitable for acetabular liners. Our Raman experiments de70

tected an equivalent crystalline fraction (~54%) in the bulk regions of VEI and VEB liners despite the different type and amounts radiation doses (300 and 133kGy) applied to the same type of resin (GUR 1050). In the context of interest here, important differences came into view regarding αa and αt fractions in the bulk. Note that the VEB sample possessed about 10% higher amount of “rigid” amorphous phase in its bulk (i.e., a 10% higher amount of third phase at the expenses of a lower amount of amorphous phase). Nevertheless, we have found a lower shape-recovery capacity for the VEB liner against an applied uniaxial strain. Note that this is one of the most important characteristics in a UHMWPE structure for minimizing the mismatch of contact curvatures between acetabular liner and femoral head. Accordingly, the increased degree of crosslinking should be the main responsible in restricting the mobility of the molecular chain in the amorphous region of the VEI sample, thus resisting molecular reorientation during compressive loading and providing an increased ability to undergo shape recovery after plastic deformation (i.e., from which the lower εf/εi slope). Accordingly, we can state that the higher crosslink density of the VEI liner is advantageous for creep resistance and recovery capacity, in line with data previously shown by other authors.[197, 198] Locking by crosslinks in the amorphous structure, preponderant in the VEI structure, is counterbalanced by the above-mentioned “plasticizing” (or lubricant-like) effect of vitamin E, which was the main feature in the VEB structure. Figures 46(b) and (c) show an explanatory draft of the crosslinking vs. plasticizing behavior of the studied VEI and VEB microstructures. In conclusion, on the basis of our findings, it is suggested that Raman spectroscopy could be useful in tailoring a balanced microstructure, which could appropriately combine crosslink density and anti-oxidant additions in order to attain superior creep and wear performances in hip joint components. 5. Innovative design approaches to polyethylene components 5.1 Grafting the UHMWPE surface with a phospholipid polymer A recently launched artificial polyethylene hip-joint liner component (Aquala®; Kyocera Medical, Kyoto, Japan) possessing a surface grafted biocompatible phospholipid polymer 2-methacryloyloxyethyl phosphorylcholine (MPC) has been reported to provide increased hydrophilicity and reduced frictional forces.[199] In hip simulator experiments, polyethylene wear was shown to be dramatically suppressed using MPC-grafting as compared to non-grafted controls.[200, 201] Surface chemical analyses using XPS on in vitro tested surfaces confirmed the physical origin of this improved wear behavior; it resulted from the lubricating action of the MPC strands, which are covalently bonded to the polyethylene free surface. Despite the apparent superiority of MPC-grafted polyethylene in vitro, only limited indirect radiological evidence of its positive effect in vivo has been obtained.[202] As data on short-term retrievals are now collected by different research groups,[203, 204] such studies on retrievals are referred in this sub-section and provide us with the opportunity to directly examine whether or not the MPC-grafting morphology has been preserved after in vivo exposure. 71

The main analytical tool utilized by the original developers of the MPC-coating was XPS, which was employed to confirm the presence or absence of the nanometer thick grafted MPC polymer. We review in this sub-section recently published XPS and confocal Raman spectroscopy data on short-term retrievals,[204] which enabled to check the in vivo effect of the MPC-grafted polymer on the near-surface structure of the retrieved polyethylene liners. These data were in line with data collected by other groups.[203-205] In Ref. [204], short-term in vivo exposed and retrieved acetabular liners were compared with virgin unexposed liners. In the retrieved liners, distinction was made between MWZ and NWZ in accordance with pre-explant X-ray radiographs and post-explant preliminary laser microscopy. Three specific retrievals were examined: (i) a liner from a 68-year-old osteoarthritic male obtained after 1.9 years in vivo due to aseptic stem loosening. This patient’s primary surgery components included a Sqrum® cup, Aquala® liner, and J-Taper® stem with a Bioceram® AZ209 zirconia-toughened alumina (ZTA) head (Kyocera Medical, Osaka, Japan); (ii) a liner, belonging to the same type of hip implant, retrieved due to a hematogenous infection 1.2 years after primary THA for steroid induced osteonecrosis of the femoral head in a 53-year-old female with multiple sclerosis. The implants from both patients (i) and (ii) were reported to be stable at the time of revision surgery; and, (iii) a liner from the same implants (i) and (ii), which belonged to a 53-year-old female, which was retrieved after 1 year of in vivo implantation because of cup loosening. A comparison of the XPS results performed on a virgin liner, and on the NWZ and MWZ of the first retrieved liner (i.e., item (i) above) is replotted from Ref. 206 in Figs. 47(a), (b), and (c), respectively. XPS measurements, repeated 5 times for each sample for each MWZ and NWZ, are plotted as averages for each set of measurements. In the plots, the normalized XPS intensity of detected electrons and their binding energies are provided in the ordinate and abscissa axes, respectively. The selected spectral range highlights the signals for carbon, oxygen, nitrogen, and phosphorous (i.e., C1s, O1s, N1s, and P2p, respectively). It should be noted that P and N atoms are only possible in the MPC-grafted polyethylene, while C and O atoms are present in both the MPC-grafted and bulk polyethylenes, although with different molecular configurations. In the C1s region of both virgin and retrieved liners, a strong signal was observed at 284 eV, which arises from carbon atoms in the C-C or C-H bonds. In the O1s region, a band assigned to the C-O group was observed at 532 eV, which could be ascribed to MPC units at the grafted surface, but is also contributed by bulk polyethylene oxidation. The XPS C1s region is presented in an expanded view in Figs. 48(a) and (b) for the virgin and the MWZ of the retrieved sample (item (i) above). Signals for the N1s and P2p regions are located at energies of 403 and 134 eV and are assigned to the -N+(CH3)3 and phosphate groups, respectively. These latter two emissions are peculiar to the phosphorylcholine in the MPC units and reveal the presence or absence of the grafted polymer. At the surface of the as-received MPC-grafted liner, the measured amounts of N and P were 1.34 and 0.54 atomic percent (at.%), respectively. The P content is almost equivalent to the theoretical value estimated for the MPC polymer, as reported by Kyomoto et al.,[206] while the N content was higher by a factor of two

72

probably due to contamination of the surface during sterilization by γ -irradiation in the N2 atmosphere. The striking feature of the XPS data is that even after short-term exposure, namely 1.9 y in vivo, the P signal has completely disappeared, and also the N emission has almost disappeared (cf. Figs. 47(a)~(c)). Also the C-O signal at 532 eV was significantly reduced in both NWZ and MWZ zones (Figs. 47(b)~(c)) as compared to the virgin sample (Fig. 47(a); cf. also expanded view in Fig. 48), although this band cannot provide any quantitative information about the MPC coating because of the presence of oxidation sites at the polyethylene’s surface. Nearly identical XPS results were reported in Ref. [204]for the other two short-term retrievals (items (ii) and (iii) above). Table XII gives a summary of the XPS data collected in different zones of all the three studied retrievals in comparison with the virgin sample. These data suggest that even after short-term implantation (i.e., < 1 year), the MPC graft has been conspicuously removed. Consequently the perceived benefits of increased surface hydrophilicity and reduced frictional forces have lasted for an insignificant amount of in vivo time when compared to the expected lifetime of the artificial joint.[204] Confocal Raman spectroscopy data elucidated the changes in the polyethylene microstructure at the surface of the liners after in vivo exposure.[204] In all retrievals, an average of 15 measurements within each wear zone revealed a significant increase in the amorphous phase fraction at the sliding surface (i.e., within the first 20 µm of the free surface) when compared to the as-received liners, with this phenomenon being more evident in the MWZ than in the NWZ (53 and 42%, respectively, vs. 24% in the virgin liners) (cf. average data as a function of in-depth abscissa, z, in Figs. 49(a), (b), and (c) for virgin, NWZ, and MWZ, respectively). The combined outputs of XPS and confocal Raman analyses, performed at the surface of three short-term retrievals in comparison to virgin control samples, revealed that the surface of MPC-grafted liners were rapidly relegated to that of a conventional polyethylene surface, while concurrently undergoing a clear process of surface amorphization. Accordingly, it is conceivable to question the effectiveness of the MPC-grafting once the liners become operative in vivo. The marked difference in tribological performance of the MPC-grafted surface between previously reported in vitro tests[199-201] and the in vivo characterizations[203-205] can be reasonably related to the different lubrication, chemical, and micromechanical conditions encountered in vivo when compared to the tribolayer environment reproduced in standardized hip-simulation. Note that this is a further proof that the standardized hip-simulator testing is far from the in vivo reality, as previously discussed in different contexts of this review paper. A schematic diagram visualizing the in vivo sliding conditions and the mechanism of amorphization only observed at the surface of the in vivo exposed liners is drawn in Fig. 50. Initially, the MPC-grafted polymer adheres to the surface of the polyethylene through a strong covalent (but quite rigid) bond. On the one hand, an abundance of lubricating fluid (i.e., bovine serum) in standardized in vitro tests allows for a confined flow regime between the sliding couple, which supports the MPC strands during their rotational displacement. This is indeed, together with a limited 73

bending displacement, the only movement allowed for a rigid covalent bond linking the MPC-graft to the polyethylene surface. On the other hand, frictional forces developed in a scarcity of in vivo lubrication evidently peel off the MPC-grafted polymer. Only modest in vivo friction seems to be sufficient to remove the MPC-graft since its disappearance is noted not only in the MWZs, but also in the NWZs. As schematically depicted in Fig. 50, the peeling-off process introduces tensile forces at the surface of the polyethylene that in turn rupture the long crystalline chains. Such micromechanical process leads to the observed amorphization behavior of the liner surface. In conclusion, the optimism that accompanied the early hip simulation and radiographic tests with claims of enhanced hydrophilicity and superior frictional performance for MPC-grafted polyethylene liners[199-202, 206] should be tempered in light of the new evidences obtained from short-term retrievals.[203-205] These explants demonstrate that in vivo exposure of less than two-years led to the conspicuous disappearance of the grafted polymer. Consequently, a significant increase in the lifetime of hip joints incorporating this new grafting technology appears highly unlikely. 5.2 Exploiting sliding counterparts with high oxygen affinity Engineering the chemical interaction between femoral heads and polyethylene liner could be another viable approach to elongate artificial joint lifetimes. This is an innovative topic, which includes surface chemistry and goes beyond a simplistic view of mechanical behavior or wear, seeking to describe the prosthetic device as a whole. The basic idea is to positively exploit the chemical interactions of the joint components and, specifically, the role of oxygen affinity of the femoral head. While oxygen unavoidably diffuses into the amorphous enclaves of the polyethylene liner in contact with the tribolayer, one could tailor the affinity of the femoral head in order to selectively attract oxygen during tribochemical interactions. Specifically regarding ceramic on UHMWPE articulations, it is commonly believed that an oxide ceramic femoral head is fully bioinert, and therefore it has no role in the degradative processes occurring upon in vivo service of the artificial joint.[206] However, this belief is likely based on a misconception since extensive prior research on the surface chemistry of bioceramics has unequivocally shown that oxide ceramics such as alumina (Al2O3) and zirconia-toughened alumina (referred to as ZTA in the previous sub-section) release oxygen from their surfaces when exposed to in vitro as well as in vivo biological environment, thereby acting as oxygen “polluters” into the tribolayer.[191, 207-209] Such a “chemistry” aspect of this subject and the key question of what exactly happens to the stoichiometry of the ceramic head upon sliding during joint service are crucial to design improved joints with lifetimes up to three decades or more. If the null hypothesis, which assumed that oxide ceramics are completely bioinert while in contact with UHMWPE within a hydrothermal environment, proves to be false, could the surface of a non-oxide ceramic (e.g., silicon nitride (Si3N4)) be useful in scavenging oxygen from the joint space, thus acting as oxygen “cleanser”? While the above statements challenge the notion of the general bioinertness of ceramic materials, they also offer a new paradigm for an “integrated joint space” where biomaterial surfaces synergically interact to each other in order to 74

create a friendly chemistry in the tribolayer of the hip joint. As a first step in the direction of head/liner synergic interaction, we report here about an experiment that was designed to monitor changes in crystallinity and oxidation of the UHMWPE liners during a simply static contact with oxide or non-oxide femoral heads within an in vitro hydrothermal environment. This proof-of-concept experiment, conducted in absence of frictional loading, aimed at corroborating and statistically validating a trend of higher oxidative propensity against oxide ceramics in comparison with non-oxides. Moreover, the findings of the experiments shown in this sub-section are shown to support the thesis that oxidation of UHMWPE induces a noticeable increase in overall crystallinity contents due to chain scission and secondary recrystallization (as previously discussed in Section 3.3). The recrystallization phenomenon is therefore a sensor for surface oxidation and dependably reflects the degradation of the UHMWPE surface. Two sets of three types of ceramic femoral heads, consisting of two oxides (Al2O3 BIOLOX®forte and ZTA BIOLOX®delta, CeramTec, GmbH, Plochingen, Germany) and one non-oxide (MC2®Si3N4, Amedica Corp., Salt Lake City, UT, USA) were received from the manufacturers and cut into six hemispherical sections for each type of ceramic (i.e., three pieces from each head). The new generation of highly crosslinked polyethylene, X3TM (Stryker Orthopedics, Inc., Mahwah, New Jersey, USA), was used as the reference UHMWPE liner (see also specifications in Table V). Six asreceived acetabular liners were sectioned into four hemispherical sections each, for a total of 24 pieces. All the polyethylene specimens were equal in size and shape, maintaining the original concave surface of each liner on one side. These were then coupled to the convex surfaces of the hemispherical sections of the ceramic femoral heads as schematically shown in the diagram of Fig. 51. All the polyethylene samples were γ -irradiated with an average dose of 32 kGy before performing a hydrothermal aging test, with the aim of increasing both the free radical concentration within the polymer and the reactivity of the surface exposed to oxygenated water. In addition to the ceramic samples, six identical convex polyethylene samples were mated and tested against six spherical concave polyethylene sections. The convex polyethylene samples were not irradiated before aging. A constant pressure of 25 N between the two components during the accelerated autoclave-aging test was applied using metallic clamps. All surfaces were dipped into pure water before being coupled to their respective counter surface and immediately placed into the autoclave at a temperature of 121°C under adiabatic water-vapor pressure for a short interval of 24 h. All sample couples were concurrently run in the same experimental session. Statistical analyses were performed according to the unpaired Student's t-test. The sample size for each couple was n = 18, namely 3 separate locations on each sample and six samples for each couple. In this context, a p value < 0.05 is considered statistically significant and labeled with an asterisk. Data of local crystallinity and oxidation contents, which were acquired at exactly the same locations of each couple before and after hydrothermal exposure, referred to a series of 10 maps 50 x50 µ m for each investigated couple on the surface of the 75

UHMWPE counterparts (i.e., at z=0). Increased near-surface crystallinity values were generally observed after exposure to autoclave environment, especially for the UHMWPE samples aged in contact with the oxide ceramics. Typically, the crystallinity distributions exhibited maxima as high as 75% at “hot spots” a few micrometers in size. However, there were clear differences among couple comprising different ceramic heads in the statistical distributions and average values as well. Figures 52(a)~(d) give histograms of crystallinity increase, ∆ac, with respect to the pristine samples, which were compiled from the entire series of Raman characterizations (cf. labels), namely total surface areas of ~25 x 103 µm2 for each tested couple. As seen, the statistical distribution of ∆a c similarly shifted toward higher differential values and broadened for all the UHMWPE/oxide couples, with average increases of 9.37 and 9.43% for UHMWPE/ZTA and UHMWPE/Al2O3, respectively. On the other hand, crystallinity values were significantly lower for both UHMWPE/Si3N4 and UHMWPE/ UHMWPE couples when compared to UHMWPE samples in contact with the oxide ceramic heads. Frequency distributions were similarly sharp and average values were correspondingly low for ∆ac values within the UHMWPE/UHMWPE and UHMWPE/Si3N4 couples, with average ∆ac equal to 5.47 and 6.74%, respectively. Quantitative average values for ∆ac0 (i.e., ∆ac at a sample depth, z=0) and the corresponding ∆OI0 (obtained according to the procedure shown in Section 3.3) for the UHMWPE samples belonging to different couples are presented in Fig. 53. These data are representative of the very surface of the UHMWPE samples and were obtained from deconvoluting in-depth distributions of crystallinity from its sub-surface gradients according to the probe response procedure described in Appendix A. The comparative p values (in inset to Fig. 53), computed for establishing statistical significance, indicated that the most statistically meaningful difference occurred between the UHMWPE/oxides and the UHMWPE/Si3N4 couples (p = 0.003; cf. asterisk in Fig. 53). On the other hand, the UHMWPE/UHMWPE and UHMWPE/ Si3N4 couples showed a statistically insignificant difference (p > 0.05). Recorded values for the three different UHMWPE/oxide couples were also statistically insignificant (cf. Fig. 53). The proof-of-concept experiments shown in this sub-section clearly show that, even by its mere static contact with oxide femoral head materials, increased crystallinity and oxidation occurred in pre-irradiated UHMWPE under hydrothermal test conditions. The UHMWPE control couple provided the least burden to the polymer microstructure because oxygen molecules could similarly diffuse and react with either of the identical counterfaces. At this stage, we can safely state that oxide ceramics were not as effective as Si3N4 in preventing dissolved oxygen from reaching the polyethylene surface. In previous sections, we discussed how the oxidation rate of irradiated polyethylene depended on the amount of free radicals present in the polymer and was enhanced by the presence of lipids. Here we demonstrated that the amount of oxygen and hydroperoxides available for reacting with the UHMWPE samples was greater for liners coupled with oxide versus non-oxide ceramic heads. In other words, these experiments irrefutably revealed the differing roles of oxide and non-oxide ceramics in affecting UHMWPE’s oxidative degradation. 76

In order to substantiate the Raman data, XPS assessments were conducted on the surfaces of the UHMWPE samples before and after accelerated aging using the same photoelectron spectrometry equipment used in the previous sub-section. Surfaces of the samples were cleaned by Ar+ sputtering in the pre-chamber, while actual measurements were conducted in the vacuum chamber at around 2×10-7 Pa with an analyzer pass energy of 10 eV and voltage step size of 0.1 eV. The X-ray incidence and the takeoff angles were 34° and 90°, respectively. The fraction of elemental oxygen was determined by averaging three separate measurements on each of the UHMWPE liners at the center of their concave surfaces. In addition, XPS analyses were also conducted on two sections each from unaged and aged Si3N4 femoral heads. The aged sections were coupled with UHMWPE liners and subjected to the autoclave treatment. Figure 54 shows the average elemental fractions by XPS in three different zones on three separate samples for each tested couple. These data revealed that the strong XPS signals for carbon had similar intensities among the different UHMWPE couples. The weak emissions from N and Si were likely due to surface contaminants because they tended to disappear after robust etching. However, the remarkable result was the trend for surface oxygen content. The oxygen signal was clearly stronger by at least a factor of two in the UHMWPE samples coupled to oxide ceramics when compared to either the Si3N4 couple or the UHMWPE control. XPS examinations on the series of Si3N4 counterparts were also performed for confirmation (Fig. 55), which showed the change in oxygen content at the surface of the Si3N4 ceramic. O1s spectra obtained from exactly the same Si3N4 sample both before and after autoclaving revealed an O1s peak after autoclaving of clearly greater intensity and width, and slightly shifted toward higher energy (i.e., 533 eV), which is typical of Si-O bonding in silica and silicon oxynitride.[210-212] The recorded change in intensity corresponded to ~30% increase in oxygen content and well correlated with the lower observed oxygen of its mated UHMWPE liner. This further experimental evidence strongly corroborated the hypothesized effect of oxygen scavenging by the nonoxide surface during autoclave exposure. As a further elaboration on the UHMWPE crystallization/oxidation results given throughout this review paper, microscopic investigations were conducted that identified basic patterns in correlating oxygen flow from the ceramic bearings to microstructural changes within the polyethylene. Highly spatially resolved Raman maps were collected screening for local variations in crystallinity, ∆a c, and oxidation index, ∆OI, for the UHMWPE counterface to ZTA after 24 h of autoclave aging (Figs. 56(a) and (b), respectively). Besides confirming that variations in crystallinity were related to changes in oxidation index, a comparison between fractional differences at exactly the same locations for the third (semi-crystalline) and amorphous phases (Figs. 56(c) and (d), respectively) revealed that the major fraction of the newly formed crystalline phase formed at the expense of the third phase. It was so discovered that the UHMWPE phase undergoing the most oxidation was the third phase, while only minor variations could be found in the local pattern of the amorphous phase. According to our previous discussions on the crystallization behavior of UHMWPE, the oxida77

tion driven process starts with the formation of carboxylic acids and leads to the breaking and shortening of polyethylene chains. Enhancement of their molecular mobility enables the chains to reorganize into an ordered structure of lower free energy (cf. Fig. 9). Building upon the experimental observations, it is hypothesized that in the early stages of oxidation, the decrease of the third rather than the amorphous phase correlated with an increase in polyethylene lamellar thickness. In fact, the third phase stems as the intermediate layer which separates the ordered lamellar structure form the random organization of the amorphous phase.[34] This connecting phase is composed by molecules which are aligned in the same direction as the molecules inside the lamella, but they have lost lateral order of the orthorhombic structure presumably due to boundary stresses generated by the highly entangled chains of the adjacent amorphous phase (cf. Fig. 1). The onset of oxidation and reduction of molecular weight may have released these stresses enabling the molecular chains to reacquire their lateral order, which led to lamellar thickening. Moreover, the concentration of free radicals may be higher in the third phase, in which they quickly migrate from the adjacent crystalline phase. As a matter of fact, free radicals generated in the lamellae during irradiation cannot form cross-links because the C-C bond length of a cross-link is shorter than the intermolecular distance inside the crystalline lamellae.[213] According to the results in Fig. 56, we can now draw a more precise picture of the recrystallization process as driven by oxidation in the third-phase volume (Fig. 57). Chain-breaking and subsequent formation of carboxylic acid sites preferentially occur in correspondence of third-phase regions. Subsequent to the shortening of polymeric chains, small and newly formed orthorhombic crystals could form upon chain rearrangement in the neighborhood of pre-existing larger crystals, namely in correspondence of the highly strained zones at the interface between crystalline and amorphous phase previously occupied by the third phase. Figures 58(a) and (b) provide a hypothesis for the cascading set of events that occurred at the wet interface of UHMWPE with oxide and non-oxide counterparts, respectively during hydrothermal activation. Chemisorption of water molecular and dehydroxylation on the Al2O3 surface created oxygen vacancies at its surface and released free oxygen molecules into the tribolayer (Fig. 58(a)). Then, this oxygen flowed toward and reacted with the UHMWPE surface in accordance with the oxidation mechanisms described above. It is noteworthy that the water interface between the Al2O3 and UHMWPE was sufficiently thermally activated to generate oxygen vacancies in Al2O3 and release oxygen from the Al2 O3 surface into the water interlayer even under static conditions. This resulted in increased crystallization and oxidation of the UHWMPE. According to the presented data, ZTA ceramics generated crystallization and oxidation indices in their respective UHMWPEs that were not statistically different than those produced in the Al2O3/UHMWPE couple. On the other hand, an opposite model is presented in Fig. 58(b) showing the events leading to oxygen scavenging by Si3N4 in contact with its UHMWPE counterpart during hydrothermal activation. In the autoclave environment, the wet interface produced a flow of oxygen out of the tribolayer toward the non-oxide ceramic. This free oxygen reacted with the Si3N4 to form a silicon oxynitride glassy phase at its surface. Therefore, this process 78

protected the UHMWPE surface from a fraction of the oxygen dissolved in the water interlayer, and consequently limited the extent of the chain-scission/re-crystallization occurring at the surface of its UHWMPE counterpart. As a general consideration, the experimental evidences provided in this sub-section clearly substantiate the importance of oxygen chemistry at the interface of UHMWPE and bioceramic couples even under static circumstances. The shown data also confirm previously shown cathodoluminescence data showing “pollution” of oxygen by offstoichiometry drifts of oxide-ceramic surfaces vs. “scavenging” of oxygen by nonoxide surfaces.[191] Consistent with a new concept of an “integrated joint space,” the shown proof-of-concept experiments provide phenomenological evidence against the common belief that bioceramics currently employed in THA devices are bioinert. Instead of no interaction, the results suggest that ceramic surface chemistry plays an important off-stoichiometric role in either enhancing or retarding the oxidative degradation of UHMWPE liners by releasing or scavenging oxygen from the tribolayer. The positive outcome of the presented experiments was the appearance of a new research path, which aims at elongating the lifetime of artificial hip joints through a synergistic effect between ceramic femoral head and polyethylene liner. In contrast to oxide ceramics, which release oxygen from their surface lattice structures, the surface of Si3N4 undergoes a steady growth of an amphoteric SiO2-rich layer by attracting oxygen from the surrounding environment. In simple terms, the released oxygen contributes to UHMWPE degradation whereas more friendly ceramics (e.g., non-oxide Si3N4) trap oxygen thereby providing a protective benefit to the polyethylene counterpart. The new paradigm of an “integrated joint space” might be further extended to the interactions of various biomaterials in the hip artificial joint at the molecular level during their lifetime service in the human body. 5.3 Free radical scavengers and a new method for their evaluation In sub-section 4.4, materials belonging to a second generation of highly crosslinked UHMWPE have been evaluated with respect to their resistance to oxidation, and the effectiveness of vitamin E as an antioxidant quantitatively discussed. Secondgeneration UHMWPEs were developed to eliminate the shortcomings of the irradiated and thermally treated materials, which belonged to the first-generation. The main alternative to thermal treatments to stabilize orthopedic UHMWPE has been recognized in the addition of antioxidants, and vitamin E ( α -tocopherol) has quickly become the most widely used stabilizer.[186, 214] However, also other types of antioxidants are currently emerging. They include ascorbic acid (vitamin C),[215] nitroxides (e.g., (2,2,6,6-tetramethylpiperidin-1-yl)-oxyl; C9H18NO also referred to as TEMPO),[216, 217] phenolic compounds (e.g., Irganox 1076® (octadecyl-3-(3,5-ditert.butyl-4-hydroxyphenyl)-propionate),[218] as well as some lanthanides (e.g., Europium II and Europium III added to UHMWPE as chloride or stearate).[219, 220] Investigations have also been presented on the antioxidant properties of carbon compounds such as multi-walled carbon nanotubes (MWCNT) and graphene, as free radical scavengers dispersed in UHMWPE matrices.[221, 222] Regarding vitamin C addition, the results presented in Ref. [215] have provided 79

strong evidence about the remarkable antioxidant efficiency of this compound. However, its oxidation mechanism appears to be a rather complex one and is governed by a two-stages kinetics process with different first-order reaction patterns. Also the antioxidant reactions involved with TEMPO are complex and have been the object of different hypotheses. In a recent paper, Haidasz et al.[223] have provided evidence in favor of a reaction mechanism involving the acid-catalyzed reaction of a nitroxide with a peroxyl radical to yield first an oxoammonium ion, then followed by electron transfer from an alkyl radical to the oxoammonium ion to reform the nitroxide. It should be noted that protonation of the nitroxide creates a potent formal H atom donor, which can quickly react with a peroxyl radical. The resultant oxoammonium ion oxidizes an alkyl radical, regenerating the nitroxide by a process of electron transfer whose speed is competitive with O2 incorporation during UHMWPE autoxidation. Regarding phenolics, they typically react with oxygen-centered free radicals. Accordingly, they are able to interrupt the autoxidation cycle in UHMWPE. Phenolic antioxidants like as Irganox 1076 quench free radicals by donating hydrogen atoms. This process is thermodynamically favorable and occurs because the resulting phenoxy radical is more stable than the oxygen-centered free radical object of quenching, primarily through resonance structures in the phenyl ring. Among lanthanides, Europium is a rare earth element, which possesses an unusual electron configuration related to its 4f electron shell. This shell is buried in the xenonlike core of the atom as a consequence of its poor shielding properties. This physical circumstance is at the origin of both a substantial lack of directional bonding and a strong affinity to oxygen.[224] These characteristics in turn make the Eu element a very suitable one for producing an antioxidative effect in UHMWPE.[219, 225] Note that this is exactly the opposite effect of d-transition metals for which the d-electron shell is so strongly prone to directional bonding and to reactivity that makes them prooxidants.[226] Data published in Ref. [219] provide evidence that the addition of Eu(III) stearate to UHMWPE reduced hydroperoxide and ketone generation rates in comparison to a non-doped control. The capacity of scavenging oxygen as well as the subsequent improvement in oxidation resistance of UHMWPE upon Europium stearate doping is the obvious consequence of the strong coordination of Eu3+ to oxygen and its capacity to reach higher (>6) coordination numbers. High affinity to oxygen and free-radical (especially allyl radicals) scavenging are the common antioxidant mechanisms of carbon-based materials like as MWCNT and graphene. Similar to Vitamin E, carbon-based free-radical scavengers might lower the efficiency in cross-linking generation. However, MWCNTs added to UHMWPE were found to induce an additional mechanism that compensates for such a negative effect.[221] It was suggested that this mechanism could be related to changes in the nanotube structure introduced by γ-irradiation, which affect graphitization and the inter-wall distance. Such rearrangements make the nanotubes interacting simultaneously with different polymer chains in their surroundings, providing a crosslinking network that is additional to and corroborates that induced by γ-irradiation. On the other hand, the graphite structure strongly attracts oxygen atoms linking to them in direct and 80

hydroxylated fashion. Its oxidation leads to exfoliation of its layered structure at the molecular scale with the subsequent formation of graphene oxide.[227] Figure 59 gives a summary of the anti-oxidizing mechanisms exploited upon addition of nitroxide (a), vitamin C (b), phenolics (c), and graphene (d), as potentially innovative approaches to improve the oxidation resistance of the next-generation UHMWPEs. In the context of this review, it is important to note that several of the antioxidant compounds mentioned above present strong Raman bands. For example, it has recent• ly been reported that the group frequency of the nitroxide N-O stretching vibration, • ν(N-O ) occurs in the range 1450~1340 cm-1.[228] Raman spectroscopy of phenolic antioxidant Irganox 1076 ® has recently revealed the existence of three different polymorphs for this compound.[229] This newly developed spectroscopic knowledge was applied to the analysis of commercial polyurethane catheters, which exhibited a blooming phenomenon. Raman spectra revealed a polymorph on the surface which was different from the commercially available Irganox 1076®, thus proving the importance of the Raman screening for polymorphs to check the biocompatibility of antioxidants used in biomedical devices. Graphene and MWCNT are also very well known as strong Raman scatterers and solid-state physics foundations have been laid in the interpretation of their Raman spectra.[230-233] From the application viewpoint, the so-called D band of graphene at ~1359 cm-1 is due to first-order zone boundary phonons and is absent in defect-free graphene. Being activated by defects, vacancy, and structural disorder in the graphene structure, this band could be used to monitor the interaction with UHMWPE upon oxidation.[234] Moreover, concurrent Raman monitoring of antioxidant emission and UHMWPE oxidation could allow to follow up in real time the oxygen chemistry evolution in the UHMWPE structure. Tailoring reduction mechanism could thus enable a selection of the best reducing free radicals in terms of efficiency.[235] The presence of free radicals induced by irradiation treatments to UHMWPE is usually monitored by electron spin resonance spectroscopy (ESR).[236, 237] The nature and the concentration of different types of radicals can be unveiled by ESR features in a straightforward way. However, the overlapping dependences on radiation dose, time elapsed after irradiation, and atmosphere of irradiation and storage might render this a cumbersome task, and eventually hamper unambiguous interpretations and clear conclusions.[238] In addition to the useful information that can be obtained by ESR about the total relative concentration of the radical and the nature of dominant contributions, a practical method is also needed to more specifically estimate the resistance of different UHMWPE structures to free-radical formation as well as the scavenging capacity of different anti-oxidant dopants and compounds. In previous sections, we have shown some practical evaluation of oxidation resistance based on a combined procedure based on Raman and FT-IR spectroscopy. The antioxidative stability of UHMWPE is thus typically measured by calculating the OI and the related crystallization extent after a period of accelerated aging. However, this method can merely elucidate whether UHMWPE is oxidized after compulsory aging or not, while it can hardly predict how long UHMWPEs will withstand unoxidized 81

before the oxidation process will actually begin. Uetsuki et al.[239] have investigated the potential stability of UHMWPE against oxidation by determining the so-called oxidative induction time (OIT) by means of a thermo-gravimetric analysis. In this new method, the analysis is conducted in a thermo-gravimetry/differential scanning calorimetry device according to the standard ASTM D3895. Thin UHMWPE sample slices (~250 µm thick) are used, eventually pre-irradiated to produce the free radicals that simulate the effect of lipids in the human body. The test starts with a heating cycle in N2 gas. Then, the atmosphere is suddenly switched to oxygen while keeping constant the temperature and monitoring the oxidative exothermic reaction. The changeover point to oxygen atmosphere corresponds to the time at which the OIT measurement starts, namely the differential heat is monitored to detect the onset for oxidative reaction. By definition, OIT is given by the time corresponding to the take off of the steepest (linear) slope of the observed exothermic reaction. Figure 60(a) schematically shows the cycle followed in this innovative measurement method and the method adopted to compute OIT. Figure 60(b) reports some typical examples of recorded thermal curves as a function of time at 200 oC isothermal heating. Specifically, a comparison is given among a non-irradiated vitamin E-free sample (GUR 1050 directly compression-molded), a vitamin E blended (3000 ppm) non-irradiated sample from the same resin and prepared by the same method, and a sample the same as the latter one but irradiated by an electron beam dose of 300 kGy. The non-irradiate vitamin E-free sample was immediately oxidized after switching the gas flow to oxygen, while significantly longer OIT was necessary for reaching the onset of oxidation in the vitamin E‐blended samples, although crosslinking by electron beam irradiation partly deprived the vitamin E‐blended sample of its anti-oxidative ability. Figure 60(c) summarizes the OIT values found a complete series of samples subjected to different irradiation doses tested at 200oC. It should be noted that, regardless of irradiation dose, the OIT value of vitamin E‐free UHMWPE was indeed very short. On the other hand, the OIT test not only confirmed that vitamin E‐blended samples possessed a significantly enhanced oxidation resistance, but also gave an estimate of the time after which such process starts when adverse environmental conditions (i.e., free radical formation and oxygen availability) converge. Uetsuki et al.[239] have also shown OIT predictions extrapolated to body temperature by means of an Arrhenius equation based on testing OIT in the samples at a series of different temperatures between 180 and 240oC. These latter results predict an improvement of several orders of magnitude in the take off of the oxidation process and thus in lifetime extension upon blending UHMWPE with vitamin E. Similar to the procedure shown for vitamin E, the OIT testing method could also be applied to evaluate and compare the efficiencies of other anti-oxidants, as described in this sub-section. Considering now the method of Raman spectroscopy for precisely evaluating OI in UHMWPE through monitoring crystallinity variations (as demonstrated by Eqs. (29)~(35) of this review), an interesting extension of the OIT Uetsuki’s parameter could be the in situ Raman measurement of OI during thermal analysis. Such a spectroscopically implemented approach to OIT including the Arrhenius formalism could then lead to an actual lifetime prediction in vivo after setting a 82

threshold value of critical relevance (e.g., OI=1) for the oxidative degradation of biomedical UHMWPEs. 6. Conclusion This review was dedicated to the theoretical and experimental examination of the Raman emission from biomedical polyethylene samples. The Raman spectroscopic findings were corroborated by means of independent analytical methods of surface analysis, such as FT-IR, SEM, and XPS. Experimental evidences supported the possibility to quantitatively assess molecular textures, oxidative patterns, and plastic strain at the microscopic level in the three dimensions of the Euclidean space. Quantitative algorithms were thus established, which hold general validity and pave the way to fully quantitative UHMWPE characterizations. Overall, the performed confocal/polarized Raman analyses were found capable to advance understanding of the basic phenomena behind the performance of this important biomedical material. In a more general perspective, the computational Raman algorithms that have explicitly been put forward enable one to deconvolute crystallographic, chemical, and micromechanical information, as it comes intermixed in polarized Raman spectra. The main achievements could be listed, as follow: (i) visualization of molecular patterns at the surface of UHMWPE bearings operating against metallic components; (ii) differentiation between wear and creep deformation in retrievals; (iii) non-destructive mapping of oxidative patterns; and, (iv) the clarification of chemical interactions between oxide/non-oxide ceramic heads and advanced UHMWPE liners. A peripheral but yet important issue for practical purposes arose in this review: the poor extent to which in vitro testing and simulations were found capable to assess the UHMWPE tribological performances. This is a matter of serious concern as we came to realize the unclear physical meaning related to the cumbersome body of legalization enacted to govern the medical device industry. While acknowledging the primary purpose of joint simulation experiments, which is to ensure both safety and effectiveness of the marketed devices, we have clearly shown here the insufficiency of their protocols in both quality control and predictive capability. Raman spectroscopic research suggested that issues of much contention in pre-clinical experimental testing of hip prostheses involve physical chemistry aspects of the tribological interaction, thus calling for a clear specification of additional (and more effective) evaluation criteria and protocols (including simplifications of useless requirements). Through some of the calibrations shown here, it has been demonstrated that the particularly stringent need for controlling the state of oxidation of polyethylene liners could be easily and non-destructively achievable through Raman spectroscopy. Nowadays, deterministic levels of quality control by means of on-line Raman spectroscopic protocols are widely applied in pharmaceutical and electronic products. They should equally be applied to UHMWPE joint components. Accordingly, in vitro standards for tribological tests should be complemented with analytical screening at the molecular level in order to validate updated “equivalency” criteria for the simulator testing procedures. In conclusion, this review have first laid the theoretical foundations for the Raman 83

analysis of biomedical polyethylenes, then examined the performance of commercially available polyethylene components (including some recently launched innovative approaches), and finally showed that new protocols are needed for both designing and monitoring UHMWPE components at the molecular scale. The take home lesson here is that new criteria in design, quality control, and in vivo durability of biomedical UHMWPEs, as well as of other biomedical materials such as bioceramics, should mandatorily incorporate monitoring of physical chemistry parameters, a so far conspicuously neglected task that Raman spectroscopy could effectively accomplish. Acknowledgments: The author gratefully thanks his collaborators Prof. Dr. Wenliang Zhu, Dr. Leonardo Puppulin, Dr. Yasuhito Takahashi, Dr. Bryan J. McEntire, Dr. Elia Marin, Shine Tone MD, and Dr. Keita Uetsuki, for their precious contributions during the course of this work. Sincere thanks are also due to Prof. Ian C. Clarke PhD, Prof. Nobuhiko Sugano MD PhD, Prof. Kengo Yamamoto MD PhD, Prof. Masahiro Hasegawa MD PhD, and Prof. B. Sonny Bal MD PhD for their long-term collaboration, their precious discussions on clinical issues, and for providing many retrieval samples to the author.

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[240] Lipkin DM, Clarke DR. Sample-probe interactions in spectroscopy: Sampling microscopic property gradients. Journal of applied physics 1995;77:1855-63. [241] Atkinson A, Jain S. Spatially resolved stress analysis using Raman spectroscopy. Journal of Raman spectroscopy 1999;30:885-91. [242] Wan K, Zhu W, Pezzotti G. Determination of in-depth probe response function using spectral perturbation methods. Journal of applied physics 2005;98:113101. Appendix A The Raman probe in a polyethylene medium In Raman microprobe spectroscopy, a research grade optical microscope is coupled to an excitation laser and to a spectrometer producing a platform capable of obtaining conventional visible images and, in addition, to generate Raman spectra from observed sample areas. The combination of a Raman microscope, a motorized three-axis stage, and a confocal pinhole configuration in the optical circuit allows for the generation of 2-D and 3-D maps, which can yield information on the distribution of different materials, crystallographic phases, stress/strain fields, and chemical gradients in a heterogeneous sample over a defined microscopic area. If a laser is focused in air, beam waist diameter and beam length only relate to the numerical aperture of the lens and to the wavelength of radiation. If the laser is instead focused onto the surface of a condensed phase material, the beam length below the sample surface will be affected by the refractive index of the material and its absorption characteristics. Raman scattering will thus occur within the probe volume and detected with different intensities along the beam length and across the focal plane. At this time, the radiation may be fully captured by the collection lens. Therefore, the spectrum measured from an individual point P0 (x0, y0) on the sample surface will actually be the convolution of information from a stream of z-planes below it, thus resulting in this form of little practical use in probing inhomogeneous samples (cf. Fig. A1(a)). However, by employing a technique known as “confocal microprobe spectroscopy”, it is possible to probe discrete z planes. In this technique, a conjugate aperture (a pinhole) is used to reject the out-of-focus radiations originating from non-target z-planes from reaching the detector. The radiation originating from the volume below the sample surface, which is not in focus, is rejected before the pinhole. Consequently, the measured signal from nontarget sub-surface layers is significantly attenuated, while the signal from the surface is brought to a focus at the aperture and passes without significant attenuation (Fig. A1(a)). As shown in the draft of Fig. A1(a), the main advantage of using a confocal aperture is the spatial discrimination of the experiment to a well-defined volume of a potentially heterogeneous sample. However, a quantitative deconvolution of Raman maps either within a given focal plane and/or into individual z-planes inside the sample requires the precise knowledge of the probe response function (PRF; i.e., the morphological function characterizing the laser probe geometry when the probe interacts with the sample). The PRF must be experimentally determined on a case-by-case basis for any given material. The PRF is composed of two main components, both depending on the geometry and the physical character of the probed sample: (i) the inplane probe response, Gip(x,y,x0,y0), which gives the lateral resolution of the probe, 98

and can be determined by moving the probe across a sharp and straight interface in the sample and recording the Raman intensity as a function of the abscissa, x0 (Fig. A1(b)); and, (ii) the in-depth probe response, Gid(z,z0), which gives the resolution along the defocusing axis, z0, perpendicular to the sample surface (Fig. A1(c)). This latter probe response function can be determined experimentally by graphing the intensity of the spectral signal vs. the defocus distance and taking the derivative of the curve obtained.[240] Note that in-plane and in in-depth calibrations should be performed not only for each investigated material, but also for each investigated Raman band of the material. Regarding the general morphology of the PRF, the observed intensity of the Raman spectrum depends on the intensity distribution of scattered light around the irradiation point P0(x0,y0,z0). The intensity distribution in a three-dimensional Euclidean space, namely the above-mentioned PRF, G(x,y,z,x0,y0,z0), represents the cumulative morphology of in-plane and in-depth probe functions. The PRF is the function weighting the intensity of the light scattered from a given point P(x,y,z) when the incident beam is focused at the point (x0,y0,z0):[241, 242] ý (=, <, ;, =!,
(D D )&)(E E )& þ&

l

Û&

(F F) &)Û&

exp (−2z)

(A1)

where 2R is the laser beam diameter in the focal plane, p is the probe response parameter, (which for an unfocused beam tends to infinity), and α is the absorption coefficient of the material at the incident wavelength. For Raman bands, the term 2α in Eq. (A1) may need to be substituted by the sum of the absorption coefficients for incident and emitted light. If the variation of all the variables in the xy plane can be ignored, the PRF can be simplified and probing performed only along the z-axis (Fig. A1(c)), as follows: ý (=, <, ;, =! ,
Û&

Û& )(F F )&

(A2)

The observed spectral intensity at band maximum can be then obtained according to a simple volumetric integration: 40¶ (߱Û ) ∝ — ¡ exp (−2;) Û& )(F F )¡

Û&

)

&

b;

(A3)

where ω p is the wavenumber at maximum of the selected spectral band. The focal plane position (above or below the sample surface), z0, can be also seen as a defocusing distance with respect to laser irradiation with the focal plane placed on the sample surface. The maximum intensity, Imax≅2Isurf, of a selected band of the spectrum with respect to varying defocusing distance, z0, can be used to normalize the band intensity,

99

thus translating Eq. (A3) into a fully quantitative equation for band intensity assessment: ೚್ೞ (ఠã )

೘ೌೣ (ఠ ã)

=

öಮ

—

öಮ

—

ã&

ୣ୶୮ ( œF) & ÂF ã ö(೥ష೥ )& ã&

ୣ୶୮ ( œF) & &ÂF ã ö೥

(A4)

Note that the analytical integration of this equation generally requires numerical calculations. As the probe is swept along the in-depth axis, the collected intensity function, 40¶ (߱Û ), maps the probe response. The probe response parameter, p, and the absorption coefficient, α, can then be obtained from the best fitting (normalized) experimental intensities as compared to the calculated ones (according to Eq. (A4)). To visualize the probe size in terms of penetration depth, a probe depth, zd, can be defined according to the following equation (using, for example, 90% of the maximum intensity as a threshold value for intensity distribution): ೥

— ೏ ீ(F,F )ÂF ீ(F,F )ÂF

= 0.9

(A5)

Also this equation is usually solved numerically. As mentioned above, the in-depth resolution of the Raman probe can be greatly improved by placing a confocal pinhole at the back-focal image plane to partly cut off the light scattered from outside the laser focal area (cf. Fig. A1(a)). When the laser is focused on the specimen surface (z0=0), there exists an inner transmitted zone for the scattered/emitted light within a solid angle, θ≤θtr, varying as a function of the depth position, z. The collection solid angle, Ω, which takes into account the competitive effects of the numerical aperture (NA) of the objective lens and of the pinhole aperture, can be expressed as follows: Ω = 2Ï (1 − N-¹ ) =

‫ۓ‬ F Ü (ߩD ≥ ߩ!) 2Ï Ú1 − ۖ ۖ áF & )ఘ& ‫۔‬ F ۖ ۖ 2Ï Ú1 − & & Ü (ߩD ≤ ߩ! ) áF )ఘ೘ೌೣ ‫ە‬

; = ߩD ඨ(¯ − 1) + ቆವ &

’

 ఘ೘ೌೣ



ቇ ¯

Ë

(A6)

(A7)

where ρmax is the maximum transverse ray aberration from the optical axis (determined by the NA of the objective lens); the confocal pinhole with diameter, Φ, has a virtual back-image, 2ρ0, in the sample focal plane given by the relation: Φ = 2ρ! ¿߯, where MP is the magnification power of the objective and χ is the enlargement factor; note that only light from within the virtual circle 2ρ! on the surface can pass through the pinhole; n is the refractive index of the material, and D/f the diame100

ter/focal length of the objective lens. For any given z value, ρmax can be derived from Eq. (A7). It could be shown that the collection solid angle remains nearly constant, with little, if any variation nearby the free surface; then, for radiation from in-depth zplanes the collection solid angle falls pronouncedly because of the filtering effect of the confocal pinhole aperture; the smaller the pinhole aperture the more abrupt the Ω drop-down. By reducing the diameter of the pinhole aperture, Φ, the critical subsurface depth, z, (needed for achieving a significant reduction in the Ω value) drops down as it approaches the sample surface. In principle, reducing the diameter of the pinhole aperture could produce the effect of reducing the probe depth down to the laser wavelength. However, a significant reduction in the efficiency of the collected spectrum is also experienced upon reducing the Φ value, the effect of which greatly limits the achievable in-depth resolution. In the experimental practice, issues relating to practical acquisition time for Raman bands dictate that minimum pinhole apertures be selected in the range of 10 ≤ Φ ≤ 100 µ m. The observed spectrum is thus obtained

by combining all the spectra originating from different points within the volume of the probe in confocal configuration: 40¶ (߱Û ) ∝ —!

)¡

4(߱)Ω(;, ;! , ߩ! ) Û& )(F F Û&

)

&

exp (−2;) b;

(A8)

where 4(߱) is the local morphology of the Raman line. When the focal plane is placed on the sample surface, Eq. (A8) can be rearranged to give the observed intensity, 40¶ , as follows: 40¶ ·߱Û ¸ ∝

—! Ω(ߩD ≤ ߩ! ) exp(−2;) Û& )F & b; + —-

)¡

Û&

(A9)

Ω(ߩD ≥ ߩ!) exp(−2;) Û&)F & b; Û&

where t, namely a threshold value of the in-depth abscissa below which the collection solid angle abruptly diminishes, can be expressed as:  = ߩ!

ඨ(¯

− 1) + ቆವ

’

 ఘ &



ቇ ¯

(A10)

Equation (A9) can eventually be normalized to the maximum spectral intensity as done for Eq. (A4). When the confocal pinhole is set to a given aperture, Φ, and the focal plane is placed on the sample surface (z0=0), we can estimate the probe depth, zd, by simply solving the following equation: ೥

— ೏ ௌ(F,ఘ )×ீ(F,F) ÂF ಮ

— ௌ(F,ఘ )×ீ(F,F )ÂF

(A11)

101

where the collection cross section, Ô(;, ߩ! ), is given by:

Ô(;, ߩ! , ߩ୫ୟ୶ ) ∝ Ω(;, ߩ! , ߩ୫ୟ୶ ) exp (−α௘’’ ;)

(A12)

Here, the latter term takes into account the effect of inhomogeneous scattering. Consequently, in highly inhomogeneous materials, the absorption coefficient, α, should be replaced with the effective absorption coefficient, αeff, which takes into account inhomogeneous light scattering. In the case of a small pinhole aperture (ρ! → 0), the collection solid angle can be approximated by the following function: Ω(;, ;! , ߩ! ≈ 0) =  +

a

஼(F F )&

(A13)

Upon defining with the parameter, pc, the apparent probe response parameter retrieved from the a best-fitting routine on defocusing results in the selected confocal configuration, Eq. (A13) can be rewritten as a function of p c and p, namely the probe response parameter characteristic of a probe configuration with full pinhole aperture (henceforth, also referred to as “normal” probe configuration). Accordingly, Ω(;, ;! ), can be expressed by: Ω(;, ;! ) = ÛX& °1 + Û& ) (F FX Û&

X

Û&  Û&

)

&

±

(A14)

It should be pointed out that the above equation represents an approximation of the exact expression of the solid collection angle and is only valid at small pinhole apertures. In addition, here p c is just a numerical parameter function of the selected probe configuration. Hence, this parameter has lost its original meaning as a material property (i.e., as in the case of p). Equations (A6) and (A9) can be used to precisely determine the relevant optical parameters and material properties through a best-fitting iterative routine of experimental data. In addition, Eqs. (A5) and (A11) can serve to assess the probe geometry (in particular, the probe depth) in the cases of confocal and through-focus probe, respectively. Regarding the in-plane distribution of the Raman scattered light, namely the nature of the function, Gip(x,y,x0,y0), one needs to calibrate the radius at the waist of the Raman probe, R, in the focal plane. Note that, if in-plane sample anisotropies could be neglected within the focal plane, the function is simplified to a single abscissa variable (i.e., as shown in Fig. A1(b)). Integration of the in-plane probe response function along a given x-axis should give the observed intensity change across a sharp interface, according to the following equation: 4(߱Û) ∝ — ¡ 4(߱)exp k−2 )¡

(D D)& þ&

l b=

102

(A15)

Equation (A15) can again be normalized to the (maximum) spectral intensity collected far away from the interface, in order to convert the proportionality sign into equality (i.e., as done for Eq. (A6) for in-depth calibrations in normal probe configurations). An experimental plot of relative intensity across the interface can be fitted to Eq. (A15) to retrieve the diameter, 2R, of the laser beam waist as it develops within the focal plane. Note that the derivative of the plot in Fig. A1(b) indeed represents the inplane probe response function, Gip(x,x0). It should also be noted that the “character” of ý(=, <, ;, =!,


through focus configuration; and, R=1.0 µm, p=10.4 µm, α eff =0.0073 µm-1, and probe



depth, zd=10.1 µm for the selected confocal configuration. Note that the pc value found for the confocal configuration is much smaller than the p value found for the through-focus one. This behavior is reflected in an almost fourfold shallower probe penetration depth when the confocal geometry is adopted (cf. zd values). No significant difference could normally be found between calculations based on retrieving 103

Raman band intensity at maximum and integral band intensity. One important notion obtained in comparing the findings of these calibration procedures is that spectra collected in UHMWPE by a non-confocal probe configuration might represent average spectral information from significantly large portions of subsurface material. Accordingly, the averaging effect on the measured microstructural features could be quite pronounced, especially in the presence of steep property gradients along the sample subsurface. Given this understanding, the use of the confocal probe appears to be essential in order to make adequate examination of graded structures in UHMWPE. Moreover, it is only by means of a probe deconvolution approach that we become able to precisely acquire (and correctly interpret) spatially resolved spectroscopic data and, in turn, the properties of UHMWPE materials. The knowledge of the correct parametric values to be introduced in the Raman PRF enables deconvolutive treatments of the experimentally retrieved distributions. The “averaging” effect of the Raman probe can be rationalized for a given spatial distribution (in a system of Cartesian coordinate (x,y,z) ) of a measurable spectroscopic property, ℘(=, <, ;) (e.g., band intensity, band width, or frequency shift). When the Raman probe is centered at the loca=! ,
—షಮ —షಮ —షಮ ீ(D,E,F,D ,E,F )ÂDÂEÂF

(A16)

where the Cartesian coordinates are taken with their origin on the sample free surface (i.e., at z0=0, corresponding to the focal plane of the Raman probe), the z axis is then taken perpendicular to the free surface and oriented toward the sample sub-surface. With the knowledge of the PRF, Eq. (A16) can be quantitatively used for spatial deconvolution of spectroscopic data (namely, to derive the real property distribution, ℘(=, <, ;), and its gradients in the three-dimensional space from the (averaged) measured one). Note, however, that Eq. (A16) represents an inverse integral equation in which the unknown function displays within a triple integral. Therefore, the possibility of extracting a restored property distribution function necessarily depends on the correct selection of a trial function (i.e., on correctly guessing the so-called “character” of the real distribution function).

Figure and table captions: Figure 1: (a) Crystalline (lamellae), rigid and mobile amorphous regions in the composite structure of polyethylene; (b) chains in a planar zigzag (crystalline) configuration; and, (c) amorphous structure, essentially random but constrained by crosslinks (red segments) and restricted by the conservation of bond angles and distances. Figure 2: (a) Repeating unit in a single infinitely long polyethylene chain and Brillouin zone of an orthorhombic assembly; (b) cross-sectional view of the orthorhombic structure of polyethylene; and, (c) vibrational modes of polyethylene.

104

Figure 3: Parallel (a) and cross (b) polarized Raman spectra of a highly crystalline and aligned polyethylene fiber with orthorhombic structure. Spectra were collected at different rotation angles on the flank of the fiber, according to the conventions specified in Fig. 4(a). Different Raman modes are labeled in inset. Figure 4: (a) Schematic representations of polarized Raman experiments on a highly crystalline polyethylene fiber with our choice of Cartesian axes and Euler angles used in the determination of RTE constants; and, (b) relationship between orthorhombic cell and crystallized lamellae in the structure of polyethylene. Figure 5: In-plane angular dependencies of different Raman modes of orthorhombic polyethylene as collected on the flanks of a highly crystallized and strongly aligned fiber using different polarized probe configurations. The monitored Raman modes and the probe configuration are specified in inset. Figure 6: Oxidation species in the polyethylene chain reported in the literature[53, 54] to be infrared sensitive and their location in the infrared spectrum of polyethylene. The notations R and R’ are adopted here in their usual meaning of alkyl groups with general formula, CnH2n+1. Figure 7: In (a) and (b), cutting procedure on the acetabular liners to obtain microtomed sections from the acetabular cups; (c) schematics of the FT-IR and Raman spectroscopy protocols used to analyze the thin sections of Samples 1~5 before and after aging. Blue squares represent the FT-IR probe (200 µm in width and full pass through the slice thickness), while the circular spots represent the Raman confocal probe (1 µm in diameter and 30 µm in depth). Figure 8: (a) Phenomenological correlations between αc and OI as obtained upon fitting the experimental data collected from Samples 1~5; and, (b) plots of oxidationinduced recrystallization rates, dαc/dOI, for Samples 1~7 as calculated from the phenomenological Eq. (29)-(35). Figure 9: Schematics of the cascade of mechanisms that links oxidation to crystallization in the amorphous phase of UHMWPE: (a) free radicals in the UHMWPE amorphous region where oxygen diffuses fast; (b) UHMWPE amorphous structure containing hydroperoxide groups (blue arrowed with broken line linking the newly formed free radical and hydroxyl) and carboxylic acid groups (red arrowed with broken line replacing the scissioned C-C bond); and, (c) shortened chain units rearrange into orthorhombic crystals (newly crystallized areas located by broken-line squares). Figure 10: (a) Plots of true strain after recovery, εf, as a function of externally (or initially) applied strain, εi, for both single-step and three-step annealed polyethylene samples under uniaxial compressive stress; and, (b) variations in crystalline phase fraction for both samples upon plastic deformation in compression. Figure 11: (a) Width (FWHM) of the 1130 cm-1 Raman band of orthorhombic polyethylene, as observed on unpolarized Raman spectra at different values of residual compressive strain, εf, after strain recovery; and, (b) the trends shown in (a) of band broadening for both types of bulk polyethylene are re-plotted as bandwidth variations, ∆FWHM, with respect to the respective initial values of bandwidth, in the as-received undeformed state of the samples.

105

Figure 12: Schematic drafts representing the internal mechanisms of deformation of biomedical bulk polyethylene at the microscopic scale. In (a), (b), and (c), the three Stages I, II, and III of strain level are depicted, respectively, as defined in Fig. 11(a) and in the forthcoming Fig. 13(a). Note the presence of both compressive and tensile microstresses as a consequence of the presence of ties in the amorphous chains, which also induce rotation of lamellae at high strain levels. Figure 13: (a) Out-of-plane (tilting) inclination angle, θp, as a function of plastic residual strain, εf, for both single-step and three-step annealed polyethylene samples subjected to uniaxial compressive stress; and, (b) trends shown in (a) of tilt angle for both types of bulk polyethylene are re-plotted as angular variations, ∆θp, with respect to the respective values of tilt angle, in the as-received undeformed state of the samples. Figure 14: (a) Plots of the out-of-plane (tilting) inclination angle, θp, at different level of (residual) plastic strain, εf; these plots show evidence of the rotational activity of orthorhombic lamellae under compressive strain according to a characteristic threestages process; and, (b) plots of residual strain as a function of variations in tilt angle of the lamellae, εf (∆θp), for two different polyethylene structures. Figure 15: Choice of Cartesian systems ((xlab,ylab,zlab) integer to the laboratory frame, (Xcry,Ycry,Zcry) integer to the local domain orientation axes, and (xp,yp,zp) locating the axes of preferential orientation of the crystal texture) and Euler angles ((θ,φ,ψ) for rotation of (Xcry,Ycry,Zcry) with respect to (xlab,ylab,zlab), (α,β,γ) for rotation of (Xcry,Ycry,Zcry) with respect to (xp,yp,zp), and (θp,φp,ψp) for rotation of (xp,yp,zp) with respect to (xlab,ylab,zlab)). The three sets of Euler angles are related to each other according to Eqs. (71) and (72). Figure 16: Maps of molecular orientation patterns as revealed by polarized Raman scattering intensities on selected areas of the four investigated retrievals in comparison with the unused acetabular cup (see labels in inset). Left and right sides of the maps in the retrieved cups are from NWZs and MWZs, respectively. Maps were also collected at similar locations in the unused cup. Full (red) line drawn on each retrieved cup represents the approximate direction of gait motion. Figure 17: Maps of degree of crystallization, αc, as revealed by Raman scattering intensities on selected areas of the four investigated retrievals in comparison with the unused acetabular cup (see labels in inset). Left and right sides of each retrieved cup are from NWZs and MWZs, respectively. Maps were similarly collected at two specular locations also in the unused cup. Figure 18: Histograms of the degree of crystallinity, αc, and of c-axis orientation angle, ψ, for both MWZs and NWZs of short-term and long-term retrievals as compared with the as-manufactured material; note the quite homogeneous structure of this latter sample in both antero-inferior and postero-superior zones (in (a) and (f), respectively). Each histogram is representative of a surface area of 5x10 4 µm2. Figure 19: (a) and (b): Experimental plots of the angular dependence of Raman scattering intensities for selected vibrational modes (see labels) of the orthorhombic structure of UHMWPE. Each plot is representative of Raman spectra averaged over an area of 5x104µm2. The full lines represent the least square fitting curves obtained with 106

using trial functions as described in the text. In (c), ODF as calculated from experimental data for the main wear zones of the 10.3 y long-term retrieval and of the 2.8 y short-term retrieval are plotted in comparison with the functions retrieved for the fiber sample and for the unused cup as an upper and lower boundary for the degree of orientation of a UHMWPE structure, respectively. The parameters locating the plotted ODF are listed in Table VIII. Each function is representative of Raman spectra averaged over an area of 5x104µm2. Figure 20: (a) Scanning electron micrograph, (b) crystallinity map, and (c) molecular orientation map collected in the same area of the main wear zone of the UHMWPE liner retrieved after 10.3 y in vivo. Broken lines evidence lumpy zones. The scales of the maps in (b) and (c) are the same of those in Figs. 50 and 51, respectively. In (d), an explanatory draft is depicted of the cross section of the worn UHMWPE surface. Figure 21: Crystallographic orientation patterns ((a) and (b)) and crystallinity fractions ((c) and (d)) evaluated from Raman spectroscopic maps collected on hipsimulator tested UHMWPE liners of the same type as the unused and retrieval liners in Figs. 16(a)~(c) and 17(a)~(c). Figure 22: Speculative drafts of in vivo (boundary lubrication conditions) and in vitro (hydrodynamic lubrication conditions); the former is based on the Raman analyses shown in Fig. 20, while the latter was elaborated according to the models given in Refs. [152] and [153]. Figure 23: Plastic strain dependences of (a) the out-of-plane tilting angle, θp, and (b) the Hermans’ parameter, < P (cos •) >, for the EtO- and γ-irradiated samples. Figure 24: (a) Observed trends of out-of-plane molecular rearrangement ∆θp with respect to the original orientation direction in the virgin (unstrained) EtO- and γirradiated samples; in (b) and (c), ODF curves obtained at different levels of strain for the EtO- and γ-irradiated samples, respectively. Figure 25: In-plane and out-of-plane Euler angles, θp and ψp, of the preferentially oriented molecular chains, as detected in the studied tibial insert retrievals. Investigated areas and definitions of Cartesian axes and Euler angles in the upper and lower side drafts, respectively. Figure 26: Residual strain, ε, stored in different zones of the investigated retrievals. Figure 27: Average ODF curves for different investigated areas on different retrievals (cf. labels; Hermans’ parameters associated with each f(β) distribution curve in inset to each plot). Figure 28: (a) Draft of orientation axes and rotation angles in the artificial knee joint (in inset, the relationship between molecular chains and orthorhombic lamellae); (b) in-depth statistical frequency of the Hermans’ parameter, < P (cos • ) > for the outof-plane orientation angle, θp, in the γ-irradiated as-received sample; and, (c) and (d) give the in-depth dependences of the average orientation angles of the molecular chains, θp and ψp, respectively, before and after in vivo exposure. Figure 29: Correlation between the percentage of compressive strain measured after 24 h recovery and the experimental band broadening for Longevity® polyethylene liners. Best-fitting is given in Eq. (85). Figure 30: (a) Draft of the protocol followed to characterize the 11 polyethylene liner 107

retrievals; pictures of a sectioned retrieval and of its cross section in (b) and (c), respectively. Figure 31: Polar plots representing profiles of creep, wear, and total penetration as interpolated from the data of the short-term retrievals. Figure 32: Polar plots representing profiles of creep, wear and total penetration obtained from the middle-term retrievals. Figure 33: Peaks of creep (a), wear (b), and total penetration (c) as a function of implantation time. Linear regression lines were calculated during the bedding-in period, the steady wear state period and the overall range of follow-up. Figure 34: (a) Graphical representation of the volume reductions due to wear and creep in retrieval Case 8; and, (b) cross section across the MWZ and NWZ of Case 8 sample showing creep and wear thickness reductions (polar profile enhanced by a factor 5 for better visualization). Figure 35: (a) Unsaturated C=C bonds in the lipid molecules react with the saturated UHMWPE molecules initiating degradation in the host polymer; (b) formation of peroxy free radicals in the lipid molecules drives the formation of hydroperoxides by abstracting hydrogen atoms from the polyethylene chains; and, (c) polymeric chains break, oxidize, and these processes lead to re-crystallization of the structure. Figure 36: Graphs of the IR-measured OI parameter for a set of 11 Longevity® liners: 7 short-term (a) and 4 medium-term (b) retrievals (cf. Table X). Figure 37: In-depth oxidation profiles, OI, recorded by IR spectroscopy at different locations in the medium-term in vivo-exposed liner Case 8 (cf. Table X); the upper inset shows the cross section of the investigated liner and the locations at which IR measurements were performed. Figure 38: In-depth profiles of oxidation index, OI, from IR spectra (a) and crystallinity profiles, αc, from Raman spectra (b); in vivo oxidative degradation (location L5 in Case 8 (cf. Fig. 37)) is compared with the as-received sample, and with in vitro induced oxidation (28 days shelf-aging at 23oC after 25 kGy γ-irradiation, and additional oxygen-bomb (5 atm) aging at 70oC after 25 kGy γ-irradiation and 28 days aging on shelves). Figure 39: (a) Anti-oxidant vitamin E and the presence of an alcoholic hydroxyl group in its chroman ring; and, (b) annihilation by free hydrogen of free radicals in the UHMWPE (peroxyl radical trapping). Figure 40: Plots of the in vitro tested degree of oxidation (by IR) as a function of the normalized in-depth abscissa, z/t, for differently manufactured liners: (a) 28 days shelf-aging at 23 oC after 25 kGy γ-irradiation, and (b) oxygen-bomb aging after 25 kGy γ-irradiation. Figure 41: Comparison between re-melted and vitamin E infused UHMWPE samples after oxygen-bomb (5 atm) aged at 70oC after 25 kGy γ-irradiation or soaking into squalene: in vitro testing of the degree of oxidation (by IR) as a function of the normalized in-depth abscissa, z/t. Figure 42: (a) Comparison between the procedures for manufacturing the VEI and VEB liners as shown in (b) and (c), respectively. The VEF sample was produced exactly in the same way as the VEB one, except for eliminating vitamin E blending. 108

Figure 43: Plots of the in-depth profiles of crystalline phase fractions in VEI, VEB, and VEF samples before (a) and after (b) compression test followed by relaxation (cf. inset). Figure 44: Plots of the in-depth profiles of amorphous phase fractions in VEI, VEB, and VEF samples before (a) and after (b) compression test followed by relaxation; the upper inset to (b) is a plot of variations in amorphous structure, ∆αa, at the surface and in the bulk. Figure 45: Plots of the in-depth profiles of third-phase fractions in VEI, VEB, and VEF samples before (a) and after (b) compression test followed by relaxation; the upper inset to (b) is a plot of variations in third-phase structure, ∆αt, at the surface and in the bulk. Figure 46: (a) Plots of true strain after recovery, εf, as a function of externally applied (or initial) strain, εi, for VEI and VEB liners (slope values in inset); and, (b) explanatory draft of the crosslinking (red features) vs. plasticizing (blue features) effects in the studied VEI and VEB microstructures. Figure 47: XPS results performed on a virgin liner (a), on the NWZ (b), and MWZ (c) of the liner retrieved after 1.9 yr in vivo. Binding energies in the abscissa axis are for selected spectral ranges highlighting C1s, O1s, N1s, and P2p. Figure 48: Enlarged view of the C1s region of the XPS spectra from a virgin liner (a) and the MWZ of a short-term retrieval (item (i)) (b). Figure 49: Confocal Raman spectroscopy data showing the phase fractions at the sliding surface (i.e., within the first 20 µm of the free surface) for virgin (a), NWZ (b), and MWZ (c); (b) and (c) refer to the Aquala® liner retrieved after 1.9 years of implantation in vivo (average data of 15 measured map locations). Figure 50: Speculative diagram visualizing the in vivo sliding conditions and the mechanism of UHMWPE amorphization observed at the surface of the 1.9 yr shortterm in vivo exposed Aquala® liners. Figure 51: Schematic diagram of the sample preparation procedure including sectioning and coupling of UHMWPE/ceramic couples in an autoclave operating in watervapor environment. Figure 52: Histograms of crystallinity increases, ∆αc, are given in (a)~(d) for the series of tested couples including the UHMWPE/UHMWPE control. Labels in the insets locate the type of couple tested. The histograms were obtained from a series of Raman maps by subtracting the crystallinity values of the pristine samples from those recorded at exactly the same locations after 24 h autoclave exposure in contact with their concave counterparts (total surface areas ~25 x103 µm2 per tested couple). Figure 53: ∆αc0 and ∆OI0 values at the very surface of various UHMWPE counterpart samples resolved from deconvoluting the sub-surface profiles at z = 0 of samples coupled with different counterfaces. The results of statistical analyses are shown in inset. Figure 54: XPS elemental data obtained for different ceramic/UHMWPE in comparison with a control UHMWPE couple. Standard deviations for the oxygen contents are shown for oxygen, n=18. Figure 55: XPS examinations on Si3N4 counterparts after 24 h autoclaving at 121 oC showing a change in oxygen content at the surface of the non-oxide ceramic. O1s 109

spectra were obtained from exactly the same Si3N4 samples both before and after autoclaving and revealed a O1s peak 30% more intense after autoclave exposure. Figure 56: Maps of variations in crystallinity, ∆αc (a) and oxidation index, ∆OI (b) as found on the UHMWPE counterpart to ZTA after 24 h of autoclave aging. The fractional variations of the third (semi-crystalline) and amorphous phases are given in (c) and (d), as recorded at exactly the same locations, respectively. Figure 57: Schematic draft of the re-crystallization process taking place after chain breaking and oxidation at the expenses of the third phase at the highly strained interface between orthorhombic crystals and amorphous enclaves. Figure 58: Hypothesis of interaction occurring at the interface between oxide ceramics and UHMWPE (a) and non-oxide ceramics and UHMWPE (b) during hydrothermal activation. An initially nearly stoichiometric Al2O3 surface diverges toward oxygen off-stoichiometry through dehydroxylation and formation of oxygen vacancies along with a flow of free oxygen molecules toward the UHMWPE structure. The pristine Si3N4 surface forms a layer of silicon oxynitride upon attracting free oxygen from the tribolayer thereby protecting the UHMWPE structure from oxidation. Figure 59: Schematic drafts of the antioxidant effects in: (a) nitroxide, (b) vitamin C, (c) phenolic compounds, and (d) graphene from exfoliation of layered graphite at the molecular scale. The drafts in (a) and (d) were re-drawn from Refs. [223]and [227], respectively. Figure 60: (a) Schematic explaining the OIT method of thermal analysis of UHMWPE proposed by Uetsuki et al.[239]; (b) curves of differential head as a function of time in thermally activated oxygen atmosphere as recorded for vitamin Edoped (3000 ppm) non-irradiated and irradiated samples in comparison with a vitamin E-free non-irradiated control sample; and, (c) plots of OIT as a function of electronbeam irradiation dose for vitamin E doped and undoped UHMWPE samples. Data in (b) and (c) are re-plotted from Ref.[239]. Figure A1: (a) Schematic draft of the confocal configuration for Raman assessments as obtained by adjusting the aperture of a confocal pinhole placed in front of the signal detector. Methods of PRF calibrations for quantitatively representing in-plane and in-depth probe structure and morphology are shown in (b) and (c), respectively. Figure A2: In-depth PRF plots for bulk biomedical polyethylene with using a 100x optical lens with a full aperture of the confocal pinhole (through-focus) and using the same lens but with a pinhole aperture of 100 µm (confocal). Solid curves represent the results of best fitting with using Eqs. (A4) (through-focus probe) and (A9) (confocal probe) as trial functions. Table I: Multiplication table for the factor group, Vh (line), which summarizes the symmetry operations for the linear structure of polyethylene schematically drawn in Fig. 11(a). Table II: Character table for the point group D2h, isomorphous with the factor group of a single polyethylene chain. Table III: Character table, number of normal modes, and selection rules for the orthorhombic structure of crystalline polyethylene. 110

Table IV: Assignment of the main features experimentally found in the Raman spectrum of polyethylene in the frequency interval 1000~1500 cm-1. Table V: Raw materials and manufacturing characteristics of single-step and threestep irradiated biomedical polyethylene samples used in uniaxial compressive strain calibrations. Crosslinking data are quoted from Ref. [89]. Table VI: Clebsch-Gordan coefficients (i.e., the constants, C, in Eq. (49)) used for expressing in a single rotation series the products of Wigner functions. Table VII: Coefficients for constructing higher-order Wigner functions, D¾9 (, •, –), as shown in Eq. (49). Table VIII: Numerical parameters characterizing the orientation distribution functions plotted in Fig. 19(c). Table IX: Summary of the investigated knee retrievals, including manufacturing characteristics and clinical data. Table X: Summary of the investigated hip retrievals, including manufacturing characteristics and clinical data. Table XI: Average creep, wear, and total penetration rates as calculated for the hip retrievals in Table X. Table XII: Summary of XPS results collected on the NWZ and MWZ of the asreceived and short-term retrieved Aquala® liners (the symbols #1, #2, and #3 refer to the three retrievals referred to as items (i), (ii), and (iii) in the text); each data value is the average of 5 measurements for each zone of each sample (data are in at.%).

111

Tables Table I E

σv

σh

σh

i

C2

C′2

C2

E

E

σv

σh

σh

i

C2

C′2

C2

σv

σv

E

C2

C′2

C2

i

σh

σh

σh

σh

C2

E

C2

C′2

σh

i

σv

σh

σh

C′2

C2

E

C2

σh

σv

i

i

i

C2

C′2

C2

E

σv

σh

σh

C2

C2

i

σh

σh

σv

E

C2

C′2

C′2

C′2

σh

i

σv

σh

C2

E

C2

C2

C2

σh

σv

i

σh

C′2

C2

E

Table II Translations and rotations

Activity

E

σv

σh

σh

i

C2

C′2

C2

Ag

+1

+1

+1

+1

+1

+1

+1

+1

Au

+1

-1

-1

-1

-1

+1

+1

+1

B1g

+1

+1

-1

-1

+1

+1

-1

-1

αC′ C

RC 2

B1u

+1

-1

+1

+1

-1

+1

-1

-1

MC 2

TC 2

B2g

+1

-1

+1

-1

+1

-1

+1

-1

B2u

+1

+1

-1

+1

-1

-1

+1

-1

B3g

+1

-1

-1

+1

+1

-1

-1

+1

B3u

+1

+1

+1

-1

-1

-1

-1

+1

αC 2 , α 2

2

C′ 2

2

αC

2

2

2

C2

MC2′

αC

2

, αC 2

RC2

RC2′

TC2′

C2′

M C2

TC2

Table III

D2h

E

C2′ ( a )

C 2′ ( b )

C2′ ( c)

i

σ (bc)

σ ( ac )

σ ( ab)

ni

T

T'

R'

n'i

IR

R

Ag

1

1

1

1

1

1

1

1

6

0

2

1

3

f

p

B1g

1

1

-1

-1

1

1

-1

-1

3

0

1

2

0

f

d

B2g

1

-1

1

-1

1

-1

1

-1

3

0

1

2

0

f

d

B3g

1

-1

-1

1

1

-1

-1

1

6

0

2

1

3

f

d

Au

1

1

1

1

-1

-1

-1

-1

3

0

1

2

0

f

f

B1u

1

1

-1

-1

-1

-1

1

1

6

Ta

1

1

3

a

f

B2u

1

-1

1

-1

-1

1

-1

1

6

Tb

1

1

3

a

f

B3u

1

-1

-1

1

-1

1

1

-1

3

Tc

0

2

0

a

f

Table IV Frequency, cm-1

Phase

Mode

Symmetry

1060

C (A)

vas(C-C)

B2g + B3g

1080

A

v(C-C)

1130

C (A)

vs(C-C)

Ag + B1g

1170

C (A)

ρ(CH2)

Ag + B1g

1296

C

τ(CH2)

B2g + B3g

1310

A

1370

C

ω(CH2)

B2g + B3g

1418

C

δ(CH2)

Ag

1440

A

Fermi resonance

B1g + Ag

1460

A

+ overtones

Ag + B1g

Table V Single-step irradiated

Three-step irradiated

Resin

GUR1050

GUR1020

Average molecular weight

5.5-6 x 106 g/mol

3.5 x 10 6 g/mol

Process of consolidation

Ram extrusion

Compression molding

Irradiation

75 kGy Gamma ray

30 kGy in 3 steps (total 90 kGy)

Post-irradiation heat treatment

Annealing (130 oC for 8 h)

Annealing after each step (130 oC for 8 h)

Sterilization

30 kGy Gamma ray in nitrogen

Gas plasma

Cross-linking density

0.11 ± 0.02 mol dm-3

0.17 ± 0.02 mol dm-3

Table VI

n = -2

n=1

n=2

1/(2݁ଶ௜ఈ sinߚ × (1 − cos β)ଶ ݁ ି௜ఊ )

1/(4݁ ଶ௜ఈ ×

1/(4݁ × (1 + cos β)ଶ ݁ଶ௜ఊ )

1/(2݁ sinߚ × (1 + cos β)ଶ ݁ ௜ఊ )

ඥ3/8 ݁ sinଶ ߚ

−1/(2݁ ଶ௜ఈ sinߚ × (1 + cos β)ଶ ݁ଶ௜ఊ )

1/(2݁ ௜ఈ × (2cosߚ − 1) × (1 + cos β)ଶ ݁ ௜ఊ )

ඥ3/2 ݁௜ఈ sinβcosβ

1/(2݁ ௜ఈ × (2cosߚ + 1) × (1 − cos β)ଶ ݁ ି௜ఊ )

1/(2݁ ௜ఈ sinߚ × (1 − cos β) ݁ ିଶ௜ఊ )

ඥ3/8 ݁ ଶ௜ఊ sinଶ ߚ

−ඥ3/2 ݁ ௜ఊ sinβcosβ

1/ (6cos ଶ ߚ − 2)

ඥ3/2 ݁ ି௜ఊ sinβcosβ

ඥ3/8 ݁ ିଶ௜ఊ sinଶ ߚ

−1/(2݁ ௜ఈ sinߚ × (1 − cos β)ଶ ݁ଶ௜ఊ )

1/(2݁ ି௜ఈ × (2cosߚ + 1) × (1 − cos β) ݁ ௜ఊ )

−ඥ3/2 ݁ ି௜ఈ sinβcosβ

1/(2݁ ି௜ఈ × (2cosߚ − 1) × (1 + cos β) ݁ ି௜ఊ )

1/(2݁ ି௜ఈ sinߚ × (1 + cos β)ଶ ݁ ିଶ௜ఊ )

1/(4݁ ିଶ௜ఈ × (1 − cos β)ଶ ݁ଶ௜ఊ )

−1/(2݁ ିଶ௜ఈ sinߚ × (1 − cos β) ݁ ௜ఊ )

ඥ3/8 ݁ sinଶ ߚ

−1 /(2݁ ିଶ௜ఈ sinߚ × (1 + cos β)ଶ ݁ ି௜ఊ )

1/(4݁ ିଶ௜ఈ × (1 + cos β)ଶ ݁ ିଶ௜ఊ )

m=2

m=1

m =0

m = -2

ଶ௜ఈ

n=0

m = -1

ଶ௜ఈ

n = -1

ଶ௜ఈ

ିଶ௜ఈ

(1 − cos β)ଶ ݁ ିଶ௜ఊ )

Table VII m

m1

m2

J=0

J=1

J=2

J=3

J=4

-4 -3 -3 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 0 1 1 1 1 2 2 2 3 3 4

-2 -1 -1 0 -1 -2 1 0 -1 -2 2 1 0 -1 -2 2 1 0 -1 2 1 0 2 1 2

-2 -2 -2 -2 -1 0 -2 -1 0 0 -2 -1 0 1 2 -1 0 1 2 0 1 2 1 2 2

1/5 -1/5 1/5 -1/5 1/5 -

1/5 -3/10 3/10 -1/5 2/5 -1/10 0 1/10 -2/5 1/5 -3/10 3/10 -1/5 -

2/7 -3/7 2/7 3/7 -1/14 -1/14 3/7 2/7 1/14 -2/7 1/14 2/7 3/7 -1/14 -1/14 3/7 2/7 -3/7 2/7 -

1/2 -1/2 1/2 0 -1/2 3/10 1/5 -1/5 -3/10 1/10 -2/5 0 -2/5 -1/10 3/10 1/5 -1/5 -3/10 1/2 0 -1/2 1/2 -1/2 -

1 1/2 1/2 3/14 4/7 3/14 1/14 3/7 3/7 1/14 1/70 8/35 18/35 8/35 1/70 1/14 3/7 3/7 1/14 3/14 4/7 3/14 1/2 1/2 1

Table VIII Sample Fiber Main wear zone Main wear zone Non-wear zone Unused liner

< P2 (cosβ ) > 0.97

< P4 (cosβ ) > 0.92

3.29×10

0.88

0.78

7.51×10

0.73

0.60

3.18×10

0.58

0.44

5.94×10

0.40

0.19

A

9.10×10

-9 -4 -3

-3 -3

l2

l4

-10.00

-10.00

-1.70

-5.00

-1.65

-3.00

-1.50

-2.00

-1.50

-0.65

Table IX

Case A Case B Case C Case D

Maker/ name of implant JMM/ KU3 JMM/ KU3

Resin

Stryker/ Scorpio NRG

GUR 1020

Smith & Nephew/ Genesis II

GUR 1020

GUR 1050 GUR 1050

Processing

Sterili zation

Compression moulding

EtO

Compression moulding

EtO

Compression moulding

γ-ray (33 kGy)

Compression moulding

EtO

Size

Small 9 mm Xsmall 9 mm 8 mm with stabili zer 9 mm H/F

Patien t

Followup

73 y, F

5 y, 8 mo

77 y, F

4 y, 7 mo

83 y, F

4y

81 y, F

7 mo

BMI 22.0 23.6 23.1

25.8

Table X

No.

In-vivo time (mo/yr)

Ex-vivo time (mo/yr)

Age (yr)

Sex

BMI (kg/m2)

Abduction Angle (°)

Thickn ess (mm)

Cause of revision

Short term Case 1

0.5 / 0.04

137 / 11.4

71

F

29

45

10.3

Cup loosening

Case 2

1.0 / 0.08

6.0 / 0.50

58

F

35

46

6.3

Infection

Case 3

1.5 / 0.13

92 / 7.70

71

F

18

35

15.4

Infection

Case 4

3.0 / 0.25

74 / 6.20

67

F

29

39

8.2

Dislocation

Case 5

6.0 / 0.50

39 / 3.30

78

F

20

30

7.2

Cup loosening

Case 6

6.5 / 0.54

94 / 7.80

71

F

26

40

15.4

Stem loosening

Case 7

8.0 / 0.67

89 / 7.40

32

M

26

47

12.4

Neuroparalysis

Middle term Case 8

49 / 4.10

50 / 4.20

72

F

33

45

6.4

Dislocation

Case 9

73 / 6.10

76 / 6.30

68

F

30

40

8.2

Stem loosening

Case1 0

77 / 6.40

78 / 6.50

61

F

25

48

7.2

Stem loosening

Case1 1

86 / 7.20

15 / 1.30

75

F

20

45

6.3

Infection

Table XI

Creep Wear Total penetration

Bedding-in Rate r 0.189 0.946 0.000 0.000

Steady wear state Rate r 0.010 0.375 0.022 0.634

Rate 0.026 0.026

r 0.798 0.857

0.189

0.027

0.046

0.849

0.946

0.534

Overall

C1s

As #1 received NWZ

#1 MWZ

#2 NWZ

#2 MWZ

#3 NWZ

#3 MWZ

C-C

71.43

76.92

86.37

87.65

88.70

83.28

88.28

C-N

16.14

13.09

6.64

6.88

5.48

7.68

6.73

C-O

7.83

5.84

3.91

3.51

3.75

5.12

2.84

C=O

4.60

4.15

3.07

1.96

2.07

3.92

2.15

Table XII