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Anelastic phenomena associated to water loss and collagen degradation in human dentin
Materials Science and Engineering C 33 (2013) 1455–1459
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering C journal homepage: www.elsevier.com/locate/msec
Anelastic phenomena associated to water loss and collagen degradation in human dentin S. Amadori a,⁎, E. Bonetti a, E.G. Campari a, I. Cappelloni b, R. Montanari b a b
Department of Physics and Astronomy, University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy Department of Industrial Engineering, University of Rome—Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy
a r t i c l e
i n f o
Article history: Received 3 July 2012 Received in revised form 4 December 2012 Accepted 14 December 2012 Available online 23 December 2012 Keywords: Dentin Collagen Internal friction Dynamic modulus
a b s t r a c t This work describes the anelastic and dynamic Young modulus behaviour of human dentin from room temperature up to 673 K. Human molars, extracted from individuals (males 55–70 years old) as part of their dental treatment, were cut to obtain bar-shaped samples subsequently used for mechanical spectroscopy experiments. In addition, thermo-gravimetric analysis (TGA) has been performed to assess a possible weight loss occurring in the same temperature range of mechanical spectroscopy tests. A broad and asymmetric internal friction (Q−1) maximum at 500 K has been observed during the heating of the as-prepared samples. This maximum is absent during the following cooling down to room temperature. It is therefore due to the occurrence of an irreversible transformation in the sample. TGA shows a remarkable weight loss in the same temperature range. This effect has been related to loss of fluids and degradation of collagen. Another set of samples, previously kept for 36 h under a vacuum of 10−2 Pa, were submitted at room temperature to test at increasing strain from 6× 10−6 to 7× 10−4. The results show transient and fully recoverable Q−1 increase and dynamic modulus (E) decrease. The phenomenon has been ascribed to the breaking of weak H-bonds between polypeptide chains forming the triple-helix with consequent increase of the mean length of vibrating chain segments. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Dentin is a complex hydrated biological composite consisting of about 50 vol.% mineral in the form of apatite, 30 vol.% organic matter, which is largely type I collagen, and about 20 vol.% fluid. Other non-collagenous proteins and organic components are also present in small amounts [1]. Its hierarchical structure is shown in Fig. 1, taken from [2]. For simplicity dentin will be described here by distinguishing three scales (macro, meso, nano) where in some texts more hierarchical levels are defined. On a macro scale (a–b) dentin can be modelled as a continuous fibre-reinforced composite, with the intertubular dentin forming the matrix and the tubule lumens with their associated cuffs of peritubular dentin forming the cylindrical fibre reinforcement [3–7]. The morphology varies with location since tubules converge on the pulp chamber varying density and orientation. On a meso scale intertubular dentin is formed by fibres randomly oriented in a plane perpendicular to the direction of dentin formation (c–d–e).
⁎ Corresponding author. Tel.: +39 0512095298; fax: +39 0512095113. E-mail address: [email protected] (S. Amadori). 0928-4931/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msec.2012.12.067
On a nanoscale the characteristic features are collagen fibrils, apatite crystals and water (f–g). Each fibre consists of several fibrils (50– 100 nm in diameter) which exhibit periodically spaced gaps. Three polypeptide chains are wound together in a triple helix. A triplehelical molecule is cylindrically shaped (diameter of ~1.5 nm, length of ~300 nm). The molecules are all parallel, but their ends are separated by holes of about 35 nm, they pack together to form a single fibril. The mineral is either within the fibrils (intrafibrillar) or between the fibrils (interfibrillar). The shape of apatite crystals is needle-like near the pulp and progressively becomes plate-like near the enamel, the thickness, ~5 nm, does not change with location. Water is the third major component and is located within and between the fibrils, between fibres and between triple-helical molecules. Several works exist in the literature regarding the mechanical properties of dentin, e.g. [8–11]; a thorough review was published by Kinney and Marshall [8]. The Young's modulus measured by different research groups spans from about 11 GPa up to 35 GPa. In general, static mechanical tests give lower values than the dynamic (particularly ultrasound) ones. Apart from artifacts, like damaged teeth, affecting the tests, it is not completely clear why there is such a spread between different measurements. The probable source for such a wide range of measured values is the anelastic behaviour of dentin. When a material exhibits such a property, its elastic constants are time dependent and different values of Young's modulus can be obtained with different techniques. In particular, static tests yield relaxed values (lower) whereas dynamic
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S. Amadori et al. / Materials Science and Engineering C 33 (2013) 1455–1459
Fig. 1. Schematic view of the highly hierarchical dentin structure [2].
tests yield unrelaxed values (higher). In spite of the importance of the topic, only few papers deal with the anelastic properties of dentin and their changes [12,13]. Therefore, an experimental campaign has been undertaken by the authors to study the anelastic behaviour of dentin under different physical conditions aiming to get ground information. The aim of this work is to add information on damping phenomena occurring in the range from room temperature up to 673 K. Although clinically relevant temperatures are between 273 and 323 K and temperatures above 500 K are rarely of interest also for the implantation of biomaterials, the anelastic behaviour of dentin has been investigated in a more extended range (up to 673 K) to get ground information about all the possible transformations of its complex structure induced by heating, including the complete degradation and combustion of collagen. For instance, such information could be useful in the study of archaeological finds or in forensic cases.
was employed. The apparatus is described in detail in [14]. Young's modulus and damping were measured. The damping Q −1 which is also the ratio of the loss modulus to the storage modulus was determined from the logarithmic decay δ of flexural vibrations: ″ ′ −1 tan δ ¼ E =E ¼ ln An =Anþ1 ¼ πQ
ð1Þ
where An and An + 1 are the amplitude of two successive vibrations, E′ and E″ are the storage and loss modulus respectively. The storage modulus (also called elastic modulus) has been determined from the resonant frequency f of the bar samples: h i 2 4 4 2 2 E ¼ 48π ρl =α h f
ð2Þ
2. Experimental Human molars were extracted from individuals (males 55–70 years old) as part of their dental treatment. The teeth were not identified by patient number or name and each patient signed a patient consent form. After disinfection by immersion in a solution of sodium hypochlorite in water for about 12 h, they were sectioned along mesial direction by using a precision diamond saw with water cooling in order to obtain 0.8 mm-thick slices. From these sections bar-shaped samples (length L = 13÷ 16 mm, width W = 3 ÷ 4 mm) have been cut for mechanical spectroscopy measurements. A single specimen was obtained from each tooth and included root dentin and crown dentin but not enamel. Teeth taken from different patients (sixty patients, one tooth per patient) have been used in the experiments. Before testing the specimens have been investigated by scanning electron microscopy and light optical microscopy and one third of the samples was rejected because of the presence of fractures or damages. The samples, mounted in free-clamped mode, have been tested by the vibrating reed technique in a vacuum chamber at a pressure of 10 −2 Pa. The vibrating reed analyzer model VRA 1604 by CANTIL srl
α is a constant, ρ is the material density, l and h are the sample length and thickness, respectively. The strain amplitude was kept below 1 × 10 −5, and the vibration frequency of the samples spans the 1–10 kHz frequency range. A first set of measurements consisted of heating–cooling cycles from 300 to 673 K with a constant heating rate of 3.33 × 10 −2 K s −1. A second set of measurements was carried out isothermally at 300 K with increasing strain amplitudes. Fifteen specimens were used for each set of tests. In the second set of measurements before starting the isotherms, specimens were kept for 1.3 × 10 5 s (about 36 h) in the spectrometer chamber at room temperature at the pressure of measurements of 10−2 Pa. These samples were submitted to a strain increase from 6 × 10 −6 to 7 × 10−4, then kept at the maximum strain for 1.2 × 103 s (20 min) and finally brought back to the initial condition. Successive measurement runs were made on the same samples. Thermo-gravimetric analysis (TGA) has been performed from room temperature up to 693 K on ten samples submitted to the same heating runs employed in mechanical spectroscopy experiments to assess a possible weight loss.
S. Amadori et al. / Materials Science and Engineering C 33 (2013) 1455–1459
3. Results and discussion 3.1. Experiments at increasing temperature The results of mechanical spectroscopy experiments obtained on different samples showed only minor differences. In particular the Q−1 and modulus data for samples from the same set are within ±3%. A greater dispersion of order of ±5% was observed for damping in the temperature range of the maximum. Fig. 2a and b shows the typical Q−1 and E vs. temperature trend during heating–cooling runs. The specimen of Fig. 2a was heated at the standard heating rate up to 360 K and then cooled down to room temperature, the specimen of Fig. 2b was heated up to 673 K. Fig. 2b shows the temperature range not covered by Fig. 2a. The difference in Q−1 and E between the two samples in the cooling data is due to the irreversible transformation occurring in the specimen of Fig. 2b when heated up to 673 K, as explained in the following. Fig. 2c shows the results of a second heating–cooling run up to 673 K performed on the same sample of Fig. 2b. The Q−1 maximum is no more present. The dynamic modulus at room temperature (E=15±2 GPa) is in agreement with the data of other investigators [15,16]. Despite the absence in literature of other dentin damping data, a comparison with Q−1 values of the rather similar human bone has been done. The data, ranging from 2×10−2 to 4×10−2 [17–19], are compatible with those of dentin determined in the present experiments (Q−1 ≈1.0×10−2). It is known that heating up to about 360 K affects only residual water present in the pores of dentin without altering the molecular structure of collagen. In general, owing to a viscous friction dissipative mechanism, hydrated bone has a lower modulus and a higher Q−1 than dried bone (Schaller et al. [20]) and the same behaviour has been observed for dentin [21]. Therefore, the initial water loss leads to a transient between 300 and 360 K with E and Q−1 changing with
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temperature, see Fig. 2a. If the samples are cooled down from 360 K and rewetted, the original characteristics are completely restored and thus the process is reversible. Above 360 K, Q −1 progressively increases and a very broad and asymmetric maximum at 500 K is observed. Modulus decreases and exhibits two slope changes around 473 and 573 K. On the basis of modulus behaviour it is reasonable to assess that the asymmetric shape of the internal friction maximum can be due to the overlapping of two different contributions. These phenomena are not present during cooling to room temperature and successive cycles. After a heating–cooling cycle up to 673 K the samples appear carbonized and both Q −1 and E have decreased values with respect to the original ones. The location of the Q−1 maximum does not shift with frequency. These results testify that an irreversible structural transformation has occurred. TGA shows a remarkable weight loss in the same temperature range of the internal friction maximum (Fig. 3). Two stages (1, 2) can be identified, corresponding to the ascending and descending parts of the internal friction maximum respectively. The two TGA stages have been observed by other investigators [22] and related to water loss (1) and protein degradation (2), respectively. To understand the anelastic behaviour of dentin above 373 K it is of great importance to know its structural evolution. Unfortunately, specific data are not available in literature. Therefore, experimental results will be discussed on the basis of the rather similar characteristics of human bone. Studies of Yamashita et al. [19] indicated that the denaturation of bone collagen begins when temperature exceeds 393 K, but significant collagen denaturation is observed after heating to 473 K. Collagen denaturation occurs within the triple helix by cleaving intramolecular hydrogen bonding. Infrared spectroscopy investigations by Lozano et al. [23] showed that from 473 to 673 K the main change is due to structural water
Fig. 2. Internal friction (black) and dynamic modulus (grey) of dentin measured on two different samples. The first sample has been heated up to 360 K and subsequently cooled to room temperature a). The second sample has been heated up to 673 K, then cooled to room temperature b). The behaviour in a second thermal run is shown in c).
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ascending part of the damping can be ascribed to an increased mobility of the molecular chains. Above 500 K water loss takes place inside the fibrils. This water guarantees the continuity of the peptide chain, so fibrils degrade and the chain is broken into fragments. At 573 K combustion occurs, further contributing to the damping decrease and giving rise to the second modulus slope change. SEM micrographs in Fig. 4(a–b) show the structure of dentin at room temperature (a) and after heating to 523 K (b). Few areas with carbonization can be observed. In the second thermal run (Fig. 2b) Q −1 exhibits a monotonous increasing trend of very low intensity, which could be due to a hysteretic effect associated to the release of water into the ceramic phase during the breakdown of residual collagen. Therefore, it is reasonable to suppose that such phenomenon is present also in the first run, contributing to the background, together with the major anelastic effect of fibril degradation connected to the maximum.
Fig. 3. Thermo-gravimetry of dentin during a heating–cooling cycle.
that has a strong chemical interaction with the proteins. The backbone of the proteins starts to break into fragments after 500 K, degradation and combustion of collagen occur from 573 to 673 K. The mineral part of dentin is not affected by heat treatments in the temperature range examined here [24], thus the Q −1 maximum must be connected to loss of water and degradation of collagen. Damping behaviour can be discussed in terms of the specific structure of dentin, which is made of several fibres consisting of bundles of fibrils. The molecular chains forming the helix structure are like strings able to oscillate under an external periodical applied stress. These strings are subjected to a complex system of constraints, which are progressively modified as temperature increases with a consequent effect on the anelastic properties of the organic phase. A similar approach to that developed by Granato-Lücke [25] for describing the changes of dynamic modulus and Q−1 of metals in terms of dislocation density and mean distance between pinning points can be used in first approximation to explain the anelastic behaviour of dentin. Specifically, in dentin molecular chains take the role played by dislocations in metals. Like dislocations the molecular chains are disordered belonging to collagen fibrils which are randomly oriented in a plane perpendicular to the direction of dentin formation [8]. The concept that elastic energy loss and modulus depend on the number of oscillating strings and on their mean length is of general validity. The reference relationships are: Q
−1
4
∝ ρl ω
ΔG=G ≅ βρl
2
ð3Þ ð4Þ
where ρ is the density of vibrating strings, l is the average string length, ω / 2π is the vibration frequency and β is a constant. The
3.2. Experiments at increasing strain amplitude Fig. 5a, displays the results of an experiment carried out at room temperature by applying three successive strain ramps. Q −1 and E/E0 are plotted vs. time; the samples were kept 36 h in vacuum before the measure started. Although the lower strain corresponds to that used in the tests at increasing temperature, it can be observed that Q−1 has a starting value (3.8 × 10−3) between those measured before heating (1.0 × 10 −2) and after cooling (1.1 × 10−3), as reported in Fig. 2b. This is due to the prolonged permanence into a high vacuum, which reduces the damping by removing water from the pores. In each strain ramp, Q −1 progressively increases while modulus decreases, as can be seen from Fig. 5b. The effects are not permanent because the original Q −1 and E values are recovered if only the strain is decreased to its starting value. The polypeptide chains forming the triple-helix are bound together by weak H-bonds (Fig. 5c) and it has been shown that the breaking of H-bonds is a crucial mechanism for the deformation of protein molecules, fibrils, and fibres [26]. Stress bond breaking is reversible and when force is released the bonds restore. Therefore, according to Eqs. (3) and (4), it is believed that the anelastic behaviour depicted in Fig. 5b could be attributed to the progressive rupture of H-bonds as strain increases with consequent increase of the mean length l of vibrating strings (segments of polypeptide chains). As the strain amplitude recovers to the starting value, H-bonds reform and anelastic properties are restored. Furthermore, Fig. 5a shows a progressive decreasing trends of both damping and modulus while samples vibrate with the lower strain applied. Since the orientation of fibres strongly affects all the mechanical characteristics of bone [27], the origin of the phenomenon could be
Fig. 4. SEM micrographs of dentin before heating (a) and after heating up to 523 K (b).
S. Amadori et al. / Materials Science and Engineering C 33 (2013) 1455–1459
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Fig. 5. a) Q−1 and dynamic modulus vs. time at room temperature. At times indicated with numbers 1, 2 and 3, a strain ramp is performed. In b) the details of the strain ramp 3 are reported. At the end of each ramp the strain is brought back to the starting value. c) H-bonds between the polypeptide chains of triple helix.
tentatively associated to their partial re-orientation favoured by the lack of viscous effect of water in the gaps between fibres. 4. Conclusions The anelastic behaviour of human dentin above room temperature can be divided into two ranges: 1- 300–360 K. Dynamic modulus and Q −1 show reversible anelastic behaviour depending on water loss in the pores without alteration of collagen. 2- 360–673 K. A broad and asymmetric Q−1 maximum is observed at 500 K together with a corresponding dynamic modulus slope change; these features are not present during cooling. In the same temperature range, TGA shows a remarkable weight loss and two stages have been identified. The behaviour corresponds to an irreversible transformation due to water loss in the gaps between fibrils inducing despiralization of the helix structure of collagen molecule (360–500 K), to water loss inside the fibrils, leading to peptide chain fragmentation (500–573 K), and finally to collagen combustion (573–673 K). It is supposed that a hysteretic effect associated to the release of water into the ceramic phase during the breakdown of collagen also occurs contributing to the background. At room temperature reversible effects on the structure of dentin are induced by vibrations with increasing amplitude. The origin of the continuous Q −1 increase and modulus decrease with strain is the progressive breaking of the weak H-bonds between polypeptide chains forming the triple-helix, which is completely recovered when strain amplitude decreases to the starting value. References [1] G.W. Marshall Jr., S.J. Marshall, J.H. Kinney, M. Balooch, J. Dent. 25 (1997) 441–458. [2] PhD Thesis of Ilaria Cappelloni “Mechanical characterization of human dentin”, p. 62. [3] G.W. Marshall Jr., Quintessence Int. 24 (1993) 606–617. [4] D.H. Pashley, Crit. Rev. Oral Biol. Med. 7 (1996) 103–133.
[5] J.H. Kinney, M. Balooch, S.J. Marshall, G.W. Marshall Jr., T.P. Weihs, Arch. Oral Biol. 41 (1996) 9–13. [6] J.H. Kinney, M. Balooch, S.J. Marshall, G.W. Marshall, Arch. Oral Biol. 44 (1999) 813–822. [7] Q.H. Qin, M.V. Swain, Biomaterials 25 (2004) 5081–5090. [8] J.H. Kinney, S.J. Marshall, G.W. Marshall, Crit. Rev. Oral Biol. Med. 14 (2003) 13–29. [9] I.M. Low, N. Duraman, U. Mahmood, Mater. Sci. Eng. C 28 (2008) 243–247. [10] I. Cappelloni, P. Deodati, R. Montanari, A. Moriani, Adv. Mater. Res. 89–91 (2010) 751–756. [11] S. Roy, B. Basu, Mater. Charact. 59 (2008) 747–756. [12] S. Amadori, E. Bonetti, I. Cappelloni, R. Montanari, Solid State Phenom. 184 (2012) 455–460. [13] H. Ryou, E. Romberg, D.H. Pashley, F.R. Tay, J. Mech. Behav. Biomed. Mater. 7 (2012) 3–16. [14] S. Amadori, E.G. Campari, A.L. Fiorini, R. Montanari, L. Pasquini, L. Savini, E. Bonetti, Mater. Sci. Eng., A 442 (2006) 543–546. [15] F. Povolo, E.B. Hermida, J. Alloys Compd. 310 (2000) 392–395. [16] J.S. Rees, P.H. Jacobsen, J. Hickman, Clin. Mater. 17 (1994) 11–15. [17] T. Wang, Z. Feng, Mater. Lett. 59 (2005) 2277–2280. [18] Y.N. Yeni, R.R. Shaffer, K.C. Baker, X.N. Dong, M.J. Grimm, C.M. Les, D.P. Fyhrie, J. Biomed. Mater. Res. 82 (2007) 530–537. [19] J. Yamashita, X. Li, B.R. Furman, H.R. Rawls, X. Wang, M. Agrawal, J. Biomed. Mater. Res. 63 (2002) 31–36. [20] R. Schaller, S. Barrault, Ph. Zysset, Mater. Sci. Eng., A 370 (2004) 569–574. [21] L.E. Bertassoni, S. Habelitz, J.H. Kinney, S.J. Marshall, G.W. Marshall Jr., Caries Res. 43 (2009) 70–77. [22] J. Lim, A.R. Liboff, J. Dent. Res. 51 (1972) 509–514. [23] L.F. Lozano, M.A. Pena-Rico, A. Heredia, J. Ocotlan-Flores, J. Gomez-Cortes, R. Velazquez, I.A. Belio, L. Bucio, J. Mater. Sci. 38 (2003) 4777–4782. [24] J. Reyes-Gasga, R. Garcıa-Garcıa, M.J. Arellano-Jimenez, E. Sanchez-Pastenes, G.E. Tiznado-Orozco, I.M. Gil-Chavarria, G. Gomez-Gasga, J. Phys. D: Appl. Phys. 41 (2008) 1–11. [25] A.S. Nowick, B.S. Berry, Anelastic Relaxation in Crystalline Solids, Eds. Academic Press, New York, 1972 Ch. 14. [26] M.E. Launey, M.J. Buehler, R.O. Ritchie, Annu. Rev. Mater. Res. 40 (2010) 25–53. [27] S. Weiner, H.D. Wagner, Annu. Rev. Mater. Sci. 28 (1998) 271–298.
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering C journal homepage: www.elsevier.com/locate/msec
Anelastic phenomena associated to water loss and collagen degradation in human dentin S. Amadori a,⁎, E. Bonetti a, E.G. Campari a, I. Cappelloni b, R. Montanari b a b
Department of Physics and Astronomy, University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy Department of Industrial Engineering, University of Rome—Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy
a r t i c l e
i n f o
Article history: Received 3 July 2012 Received in revised form 4 December 2012 Accepted 14 December 2012 Available online 23 December 2012 Keywords: Dentin Collagen Internal friction Dynamic modulus
a b s t r a c t This work describes the anelastic and dynamic Young modulus behaviour of human dentin from room temperature up to 673 K. Human molars, extracted from individuals (males 55–70 years old) as part of their dental treatment, were cut to obtain bar-shaped samples subsequently used for mechanical spectroscopy experiments. In addition, thermo-gravimetric analysis (TGA) has been performed to assess a possible weight loss occurring in the same temperature range of mechanical spectroscopy tests. A broad and asymmetric internal friction (Q−1) maximum at 500 K has been observed during the heating of the as-prepared samples. This maximum is absent during the following cooling down to room temperature. It is therefore due to the occurrence of an irreversible transformation in the sample. TGA shows a remarkable weight loss in the same temperature range. This effect has been related to loss of fluids and degradation of collagen. Another set of samples, previously kept for 36 h under a vacuum of 10−2 Pa, were submitted at room temperature to test at increasing strain from 6× 10−6 to 7× 10−4. The results show transient and fully recoverable Q−1 increase and dynamic modulus (E) decrease. The phenomenon has been ascribed to the breaking of weak H-bonds between polypeptide chains forming the triple-helix with consequent increase of the mean length of vibrating chain segments. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Dentin is a complex hydrated biological composite consisting of about 50 vol.% mineral in the form of apatite, 30 vol.% organic matter, which is largely type I collagen, and about 20 vol.% fluid. Other non-collagenous proteins and organic components are also present in small amounts [1]. Its hierarchical structure is shown in Fig. 1, taken from [2]. For simplicity dentin will be described here by distinguishing three scales (macro, meso, nano) where in some texts more hierarchical levels are defined. On a macro scale (a–b) dentin can be modelled as a continuous fibre-reinforced composite, with the intertubular dentin forming the matrix and the tubule lumens with their associated cuffs of peritubular dentin forming the cylindrical fibre reinforcement [3–7]. The morphology varies with location since tubules converge on the pulp chamber varying density and orientation. On a meso scale intertubular dentin is formed by fibres randomly oriented in a plane perpendicular to the direction of dentin formation (c–d–e).
⁎ Corresponding author. Tel.: +39 0512095298; fax: +39 0512095113. E-mail address: [email protected] (S. Amadori). 0928-4931/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msec.2012.12.067
On a nanoscale the characteristic features are collagen fibrils, apatite crystals and water (f–g). Each fibre consists of several fibrils (50– 100 nm in diameter) which exhibit periodically spaced gaps. Three polypeptide chains are wound together in a triple helix. A triplehelical molecule is cylindrically shaped (diameter of ~1.5 nm, length of ~300 nm). The molecules are all parallel, but their ends are separated by holes of about 35 nm, they pack together to form a single fibril. The mineral is either within the fibrils (intrafibrillar) or between the fibrils (interfibrillar). The shape of apatite crystals is needle-like near the pulp and progressively becomes plate-like near the enamel, the thickness, ~5 nm, does not change with location. Water is the third major component and is located within and between the fibrils, between fibres and between triple-helical molecules. Several works exist in the literature regarding the mechanical properties of dentin, e.g. [8–11]; a thorough review was published by Kinney and Marshall [8]. The Young's modulus measured by different research groups spans from about 11 GPa up to 35 GPa. In general, static mechanical tests give lower values than the dynamic (particularly ultrasound) ones. Apart from artifacts, like damaged teeth, affecting the tests, it is not completely clear why there is such a spread between different measurements. The probable source for such a wide range of measured values is the anelastic behaviour of dentin. When a material exhibits such a property, its elastic constants are time dependent and different values of Young's modulus can be obtained with different techniques. In particular, static tests yield relaxed values (lower) whereas dynamic
1456
S. Amadori et al. / Materials Science and Engineering C 33 (2013) 1455–1459
Fig. 1. Schematic view of the highly hierarchical dentin structure [2].
tests yield unrelaxed values (higher). In spite of the importance of the topic, only few papers deal with the anelastic properties of dentin and their changes [12,13]. Therefore, an experimental campaign has been undertaken by the authors to study the anelastic behaviour of dentin under different physical conditions aiming to get ground information. The aim of this work is to add information on damping phenomena occurring in the range from room temperature up to 673 K. Although clinically relevant temperatures are between 273 and 323 K and temperatures above 500 K are rarely of interest also for the implantation of biomaterials, the anelastic behaviour of dentin has been investigated in a more extended range (up to 673 K) to get ground information about all the possible transformations of its complex structure induced by heating, including the complete degradation and combustion of collagen. For instance, such information could be useful in the study of archaeological finds or in forensic cases.
was employed. The apparatus is described in detail in [14]. Young's modulus and damping were measured. The damping Q −1 which is also the ratio of the loss modulus to the storage modulus was determined from the logarithmic decay δ of flexural vibrations: ″ ′ −1 tan δ ¼ E =E ¼ ln An =Anþ1 ¼ πQ
ð1Þ
where An and An + 1 are the amplitude of two successive vibrations, E′ and E″ are the storage and loss modulus respectively. The storage modulus (also called elastic modulus) has been determined from the resonant frequency f of the bar samples: h i 2 4 4 2 2 E ¼ 48π ρl =α h f
ð2Þ
2. Experimental Human molars were extracted from individuals (males 55–70 years old) as part of their dental treatment. The teeth were not identified by patient number or name and each patient signed a patient consent form. After disinfection by immersion in a solution of sodium hypochlorite in water for about 12 h, they were sectioned along mesial direction by using a precision diamond saw with water cooling in order to obtain 0.8 mm-thick slices. From these sections bar-shaped samples (length L = 13÷ 16 mm, width W = 3 ÷ 4 mm) have been cut for mechanical spectroscopy measurements. A single specimen was obtained from each tooth and included root dentin and crown dentin but not enamel. Teeth taken from different patients (sixty patients, one tooth per patient) have been used in the experiments. Before testing the specimens have been investigated by scanning electron microscopy and light optical microscopy and one third of the samples was rejected because of the presence of fractures or damages. The samples, mounted in free-clamped mode, have been tested by the vibrating reed technique in a vacuum chamber at a pressure of 10 −2 Pa. The vibrating reed analyzer model VRA 1604 by CANTIL srl
α is a constant, ρ is the material density, l and h are the sample length and thickness, respectively. The strain amplitude was kept below 1 × 10 −5, and the vibration frequency of the samples spans the 1–10 kHz frequency range. A first set of measurements consisted of heating–cooling cycles from 300 to 673 K with a constant heating rate of 3.33 × 10 −2 K s −1. A second set of measurements was carried out isothermally at 300 K with increasing strain amplitudes. Fifteen specimens were used for each set of tests. In the second set of measurements before starting the isotherms, specimens were kept for 1.3 × 10 5 s (about 36 h) in the spectrometer chamber at room temperature at the pressure of measurements of 10−2 Pa. These samples were submitted to a strain increase from 6 × 10 −6 to 7 × 10−4, then kept at the maximum strain for 1.2 × 103 s (20 min) and finally brought back to the initial condition. Successive measurement runs were made on the same samples. Thermo-gravimetric analysis (TGA) has been performed from room temperature up to 693 K on ten samples submitted to the same heating runs employed in mechanical spectroscopy experiments to assess a possible weight loss.
S. Amadori et al. / Materials Science and Engineering C 33 (2013) 1455–1459
3. Results and discussion 3.1. Experiments at increasing temperature The results of mechanical spectroscopy experiments obtained on different samples showed only minor differences. In particular the Q−1 and modulus data for samples from the same set are within ±3%. A greater dispersion of order of ±5% was observed for damping in the temperature range of the maximum. Fig. 2a and b shows the typical Q−1 and E vs. temperature trend during heating–cooling runs. The specimen of Fig. 2a was heated at the standard heating rate up to 360 K and then cooled down to room temperature, the specimen of Fig. 2b was heated up to 673 K. Fig. 2b shows the temperature range not covered by Fig. 2a. The difference in Q−1 and E between the two samples in the cooling data is due to the irreversible transformation occurring in the specimen of Fig. 2b when heated up to 673 K, as explained in the following. Fig. 2c shows the results of a second heating–cooling run up to 673 K performed on the same sample of Fig. 2b. The Q−1 maximum is no more present. The dynamic modulus at room temperature (E=15±2 GPa) is in agreement with the data of other investigators [15,16]. Despite the absence in literature of other dentin damping data, a comparison with Q−1 values of the rather similar human bone has been done. The data, ranging from 2×10−2 to 4×10−2 [17–19], are compatible with those of dentin determined in the present experiments (Q−1 ≈1.0×10−2). It is known that heating up to about 360 K affects only residual water present in the pores of dentin without altering the molecular structure of collagen. In general, owing to a viscous friction dissipative mechanism, hydrated bone has a lower modulus and a higher Q−1 than dried bone (Schaller et al. [20]) and the same behaviour has been observed for dentin [21]. Therefore, the initial water loss leads to a transient between 300 and 360 K with E and Q−1 changing with
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temperature, see Fig. 2a. If the samples are cooled down from 360 K and rewetted, the original characteristics are completely restored and thus the process is reversible. Above 360 K, Q −1 progressively increases and a very broad and asymmetric maximum at 500 K is observed. Modulus decreases and exhibits two slope changes around 473 and 573 K. On the basis of modulus behaviour it is reasonable to assess that the asymmetric shape of the internal friction maximum can be due to the overlapping of two different contributions. These phenomena are not present during cooling to room temperature and successive cycles. After a heating–cooling cycle up to 673 K the samples appear carbonized and both Q −1 and E have decreased values with respect to the original ones. The location of the Q−1 maximum does not shift with frequency. These results testify that an irreversible structural transformation has occurred. TGA shows a remarkable weight loss in the same temperature range of the internal friction maximum (Fig. 3). Two stages (1, 2) can be identified, corresponding to the ascending and descending parts of the internal friction maximum respectively. The two TGA stages have been observed by other investigators [22] and related to water loss (1) and protein degradation (2), respectively. To understand the anelastic behaviour of dentin above 373 K it is of great importance to know its structural evolution. Unfortunately, specific data are not available in literature. Therefore, experimental results will be discussed on the basis of the rather similar characteristics of human bone. Studies of Yamashita et al. [19] indicated that the denaturation of bone collagen begins when temperature exceeds 393 K, but significant collagen denaturation is observed after heating to 473 K. Collagen denaturation occurs within the triple helix by cleaving intramolecular hydrogen bonding. Infrared spectroscopy investigations by Lozano et al. [23] showed that from 473 to 673 K the main change is due to structural water
Fig. 2. Internal friction (black) and dynamic modulus (grey) of dentin measured on two different samples. The first sample has been heated up to 360 K and subsequently cooled to room temperature a). The second sample has been heated up to 673 K, then cooled to room temperature b). The behaviour in a second thermal run is shown in c).
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ascending part of the damping can be ascribed to an increased mobility of the molecular chains. Above 500 K water loss takes place inside the fibrils. This water guarantees the continuity of the peptide chain, so fibrils degrade and the chain is broken into fragments. At 573 K combustion occurs, further contributing to the damping decrease and giving rise to the second modulus slope change. SEM micrographs in Fig. 4(a–b) show the structure of dentin at room temperature (a) and after heating to 523 K (b). Few areas with carbonization can be observed. In the second thermal run (Fig. 2b) Q −1 exhibits a monotonous increasing trend of very low intensity, which could be due to a hysteretic effect associated to the release of water into the ceramic phase during the breakdown of residual collagen. Therefore, it is reasonable to suppose that such phenomenon is present also in the first run, contributing to the background, together with the major anelastic effect of fibril degradation connected to the maximum.
Fig. 3. Thermo-gravimetry of dentin during a heating–cooling cycle.
that has a strong chemical interaction with the proteins. The backbone of the proteins starts to break into fragments after 500 K, degradation and combustion of collagen occur from 573 to 673 K. The mineral part of dentin is not affected by heat treatments in the temperature range examined here [24], thus the Q −1 maximum must be connected to loss of water and degradation of collagen. Damping behaviour can be discussed in terms of the specific structure of dentin, which is made of several fibres consisting of bundles of fibrils. The molecular chains forming the helix structure are like strings able to oscillate under an external periodical applied stress. These strings are subjected to a complex system of constraints, which are progressively modified as temperature increases with a consequent effect on the anelastic properties of the organic phase. A similar approach to that developed by Granato-Lücke [25] for describing the changes of dynamic modulus and Q−1 of metals in terms of dislocation density and mean distance between pinning points can be used in first approximation to explain the anelastic behaviour of dentin. Specifically, in dentin molecular chains take the role played by dislocations in metals. Like dislocations the molecular chains are disordered belonging to collagen fibrils which are randomly oriented in a plane perpendicular to the direction of dentin formation [8]. The concept that elastic energy loss and modulus depend on the number of oscillating strings and on their mean length is of general validity. The reference relationships are: Q
−1
4
∝ ρl ω
ΔG=G ≅ βρl
2
ð3Þ ð4Þ
where ρ is the density of vibrating strings, l is the average string length, ω / 2π is the vibration frequency and β is a constant. The
3.2. Experiments at increasing strain amplitude Fig. 5a, displays the results of an experiment carried out at room temperature by applying three successive strain ramps. Q −1 and E/E0 are plotted vs. time; the samples were kept 36 h in vacuum before the measure started. Although the lower strain corresponds to that used in the tests at increasing temperature, it can be observed that Q−1 has a starting value (3.8 × 10−3) between those measured before heating (1.0 × 10 −2) and after cooling (1.1 × 10−3), as reported in Fig. 2b. This is due to the prolonged permanence into a high vacuum, which reduces the damping by removing water from the pores. In each strain ramp, Q −1 progressively increases while modulus decreases, as can be seen from Fig. 5b. The effects are not permanent because the original Q −1 and E values are recovered if only the strain is decreased to its starting value. The polypeptide chains forming the triple-helix are bound together by weak H-bonds (Fig. 5c) and it has been shown that the breaking of H-bonds is a crucial mechanism for the deformation of protein molecules, fibrils, and fibres [26]. Stress bond breaking is reversible and when force is released the bonds restore. Therefore, according to Eqs. (3) and (4), it is believed that the anelastic behaviour depicted in Fig. 5b could be attributed to the progressive rupture of H-bonds as strain increases with consequent increase of the mean length l of vibrating strings (segments of polypeptide chains). As the strain amplitude recovers to the starting value, H-bonds reform and anelastic properties are restored. Furthermore, Fig. 5a shows a progressive decreasing trends of both damping and modulus while samples vibrate with the lower strain applied. Since the orientation of fibres strongly affects all the mechanical characteristics of bone [27], the origin of the phenomenon could be
Fig. 4. SEM micrographs of dentin before heating (a) and after heating up to 523 K (b).
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Fig. 5. a) Q−1 and dynamic modulus vs. time at room temperature. At times indicated with numbers 1, 2 and 3, a strain ramp is performed. In b) the details of the strain ramp 3 are reported. At the end of each ramp the strain is brought back to the starting value. c) H-bonds between the polypeptide chains of triple helix.
tentatively associated to their partial re-orientation favoured by the lack of viscous effect of water in the gaps between fibres. 4. Conclusions The anelastic behaviour of human dentin above room temperature can be divided into two ranges: 1- 300–360 K. Dynamic modulus and Q −1 show reversible anelastic behaviour depending on water loss in the pores without alteration of collagen. 2- 360–673 K. A broad and asymmetric Q−1 maximum is observed at 500 K together with a corresponding dynamic modulus slope change; these features are not present during cooling. In the same temperature range, TGA shows a remarkable weight loss and two stages have been identified. The behaviour corresponds to an irreversible transformation due to water loss in the gaps between fibrils inducing despiralization of the helix structure of collagen molecule (360–500 K), to water loss inside the fibrils, leading to peptide chain fragmentation (500–573 K), and finally to collagen combustion (573–673 K). It is supposed that a hysteretic effect associated to the release of water into the ceramic phase during the breakdown of collagen also occurs contributing to the background. At room temperature reversible effects on the structure of dentin are induced by vibrations with increasing amplitude. The origin of the continuous Q −1 increase and modulus decrease with strain is the progressive breaking of the weak H-bonds between polypeptide chains forming the triple-helix, which is completely recovered when strain amplitude decreases to the starting value. References [1] G.W. Marshall Jr., S.J. Marshall, J.H. Kinney, M. Balooch, J. Dent. 25 (1997) 441–458. [2] PhD Thesis of Ilaria Cappelloni “Mechanical characterization of human dentin”, p. 62. [3] G.W. Marshall Jr., Quintessence Int. 24 (1993) 606–617. [4] D.H. Pashley, Crit. Rev. Oral Biol. Med. 7 (1996) 103–133.
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