On the successful fabrication of auxetic polyurethane foams: Materials requirement, processing strategy and conversion mechanism

Polymer 87 (2016) 98e107

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On the successful fabrication of auxetic polyurethane foams: Materials requirement, processing strategy and conversion mechanism Yan Li a, b, Changchun Zeng a, b, * a b

High Performance Materials Institute, Florida State University, Tallahassee, FL 32310, USA Department of Industrial and Manufacturing Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 October 2015 Received in revised form 15 January 2016 Accepted 27 January 2016 Available online 1 February 2016

This study aims to provide fundamental understandings in several issues critical to the fabrication of auxetic polyurethane (PU) foams by thermal compression process: conversion and auxetic structure fixation mechanisms, materials characteristics essential for the successful auxetic conversion, and optimal conditions for auxetic conversion. Three flexible PU foams with similar morphology were selected for the study. First the commonalities as well as the differences between these foams in terms of their chemical composition, microstructure and thermomechanical properties were thoroughly analyzed. This is followed by the auxetic convertibility study of these three foams. Mechanisms for fixing the structure were elucidated and the windows for processing were interpreted in the context of polymer relaxation. Guided by these understandings, a series of auxetic foams were manufactured at a wide range of conditions. The processing conditions agreed very well with those suggested from the mechanistic investigation, validating the proposed auxetic conversion and structure fixation mechanisms. The mechanism was further confirmed by direct observation of the morphology of the fabricated auxetic foams. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Auxetic foam Negative poisson's ratio Polyurethane Glass transition Stress relaxation

1. Introduction Auxetics refer to a family of materials possessing negative Poisson's ratio (n) [1e4]. They expand in the transverse direction when being stretched, while shrink under compression [1e4]. Before the pioneering work by Lakes et al. on the manufacturing of artificial auxetic materials, [1] there was little interest in this type of materials in spite of many intriguing properties they possess, because their rarity in nature [5]. Since then there has been significant interest in the development of auxetic materials, because of the novel properties and promising application potential they exhibited, such as enhanced indentation resistance for applications in protective equipment and biomedical devices [6e8], improved bending stiffness and shear resistance for structural integrity construction elements [9e13], optimal dynamics, acoustic and dielectric properties for damping application and wave absorbers [14e17]. Auxetic polyurethane (PU) foams is a class of auxetic materials

* Corresponding author. High Performance Materials Institute, Florida State University, Tallahassee, FL 32310, USA. E-mail address: [email protected] (C. Zeng). http://dx.doi.org/10.1016/j.polymer.2016.01.076 0032-3861/© 2016 Elsevier Ltd. All rights reserved.

that can be manufactured from conventional flexible PU foams via a thermal mechanical process [1,18e22]. This process, first proposed by Lakes et al., involves applying tri-axial compression on a neat PU foam to partially buckle the cell struts and induce the re-entrant morphology. The compressed foam was then heated above the softening temperature of the polymer, followed by cooling in the compression state to fix the intended re-entrant structure [1,23,24]. A schematic of this process is shown in Fig. S1 in supplemental information. While there are a great deal of study on the effects of manufacturing process parameters (temperature, time and compression ratio) on the structure and properties of auxetic PU foams [1,10,20,24e31], several key questions remains. First, results from different researchers show large discrepancies. For example, published studies have shown that for successful auxetic conversion using the seemingly simple process, the required processing temperature may differ substantially from 130 to 220
C, and the processing time may vary from 6 to 60 min. While qualitatively the combination of higher temperature/shorter time was considered a general requirement for the successful conversion, the question why would certain combination would work while others would not, remains unanswered. Most researchers attributed these to the

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difference in the equipment used and properties of the starting PU foams (e.g., pore size), which only lead to more unanswered questions. For example, it was reported that PU foams with similar pore size could behave dramatically different in terms of their auxetic convertibility and associated processing conditions [32]. A recent review by Critchley et al. [32] provided a comprehensive account of the discrepancies in process parameters and auxetic properties. Moreover, the microscopic mechanism for the auxetic structure fixation is unknown, and the vaguely referenced “softening temperature’, critical for auxetic conversion, lack clear meaning in the context of the materials. To date a surprising omission in the study of auxetic PU foams is the lack of understanding of the effects of the chemistry and microstructure of the starting PU foams, as they dictate both the matrix PU properties and the cellular structure and properties. It is conceivable they are both critically important in determining 1) the suitability of auxetic conversion; 2) appropriate windows of process parameters for the conversion; and 3) the auxetic properties of the PU foams. Comprehensive understanding of the chemistry and microstructure will 1) facilitate the establishment of the selection criteria for starting PU foams for auxetic foam manufacturing, 2) elucidate definitively the physical meaning of the currently vaguely referred “softening temperature” and the molecular mechanism for the auxetic structure fixation, and 3) suggest optimal processing temperature/time combination that is based on the firm understanding of the behavior of the materials systems under consideration. This would provide a comprehensive framework that facilitates transforming the PU auxetic foam manufacturing from the current trial-and-error and user-dependent process to engineering practices that are based on fundamental polymer science and processing principle. In this study three flexible PU foams with similar morphology were investigated. First their chemical composition, microstructure and thermomechanical properties were thoroughly analyzed to identify the common and different characteristics in these foams. This is followed by the auxetic convertibility study of these three foams. Mechanisms for fixing the structure were elucidated and the windows of processing were interpreted in the context of polymer relaxation. Guided by these understandings, a series of auxetic foams were manufactured at a wide range of conditions that agreed very well with those suggested from the mechanistic investigation. Results from the study have the potential to serve as the general principle for fabrication of auxetic foams of consistent morphology and properties under optimal conditions.

99

then weighed to determine the soluble fraction of each sample. The soluble fractions for I, II and III were found to be 5 wt%, 9 wt% and 18 wt%, respectively. 2.2.2. Scanning electron microscopy (SEM) Morphologies of the samples were investigated using field emission scanning electron microscope (SEM) (JEOL 7401F). Samples were cut using a razor, and the surface was sputter-coated with a thin layer of gold before observation. 2.2.3. Fourier transform infrared (FTIR) spectroscopic analysis Fourier transform infrared (FTIR) spectra were performed using a Nicolet NEXUS 470 FTIR-spectrometer (ThermoFisher Ltd.) with the KBr pellet technique in a range from 4000 to 400 cm1 at a resolution of 4 cm1. Data were collected as average of 32 scans. FTIR with attenuated total reflectance (ATR) spectra were carried out in a spectral range from 4000 to 650 cm1 utilizing a Smart Golden Gate reflectance attachment and recorded 64 scans at a resolution of 2 cm1. All spectra had been normalized using the CH2 peak at 1969 cm1 as an internal reference peak. 2.2.4. X-ray scattering Simultaneous small- and wide-angle X-ray scattering (SAXS/ WAXS) measurements were obtained using a Bruker NanoSTAR system, operating at 45 kV and 650 mA with Ims microfocus X-ray source (Cu Ka, l ¼ 0.15412 nm). The SAXS pattern was recorded by a HiStar 2D multi-wire area detector. The WAXS pattern was recorded by a Fuji Photo Film image plate, and the plate was read with a Fuji FLA-7000 scanner. 2.3. Thermal, thermomechanical and mechanical characterizations 2.3.1. Differential scanning calorimetry (DSC) Differential scanning calorimetry was performed using a TA Q100 (TA Instruments) under nitrogen atmosphere. The foam samples (ca. 10 mg) were firstly maintained at 225
C for 5 min in order to eliminate possible thermal history effect. Subsequently they were rapidly cooled down to 80
C, and then reheated to 200
C at a heating rate of 10
C/min.

2.1. Materials

2.3.2. Dynamic mechanical analysis (DMA) The 7 mm  7 mm  25 mm rectangular DMA samples were machined using a CO2 laser (VersaLASER, Universal Laser Systems). DMA analysis was conducted using a TA Instruments Q800 Dynamic Mechanical Analyzer in tension model using a deformation of 0.2% strain, a frequency of 1 Hz, a force track of 150%, and a preload force of 0.05 N. The test was run in the temperature range of 100 to 200
C using a heating rate of 1
C/min.

In this study, three commercially available flexible PU foams with similar nominal cell diameters of 480 mm were used and they are identified as I, II and III. The densities of the three foams were also similar (44.8 kg/m3, 44.8 kg/m3 and 48.1 kg/m3, respectively). They were dried in an air-flow oven at 80
C for at least 12 h before use. Dimethylformamide (DMF) was purchased from Fisher Scientific and was used as received.

2.3.3. Uniaxial compression test Compression experiments were conducted using a TA Instruments Q800 Dynamic Mechanical Analyzer in compression model with a 15 mm compression clamp at a strain rate of 0.01 min1 and 30
C. Disk sample, 15 mm in diameter and 5 mm thick, were machined using a CO2 laser (VersaLASER, Universal Laser Systems).

2.2. Morphology and microstructure characterizations

2.4. Structure convertibility study

2.2.1. Sol-Gel analysis Samples (ca. 2 g) were immersed in 500 ml of Dimethylformamide (DMF). After 48 h, they were removed dried in a vacuum oven at 40
C for 24 h and then at 80
C for an additional 24 h. The solution, which contained the solvent DMF and the sol fraction from the PU foams, were dried to evaporate the solvent. Samples were

Structural convertibility characteristics were quantified via strain-controlled compression tests performed on an ARES-LS3 rheometer with 25 mm parallel plate fixture (TA instruments). Disk samples, with a diameter of 25 mm and 10 mm thick, were machined using a CO2 laser (VersaLASER, Universal Laser Systems). They were heated to the experiment temperatures and allowed to

2. Experimental section

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equilibrate for 10 min, and then compressed to a strain of 40% or 70% at a rate of approximately 0.5 min1. The compressed samples were then allowed to equilibrate at the testing temperature for different time. After being cooled at room temperature with the strain still imposed for an additional 10 min, the samples were removed from the fixture and stored for 24 h to allow for the completion of relaxation. Finally, the sample thickness was measured, and the structure convertibility (Rf) was calculated using the following equation:

Rf ¼ ε=ε load

(1)

where ε is the strain after unloading and εload is the initial loading strain. Values averaged from three separate measurements were used for calculation. 2.5. Auxetic foam fabrication and characterization 2.5.1. Fabrication of auxetic foam Auxetic foams were fabricated by the thermo-mechanical process described in the literature [19,22]. Samples with initial dimensions of 32 mm in diameter and 80 mm in length were inserted into a metallic tube mold and compressed to 20 mm diameter and 50 mm long. The mold was then placed in a forced-convention oven at desired temperatures for predetermined periods of time. The mold was then removed from the oven and cooled down for 1 h in ambient environment. Subsequently the converted foams were retrieved from the mold. A schematic of the process is shown in Fig. S2. 2.5.2. Poisson's ratio determination Videos were acquired from a video extensometer system (Shimadzu DV-201) machine during tensile tests using a tensile tester (Shimadzu ASG-J, with a strain rate of 6 mm/min and maximum strain of 10%) (See Fig. S3 in supplemental information). For the calculation of Poisson's ratio, the videos were first transformed into a series of static images (for different strains) via the software MATLAB R2013b. A MATLAB routine we developed [33] was used to calculate the length (l) and diameter (d) of the sample for every image. Then, the transverse strain (εx) and longitudinal strain (εy) were calculated using the following equations, respectively:

εx ¼

Dl lo

(2)

εy ¼

Dd do

(3)

where, l0 is the original length and d0 is the original diameter. The section for l0 determination was selected such that it is away from both clamps to eliminate the end effect. Finally, the average Poisson's ratio was calculated from the strainestrain curve by the classical definition of Poisson's ratio [34].

v¼

εx εy

(4)

3. Results and discussion 3.1. Characterization of chemistry and structure Morphology of the three PU foams were studied by SEM. Fig. 1 shows the results. All foams showed similar cellular structure

Fig. 1. Cross-sectional SEM images of the three flexible PU foams in the study. Top row: the three foams showed similar cellular structure; Middle row: high magnification SEM micrographs showed that the rib/strut region of I had a smooth surface, while there were particles present in II and III; Bottom row: high magnification SEM micrographs of the rib/strut regions of the three foams after subjected to DMF extraction. The morphology of I remained unchanged, while holes were observed in II and III. These hole appeared to result from the particles being extracted from the samples. The holes in both II and III were considerably fewer than the original particles, suggesting some particles are not extractable by DMF.

(Fig. 1, top row). However, a clear difference was identified in the higher magnification images taken from the rib/strut regions (Fig. 1, middle row). While foam I showed a smooth surface, both II and III contained well dispersed sub-micron sized spherical particles. The amount of particles was higher in III than in II. After extraction by DMF, the morphology of I remained unchanged, while holes were observed in both II and III. The number of holes appeared to be considerably less than that of the particles in the respective samples before extraction. Nevertheless the locations of the holes appeared to coincide with those of the particles with similar sizes. There were more holes in the extracted III than in II. The flexible PU foams are chemically and structurally complex multi-scale, multiphase materials formed from two competing reaction between a diisocyanate and both polyol and water [35,36]. Aside from the obvious macroscale cellular structure, microscopically the flexible PU matrix shows a dominant phase-separated structure consisting of hard-segment domains dispersed in and linked to a continuous soft-segment phase by covalent bonds and physical interactions [37e41]. If a high water content is used in the formulation, aggregates of the hard segments or “urea balls”, which are rich in urea and much larger in size and higher in crystallinity, may form [35,36]. Particles such as styrene and acrylonitrile copolymer (SAN) copolymer particles may also be added in order to improve the foams' load bearing property and cell openness [41]. Fig. 2a shows the ATR-FTIR spectra of the original foams. In the NH stretching vibration region (from 3500 to 3150 cm1), all foams showed a peak around 3295 cm1, which was attributed to the NH group that is hydrogen bonded with the ether oxygen (NH—O) (hard e soft segment hydrogen bonding) [37]. In the carbonyl (C] O) stretch region (from 1800 to 1600 cm1), all samples showed

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Fig. 2. (a) ATR-FTIR spectra of flexible PU foams. (b) FTIR spectra of the extractants of flexible PU foams by DMF.

two peaks. The first peak at 1720 cm1 is assigned to the free urethane C]O. The second peak around 1642 cm1 is associated with the urea C]O group hydrogen bonded to NH group in the ordered hardehard segments (C]O—HN, urea aggregates) [37e39]. The FITR results not only confirmed all three PU foams possess the typical phase-separated structure of flexible PU foams [37e41], but identified in all materials the presence of two types of hydrogen bonds, one between hard - soft segment, and the other between hard - hard segment. I has slightly less hard-soft segment hydrogen bonding than II and III. On the other hand, III has significantly lower free urethane content and higher content of hard-segment domains, evidenced by the much lower relative intensity of the free urethane C]O and much higher relative intensity of the ordered C]O—HN peak. Despite the slight differences the overall phaseseparated structure are similar in all three foams. Aside from the common features, FTIR also revealed one key difference between foam I, and foams II and III. A nitrile (CN) peak centered at 2240 cm1 was present in II and III, but absent in I. This peak is more distinct in the extracted sol of both II and III (Fig. 2b). It is known that SAN copolymer particles were often used in PU formulations to improve the load bearing property and cell openness of flexible PU foam [41], and the FTIR provided a direct evidence that SAN particles were present in II and III but not in I. Comparing to II, III has a higher CN signal, indicating a higher SAN content. In light of this, it can be concluded that the particles observed on the cell walls of II and III (Fig. 1, middle row) are SAN particles, which are of significantly higher number in III than in II. Furthermore, the connection of the SAN particles to the PU matrix can be inferred from the morphology of the foams after extraction (Fig. 1, bottom row) and the FTIR spectra of the extracted sol (Fig. 2b). SAN particles were present in the extracted sol and the amount of extractable SAN was substantially higher in III than in II. At the same time, the sol from III also contained considerably higher amount of soluble hydrogen-bonded C]O (hard-segment) than both II and I. These results suggest that some SAN copolymer particles are linked to the PU matrix by physical means such as hydrogen bonding [40,41]. They can be extracted from the PU matrix, leaving behind holes observed on the cell walls of II and III (Fig. 1, bottom row). Moreover the fact that in both II and III, the holes were considerably fewer than the particles in the original foam suggests majority of the SAN particles are linked to the PU

matrix by chemical grafting, and are not extractable by DMF. These observations are all in good agreement with previous studies on flexible PU foams involving SAN copolymer particles [40,41]. Structural information was further probed by DSC. Fig. 3 shows the DSC temperature scans. Melting peak was not detected in any of the foams in temperature range up to 200
C. This suggests that unlike some flexible PU foams prepared with high water concentration that contain large urea-rich aggregates or “urea balls” structure [35,36], all three foams studied herein lack sizable urea aggregates and the resultant crystallinity. All foams show a transition temperature of about 50
C, which is the glass transition of the soft segment [41] and is denoted as Tg, soft. An additional transition was observed in II and III at a temperature of about 103e104
C, but not detected in I. This temperature, which agrees well with previous reports [40e42], was the glass transition temperature of SAN (denoted as Tg, SAN). The DSC results thus further confirmed the presence of SAN copolymers in II and III.

Fig. 3. DSC thermograms for the three PU foams under investigation.

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The transition behaviors were also investigated by dynamic mechanical analysis (See Supplemental Information Fig. S4). Consistent with the DSC results, all foam showed a soft segment glass transition, while the SAN glass transitions were observed in both II and III but was absent in I. Furthermore by considering the reinforcement effect of the SAN particles, the volume fractions of SAN particles in the foams were calculated using the Guth equation [43] to be 0 vol % in foam I, 12 vol % in foam II and 32 vol % in foam III. Foam III has almost three times the amount of SAN particles as foam II. Details on the calculation can be found in supplemental information. To further understand the fine features of the foams' microstructure, we employed simultaneous small and wide-angle x-ray scattering measurements (SAXS and WAXS). Fig. 4a shows the SAXS profiles for the three foams I, II and III. All samples display a shoulder at 0.5e1 nm1, suggesting a phase separated structure with weak interconnectivities between hard-segments [44]. Fig. 4b shows the 2D WAXS patterns for the three foams. In all cases only an amorphous halo at 2q ~20
were observed. This demonstrates that in these foams very little orders exist in the hard-segment domains [45]. Using Scherrer equation (D z kl/bcosq, where k is a material parameter, commonly 1 for polymer, l is the wavelength of the X-ray, and b is the full width at half-maximum of the WAXS peak, the hard segment domain size, estimated by the correlation length D, was found to be about 1 nm for all three foams. This is far less than the smallest structural heterogeneity resolvable through Tg measurements (~10 nm) [46]. Note also that the presence of the SAN particles in II and III has at most, very limited effect on the hard segment e soft segment phase separated structure, as both SAXS and WAXS results for the three foams are similar. From the systematic characterizaton studies, the structural features of the three PU foams were reavled and confirmed, and summerized herein. All three foams possess a phase separated structure consisting of large fraction of soft-segments with hardsegments dispersed within, typical of felxible PU foams. The hard segment domain has a size of ~1 nm with limited structural order. Large-size urea-rich aggregates are not present in any of these foams. There is one distinct difference between Foam I, and Foams

II and III. Foams II and III contains sub-micron sized SAN copolymer particles, while the particles are absent in Foam I. The SAN copolymer particles are embedded in the PU matrix by both chemical and physical crosslinkings. Their presentce does not impact the basic phase-separated structure of the PU matrix. Foam III has a substantially higher amount of SAN than II. The muti-scale, muliphase structures of the three foams are schematically shown in Fig. 5. 3.2. Structure convertibility Two compressive strains, 40% and 70%, were used for the study of structural convertibility (Rf). Both are beyond the yield point on the compressive stressestrain curve (the strains are in collapse plaeau regime and densification regime, respectively. See Fig. S5 in supplimental information). This is important because it is in these regimes that bulkling of the cell cells and ribs/struts and their contact would take places, which allow for deformation that can be retained (fixed) after removal of the stress. Fig. 6 shows the results from the convertiblity studies. For all three materials, the structure convertibility benefited from the use of higher preload strain, which helped achieving a higher Rf in a shorter amount of time. This effect was the most prominent for I, only moderate for II, and barely noticeable for III. At either preload strain, III showed excellent convertibility. Within minutes the structural transformation would be completed with near perfection (Rf approaches to 1). By comparision, I had poor structural convertibility (long conversion time and low Rf), particularly at lower preload strain. The structural convertiblity and fixing rates of II are both inferior to III, but superior to I. Albeit some major, distinct difference, auxetic foams share some similarity with thermally induced shape memory polymer (SMP) and SMP foams. Both concerns shape fixing using external stress. In SMP the fixed shape is temporary and the major interest is in the elastic shape change between the two states (temporary and permant shape) and associated charactersitics such as fixity, recovery dynamics and percent of recovery, hyterisis etc. [47,48] By contract, the auxetic foams are used exclusively in the fixed shape

Fig. 4. (a) SAXS scattered intensity profiles, (b) WAXS patterns and (c) WAXS scattered intensity profiles for three flexible PU foams.

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Fig. 5. Schematics illustrating the structure features in foams I, II, and III. The basic microstructure of the PU matrix is a phase separated structure with small hard segment domains dispersed in a continuous soft segment phase. This is typical of flexible PU foams. The hard segment domain has a size of ~1 nm with limited structural order. Large-size urea-rich aggregates are not present in any of these foams. Aside from the common features, II and III contains SAN particles that are linked to the PU matrix by both physical and chemical grafting.

Fig. 6. Structural convertibility of the three foams at 135
C.

and concerned mostly fixity and the properties of the fixed auxetic state. The auxetic foam conversion process resemble the “dual-shape creation process” (DSCP) for thermally induced SMP. During DSCP the thermally induced SMP are deformed from the unperturbed initial state to fixed temporary state by application of external stress. The fixation relies on the presence of so called “switching domains”, and the utilization of cooling the materials below a characteristic thermal transition temperature of the switching domains so that these domains solidify and form physical

crosslinks [47,48]. These additional crosslinks dominate the netpoints dermining the permanent shape, thereby enabling the temporary fixation of an elastic deformation that can be recovered by reheating. The most commonly encounted switching mechanisms are glass transition of amorphous domains and melting/ crystallization of crystalline domains. It is plausbile that the auxetic conversion follows the similar overall change scheme with its unique fixing mechanisms. These mechanisms are more appropriately called “fixing” rather than “switching” because 1) some mechanisms are not entirely reversible, and 2) in auxetic foams, one tries to use the materials in the fixed state exclusively, and avoid triggering the return to the initial permanent shape. Under the experimental conditions, in the case of I with low prestrain (40%), the primary fixing mechanism is the hard-segment e soft-segment hydrogen bonding interactions. These hydrogen bonds weaken as temperature increases, allowing the hard-segment phase to move relative to the soft-segment phase. When the temperature is reduced, the hard- and soft-segment phases reestablished their hydrogen bonding interactions in the new deformed geometry, thereby fixing the structure. These forces are however, normally weak relative to the overall strength of the elastic matrix's restoring force, resulting in low fixing rate and low Rf. The hydrogen bonds also are easily affected by humidity [39], which decreases the interaction and reduce the convertibility and stability. At 70% preload strain, buckling of cell walls and ribs took place (Fig. S5). This may lead to possible weak van der Waals interactions or even contacts between neighboring structures at the experimental temperature. Such weak adhesion may have facilitated (to some degree) the improvement in structure fixation. However it should be noted that even the adhesion may play a role, it is

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ineffective in promoting the fixity and may cause problems in the process. First, the van der Waals forces are too weak to offset the elastic restoring force. In addition, fixation by establishment of contacts during conversion is intrinsically a random process. It is also highly individual foam materials dependent and highly uncontrollable. It would fundamentally alter the cellular structure and excessive contacts may completely destroy the foam structure. Therefore for consistent auxetic fabrication, processing conditions shall be selected to prevent adhesion mechanism taking place. While the two aforementioned mechanisms were also present in the conversion of II and III, additional mechanisms must exist, which dominate the conversion process and are responsible for the rapid conversion and high Rf, particularly in III. As elucidated in the structure analysis section, substantial amount of SAN copolymer are present in II and III. These copolymer exist as particles and are linked to the PU matrix by both physical and chemical bonds. At the experimental temperature, ca. 30
C above the glass transition temperature of the SAN copolymer, the particles are in the rubbery state. The compressive stresses not only deformed the foam cellular structure and PU cell walls and ribs, but also cause the deformation of the viscoelastic SAN particles via time-dependent stress relaxation. The deformed SAN particles, whose shape changed from spherical from ellipsoidal, were observed in samples after convertibility study. Fig. 7a shows an example image and Fig. 7b shows a schematic illustrating this process. Such stressed induced particle deformation has been previously reported for polystyrene

(PS) filled poly(dimethylsiloxane) (PDMS) system [49,50]. When the system was cooled down to below the glass transition temperature of SAN, the particles were vitrified fixing the overall geometry of the foam samples. Thus in foam III the SAN particles serves the same role as the switching domain in SMP. Their relaxation behavior dominate the overall materials response. The stiff SAN particles (at T < Tg, SAN) would withstand and completely offset the elastic restoring force, maintaining the foam in the converted geometry and thereby an excellent Rf (close to 1). The effects of the other two mechanisms became negligible. In the auxetic conversion of II, all three mechanisms may play a role. The SAN particles while greatly expedite the structure fixing and substantially higher Rf than I, the effect is not as dominant as that in III. To study in detail the essential role of the SAN particles on the auxetic conversion in II and particularly in III, we conducted systematic convertibility study at different temperature using theses two foams. A preload strain of 40% was used so that the effect of adhesion on the structural convertibility is negligible. As shown in Fig. 8a and b, either a longer heating time or a higher temperature resulted in a higher structural convertibility, providing further support for a SAN particle relaxation controlled process. To better comprehend the particle relaxation behavior, we make use of a well-known empirical relationship, the Kohlrausch, Williams and Watts (KWW) stretched exponential function [51,52]. It is widely used to describe the structural relaxation in amorphous systems and takes the following form.

"



t 1  Rf ¼ exp  tðTÞ

Fig. 7. (a) An example SEM micrograph showing the deformed SAN particles in the PU foam after compression at 135
C; (b) a schematic showing the concurrent occurrence of the deformation of both the foam cellular structure and the SAN particles.

b # (5)

where b (0 < b  1) is the stretch exponent, t is the relaxation time and T is the temperature. Data were replotted in double-logarithmic as log[-ln(1-Rf)] vs. log(t) and were shown in Fig. 8c and d. The data for both foams (at all temperatures) exhibited good linear relationships and fit well using the KWW stretched exponential, from which the temperature dependent relaxation times for both foams were calculated and are shown in Fig. 8e and f. For both foams the relaxation times exhibited a critical “slowing down” when the temperature approaches to the glass transition temperature of SAN, agreeing well with the argument that the relaxation behavior observed in these experiments originated from the SAN copolymer. While displaying similar temperature dependence, the particle relaxation times in III are several magnitude lower than those in II. The relaxation process was extremely rapid unless the temperature reached to close the SAN glass transition temperature. We emphasize that the relaxation times discussed here (Fig. 8e and f) are not the SAN copolymer molecular chain relaxation times. Instead, they are particle relaxation times in the two foams, the characteristic times (t) for the particles to reach particular levels of deformations (εt,p). As mentioned earlier, the deformations of the SAN particles collectively fix the foams in the deformed state. They provide a mechanism for “restraining stress” that can counter/ offset the spring-back force originated from the elasticity of the PU foams upon removal of the external stresses after auxetic conversion. As a first order estimation, such restraining stress F can be considered equal to the stress necessary to return the deformed SAN particles to the original undeformed state at the auxetic foam service temperature, under which the SAN copolymer is typically in glassy state. Fff(ESAN,glassy, fp, εt,p), F is a function of the molus of SAN particle in the glassy state (ESAN,glassy), the number of the SAN particles (or volume fraction of SAN particles, fp), and the characteristic deformation of each SAN particle (εt,p). The characteristic times deduced from the convertibility study are the relaxation

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105

Fig. 8. Structural convertibility of PU foam (a) II and (b) III at different shape holding temperature (shape strain 40%); Plots of log[-ln(1-Rf)] vs. log(t) for PU foam (c) II and (d) III. The dash lines are the KWW stretched exponential fits; Relaxation time as a function of temperature for PU foam (e) II and (f) III. The values of t were calculated by fitting the data in a doubleelogarithmic plot presented in (c) and (d).

times to achieve a particular εt,p. As the stress is contributed collectively by all SAN particles, to empower the same level of restraining stress the required deformation εt,p from each particle would decrease with increasing particle volume fraction fp. For foams containing large amount of SAN particle such as foam III in the present study, the required deformation εt,p may be very small, and could be rapidly achieved at the processing conditions. To summarize, in this section we aim to elucidate the underlying mechanisms responsible for the structural convertibility of flexible PU foams. Our study suggests that the structure fixation may be realized by: 1) hydrogen bonding between hard- and softsegments; 2) adhesion between the cell walls/ribs from van der Waals interactions and contacts; and 3) stressed induced deformation and relaxation of SAN particles. The first two forces are rather weak and inefficient in structural fixation. By contrast, the stress induced SAN particles deformation and relaxation is a powerful means to fix the structure whose effectiveness is profoundly affected by the amount of SAN particle in the materials. Extremely rapid structure conversion with Rf/1 can be achieved.

These findings would provide valuable insights to guide auxetic foams fabrication. 3.3. Auxetic foams manufacture Aiming to utilize the mechanisms illustrated in the previous section to guide the auxetic foam manufacturing, we used the triaxial compression process to fabricate a series of auxetic samples using foams I, II and III. It was found that conversion of foam I to auxetic foam was not possible under any of the experiment conditions. This coincides with the previous finding of the poor structural convertibility of this material. The hard-soft segments hydrogen bonding is too weak and inept for auxetic conversion. Fabrication of auxetic foams using II and III were successful under a variety of processing time/temperature combination. Fig. 9 shows the results. The auxetic conversion of III was substantially faster than that of II. Notably, the processing times (Fig. 9) are comparable to the particle relaxation times (Fig. 8). The slight difference may be attributed to the difference in the equipment used and their

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and “freeze” the re-entrant structure formed when the foam is cooled to below the SAN glass transition temperature. 4. Conclusions

Fig. 9. Auxetic foams were fabricated under a variety of processing conditions (time/ temperature) from II and III. Numbers in the graph are measured Poisson's ratio.

heating capability. The relaxation time experiments utilized a DMA that can provide almost instantaneous heating whereas thermal lag was much more prominent for the oven used for the auxetic foam fabrication. Nevertheless to a large extent results from the auxetic foam fabrication study mirror those from the structural convertibility study, further confirming the critical role of the SAN particles and their stress induced deformation/relaxation in determining the success of auxetic conversion and the selection of conversion conditions. Fig. 10 shows the SEM images of a fabricated auxetic foam. The typical re-entrant structure was clearly prevailing in the foam. High magnification images (Fig. 10c and d) showed that the SAN particles, which were ellipsoidal in shape, aligned in a preferential direction (plausibly along the local stress direction). Indeed the deformed SAN particles effectively serve as curing/locking agents

By a plethora of detailed characterization and analysis that reveals the materials microstructures, chemistries, morphologies, and thermomechanical properties of several flexible PU foams, this study affords answers to questions critical in manufacturing of auxetic PU foams from flexible PU foams. The study, for the first time, elucidated several microscopic, molecular level mechanisms for auxetic conversion. Both hydrogen bonding interaction and adhesion by van der Waals interaction and contacts are ineffective and highly uncontrollable in achieving auxetic conversion during processing and maintaining the auxetic structure thereafter. The significant role of SAN copolymer particles in the structural conversion of the flexible PU foams was identified and thoroughly analyzed for the first time. It was found that stress induced deformation and relaxation of the SAN particles is an extremely powerful mechanism for successful conversion of the PU foam to auxetic foams with high convertibility and high time efficiency. SAN containing flexible PU foams are therefore excellent choices for use in the fabrication of auxetic PU foams. The processing timeetemperature relationship of SAN containing PU foams largely coincide with that of the SAN particle relaxation time e temperature relationship, which can be attained by utilizing a simple yet highly useful stretched exponential function and used to design the auxetic foam manufacturing process. The methodology can serve as a general guideline for manufacturing of auxetic PU foams from SAN containing flexible PU foams. The study also unequivocally demonstrated that how PU foams with similar macroscopic pore morphology would differ tremendously in the chemical and physical characteristics, which in turn would enable different conversion mechanisms that dictate the suitability of, and associated processing conditions for auxetic conversion using a particular flexible PU foam. The “softening” temperatures discussed in the literature is ill-defined and vague because they may be related to different thermal transition phenomena in different materials systems. For rational design of auxetic foam manufacturing process and product consistency, critical for the adoption of this type of materials, a thorough understanding of the starting PU foam from the materials perspective is a indispensable. Acknowledgment This work was supported by the U.S. Department of Veterans Affairs (VA118-12-C-0066). The authors are grateful for Md Deloyer Jahan and Hui Wang in assisting Poisson's ratio determination. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.polymer.2016.01.076. References

Fig. 10. SEM images of an auxetic foam fabricated from foam III. (a) A typical image showing the re-entrant foam structure; (b) a higher magnification view of the cell wall regions; (c) and (d) high magnification views of circled regions in (b) showing that the ellipsoidal SAN particles preferentially align in one direction (presumably the local stress direction).

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