Kinetics of Strain-Induced Crystallization in Natural Rubber Studied by

Article pubs.acs.org/Macromolecules

Kinetics of Strain-Induced Crystallization in Natural Rubber Studied by WAXD: Dynamic and Impact Tensile Experiments Karsten Brüning,†,‡ Konrad Schneider,*,† Stephan V. Roth,§ and Gert Heinrich†,‡ †

Leibniz-Institut für Polymerforschung Dresden e.V., Dresden, Germany Institut für Werkstoffwissenschaft, Technische Universität Dresden, Dresden, Germany, and § Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany ‡

S Supporting Information *

ABSTRACT: The time-dependence of strain-induced crystallization in cross-linked natural rubber was studied using synchrotron wide-angle X-ray diffraction (WAXD) with an unprecedented time resolution in the ms range. In-situ dynamic mechanical tests and tensile impact tests were carried out. In tensile impact tests, consisting of a strain step within less than 10 ms, it was found that roughly half of the crystallization process was complete within less than 5 ms, provided the strain is large enough. Afterward, crystallization proceeded on a time scale of a few seconds. This implies that under dynamic loading at frequencies which are typically encountered in the application of rubbers, the degree of crystallinity is considerably lower than under equilibrium conditions. This was directly confirmed by in situ dynamic cyclic experiments at a frequency of approximately 1 Hz. Since crystallization is a major factor contributing to the outstanding mechanical properties of natural rubber, these findings can aid in the interpretation and prediction of the frequency-dependence of mechanical properties.

■

INTRODUCTION The ability to undergo strain-induced crystallization (SIC) is a key property of natural rubber, contributing to its outstanding mechanical properties. Since the first experiments by Katz in 1925,1 numerous studies in this field have been done, investigating, e.g., the influence of temperature,2 cross-linking density,3 filler,4−6 rubber type,7 or strain field.8,9 The overall goal of these studies was to contribute to a better understanding of the relationship between structure and properties. Having in mind that the majority of the world’s yearly rubber production goes into the production of tires, which represent a highly dynamically loaded system, one should be aware of the time-dependency of SIC, which so far has received little attention due to the limited accessibility of short time scales in experiments, especially scattering experiments. However, with the advent of more powerful synchrotron sources and faster detectors, it is nowadays possible to obtain structural information with a time resolution of less than 10 ms, opening up new ways to study the kinetics of SIC. The first study on SIC under dynamic load is due to Acken in 1932, who used a stroboscopic technique to accumulate scattering patterns over several cycles.10 He reported that the SIC onset under cyclic loading was shifted to greater strains compared to quasistatic loading. Performing experiments at strains slightly larger than the SIC onset, he found an incubation time between 1 and 10 s for SIC to take place. Since then, the stroboscopic technique was applied by several investigators. Kawai et al.11,12 reported that crystallization is in phase with stress and not with strain. Using different phase © 2012 American Chemical Society

shifts between the stretching of the sample and the stroboscopic shutter, they were able to probe the evolution of crystallinity over the complete deformation cycle. They further reported that at frequencies below 2 Hz crystallization is independent of frequency. Recently, Candau et al. used the stroboscopic approach and deduced SIC incubation times of 50 ms,13 followed by an exponential increase of crystallinity over time according to a stretched exponential function with an exponent around 3. The inherent disadvantage of the stroboscopic technique is the accumulation over several cycles, such that no distinction can be made between structural evolution during any one cycle and a possible structural change over the course of several cycles. This can now be overcome using powerful synchrotron sources with high flux and fast detectors to resolve each cycle individually. Numerous SIC studies have been done under cyclic stretching at quasistatic strain rates.14−17 The first work regarding SIC after a fast strain step was published by Dunning in 1967.18 Because of the limited beam flux, he performed WAXD on a continuously stretched rubber band that was passed between two rolls rotating at different angular velocities, stretching the rubber band within a few milliseconds up to 500%. He reported an SIC incubation time of at least 0.1 s and found that the crystallinity increased constantly over more than 1 h. In the same time, Mitchell used Received: June 5, 2012 Revised: September 11, 2012 Published: September 19, 2012 7914

dx.doi.org/10.1021/ma3011476 | Macromolecules 2012, 45, 7914−7919

Macromolecules

Article

vulcameter tests (Scarabaeus SIS-MDR, Germany). The vulcanized sheets were then die-punched to obtain miniature tensile bars with beaded ends in the clamping area. Beamline Setup. The dynamic and impact experiments were performed at the Micro - and Nanofocus Beamline (MiNaXS) at PETRA III at Hasylab, Hamburg, Germany. The detector was a Pilatus 300 K pixel detector (Paul Scherrer Institute, Switzerland) with a readout time of 3 ms. The detector distance was around 170 mm. The angles between the detector plane and fiber axis were 0° and 6.66°, respectively. The latter setup was chosen to observe the (002) peak. Photon flux was around 5 × 1012 photons per second at a wavelength of 0.0954 nm. The beam size was variable between 20 and 300 μm; no significant peak broadening due to the finite peak size was detected and thus no deconvolution was carried out. The image acquisition rate was 140 fps (impact test) or 50 fps (dynamic tests), respectively. Each image series consisted of 10 000 patterns. Tensile impact tests were performed on an in-house developed machine, stretching the sample from 0% strain to a predetermined strain (between 150% and 550% engineering strain in steps of 50%) within 5 to 10 ms (depending on the magnitude of the strain step). The machine is driven by a spring, which is released by a servo motor, and can be equipped with a dynamic load cell (Instron Dynacell, time resolution 0.5 ms) and a high-speed camera for optical strain measurements. However, during in situ experiments, the load cell was not used and only the final strain after deformation was recorded. Dynamic tests were done on a self-made electrodynamic machine with a sinusoidal waveform. Quasistatic tests were performed on a custom-made tensile machine at the BW4 beamline at Hasylab in the step-hold technique, i.e. the sample was stretched in steps of 5 mm at a rate of 0.1 mm/s, interrupted by holding periods of 30 s, during which the patterns were acquired.28,29 All strains were recorded optically, using markers on the sample and a videocamera system with 24 fps. Ex-situ dynamic and quasistatic tensile tests were done on an Instron Electropuls E1000 machine. Data Processing. The scattering patterns were processed using self-written code in PV-Wave. This includes median filtering, background correction, normalization with respect to beam intensity and sample thickness, masking of invalid regions, reconstruction of the complete diffraction pattern and projection to obtain equatorial diffraction curves. The procedures are partly based on code developed by Stribeck.30,31 The degree of crystallinity Φ was obtained by subtraction of the amorphous scattering pattern (obtained before stretching) from the actual scattering patterns after normalization and background correction. The crystallinity was taken to be proportional to the integrated scattering intensity in the region of the (120) peak.

thermal techniques to measure SIC after a strain step and found that crystallization was almost complete within less than 0.5 s. The incubation time was detected to be well below 0.1 s.19 Several other studies approached SIC indirectly by volume measurements or stress relaxation experiments.20−22 Most of these studies gave crystallization half times longer than 10 min. The incorrectness of the assumed underlying relationship between stress and crystallinity was later clarified by Yeh.23 Very recently, a direct investigation of tensile impact tests was done by Tosaka et al.24−26 In their latest setup, it took around 500 ms for the strain step to complete. According to them, crystallization proceeds on two time scales of approximately 0.1 and 4 s, respectively. However, an interpretation of strain-induced crystallization on the molecular level, e.g., in analogy to the well-known nucleation and growth models for quiescent crystallization, is still lacking.27 In order to study the evolution of crystallinity over time, we followed two approaches: (a) dynamic mechanical experiments at a frequency of approximately 1 Hz, which are typically also carried out in the context of fatigue analysis; (b) tensile impact experiments, consisting of a fast step-strain within less than 10 ms.

■

EXPERIMENTAL SECTION

Materials. Unfilled and filled natural rubber (NR and NR-F) as well as unfilled synthetic isoprene rubber (IR) were used for the mechanical and diffraction experiments acc. to the recipe given in Table 1. The samples for SEM investigations were based on a recipe of

Table 1. Recipes and Vulcanization Times natural rubber [phr] isoprene rubber [phr] dicumyl peroxide [phr] N234 carbon black [phr] curing time [min]

NR

NR-F

100

100

2

2 20 19

24

IR 100 2 19

100 phr NR, 150 phr N772, 1.5 phr DCP and 15 phr stearic acid as processing aid; vulcanization time was 13 min. Pale crepe natural rubber was supplied by Weber and Schaer, Germany. Synthetic polyisoprene rubber (Natsyn 2200) was purchased from Goodyear Chemical. The rubber was masticated in an internal mixer and afterward the peroxide cross-linker was added on a heated two-roll mill. Vulcanization was performed in a hot press at 160 °C for the times listed, as determined from the optimum curing time t90 in

Figure 1. Φ vs time for NR for a strain step of 410% along with fits acc. to eq 3 (solid line) and Avrami fit (dashed line, n = 0.18): (a) logarithmic time scale; (b) linear time scale. 7915

dx.doi.org/10.1021/ma3011476 | Macromolecules 2012, 45, 7914−7919

Macromolecules

■

Article

is of the same order as the tube diameter,34 local segmental motion can contribute to crystal growth. (d) Crystallites grow from the oriented network, resulting in a fibrillar structure rather than a lamellar structure. The presence of a significant amount of crystallinity directly after the strain step leads us to the hypothesis that crystallization is a two step process consisting of nucleation and growth. The major part of the nucleation occurs during the strain step, supporting the idea of an instantaneous coil−stretch transition as proposed by De Gennes.35 Later Hsiao et al. proposed to apply this transition to chain segments between cross-links,36 considering that the crystallites are much smaller than the typical distance between cross-links or entanglements, which is of the order of 20−150 nm.34,37,38 In analogy to flowinduced crystallization (FIC) we propose the formation of shish crystals.39,40 Lamellar overgrowth (kebab), typically observed as the second step in FIC, is impeded by the reduced mobility due to the cross-links. In fact, only after very prolonged stretching41 or after thermal treatment39,40 was the formation of lamellar overgrowth observed in natural rubber . A SEM micrograph of a highly stretched filled NR is shown in Figure 2. The similarity

RESULTS AND DISCUSSION Tensile Impact Experiments. A. Short-Time Behavior. Provided the strain step was large enough, the very first pattern, acquired approximately 5 ms after the impact, already showed first signs of crystallinity, as exemplified in Supporting Information, supplementary Figures 1 and 2. The required minimum strain to observe crystallinity already in the first diffraction pattern after approximately 5 ms is 400% for NR, 300% for NR-F and 570% for IR (s. Supporting Information, supplementary Figure 2). Despite the short time interval, the crystallinity Φ was already considerable, usually around half of the final crystallinity Φf (defined as the crystallinity 60 s after the strain step was applied). In a narrow window of strains smaller than those listed above, SIC took up to 200 ms until the first signs of crystallinity were recognizable from the diffraction patterns. This is in contrast to the results by Tosaka et al.26 They did not detect any crystallinity directly after the strain step was complete. This contradiction becomes even more puzzling when considering that at the point of completion of the strain step their samples have resided several 100 ms above the strain of crystallization onset due to the limited strain rate. Given that both experiments were carried out at high-flux synchrotron sources and that we also observed very fast crystallization in sulfur-cured samples, this discrepancy remains unsolved. B. Crystallization Kinetics. The development of crystallinity over time is shown in Figure 1, at first sight suggesting a linear relation between crystallinity and the logarithm of time. However, the data can be fitted to a multitude of models. When fitting it to the Avrami equation Φfit (t ) = Φf (1 − exp(− (kt )n ))

(1)

as shown in Figure 1, unrealistically low exponents n < 0.5 are the outcome, suggesting that the mechanism is different from quiescent crystallization. The Avrami model in its original form is typically applied to the growth of crystallites (mainly spherulites) on length scales much larger than individual crystallizable chain segments. It assumes a linear growth of the crystallite over time, i.e., the attachment of crystallizable entities on the growth face is the rate-determining step. However, the SIC kinetics in networks can be expected to be governed by a different mechanism, since there are some peculiar differences to quiescent crystallization: (a) The crystallites are much smaller. Thus, the description of the growth process has to deal with the attachment of segments of sizes below 1 nm, i.e., on the size scale of individual unit cells. (b) The mobility of the melt is reduced due to cross-links, reducing the diffusion coefficient and rendering largescale diffusion impossible.32 Thus, also a modified Avrami equation with diffusion as the rate limiting step is not applicable. (c) The mobility of the chains becomes anisotropic due to the presence of strain. In contrast to flow-induced crystallization, where the external strain typically is temporary and crystallization proceeds after removal of the strain, in this study the strain is permanent. In terms of the concepts of long-time/large scale dynamics in tube-like constrained polymer networks the constraining tube is preferentially aligned along the tensile direction and thus diffusion normal to the tensile direction is strongly reduced.33 However, because the crystallite size

Figure 2. SEM micrograph of a highly strained natural rubber with 150 phr of N772 carbon black. The scale bar represents 1 μm. Stretching direction is horizontal.

between the shish structures obtained in FIC and the fibrillar network obtained in stretched NR is obvious.36 The diameter of the fibrils is around 20−50 nm. It is assumed that the shish structure is surrounded by an oriented amorphous shell. Because of the row-like arrangement of the individual shish segments, separated by defects (such as entanglements or crosslinks) present in the amorphous precursors,42,43 crystallite growth is restricted to the a and b crystallographic directions. This is supported by the data on the crystallite size, obtained from the Scherrer equation (Figure 3). Further results of the Scherrer equation are, that the size of the crystallites is constant in the tensile direction irrespective of the magnitude of the strain step, whereas in the a and b directions the size increases slightly with increasing strain step height. Thus, the main reason behind the increase in crystallinity with strain must be a larger number of crystallites, which is in line with literature on quasistatic experiments.44 Following the concept that the crystallization rate is, due to the hindered mobility, determined by the availability of crystallizable chains (Φf − Φ), the rate equation is given by 7916

dx.doi.org/10.1021/ma3011476 | Macromolecules 2012, 45, 7914−7919

Macromolecules

Article

obtain even a basic understanding of the mechanisms of straininduced crystallization.27 In agreement with quasistatic studies,4,7 no significant orientation of the amorphous halo could be detected, whereas the crystallites were highly oriented. This, however, does not rule out the existence of oriented amorphous precursor structures, since due to the small persistence length in NR an orientation of the amorphous chains is hardly reflected in the WAXD diffractogram.47 C. Comparison with Quasistatic Behavior. After roughly 1 min, Φ was almost constant and increased only at a very low rate, thus termed final crystallinity Φf. The crystallinity-strain curves obtained from Φf after a strain step or Φ during quasistatic stretching, respectively, are similar (Supporting Information, supplemental Figure 4). This shows that despite the fast stretching and thus despite being so far off equilibrium, the system finally returns to a comparable state as in quasistatic stretching. This is in contrast to thermal quenching, where the system remains in a metastable state. However, it remains speculative, whether the applied strain rate of 350 s−1 is sufficiently large. It also is questionable whether the chain mobility in the stretched state is reduced in a similar fashion as it is by cooling. D. Melting Kinetics. In order to gradually approach cyclic loading, the melting kinetics after a sudden removal of the load were investigated. First, the sample was quasistatically loaded to a fixed strain, and then unloaded. The magnitude of the unloading strain rate was similar to the loading case described in the previous sections, i. e. the unloading step was completed in less than 10 ms. The WAXD patterns clearly show that the melting of the strain-induced crystallites occurs instantaneously (on the experimentally accessible time scale). As exemplified in Figure 5, melting is complete within about 10 ms. This does not only apply to IR, but is also true for NR and filled NR.

Figure 3. Lhkl vs time curves for NR for a strain step of 410%.

dΦ = (k(Φf − Φ))n dt

(2)

Integration yields Φ(t ) = Φf − ((n − 1)knt + (Φf − Φ0)1 − n )1/1 − n

(3)

where Φ0 is the initial crystallinity due to nucleation after completion of the strain step and t is the time. k and n are fit parameters. n describes the different propensity of the amorphous chain segments to crystallize, owing to the orientational distribution of the chain segments. n was found to be close to 4 for all cases. The quality of the fit is exemplified in Figure 1. The obtained values for Φ0 and Φf are plotted in Figure 4. As expected, both Φ0 and Φf increase with strain. In

Figure 4. Initial crystallinity Φ0 (dashed lines) and final crystallinity Φf (solid lines) vs strain step height for NR (open symbols) and NR-F (filled symbols).

Figure 5. Crystallinity vs time in IR after steplike unloading from 500% to 0% at t = 0 s. The crystallites disappear instantaneously. The time between two consecutive points is 7 ms.

agreement with quasistatic tensile experiments, the SIC onset occurs at lower strains in NR-F, but at larger strains the crystallinity in the unfilled rubber is higher.45 Similar to thermal crystallization, strain-induced crystallization is much slower in IR as compared to NR when stretched to the same strain.46 However, when a higher strain is applied to the IR sample, which is necessary in order to compensate for the lower melting temperature of IR,16 the kinetics of NR and IR are very similar (Supporting Information, supplemental Figure 3). Even though the data fits the nucleation and growth model well, there is no direct proof of the proposed mechanism. We agree with Mandelkern that there still remains a lot of work to be done in terms of experimental work as well as modeling to

The reason for the difference in the observed crystallization and melting kinetics can be 2-fold: (a) The dissolution of the crystalline order is indeed faster than its establishment after the strain step. This could be explained by the faster chain segment dynamics in the undeformed state. (b) The observed disbalance is methodological in nature. Since the diffraction condition is only fulfilled when the crystalline order is fully established, it takes some time to observe crystalline peaks. On the other hand, disturbances in the crystalline order after removal of the strain can erase any diffraction signal while some residual short-range order might continue to exist. We believe that both effects make contributions. 7917

dx.doi.org/10.1021/ma3011476 | Macromolecules 2012, 45, 7914−7919

Macromolecules

Article

Dynamic Tensile Experiments. In the dynamic tensile experiments, we varied the amplitude, the strain level and the sample history (i.e., strain level before cyclic deformation started). For clarification, the minimum strain value during cyclic stretching is hereafter referred to as εmin, its maximum as εmax. The strain level before cycling is termed as εi. Consequently, the amplitude is 0.5(εmax − εmin). The frequency was kept between 0.75 and 0.85 Hz and can be considered constant. A. Dynamic Stretching with Minimum Strain = 0. As depicted in Figure 6, at t < 0, the sample was held at εi = 365%

Figure 8. SIC during cyclic stretching (εmin = 0%, εmax = 300%) in NRF; strain and crystallinity, each normalized to the maximum values, vs time.

tests, and considering the reinforcing effect of the crystallites, one expects to see an influence on the mechanical properties. In fact, when the strain amplitude of the dynamic tests exceeds the strain of SIC onset (approximately 170% for NR-F), the lower crystallinity leads to a reduction in reinforcement and thus reduces the stress as compared to a quasistatic test, where sufficient time was given to reach crystallization equilibrium. This is exemplified in Figure 9, where the same specimen was Figure 6. Crystallinity Φ vs time in NR during dynamic stretching (εmin = 0%, εmax = 365%). The first and last two cycles of a 90 s period are shown. Before cycling started (t < 0), the sample was kept stretched at εi = 365%.

for approximately 5 min, until at t = 0 cyclic stretching (εmin = 0%, εmax = 365%) began. It is clearly visible that under dynamic load the maximum Φ is considerably lower than the initial level despite the same maximum strain. B. Dynamic Stretching above the SIC Onset. Figure 7 shows the evolution of Φ vs strain in NR from cyclic

Figure 9. Force and crystallinity vs engineering strain for NR-F. Dynamic and quasistatic experiments were performed as described in the text. For the dynamic experiments, for clarity, only the loading paths of six cycles are shown.

first cycled for 20 cycles (″demullinization″, εeng,min = 0%, εeng,max = 250%), then the quasistatic force-displacement curve (with 30 s holding time in analogy to the beamline experiments) was recorded and finally the sample was cycled for another 20 cycles, 10 of which are shown. These mechanical experiments were performed ex situ. In order to avoid experimental inaccuracies, the engineering strain εeng from the readouts of the tensile machine are plotted. However, we confirmed that these are related to the optical strain data by a constant factor only. The amplitude of the in situ dynamic experiments was slightly larger (εeng,min = 0%, εeng,max = 285%).

Figure 7. Crystallinity Φ vs strain in NR during dynamic stretching (εmin = 290%, εmax = 365%). Five cycles after approximately 40 s are shown.

■

experiments with εmin = 290% and εmax = 365%. The maximum Φ during cycling is roughly two times larger than in case A despite the same maximum strain εmax. This can be ascribed to two reasons: (i) Because of the smaller amplitude, the strain rate is lower and consequently the samples resides a longer time at a given strain above εmin. (ii) Since stretching takes place above the crystallization strain, crystallites are present at all times, and thus no nucleation is required. C. Phase Lag between Strain and Crystallinity. The previously reported hysteresis in the Φ vs strain curve also occurs under dynamic loading.14−17 It is reflected in a phase lag between strain and Φ under cyclic load (Figure 8). Because the melting kinetics are much faster than the crystallization kinetics, the lag is only present on the loading branch. D. Mechanical Consequences of the Crystallization Kinetics. Given that crystallinity does not reach Φf in dynamic

CONCLUSION Owing to the high photon flux of modern synchrotron sources, it was for the first time possible to follow the strain-induced crystallization in natural rubber during cyclic dynamic mechanical experiments without the necessity to modify the mechanical experiment or to average over several cycles. The results from the tensile impact tests clearly show that crystallization is an initially very fast process. However, the time in a dynamic cycle is not sufficient to reach equilibrium. This finding has direct impact on the properties of natural rubber. It was shown that the stress−strain behavior changes accordingly. It is safe to assume that also the crack propagation behavior is affected. In particular, the fact that natural rubber is almost unable to undergo stable static crack growth, whereas under cyclic loading stable crack growth is observed, can be 7918

dx.doi.org/10.1021/ma3011476 | Macromolecules 2012, 45, 7914−7919

Macromolecules

Article

(17) Toki, S.; Burger, C.; Hsiao, B.; Amnuaypornsri, S.; Sakdapipanich, J.; Tanaka, Y. J. Polym. Sci., Part A: Polym. Chem. 2008, 46, 2456−2464. (18) Dunning, D.; Pennells, P. Rubber Chem. Technol. 1967, 40, 1381. (19) Mitchell, J.; Meier, D. J. Polym. Sci., Part A-2: Polym. Phys. 1968, 6, 1689−1703. (20) Gent, A. Trans. Faraday Soc. 1954, 50, 521−533. (21) Luch, D.; Yeh, G. J. Polym. Sci., Polym. Phys. Ed. 1973, 11, 467− 486. (22) Kim, H.; Mandelkern, L. J. Polym. Sci., Part A-2: Polym. Phys. 1968, 6, 181−196. (23) Yeh, G. Rubber Chem. Technol. 1977, 50, 863−873. (24) Tosaka, M.; Senoo, K.; Kohjiya, S.; Ikeda, Y. J. Appl. Phys. 2007, 101, 084909. (25) Tosaka, M.; Kawakami, D.; Senoo, K.; Kohjiya, S.; Ikeda, Y.; Toki, S.; Hsiao, B. Macromolecules 2006, 39, 5100−5105. (26) Tosaka, M.; Senoo, K.; Sato, K.; Noda, M.; Ohta, N. Polymer 2012, 53, 864−872. (27) Mandelkern, L. Crystallization of Polymers Vol. 2: Kinetics and Mechanisms; Cambridge University Press: Cambridge, U.K., 2004; Vol. 2. (28) Schneider, K. J. Polym. Sci., Part B: Polym. Phys. 2010, 48, 1574− 1586. (29) Schneider, K.; Zafeiropoulos, N.; Stamm, M. Adv. Eng. Mater. 2009, 11, 502−506. (30) Stribeck, N. X-ray Scattering of Soft Matter; Springer: Berlin, 2007. (31) Stribeck, N. Fibre Diffr. Rev. 1997, 6, 20−24. (32) De Gennes, P.; Leger, L. Annu. Rev. Phys. Chem. 1982, 33, 49− 61. (33) Heinrich, G.; Vilgis, T. Macromolecules 1992, 25, 404−407. (34) Rubinstein, M.; Colby, R. Polymer Physics; Oxford University Press: Oxford, U.K., 2003. (35) De Gennes, P. J. Chem. Phys. 1974, 60, 5030−5042. (36) Somani, R.; Yang, L.; Zhu, L.; Hsiao, B. Polymer 2005, 46, 8587−8623. (37) Tosaka, M. Polym. J. 2007, 39, 1207−1220. (38) Sanders, J.; Ferry, J.; Valentine, R. J. Polym. Sci., Part A-2: Polym. Phys. 1968, 6, 967−980. (39) Shimizu, T.; Tosaka, M.; Tsuji, M.; Kohjiya, S. Rubber Chem. Technol. 2000, 73, 926−936. (40) Tsuji, M.; Shimizu, T.; Kohjiya, S. Polym. J. 2000, 32, 505−512. (41) Valladares, D.; Yalcin, B.; Cakmak, M. Macromolecules 2005, 38, 9229−9242. (42) Yeh, G.; Hong, K. Polym. Eng. Sci. 1979, 19, 395−400. (43) Andrews, E. Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 1964, 277, 562−570. (44) Huneau, B. Rubber Chem. Technol. 2011, 84, 425−452. (45) Brüning, K.; Schneider, K.; Heinrich, G. J. Polym. Sci., Part B: Polym. Phys. 2012, in press. (46) Gent, A.; Kawahara, S.; Zhao, J. Rubber Chem. Technol. 1998, 71, 668−678. (47) Mitchell, G. Polymer 1984, 25, 1562−1572. (48) Persson, B.; Albohr, O.; Heinrich, G.; Ueba, H. J. Phys. Condens. Matter 2005, 17, R1071−R1142. (49) Harbour, R.; Fatemi, A.; Mars, W. Fatigue Fract. Eng. Mater. Struct. 2007, 30, 640−652.

ascribed to the lower crystallinity in the crack tip when it is loaded dynamically.48 Similarly, the observation that the crack growth rate in natural rubber is considerably reduced when the sample is not fully unloaded, can be attributed to the delay in crystallization.49 Obviously, after the complete unloading, the crack advances faster because the reinforcement by crystallization is not instantaneously fully established due to the finite crystallization kinetics.

■

ASSOCIATED CONTENT

* Supporting Information S

Diffraction curve in equatorial direction and plots of incubation time vs strain step height, crystallinity vs time, and final crystallinity after impact. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

■

REFERENCES

The authors are indebted to Hasylab for the assigned beamtime. The support of A. Buffet and A. Rothkirch from Hasylab is highly appreciated. They also acknowledge the pioneering work of N. Stribeck (University of Hamburg) for automated scattering data processing in PV-wave. This work was funded by the DFG in the framework of the DFG Forschergruppe 597, Fracture Mechanics and Statistical Mechanics of Reinforced Elastomeric Blends.

(1) Katz, J. Naturwissenschaften 1925, 13, 410−416. (2) Trabelsi, S.; Albouy, P.; Rault, J. Macromolecules 2003, 36, 7624− 7639. (3) Tosaka, M.; Murakami, S.; Poompradub, S.; Kohjiya, S.; Ikeda, Y.; Toki, S.; Sics, I.; Hsiao, B. Macromolecules 2004, 37, 3299−3309. (4) Poompradub, S.; Tosaka, M.; Kohjiya, S.; Ikeda, Y.; Toki, S.; Sics, I.; Hsiao, B. J. Appl. Phys. 2005, 97, 103529. (5) Carretero-Gonzalez, J.; Verdejo, R.; Toki, S.; Hsiao, B.; Giannelis, E.; López-Manchado, M. Macromolecules 2008, 41, 2295−2298. (6) Trabelsi, S.; Albouy, P.; Rault, J. Macromolecules 2003, 36, 9093− 9099. (7) Toki, S.; Sics, I.; Ran, S.; Liu, L.; Hsiao, B. Polymer 2003, 44, 6003−6011. (8) Trabelsi, S.; Albouy, P.; Rault, J. Macromolecules 2002, 35, 10054−10061. (9) Beurrot, S.; Huneau, B.; Verron, E. Proc. VII Eur. Conf. Constitutive Models Rubber 2011, 23−28. (10) Acken, M.; Singer, W.; Davey, W. Ind. Eng. Chem. 1932, 24, 54− 57. (11) Hiratsuka, H.; Hashiyama, M.; Tomita, S.; Kawai, H. J. Macromol. Sci., Part B 1973, 8, 101−126. (12) Kawai, H. Rheol. Acta 1975, 14, 27−47. (13) Candau, N.; Chazeau, L.; Chenal, J.; Gauthier, C.; Munch, E.; Rochas, C. Polymer 2012, 53, 2540−2543. (14) Toki, S.; Fujimaki, T.; Okuyama, M. Polymer 2000, 41, 5423− 5429. (15) Toki, S.; Sics, I.; Ran, S.; Liu, L.; Hsiao, B.; Murakami, S.; Senoo, K.; Kohjiya, S. Macromolecules 2002, 35, 6578−6584. (16) Trabelsi, S.; Albouy, P.; Rault, J. Rubber Chem. Technol. 2004, 77, 303−316. 7919

dx.doi.org/10.1021/ma3011476 | Macromolecules 2012, 45, 7914−7919