Effects of Molecular Weight Reduction on Brittle–Ductile Transition

Mar 7, 2017 - ... the cold-drawing of these polymer glasses into the strain hardening regime by investigating the elastic yielding behavior of these c...
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Effects of Molecular Weight Reduction on Brittle−Ductile Transition and Elastic Yielding Due to Noninvasive γ Irradiation on Polymer Glasses Panpan Lin,† Quan Xu,‡ Shiwang Cheng,§ Xiaoxiao Li,† Zhichen Zhao,† Shuangyi Sun,† Chao Peng,† Abraham Joy,*,† and Shi-Qing Wang*,† †

Department of Polymer Science, University of Akron, Akron, Ohio 44325-3909, United States State Key Laboratory of Heavy Oil Processing, Institute of New Energy Beijing Key Laboratory of Biogas Upgrading Utilization, China University of Petroleum (Beijing), Beijing 102249, China § Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ‡

S Supporting Information *

ABSTRACT: By exposing specimens to the γ irradiation, we show that polymer glasses including bisphenol A polycarbonate (PC) and poly(methyl methacrylate) (PMMA) turn from ductile to brittle due to chain scission by the irradiation that has noninvasively reduced their molecular weight. More importantly, by causing chain scission with the γ irradiation, we examine the origin of mechanical stress produced from cold drawing of four ductile polymer glasses (PC, PMMA, polystyrene, and poly(2,6dimethyl-1,4-phenylene oxide)). Specifically, we elucidate the origin of the residual stress embedded in the glassy state from the cold-drawing of these polymer glasses into the strain hardening regime by investigating the elastic yielding behavior of these colddrawn specimens. In contrast to the emergent retractive stress observed during annealing of the cold-drawn specimens above their storage temperature but still well below their glass transition temperatures, we find significantly lower retractive stress level and longer induction time for the retractive stress to show up when these specimens undergo sufficient dosage of the γ irradiation whose effect on the molecular weight and its distribution has been measured with gel permeation chromatography.

1. INTRODUCTION Mechanical behavior of polymer glasses has been studied for several decades.1−3 Apart from the past decade of computer simulations4−23 and development24−30 of a microscopic forcebased constitutive equation theory as well as recent direct molecular mobility measurements by the optical photobleaching technique,31−33 most research activities34−45 have been carried out to achieve a continuum level description of mechanical responses of polymer glasses to various forms of large deformation that produces ductile plastic deformation. For a long period, in the absence of a microscopic theory, the phenomenon of stress growth in the postyield regime, known as strain hardening, had been thought to manifest entropic stress associated with chain deformation.3,34,46,47 Such a characterization of the strain hardening behavior has been criticized.48 The recent consensus6,27 that strain hardening is a © XXXX American Chemical Society

dissipative process is reached on the basis of the following reasons: (a) a theoretical study shows that intersegmental interactions alone can produce an increase of the stress with growing strain beyond the yield point;27 (b) in computer simulations the strain hardening character even occurs in systems made of short chains.6 On the other hand, a recent study based on simultaneous mechanical and thermal measurements of ductile extension of bisphenol A polycarbonate revealed considerable internal potential energy buildup.49−52 Such an internal energy increase can be both intermolecular and intramolecular in origin. Without a theoretical model that accounts for both intermolecular and intramolecular interactions, it is not feasible to assess how much of the stored Received: January 31, 2017

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2. EXPERIMENTAL SECTION

energy is intramolecular in origin because intermolecular contribution is clearly present.27,52 Thus, it remains elusive whether postyield deformation is always largely intermolecular or not. In dealing with the challenge to explicitly demonstrate how the polymeric nature manifests itself in large deformation of common glassy polymers, elastic yielding is one of the most insightful phenomena. The elastic yielding behavior refers to the emergence of a significant retractive stress during annealing of a cold-drawn polymer glass above the storage temperature.53−62 The behavior of elastic yielding is interesting in its own right because it affords us an opportunity to investigate whether the retractive stress is due (at least in part) to chain networking or not. Further study of the elastic yielding may also help us explore the origin of strain hardening in uniaxial extension of ductile polymer glasses. Molecular interactions in the glassy state involve both shortranged van der Waals intersegmental interactions and intrasegmental covalent bonding that produces their long-range effects through interchain uncrossability. It has been elusive to demonstrate any intrasegmental contributions even in the postyield plastic deformation regime because of the demonstration from the microscopic theory24−30 and computer simulations4−23 that strain hardening6,27 can emerge without explicitly taking the chain networking into account. On the other hand, it is apparent that long chains in polymer glasses may form a network and undergo affine deformation at the covalent bond level.63,64 Consequently, we assert in the absence of a first-principles molecular theory that there could be nonnegligible intrasegmental stress during strain hardening in the postyield regime. There is indirect support for such a picture that views polymer glasses of high molar mass as a structural hybrid, made of a glassy primary structure (held by van der Waals bonding) and a chain network.63,64 For example, a recent molecular model found a correlation between the tensile stress at the brittle−ductile transition and the structure (i.e., areal density of load-bearing strands) of the chain network and concluded that the chain tension necessary for pullout is at a universal level of 0.2−0.3 nN.64 The phenomenon of elastic yielding is consistent with such a picture and points to the explicit role of the chain network in producing the strain hardening phenomenon. However, it can be argued that residual intersegmental stress could perhaps also produce elastic yielding: Chen et al. 42 predicted, based on a consideration of only intersegmental interactions, that there would exist sizable residual strain after postyield creep. In the present work, we set out to learn more about the nature of mechanical stress produced by large extension of various polymer glasses. We resort to γ irradiation to cause chain scission because the high-energy irradiation can penetrate samples and induce appreciable chain degradation in a noninvasive manner.65−69 The effect of any chain scission should show up in the cold drawing of γ-irradiated polymer glasses. In other words, a polymer glass after γ irradiation may show different mechanical characteristics. More important, if a precold-drawn polymer glass is subjected to sufficient γ irradiation, the retractive stress level may change during elastic yielding. We have previously assumed that the elastic yielding arises because the distorted chain network by cold drawing has caused the sample to undergo yielding. Since chain scission by the γ irradiation should weaken the chain network, the elastic yielding behavior should diminish in magnitude upon γ irradiation of the cold-drawn specimen.

2.1. Materials and Methods. Four types of polymer glasses bisphenol A polycarbonate (PC), polystyrene (PS), poly(methyl methacrylate) (PMMA), and poly(2,6-dimethyl-1,4-phenylene oxide) (PPE)were studied in this work. The PC was Lexan TM 141 111, received from Sabic. The PS was Dow Styron 663. The PMMA was from Plaskolite West, Inc., with a product number of CA-86. The PPE was obtained from SABIC (PPO630). Relevant sample properties are listed in Table 1.

Table 1. Sample Characteristics of Polymer Glasses sample

Mw (kg/mol)

Me (kg/mol)

PDI

Tg (°C)

PC PS PMMA PPE

50 194 125 47.6

1.3 13 13 5.3

2.01 1.27 1.13 2.75

149 103 113 214

PC pellets were first pressed into a 100 mm × 100 mm × 0.5 mm compression mold at 200 °C in a TMP vacuum compression press for 1 h and then cooled down to room temperature. Dog-bone-shaped samples were obtained by a punch press at room temperature with a dog-bone mold (ASTM D-412) involving an effective length of 39 mm. Similarly, PPE specimens were prepared in the same way except for the higher temperature of 280 °C used in the compression molding. PS pellets were pressed into a 100 mm × 100 mm × 1.0 mm compression mold at 180 °C in a TMP vacuum compression press for 1 h and then cooled down to room temperature. Dog-bone-shaped samples were obtained by a punch press at room temperature with a dog-bone mold (ASTM D-638) involving an effective length of 13.7 mm. Such samples were then melt-stretched to a stretching ratio of 5.0 at 135 °C with a crosshead speed of 600 mm/min. At the end of melt stretching cold water of 0 °C was sprayed onto the sample to rapidly quench the melt below Tg so that the rheological effect of melt stretching was retained. Cylindrical PMMA are extruded by a Monsanto capillary rheometer. The pellets of PMMA were first heated up to 210 °C in the rheometer. A pressure of 123 bar was then applied to compress the resin in the barrel to remove the air. After relaxation for 30 min, the sample was extruded at a wall stress of 0.078 MPa, using a capillary die with a length of 15 mm and a diameter of 1 mm. 2.2. Apparatus. The melt stretching preparation of PS was done on an Instron 5543 in a homemade oven with temperature control ranging from −100 to 200 °C. All cold-drawn measurements were carried out by an Instron 5543 at either 80 °C for extruded PMMA or 23 °C for other samples. Cold water of 0 °C was sprayed onto the PMMA samples instantly after deformation. Elastic yielding tests involve bringing precold-drawn samples into a homemade heater while holding the sample between the two clamps in an Instron 5543. For a typical sample length of 70 mm, the middle section of length ca. 30 mm was heated to produce the elastic yielding phenomenon. All precold-drawn samples were stored at room temperature for around 60 days. This period of two months included the time during which samples underwent the γ irradiation. The γ irradiation was carried out in Beijing Radiation Application Research Center with 60Co source. The total energy absorbed by the sample during the γ irradiation can be expressed in the unit of gray (Gy), which is energy per unit mass: 1 kGy = 1 J/g. Denoting the molar mass of a backbone bond as m in the unit of g/mol, then, on the average, each bond would receive a level of energy given by m J/mol at 1 kGy. Thus, at 100 kGy, if the energy absorption efficiency is 30%, for PS that has m = 52 g/mol, the average energy per bond would be ca. 1.5 kJ/mol, which is significantly lower than the chain-scission energy Ecs ∼ 300 kJ/mol. Thus, there could be one bond breakage for every 200 bonds. At a dosage rate of 1.5 kGy/h, a sample labeled to have undergone γ irradiation at the level of 1000 kGy has been exposed to the source for 667 h or ca. 28 days. B

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Macromolecules The degradation effect to the γ irradiation on PC and PMMA has been verified with measurements of the resulting molecular weights. The molecular weight of PC and PMMA was determined on a TOSOH EcoSec HLC-8320 gel permeation chromatography (GPC) equipped with one TSK-GEL super H 4000 column and two TSKGEL super H 3000 columns with chloroform as solvent. A TA Q200 differential scanning calorimeter was used to determine the glass transition temperatures of PC before and after the γ irradiation.

3. RESULTS To demonstrate the universality of the effect of the γ irradiation on elastic yielding, we subject four different polymer glasses to uniaxial extension. Because the temperature window for ductility is very narrow for PS, we have invoked melt-stretching to make PS ductile at room temperature.63 Figure 1 shows the

Figure 2. Engineering stress vs draw ratio curves of PC after γ irradiation with different dosages at a crosshead speed of 6 mm/min at 23 °C.

treated PMMA is already brittle and becomes fragile after a dosage of 200 kGy, as shown in Figure 3.

Figure 1. Engineering stress σengr as a function of draw ratio L/L0 for four types of polymer glasses: (1) melt-stretched PS; (2) PPE; (3) PC; (4) extruded PMMA. All these extension tests involve a crosshead speed of 6 mm/min. The parentheses show the experimental temperatures during uniaxial extension.

Figure 3. Engineering stress vs draw ratio curves of PMMA after γ irradiation with different dosages at a crosshead speed of 6 mm/min at 80 °C.

tensile (engineering) stress vs draw ratio at either room temperature (ca. 23 °C) for ms-PS, PC, and PPE or for PMMA at 80 °C. All of these tests were carried out using a crosshead speed of 6 mm/min. Significant tensile stress is built into these cold-drawn specimens when postyield drawing continues until the necking is complete at a draw ratio of λneck, which ranges from 1.35 to 1.7. The initial effective length of the dog-bone-shaped PMMA was 50 mm. For ms-PS before cold draw was 69 mm. The PC and PPE specimens were prepared with a dog-bone mold (ASTM D-412) with an effective length 39 mm. After cold draw, each of the samples was cut into a piece with length of around 70 mm for the elastic yielding experiment. 3.1. Effect by γ Irradiation on Ductility. To evaluate the effect of the γ irradiation that is expected to cause chain scission at high kGy, we subject the PC specimens to various levels of irradiation. Figure 2 shows the effect the γ irradiation in terms of the stress vs drawing ratio curves. As shown in Figure 2, at 200 kGy of γ irradiation, the yield stress, i.e., the maximum of σengr, shows a measurable drop. With 500 kGy of γ irradiation, after shear yielding and necking, the neck front cannot propagate over a longer draw ratio than 1.17 before the specimen suffers a structural failure at the neck front. Upon increasing the γ irradiation to 1000 kGy, the PC specimen turns brittle at room temperature. We have also examined the effect of the γ irradiation on isotropic PMMA specimen. The uniaxial extension of PMMA is far more sensitive to the γ irradiation. At 20 kGy, the γ-ray-

3.2. Reduction of Retractive Stress during Elastic Yielding Due to γ Irradiation. Previous studies show that a sizable retractive stress emerges in the cold-drawn polymer glasses upon annealing above the storage temperature.61,62 It was proposed that the emergent retractive stress in the elastic yielding phenomenon was intrasegmental without any direct evidence. If this conclusion is valid, the noninvasive chain cleavage of the cold-drawn polymers by the γ irradiation should lead to a measurable decrease of the retractive stress. After different levels of γ irradiation on the cold-drawn PC specimens, we anneal them at 75 °C. Figure 4 shows that the retractive stress significantly decreases systematically with increasing dosage of the γ irradiation. In particular, at 500 kGy, the retractive stress has reduced to 3.5 MPa, relative to the reference of 0 kGy that achieves 9.5 MPa. To varying degrees, the γ irradiation is also expected to cause chain scission in the other three polymer glasses. For example, after the γ irradiation at 200 kGy, the cold-drawn meltstretched PS specimens also display reduced retractive stress as well as longer induction time for the emergence of the retractive stress when annealed at 75 °C, as shown in Figure 5. At smaller dosages, e.g., at 20 kGy, the effect of the γ irradiation is immeasurably small. Presumably, little chain scission occurred, which can be verified by making GPC measurements of the postirradiation samples, as discussed in the Discussion section. PPE shows an even more remarkable increase in the induction time (squares) in Figure 6 where the retractive stress C

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The case of PMMA is more remarkable. Figure 7 shows the retractive stress hardly changes with the dosage relative to that

Figure 4. Retractive stress as a function of time at temperature Tel‑yield = 75 °C of cold-drawn PC that received different dosages of γ irradiation. The condition to produce the cold-drawn PC specimens is given in Figure 1, involving a draw ratio of L/L0 = 1.7.

Figure 7. Retractive stress as a function of time at temperature Tel‑yield = 75 °C of cold-drawn PMMA that received different dosages of γ irradiation. The condition to produce the cold-drawn PMMA specimens is given in Figure 1, involving a draw ratio of L/L0 = 2.2.

of the untreated PMMA for dosages up to 20 kGy. Such a result is unsurprising, given the estimate made near the end of section 2.2. However, with the severe γ irradiation treatment of 200 kGy, not only the retractive stress shows a sign to saturate to a significantly lower value but the specimen actually suffered a macroscopic breakdown during the elastic yielding. It is necessary to indicate that the failure, observed in multiple specimens under the same condition, did not occur in the annealed portion of the irradiated specimen. The breaking took place outside the heated region at the clamps. Apparently, the retractive stress produced by the elastic yielding was high enough to cause the premature brittle fracture of the irradiated PMMA that did not undergo cold drawing.

Figure 5. Retractive stress as a function of time at temperature Tel‑yield = 75 °C of cold-drawn melt-stretched PS that received different dosages of γ irradiation. The condition to produce the cold-drawn PS specimens is given in Figure 1, involving a draw ratio of L/L0 = 1.35.

4. DISCUSSION The origin of stress arising from large deformation of ductile polymer glasses has remained elusive. If the stress emergent during strain hardening may have the same origin as the retractive stress observed during the elastic yielding, we may examine the origin of stress during postyield extension by investigating the nature of elastic yielding. The data presented in the preceding section clearly show that the driving force for elastic yielding diminishes when the γ irradiation has caused chain scission in the precold-drawn glasses. Thus, the present results are consistent with the idea that intrachain tension built during postyield cold drawing may play a role in driving the observed elastic yielding.61,62 A number of additional comments are in order. First of all, both Figures 2 and 3 indicate that the γ irradiation has little effect at the low dosages, as expected. On the other hand, Figure 2 shows a systematic decrease of the yield stress with increasing dosage. DSC measurements confirm in Figure 8a a notable shift in the glass transition temperature from 147.7 °C (0 kGy) to 141.7 °C (500 kGy). Such information is consistent with the observed lowering of the yield stress. The behavior shown in Figure 4 indicates that the dominant effect of the γ irradiation is not the reduction in PC’s glass transition temperature Tg. With reduced Tg, the elastic yielding in Figure 4 should take place more readily: the retractive stress should have appeared within a shorter induction time and risen more rapidly in comparison to the control, i.e., the PC that was not exposed to the γ irradiation. The opposite was observed: the retractive stress

Figure 6. Retractive stress as a function of time at temperature Tel‑yield = 75 °C of cold-drawn PPE that received different dosages of γ irradiation. The cold-drawn PPE is predeformed at a constant crosshead speed of 6 mm/min at 23 °C to a draw ratio of 1.6.

is still growing before the tests were terminated. Compared with a previous report of elastic yielding in PPE,62 we observe much longer induction periods. The difference is due to aging. The previously published data on elastic yielding of PPE involves a younger sample that has been stored for only 1 day at room temperature after cold drawing instead of 2 months. In contrast, we note that the duration of storage does not strongly affect the induction period for elastic yielding of cold-drawn PC, as shown in a previous study,59 although the attainable retractive stress can decrease with the storage time. D

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Figure 8. (a) Differential scanning calorimetric measurements of three PC specimens that have been subjected to the γ irradiation at 20 and 500 kGy or no irradiation (0 kGy). (b) Observed shift in Tg as a result of molecular weight reduction is consistent with the literature data labeled as 197670 and as 2012.71

ductile. At 200 kGy, according to Figure 10, PMMA should be fragile because the molecular weight has dropped to a level comparable to the entanglement molecular weight Me ∼ 15 kg/ mol. In other words, the GPC data explain why the treated PMMA could break up during elastic yielding. The data (downpointed triangle) in Figure 7 indeed reveal specimen failure during the elastic yielding. The GPC results in Figure 11 also explain well the weakened elastic yielding in PS. At 20 kGy, there is hardly any change in

shows up more slowly and is weaker with increasing dosage. It seems that the dominant effect of the γ irradiation is to cause chain scission. To confirm this effect of the γ irradiation, GPC measurements have been carried out for all four types of polymers. The result in Figure 9 explains in the trend observed in Figure 8b

Figure 9. GPC determination of the change in the molecular weight of the γ-irradiated PC as a function of the dosage.

showing the shift of Tg due to the reduction in the molecular weight. Although the sample at 500 kGy is ductile as shown in Figure 2, the observable molecular weight decrease may explain the reduced magnitude of the elastic yielding in Figure 4. According to Figures 3 and 7, the irradiation effect on PMMA is stronger. The GPC measurements of the irradiated PMMA in Figure 10 confirm that PMMA has dropped to such a low molecular weight (ca. Mw and Mn equal to 70 and 37 kg/mol, respectively) at 20 kGy below a threshold for PMMA to be

Figure 11. GPC determination of the change in the molecular weight of the γ-irradiated PS as a function of the dosage.

the elastic yielding behavior. A measurable effect is seen for PS at 200 kGy as shown in Figure 4. Finally, there is a sharp drop in the molecular weight of PPE as shown in Figure 12. Such information explains the observed elastic yielding behavior in Figure 6. In principle, the reduced magnitude of elastic yielding could stem from physical aging. But any accelerated physical aging due to the γ irradiation can be ruled out for a couple of reasons. If sufficient physical aging took place, the yield stress should be noticeably higher in Figures 2 and 3 at 2 and 5 kGy, which is not the case. Physical aging should not have been accelerated by the γ irradiation because the rate of energy adsorption is too low to cause the specimen to heat up. Given the γ irradiation rate at ḋ = 1.5 kGy/h = 0.42 J/kg·s and mass density ρ ∼ 103 kg/m3, we can compare this rate of energy absorption with the efficiency of air cooling given by hΔT/ρH. For a typical specimen thickness of H ∼ 1 mm and a temperature increase of ΔT = 0.1 °C, we have hΔT/ρH ∼ 2 J/kg·s > ḋ, given a characteristic value of h = 20 J/(m2 s K). Therefore, air cooling

Figure 10. GPC determination of the change in the molecular weight of the γ-irradiated PMMA as a function of the dosage. E

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strain recovery of as much as 2% could be driven by processes that is intersegmental in origin. We carry out further experiment, aiming to isolate the observed elastic yielding from effects that can be produced by intersegmental driving force. Dog-bone-shaped PC specimens with effective length equal 39 mm are subjected at room temperature to tensile extension at three speeds V = 6, 60, and 300 mm/min to a draw ratio of 1.6 during which necking forms and propagates. At the end of the drawing, the crosshead reverses its traveling direction at the same respective speeds of 6, 60, and 300 mm/min by 6.25% (i.e., traveling backward by 3.9 mm) to cause bending of the specimen. For the specimen involving 6 mm/min the bending lasted nearly 103 s before the specimen straightened and exhibited retractive force as shown in Figure 13a. It takes progressively less time for the bent specimen to turn straightened and for us to observe rising retractive force at the higher speeds, as shown in Figure 13b,c. These additional tests reveal further information to suggest that the cold-drawn chain network may be the cause for drawn samples to yield in their glassy states. In the absence of yielding, no measurable retractive force would have emerged. More stress is stored when the crosshead is more quickly reversed. With the speed V0 = 6 mm/min, it takes 39 s to return by 6.25%. Data in Figure 13a indicate that for the first 36 s of the 39 s, the stress was positive because the specimen was still under tension. The movie in the Supporting Information records the entire test involving drawing, bending, and straightening for the case of 60 mm/min.

Figure 12. GPC determination of the change in the molecular weight of the γ-irradiated PPE as a function of the dosage.

would not allow the specimen to heat up by even 0.1 °C during the γ irradiation. Although the γ irradiation does not warm up the specimens to affect physical aging, physical aging as well as relaxation of intrasegmental tension may take place during storage. Consequently, all the comparison between zero and finite kGy in Figures 4−7 involves the same duration of storage. The effect of physical aging is indeed evident in Figure 6: a previous report indicated that after unloading from a cold drawing to L/ L0 = 1.65 and storage for 24 h at room temperature the prenecked PPE could show the elastic yielding effect at 70 °C with an induction time of 40 s and reaching 8 MPa in 1000 s. In contrast, Figure 6 shows an induction time of several hundred seconds at 2 kGy. The further increased induction time to 2000 s (diamonds) at 500 kGy relative to the behavior at 2 kGy is due to the effect of the γ irradiation, i.e., the irradiation-induced chain scission, as supported by the GPC data in Figure 12. Although a largely deformed polymer glass of high molecular weight can restore its undeformed dimensions upon heating above Tg, the increase of stress in the postyield regime is not simply due to rubbery elastic stretching. Both computer simulations5−9 and a microscopic free-energy-based theory27 have asserted that the strain hardening can arise from intersegmental interactions alone.72 Moreover, according to the segmental-scale constitutive equation theory of Chen and Schweizer24−30,73 that does not explicitly account for chain networking, strain recovery from postyield creep is only partial,42 implying that (a) there is residual stress of intersegmental origin and (b) elastic yielding could occur due to such a residual stress. Indeed, we could argue that additional

5. CONCLUSION We first subjected isotropic polymer glasses to the γ irradiation in order to study the effects of molecular weight, in a noninvasive way, on the brittle−ductile transition. Before the irradiation both PC (at room temperature) and PMMA (at 80 °C) are ductile and turn brittle in tensile extension upon sufficient dosages of the γ irradiation. This result is consistent with the recently proposed model64,74 that acknowledges the chain networking as indispensable in driving a polymer glass to undergo yielding and ductile deformation. The present results also support the notion that a polymer glass is only brittle below a threshold molecular weight. To study the origin of stress arising from large ductile extension of polymer glasses, we investigated the nature of the elastic yielding phenomenon53−62 by exposing four different precold-drawn polymer glasses to γ irradiation of different dosages. In each case, the γ irradiation at sufficient dosages causes the molecular weight to decrease considerably, as

Figure 13. Stress vs time curves during one cycle when PC specimens of length L0 = 39 mm is first drawn to a draw ratio 1.6 at (a) 6, (b) 60, and (c) 300 mm/min before undergoing compression at the same speeds over a distance of ΔL = 3.9 mm. The compression of this magnitude, i.e., ΔL/L = 6.25%, causes the specimen to bend considerably at the beginning. All three specimens were able to straighten over time and show retractive forces. F

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(5) Hoy, R. S.; Robbins, M. O. Strain hardening of polymer glasses: Effect of entanglement density, temperature, and rate. J. Polym. Sci., Part B: Polym. Phys. 2006, 44 (24), 3487−3500. (6) Hoy, R. S.; Robbins, M. O. Strain Hardening in Polymer Glasses: Limitations of Network Models. Phys. Rev. Lett. 2007, 99 (11), 117801. (7) Hoy, R. S.; Robbins, M. O. Strain hardening of polymer glasses: Entanglements, energetics, and plasticity. Phys. Rev. E 2008, 77 (3), 031801. (8) Hoy, R. S.; Robbins, M. O. Strain hardening in bidisperse polymer glasses: Separating the roles of chain orientation and interchain entanglement. J. Chem. Phys. 2009, 131 (24), 244901. (9) Robbins, M. O.; Hoy, R. S. Scaling of the strain hardening modulus of glassy polymers with the flow stress. J. Polym. Sci., Part B: Polym. Phys. 2009, 47 (14), 1406−1411. (10) Barrat, J.-L.; Baschnagel, J.; Lyulin, A. Molecular dynamics simulations of glassy polymers. Soft Matter 2010, 6 (15), 3430−3446. (11) Vorselaars, B.; Lyulin, A. V.; Michels, M. A. J. Deforming glassy polystyrene: Influence of pressure, thermal history, and deformation mode on yielding and hardening. J. Chem. Phys. 2009, 130 (7), 074905. (12) Lyulin, A. V.; Vorselaars, B.; Mazo, M. A.; Balabaev, N. K.; Michels, M. A. J. Strain softening and hardening of amorphous polymers: Atomistic simulation of bulk mechanics and local dynamics. EPL (Europhysics Letters) 2005, 71 (4), 618−624. (13) Vorselaars, B.; Lyulin, A. V.; Michels, M. A. J. Microscopic Mechanisms of Strain Hardening in Glassy Polymers. Macromolecules 2009, 42 (15), 5829−5842. (14) Lyulin, A. V.; Michels, M. A. J. Time Scales and Mechanisms of Relaxation in the Energy Landscape of Polymer Glass under Deformation: Direct Atomistic Modeling. Phys. Rev. Lett. 2007, 99 (8), 085504. (15) Vorselaars, B.; Lyulin, A. V.; Michels, M. A. J. Development of Heterogeneity near the Glass Transition: Phenyl-Ring-Flip Motions in Polystyrene. Macromolecules 2007, 40 (16), 6001−6011. (16) Chung, Y. G.; Lacks, D. J. How Deformation Enhances Mobility in a Polymer Glass. Macromolecules 2012, 45 (10), 4416−4421. (17) Chung, Y. G.; Lacks, D. J. Atomic Mobility in a Polymer Glass after Shear and Thermal Cycles. J. Phys. Chem. B 2012, 116 (48), 14201−14205. (18) Chung, Y. G.; Lacks, D. J. Sheared polymer glass and the question of mechanical rejuvenation. J. Chem. Phys. 2012, 136 (12), 124907. (19) Lee, H.-N.; Riggleman, R. A.; de Pablo, J. J.; Ediger, M. D. Deformation-Induced Mobility in Polymer Glasses during Multistep Creep Experiments and Simulations. Macromolecules 2009, 42 (12), 4328−4336. (20) Riggleman, R. A.; Lee, H.-N.; Ediger, M. D.; de Pablo, J. J. Heterogeneous dynamics during deformation of a polymer glass. Soft Matter 2010, 6 (2), 287−291. (21) Warren, M.; Rottler, J. Microscopic View of Accelerated Dynamics in Deformed Polymer Glasses. Phys. Rev. Lett. 2010, 104 (20), 205501. (22) Warren, M.; Rottler, J. Deformation-induced accelerated dynamics in polymer glasses. J. Chem. Phys. 2010, 133 (16), 164513. (23) Smessaert, A.; Rottler, J. Recovery of Polymer Glasses from Mechanical Perturbation. Macromolecules 2012, 45, 2928−2935. (24) Chen, K.; Schweizer, K. S. Molecular Theory of Physical Aging in Polymer Glasses. Phys. Rev. Lett. 2007, 98 (16), 167802. (25) Chen, K.; Schweizer, K. S. Microscopic Constitutive Equation Theory for the Nonlinear Mechanical Response of Polymer Glasses. Macromolecules 2008, 41 (15), 5908−5918. (26) Chen, K.; Schweizer, K. S. Theory of physical aging in polymer glasses. Phys. Rev. E 2008, 78 (3), 031802. (27) Chen, K.; Schweizer, K. S. Suppressed Segmental Relaxation as the Origin of Strain Hardening in Polymer Glasses. Phys. Rev. Lett. 2009, 102 (3), 038301. (28) Chen, K.; Saltzman, E. J.; Schweizer, K. S. Molecular Theories of Segmental Dynamics and Mechanical Response in Deeply Super-

confirmed by GPC measurements. Apparently such degradation has caused chain scission produced by the γ irradiation apparently can reduce the magnitude of elastic yielding, quantifiable in terms of the level of the retractive stress as well as the induction time for the emergence of the retractive stress. If we make the assumption that the γ irradiation does not affect intersegmental interactions and therefore does not reduce residual intersegmental stress, the observed effect of γ irradiation is consistent with the explanation that the emerging retractive stress is related to the residual chain tension of the load-bearing strands in the chain network. A competing explanation for the retractive stress is residual intersegmental forces. During the cold-drawing, packing at the segmental level is brought out of the initial state. Unloading only allows a partial return to the initial configuration. Upon annealing, the tendency to return to a less strained state shows up as a retractive stress. Although macroscopic tests reveal definitive molecular mechanism for the elastic yielding, it is instructive to learn from Figure 13a−c that cold-drawn specimens can still straighten up and show significant retractive stress after they have been intentionally bent by constraining their ends at a length 6.25% shorter.

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00238. Movie S1 (WMV)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (S.-Q.W.). *E-mail [email protected] (A.J.). ORCID

Shiwang Cheng: 0000-0001-7396-4407 Abraham Joy: 0000-0001-7781-3817 Shi-Qing Wang: 0000-0002-0572-7108 Author Contributions

P.L., Q.X., and S.C.: leading authors who have made equally important contributions in this work. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is in part supported by a grant from ACS-PRF (54047-ND7). Q.X. thanks Science Foundation of China No. 51505501 and Beijing Nova Program No. Z171100001117058 for the support. S.C. thanks the support from the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science & Engineering Division.

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