Directly Measuring the Complete Stress–Strain Response of Ultrathin

Article pubs.acs.org/Macromolecules

Directly Measuring the Complete Stress−Strain Response of Ultrathin Polymer Films Yujie Liu, Yu-Cheng Chen, Shelby Hutchens, Jimmy Lawrence, Todd Emrick, and Alfred J. Crosby* Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, United States S Supporting Information *

ABSTRACT: The inherently fragile nature of ultrathin polymer films presents difficulties to the measurement of their mechanical properties, which are of interest in packaging, electronics, separations, and other manufacturing fields. More fundamentally, the direct measurement of ultrathin film mechanical properties is necessary for understanding changes in intrinsic material properties at reduced size scales, for example, when the film thickness alters the equilibrium configuration of the polymer chains. We introduce a method for ultrathin film tensile testing that stretches a twodimensionally macroscopic, yet nanoscopically thin, polymer film on the surface of water. For polystyrene films, we observe a precipitous decrease in mechanical properties (Young’s modulus, strain at failure, and nominal stress at failure) for film thicknesses down to 15 nm, less than the characteristic size of an individual polymer chain, yielding new insights into the changes in polymer chain entanglements in confined states.

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strain increases as film thickness decreases below 40 nm. Si et al.29 used the dimensional contraction of crazes in polystyrene films to estimate the change in polymer entanglements as thickness decreases below 100 nm and extrapolated their predictions to suggest that the maximum stretch would increase for ultrathin films. These findings contradict the classical predictions and findings of Chan et al.,30 who used microdensiometry to investigate crazes in polystyrene films down to thicknesses of 110 nm. Given the importance of thin polymer glasses and the contradicting results of current indirect methods, a critical need exists for the direct measurement of mechanical properties in these materials.

INTRODUCTION Polymeric thin films find application ranging from environmental barriers in packaging1 to critical filter components in separations1,2 where thinner films can lead to cheaper material costs or higher volume production.3 Polymer glasses are often used in these applications due to their combination of processing ease and mechanical strength.4,5 Although performance gains could be significant for thinner films in many applications,1−5 limited fundamental understanding of materials property changes in these confined states has inhibited the ability to confidently engineer ultrathin polymer glasses. Numerous studies have focused on understanding transitions in the physical properties of dimensionally confined polymer glasses.6−18 Considerable attention has been placed on the glass transition temperature, Tg, as film thickness decreases below the polymer chain’s average conformational length,13,19−23 while much less attention has been placed on the mechanical properties in this limit. Measurements of the mechanical properties of thin films above Tg have been provided by novel techniques developed by McKenna and co-workers.24−27 These measurements require interpretation of the biaxial membrane stress from an applied inflation pressure; however, they provide clear trends with regards to many transitions in mechanical properties. Young’s modulus, E, is one of the few mechanical properties that has been measured far below Tg for thin polymer glasses; however, these studies, which relied upon indirect measurements of films, have contradicting results with E either increasing or decreasing with decreasing film thickness.7,9−12 Similarly, indirect methods have been used to measure how the nonlinear and failure properties, perhaps the most important for applications, change for ultrathin polymer glasses. Lee et al.28 used crack spacing in thin, elastomersupported films of polystyrene to suggest that the critical failure © XXXX American Chemical Society

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RESULTS AND DISCUSSION We introduce a new method, called the ultrathin film tensile (UFT) test (Figure 1), which permits, for the first time, measurement of the complete uniaxial stress−strain response of thin polymer glasses, as thin as 15 nm. UFT takes advantage of liquid supporting layers and a laser reflective cantilever to measure the stretching forces of films with macroscopic lateral dimensions in a gentle and stable manner. We use this device to investigate the changes in E as well as the failure stress and failure strain for polystyrene films ranging from 230 to 15 nm in thickness. These direct measurements allow us to determine that polystyrene thin films embrittle significantly in the thin film state, and we use these quantified changes to determine the change in load-bearing entanglements as polymer chains are confined in ultrathin films. These findings provide important contributions to the fundamental understanding of polymer Received: July 5, 2015 Revised: August 24, 2015

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DOI: 10.1021/acs.macromol.5b01473 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Ultrathin film tensile tester (UFT) and representative stress−strain responses. (a) Six polystyrene (PS) films of varying thicknesses stretching until break, each yields a stress−strain response. (b) Rectangular thin film of polydimethylsiloxane (PDMS) (9 μm in thickness, 2.2 cm in width, and 4 cm in length) on UFT. The image is taken under UV light and fluorescent dye (Coumarin 153) is added into the PDMS. (c) A schematic of UFT for ultrathin films. The capable testing film thickness hF is comparable to the bulk polymer chain end to end distance Ree.

Figure 2. Different material stress−strain responses of thin films (red circles) versus their bulk counterparts (black squares). Thin films are characterized by UFT, and their bulk counterparts are characterized by traditional tensile testing procedures. (a) Brittle polystyrene (PS). (b) Ductile polycarbonate (PC). (c) Rubbery polydimethylsiloxane (PDMS).

explore a wide range of materials, such as PC,31 where mechanical property transitions have been suggested. Future measurements on PC thin films could further investigate this transition. The UFT (Figure 1) quantifies the complete mechanical response of ultrathin polymer films under uniaxial tension. Representative results for measurements on polystyrene are provided in Figure 1a and in Figure S1 for polycarbonate and polydimethylsiloxane, including comparisons to ASTM measurements on bulk samples (Table S1). Our method stretches ultrathin polymer films as they rest on a water surface, similar to a method for stretching thin metal films.32 The films themselves are of macroscale size (∼cm2) in two dimensions, allowing the elastic energy contribution to dominate surface energy contributions due to the stretching of the ultrathin films (Figure S1). We note that liquid other than water, such as

glasses, while also providing a new measurement method that can be confidently applied to a wide range of dimensionally confined materials, including ductile polymers and elastomers, such as polycarbonate (PC) and polydimethylsiloxane (PDMS). Figure 2 illustrates the UFT’s sensitivity to linear and nonlinear responses, exemplified by the plastic deformation of PC (Figure 2b) and nonlinear elastic deformation of PDMS (Figure 2c). In the linear regime, Young’s modulus (E) values for films with thickness greater than the confinement length agree well with bulk values (Table S1), but for films thinner than the confinement length E decreases compared to the bulk (Figure 2a). The UFT method also allows nonlinear mechanisms, such as dissipative processes, to be quantified. For PC, we observe striking changes in the yield transition, likely associated with aging differences between the thin film and bulk samples. The versatility of this method allows us to B

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Figure 3. Agreement between experiments and finite element analysis (FEA). (a, b) Two representative sets of images from experiments and FEA, respectively, focusing on the upper left corner of the rectangular composite thin film (a, 50 nm thick, 0.3 μm wide, and 100 μm spaced QDs grids patterned on 4.5 μm thick, 2.2 cm wide and 4 cm long PDMS film). (a) Music and L-shaped markers indicate the same location on the film from unloaded to progressively strained states. Insets of the L-shaped marker have a length of 1.8 mm. (b) FEA results of the film under identical applied strains. (c) Comparison of measured strains (data points) at music marker locations to FEA calculated strains (solid lines). (d) Comparison of average measured strains (solid data points with error bars) at L-shaped marker locations, FEA determined strains (open data points), applied strains (red solid line), and calculated strains (the black solid line, for neo-Hookean strain energy function). The error bars denote standard deviation for five measurements. (e) Ratio of nominal modulus from the rectangular thin film boundary E′ and material input modulus E for both PS and PDMS as a function of sample aspect ratio (LF/WF) from FEA.

subtracting the cantilever displacement from the total displacement, allowing the strain in the x1 direction on the x1 plane, ε11, to be determined by ε11 = δF/LF, where LF is the initial film length before stretching. The nominal stress in the x1 direction acting on the x1 plane is σ11 = PF/(wFhF), where wF is the initial film width and hF is the initial film thickness. For the ultrathin samples used in the UFT, it is challenging to create samples with shapes that ensure a uniaxial state of stress, such as a dog-bone shape. However, a validation of the observed deformation response using finite element analysis (FEA) allows us to calculate a corrected Young’s modulus that accounts for the nonideal, rectangular sample geometry even in the case of finite deformations. We compare finite element (FE) predictions to kinematic measurements on specially designed films of PDMS (to allow for finite deformation) with flow-coated fluorescent nanoparticle (NP) grids38 incorporated into the near-surface layer (Figure 3 and Figure S4 for preparation details). The FEA results (parameters listed in the Supporting Information) and kinematic measurements show excellent agreement (Figure 3c,d). The FEA model is used to calculate the nominal Young’s modulus, E′, from the nominal stress at the film edge and the applied nominal strain. Figure 3e compares this calculated value to the model material’s intrinsic modulus, E, as a function of the film’s lateral aspect ratio, LF/WF. As expected, the difference between E′ and E increases as the film’s width becomes larger

glycerol, have been used and can provide benefits for future study.33−37 This macroscale dimension also permits the application of extremely small strains and strain rates, thus allowing a wide range of materials, including brittle ones, to be characterized in a precise manner. The UFT (real apparatus in Figure 1b and schematic in Figure 1c) utilizes the laser reflection from a displacing cantilever for force sensing (resolution ∼10 μN) and a linear actuator for applying displacement (resolution ∼48 nm). To mount the film into the tester, water is used to release the film from the substrate, leaving the film floating on the water surface that is raised through the addition of water until it contacts the two boundaries that act as grips (Movie S1). One grip, labeled as the clamp, is made from a silicon wafer and is rigidly connected to the liquid reservoir. The entire reservoir is translated by the linear actuator. The other grip is a long, reflective cantilever (aluminum coated cover glass), used to measure forces exerted on the film. The surfaces of both grips are coated with polystyrene (PS) to ensure sufficient adhesion between the boundaries and the film. The film stretches when the reservoir and fixed clamp translate a total displacement δT at constant velocity. Fixed strain rates were used (0.0033 s−1). Movement of the laser dot reflected from the cantilever determines deflection of the cantilever, δC, which is used to determine the applied load, PF (Figures S2 and S3 and Movie S2). The displacement in the film, δF, is calculated from C

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Macromolecules relative to its length. For the UFT samples described experimentally in this work, the average aspect ratio is unity, corresponding to a determined moduli ratio of approximately 1.06 for PS films. Modulus values plotted in Figure 5a have been corrected accordingly. The sensitivity and carefully controlled loading of thin films enabled by the UFT allow us to directly explore size-dependent mechanical properties for comparison with previous measurements and predictions. The stress−strain response until break for PS films ranging in thickness from 15 to 220 nm was measured (Figure 1a). The modulus, E, is observed to undergo a precipitous decrease as a function of film thickness starting at hF = 23 nm (Figure 5a). We note that this transition length scale is similar to that observed in size-dependent observations of Tg, which is near the representative size scale of the polymer chains in bulk materials (Ree = 25 nm, Ree is the end-to-end distance).20,39 Maximum strain ε11,Max and the maximum stress σ11,Max, which comprise the point of failure, decrease with decreasing PS thickness and show an increased rate of deterioration at hF = 38 nm (Figure 4b). (Vacuum annealing of the film above Tg of the thickest PS film had no influence on the stress−strain response (Figure S5).) The work to failure per unit cross-sectional area, W = LF∫ ε011,Maxσ11 dε11, is also found to decrease as thickness decreases (Figure 4c). Strikingly, the amount of energy required for failure decreases by more than 2 orders of magnitude, as compared to changes of a factor of 2 for the elastic modulus, for ultrathin films. Surface mobility theory states that polymer chains near a free surface, which have increased mobility, dictate the response of a polymer film as thickness decreases. The decrease in the modulus measured with the UFT is consistent with previous predictions from surface mobility theory19,20,39−42 for a polymer below Tg with the modulus being dictated by van der Waals interactions between neighboring chain segments. The strength of these interactions are proportional to the intersegmental distance. Thus, if a fraction of a polymer thin film (e.g., near the free surface) has increased intersegmental distance (associated with increased mobility), then the modulus of this film fraction will decrease. Volumetric scaling arguments, assuming a film composed of soft surface layers and a bulk-like midsection layer, have been shown to qualitatively describe this mechanism.13,19−21 Our modulus trend is consistent with these arguments.12 However, other researchers have noted the effect of molecular weight20,21,43,44 and supporting media33−37 on these transitions. Regardless, current surface mobility theory is insufficient to predict the precipitous decrease in ε11,Max we observe. Previous researchers have suggested that the surface mobility theory would be associated qualitatively with an increase in strain to failure for glassy films as thickness decreases.28,45 These studies relied upon indirect methods to support this prediction, while our direct measurement method contradicts these previous hypotheses and findings. We find that as the film thickness decreases the maximum strain and stress to failure decrease significantly. As argued previously,28 an increase in surface mobility could allow for chains near the surface to relax stresses, thus effectively blunting the concentration of stress near existing defects and allowing greater nominal strains to be achieved before ultimate failure. To investigate these mechanisms of stress relaxation or irreversible losses, we performed multiple load−unload cycles for the same thin film and measured the hysteresis, or loss energy, as the difference between strain energy stored and recovered with each cycle.

Figure 4. Mechanical property dependence on PS thickness. (a) Modulus E (red filled squares) versus PS thickness. Error bars denote standard deviations for five independent films. For thicknesses above 19 nm, each film has seven measurements (six measurements from cycling at small strains and one measurement from stretching until break). Blue open triangles are replotted from Figure 3 of ref 12. (b) Strain at break ε11,Max (black squares) and maximum stress σ11,Max (red circles) of PS films as a function of thickness. Error bars denote standard deviations for five independent films. (c) The work to failure per unit cross-sectional area W versus PS thickness. Error bars denote standard deviations for five independent films.

Over three cycles, PS demonstrates negligible hysteresis (Figure 5), indicating that the molecules with increased mobility in these thin films do not contribute to increased plastic losses, within the resolution of the UFT. Since plastic losses across the macroscopic film are negligible prior to failure, W can be considered to be approximately equal to the stored elastic energy in the film prior to failure. This failure energy decreases by more than a factor of 100 as the film thickness decreases. To explain this dramatic embrittlement of ultrathin films of polystyrene, we recall that polystyrene fails through the development and breakdown of crazes, which are networks of nanoscale fibrils. The stability of craze fibrils is controlled by the maximum stretch ratio of the molecular network: λ ∼ le/d0, where le is the contour length of the chain between entanglements and d0 is the characteristic size scale of D

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Therefore, the fraction of load bearing entangled chains scales as ϕe ∼ (Sf/Sf,0)2/3, where Sf,0 is the craze failure stress for bulk materials. Figure 6 shows the determined fraction of load

Figure 6. Fraction of interchain molecular entanglements, ϕe, as a function of confinement, h/Ree. The error bars denote standard deviations for five independent films.

bearing entangled chains, ϕe, as a function of normalized thickness, hF/Ree. Consistent with recent theoretical studies,49 as well as an experimental study29 that used indirect morphology data to determine the density of load bearing entanglements, we find that the number of interchain entanglements decreases significantly as thickness decreases. In support of scaling arguments put forward by DeGennes,50 as film thickness decreases, the statistical configuration of the chains within the film changes such that chains interact more with themselves rather than neighboring chains. As Si et al.29 describe, this configurational change results in fewer interchain entanglements (i.e., load bearing entanglements) and more intrachain entanglements, while their sum remains approximately constant. Therefore, the loss of interchain entanglements does not allow polymers to be strained further as others have proposed, but rather polymers become increasingly brittle.

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SUMMARY In summary, we utilized the newly developed UFT method to directly measure the size dependence of glassy, polymeric thin films of thickness on the order of an individual chain. We show that the UFT is capable of determining the complete uniaxial stress−strain relationship within confined molecular networks, including rubbery, ductile, and brittle polymers. For brittle polystyrene, we directly quantify the decrease in the elastic modulus as the film thickness decreases, and we provide the first direct measurements of the decrease in the stress and strain at failure with decreasing thickness. These changes in the failure properties provide direct confirmation of the decrease in interchain molecular entanglements as film thickness decreases. Our findings suggest a limit in the thickness of singlecomponent, glassy polymer films for flexible electronics and membrane applications due to significant decreases in mechanical robustness at length scales approaching Ree.

Figure 5. Hysteresis via cycling. (a) Schematic of hysteresis (solid blue area) from the cycle of load (red curve) and unload (black curve). A normalized hysteresis, H, is determined by H = [(∫ ε011,cycleσ11,L dε11,L) − ε ε (∫ 011,cycleσ11,Udε11,U)]/(∫ 011,cycleσ11,Ldε11,L). (b) Typical stress−strain response of three load and unload cycles (ε11,cycle = 0.4%, hf = 23 nm PS). (c) Normalized hysteresis H versus PS thickness. The error bars denote standard deviations for five independent films. The applied maximum strain for these cycling experiments was held approximately constant, with specific values provided in Figure S7.

the chain between entanglements in the nonstrained configuration.46,47 As proposed by Donald and Kramer,46 the breakdown of the craze fibrils is controlled by the true force exerted on the chains in the load bearing molecular network, f m, within the craze. For a first-order approximation, f m = πD02S/ (4ne), where S is the surface stress of the craze, D0 is the diameter of an unstrained cylinder of material that will form a craze fibril, and ne is the total number of effectively entangled chains per area of deformed craze fibril.46 D0 can be considered a material constant, and ne ≈ (π/24)ve,0ϕe3/2D04/d0, where ve,0 is the density of entangled chains in a thick film and ϕe is the fraction of entangled chains that participate in load sharing. If the craze fibril breaks down when f m ≥ f B, where f B is the force to break a backbone bond of a polymer chain (∼3 × 10−9 N for PS48), then the stress at failure is Sf ≈ (f Bve,0D02/6d0)ϕe3/2.

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EXPERIMENTAL SECTION

Materials. We demonstrate the UFT’s ability to characterize the full mechanical response of ultrathin films of three different polymers (Figure 1C−E): brittle PS (Polymer Source, weight-average molecular weight MW = 136 500 g/mol, polydispersity index (PDI) = 1.05), ductile polycarbonate (PC) (G.E., Lexan sheet, grade 103), and rubbery, cross-linked polydimethylsiloxane (PDMS) (Dow Corning, Sylgard 184). By selecting an appropriate cantilever bending stiffness, E

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ment divided by slope S1, while total displacement (δT) can be calculated from the translating actuator velocity multiplied time. As film displacement (δF) equaled the total displacement (δT) minus the cantilever displacement (δC), we determined the thin film strain (ε11 = δF/LF) by dividing film displacement (δF) by film length (LF). Similarly, force exerted on the film (PF) could be calculated from laser point pixel displacement divided by slope S2. From the PF, we determined the stress on the film, σ11, by dividing PF by the film width (WF) and film thickness (HF) (σ11 = PF/WFHF). We determined the cantilever stiffness (mN/μm) from these two cantilever calibrations and compare this measured stiffness to theoretical predicted stiffness by SC = PC/δC = 3ECIC/LC3, where SC is the theoretical predicted stiffness of the cantilever, PC is applied force on the cantilever (which equals PF), δC is cantilever displacement, EC is the cantilever modulus, IC = bh3/12 is the moment of inertia of the rectangular cantilever with b as the cantilever width and h as the cantilever thickness, and LC is cantilever length. Cantilever Choice. In our system, we controlled the total displacement. To accurately quantify displacement as well as force exerted on the film in our system, we chose a cantilever with stiffness typically 2 times the estimated stiffness of the thin film. The stiffness of the cantilever was tuned by shortening the cantilever length. The stiffness of the film (SF) was estimated by SF = WFHFEF/LF.

the UFT is capable of measuring a wide range of moduli (in this work, 0.3 MPa to 4 GPa). Solutions of PS in toluene, solutions of PC in dichloromethane, or PDMS were spun-cast onto substrates (glass or Si wafers) coated with sacrificial layers of poly(acrylic acid) (PAA) to prepare the films. We note that the use of a PAA sacrificial layer has not been shown to affect our measurements. We have confirmed this by floating films from a mica surface without a PAA sacrificial layer, and we noted no difference in our measurements. WF and LF were 22 mm and 30 mm (PS) or 22 mm and 40 mm (PC and PDMS), respectively, after film release and attachment to the UFT boundaries. The bulk counterparts of thin films (note: PS bulk is prepared from Aldrich, MW = 350 000 g/mol, PDI = 1.7) were prepared as 3 mm thick dog-bone-shaped samples without solvent (PS and PC follow ASTM D638, PDMS follows ASTM D1708) and stretched by a macroscale tensile tester (Instron, model 5500R). Floating Thin Polymer Films on Water. Thin polymer films were first cut into rectangular shape by a razor blade, and water was added along edges of the thin films. We waited until water dissolved the sacrificial layer and the thin film was floated completely (the film detached from the substrate) and then added water to the same level of the reservoir. The reservoir was an aluminum box with a clamp (a rectangular silicon wafer with dimension of 1 cm by 7 cm) fixed to the reservoir top by epoxy. Next, we utilized tweezers to position the thin film to align with the clamp, followed by adding water to raise the film and attach one end to the clamp. After one end of the film was attached to the clamp, we carefully placed the reservoir on the linear actuator stage and brought the other end of the film in contact with the cantilever (Figure 1c). Video Capture and Detection. The laser point was directed from a helium neon laser system (ThorLabs HGR005) at wavelength of 543 nm with beam diameter of 0.64 mm. Experiments were conducted after waiting 30 min for the laser system to warm up. Laser point movement was captured by a HD camcorder (Canon VIXIA HF R400) with resolution of 1920 × 1080 pixels. Frame rate was chosen to be 60 frames/s (fps) for stretching PS thin films and 30 fps for stretching PC and PDMS thin films. Images were extracted from videos at 30 fps for PS and 10 fps for PC and PDMS. As the intensity profile of the laser point followed a Gaussian distribution, we fitted the intensity profile to a Gaussian function, determined the maximum intensity pixel position, and quantified this position as the center of the laser point. The standard deviation of Gaussian function for the laser point was typically 7 pixels. In this case, to determine thin film strain, we classified the laser point movement by at least 10 pixels difference between two adjacent extracted laser point images. Then we determined the laser point pixel displacement as a function of time through the whole video (Figure S3). Incorporating the two calibrations of cantilevers (cantilever displacement to laser point movement, and cantilever applied load to laser point movement in Figure S4), we convert the pixel and time relationship to the stress and strain relationship (Figure S3). Cantilever Calibrations. Calibrations of the cantilever were conducted to relate pixel displacement (pixel) to known displacement (μm) and to relate pixel displacement (pixel) to known force (mN). A white screen was placed to reach maximum pixel displacement of the laser point when the cantilever bent under the maximum weight (estimated by 2EFε11HFWF (where EF is an initial estimated value for aligning laser path (usually EF = bulk material modulus) and ε11 = 2% for PS or 20% for PC or 60% for PDMS) was applied in the x1 direction. First, by applying known displacement in x1 direction to the cantilever, the pixel displacement on the white screen is determined. Second, by applying known weights (each weight was applied 5 times) in the x1 direction to the cantilever, the pixel displacement on the white screen was determined (Figure S4). Five different weights for each cantilever was used with 0 g as the minimum and with 2EF/ ε11HFWF as the maximum. The other three weights were chosen to be evenly distributed between minimum and maximum weights. Using image analysis, both calibrations of the cantilever were fitted to linear lines with intercepts equal to 0 (slope S1 for first calibration of pixel to μm and slope S2 for second calibration of pixel to mN). Cantilever displacement (δC) can be calculated from laser point pixel displace-

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01473. Figures S1−S6 and Table S1 (PDF) Movie S1 Movie S2

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (A.J.C.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank G. C. Evans, Y. Zhang, Z. H. Yang, and Y. Gong for help during the experiments. We acknowledge financial support from Center for Hierarchical Manufacturing, an NSF Nanoscale Science and Engineering Center (CMMI-1025020). J. Lawrence acknowledges financial support from Army Research Office (USA), W911NF-14-1-0185. We gratefully acknowledge useful conversations with J. Pham, D. R. King, D. Chen, and B. Davidovitch.

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REFERENCES

(1) Wang, H.; Keum, J. K.; Hiltner, A.; Baer, E.; Freeman, B.; Rozanski, A.; Galeski, A. Science 2009, 323, 757−760. (2) Lee, H.; Alcoutlabi, M.; Watson, J. V.; Zhang, X. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 349−357. (3) Rogers, J. A.; Bao, Z.; Baldwin, K.; Dodabalapur, A.; Crone, B.; Raju, V. R.; Kuck, V.; Katz, H.; Amundson, K.; Ewing, J.; Drzaic, P. Proc. Natl. Acad. Sci. U. S. A. 2001, 98, 4835−4840. (4) Duan, X.; Niu, C.; Sahi, V.; Chen, J.; Parce, J. W.; Empedocles, S.; Goldman, J. L. Nature 2003, 425, 274−278. (5) Cao, Q.; Kim, H.; Pimparkar, N.; Kulkarni, J. P.; Wang, C.; Shim, M.; Roy, K.; Alam, M. A.; Rogers, J. A. Nature 2008, 454, 495−500. (6) Lee, H.-N.; Paeng, K.; Swallen, S. F.; Ediger, M. D. Science (Washington, DC, U. S.) 2009, 323, 231−234. (7) O’Connell, P. A.; McKenna, G. B. Science 2005, 307, 1760−1763.

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DOI: 10.1021/acs.macromol.5b01473 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules (8) Yang, Z.; Fujii, Y.; Lee, F. K.; Lam, C.-H.; Tsui, O. K. C. Science 2010, 328, 1676−1679. (9) Stafford, C. M.; Harrison, C.; Beers, K. L.; Karim, A.; Amis, E. J.; Vanlandingham, M. R.; Kim, H.-C.; Volksen, W.; Miller, R. D.; Simonyi, E. E. Nat. Mater. 2004, 3, 545−550. (10) Huang, J.; Juszkiewicz, M.; de Jeu, W. H.; Cerda, E.; Emrick, T.; Menon, N.; Russell, T. P. Science 2007, 317, 650−653. (11) Tweedie, C. A.; Constantinides, G.; Lehman, K. E.; Brill, D. J.; Blackman, G. S.; Van Vliet, K. J. Adv. Mater. 2007, 19, 2540−2546. (12) Stafford, C. M.; Vogt, B. D.; Harrison, C.; April, R. V.; Re, V.; Recei, M.; June, V. Macromolecules 2006, 39, 5095−5099. (13) Ellison, C. J.; Torkelson, J. M. Nat. Mater. 2003, 2, 695−700. (14) Ngai, K. L.; Prevosto, D.; Grassia, L. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 214−224. (15) Connell, P. A. O.; Hutcheson, S. A.; McKenna, G. B. J. Polym. Sci., Part B: Polym. Phys. 2008, 46, 1952−1965. (16) Rowland, H. D.; King, W. P.; Pethica, J. B.; Cross, G. L. W. Science (Washington, DC, U. S.) 2008, 322, 720−724. (17) Gray, L. a G.; Roth, C. B. Soft Matter 2014, 10, 1572−1578. (18) Riggleman, R. A.; Yoshimoto, K.; Douglas, J. F.; De Pablo, J. J. Phys. Rev. Lett. 2006, 97, 1−4. (19) Gao, S.; Koh, Y. P.; Simon, S. L. Macromolecules 2013, 46, 562− 570. (20) Forrest, J.; Dalnoki-Veress, K.; Stevens, J.; Dutcher, J. Phys. Rev. Lett. 1996, 77, 2002−2005. (21) Pye, J. E.; Roth, C. B. Phys. Rev. Lett. 2011, 107, 235701. (22) Ngai, K. L. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 2980− 2995. (23) Prevosto, D.; Capaccioli, S.; Ngai, K. L. J. Chem. Phys. 2014, 140, 074903. (24) Xu, S.; O’Connell, P. A.; McKenna, G. B. J. Chem. Phys. 2010, 132, 184902. (25) Li, X.; Warzywoda, J.; Mckenna, G. B. Polymer 2014, 55, 4976− 4982. (26) Zhai, M.; McKenna, G. B. Polymer 2014, 55, 2725−2733. (27) O’Connell, P. A.; McKenna, G. B. J. Polym. Sci., Part B: Polym. Phys. 2009, 47, 2441−2448. (28) Lee, J.-H.; Chung, J. Y.; Stafford, C. M. ACS Macro Lett. 2012, 1, 122−126. (29) Si, L.; Massa, M. V.; Dalnoki-Veress, K.; Brown, H. R.; Jones, R. A. L. Phys. Rev. Lett. 2005, 94, 127801. (30) Chan, T.; Donald, A. M.; Kramer, E. J. J. Mater. Sci. 1981, 16, 676−686. (31) Soles, C. L.; Douglas, J. F.; Wu, W.; Dimeo, R. M. Phys. Rev. Lett. 2002, 88, 037401. (32) Kim, J.-H.; Nizami, A.; Hwangbo, Y.; Jang, B.; Lee, H.-J.; Woo, C.-S.; Hyun, S.; Kim, T.-S. Nat. Commun. 2013, 4, 2520. (33) Bodiguel, H.; Fretigny, C. Macromolecules 2007, 40, 7291−7298. (34) Bodiguel, H.; Fretigny, C. Phys. Rev. Lett. 2006, 97, 1−4. (35) Bodiguel, H.; Fretigny, C. Eur. Phys. J. E: Soft Matter Biol. Phys. 2006, 19, 185−193. (36) Wang, J.; McKenna, G. B. Macromolecules 2013, 46, 2485−2495. (37) Wang, J.; McKenna, G. B. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1343−1349. (38) Kim, H.; Lee, C.; Sudeep, P.; Emrick, T.; Crosby, A. J. Adv. Mater. 2010, 22, 4600−4604. (39) Forrest, J. A.; Dutcher, J. R. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1997, 56, 5705−5716. (40) Ellison, C. J.; Torkelson, J. M. Nat. Mater. 2003, 2, 695−700. (41) Fakhraai, Z.; Forrest, J. A. Science 2008, 319, 600−604. (42) Yang, Z.; Fujii, Y.; Lee, F. K.; Lam, C.-H.; Tsui, O. K. C. Science 2010, 328, 1676−1679. (43) Ellison, C. J.; Mundra, M. K.; Torkelson, J. M. Macromolecules 2005, 38, 1767−1778. (44) Torres, J. M.; Stafford, C. M.; Vogt, B. D. Polymer 2010, 51, 4211−4217. (45) Gurmessa, B.; Croll, A. Phys. Rev. Lett. 2013, 110, 074301. (46) Kramer, E. J. Adv. Polym. Sci. 1983, 52−53, 1−56. (47) Donald, A. M.; Kramer, E. J. Polymer 1982, 23, 461−465.

(48) Kausch, H.-H. Polymer Fracture; Springer: Berlin, 1978. (49) Sussman, D. M.; Tung, W.; Winey, K. I.; Schweizer, K. S.; Riggleman, R. A. Macromolecules 2014, 47, 6462−6472. (50) DeGennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979.

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DOI: 10.1021/acs.macromol.5b01473 Macromolecules XXXX, XXX, XXX−XXX