On the Necking Phenomenon in Pseudo-Semi-Interpenetrating

Aug 1, 2013 - salt (SAPS) and acrylamide (AAm) with different molecular weights. Uniaxial tensile tests for DN hydrogels already damaged by a compress...
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On the Necking Phenomenon in Pseudo-Semi-Interpenetrating Double-Network Hydrogels S. Shams Es-haghi, A. I. Leonov,* and R. A. Weiss* Department of Polymer Engineering, 250 S. Forge St., The University of Akron, Akron, Ohio 44325-0301, United States ABSTRACT: A detailed physical picture of necking phenomenon in semi-interpenetrating double-network (SIDN) hydrogels was developed using the tensile mechanics of DN hydrogels synthesized from 3-sulfopropyl acrylate potassium salt (SAPS) and acrylamide (AAm) with different molecular weights. Uniaxial tensile tests for DN hydrogels already damaged by a compression load demonstrated the necking required a first network with a brittle structure. Although necking originates from the brittle nature of the first network, the molecular weight of polymer chains of the second network is an important factor for neck propagation. The finite deformation of DN hydrogels is characterized by two regimes of deformation: one where the neck initiates and a second where it propagates.

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INTRODUCTION Hydrogels are hydrophilic polymeric networks that absorb large amounts of water but are insoluble. The network structure can be formed by chemical cross-links or physical cross-links due to electrostatic, hydrophobic, or dipole−dipole interactions.1 The similarity of hydrogels to biological tissues makes them attractive candidates for applications such as soft robotics, molecular filters, drug delivery, and tissue engineering.2 The main deficiency of hydrogels is their usually poor mechanical properties, which is due to their large water content.3 The problem of poor mechanical properties was resolved by Gong et al.,4 who developed a new generation of hydrogels based on interpenetrating networks of a soft neutral polymer network and a more highly cross-linked polyelectrolyte network that they termed a double-network (DN) hydrogel. DN hydrogels possess excellent strength and toughness, and a particularly notable characteristic of their mechanical behavior is that they exhibit necking in uniaxial tension. This was first reported by Na et al.,5 who purposely reduced the cross-link density of the polyelectrolyte network made from 2-acrylamido2-methylpropanesulfonic acid (AMPS). They concluded that very low, though finite cross-linking of the second, neutral network, in their case polyacrylamide (PAAm), was necessary for achieving necking. Semi-interpenetrating double-network (SIDN) hydrogels prepared with un-cross-linked AAm were fragile and did not show necking. Similar to the conclusions of Na et al.,5 Webber et al.6 reported that without reducing the cross-link density of the polyelectrolyte network DN hydrogels based on AMPS and AAm did not neck in tensile tests, though they speculated that necking might occur at higher strains. Kawauchi et al.,7 however, observed necking in a similar DN hydrogel without reducing the cross-link density of the polyelectrolyte network. In contrast to the report by Na et al.,5 Tanaka et al.8 reported that necking occurred with a SIDN hydrogel composed of linear polyacryamide (PAAm) in crosslinked AMPS. For each of the studies in refs 2−8 an AMPS/ © XXXX American Chemical Society

AAm DN formulation was used, and the networks were prepared by long-term exposure (7−10 h) to UV radiation. However, none of the studies reported the intensity of the radiation used. Also, for reasons that will be explained below, it is doubtful that either Kawauchi et al.7 or Tanaka et al.8 actually made SIDN hydrogels containing free PAAm chains. Rather, it is more likely that at least some of the PAAm chains were covalently grafted to the AMPS network. Myung et al.9 and Waters et al.10 independently studied the mechanical properties of DN hydrogels made from poly(ethylene glycol) as the first, rigid network and poly(acrylic acid) as the second, soft network using short-time (5 min) photopolymerization with a light intensity of 10 mW/cm2. The construction of those DNs was opposite of the conventional DNs reported by Gong and her co-workers in that the polyelectrolyte network in the latter was always the more highly cross-linked, rigid network and the neutral network was the soft network. Myung et al.9 did not report necking in their tensile tests, and Waters et al.10 only measured the compressive behavior of their gels. Brown11 and Tanaka3 have independently proposed simple phenomenological models to explain the extraordinary toughness and high fracture energy of DN hydrogels, but neither of these models addresses the origin of necking and why necking occurs in some DN hydrogels. It is also important to note that both authors were considering interpenetrating polymer network (IPN) hydrogels as originally reported by Gong et al.,4 but which is now known not to be the correct structure of those materials.12 Therefore, the physics underlying the necking phenomenon is still not well understood, and as demonstrated by the literature cited in the previous paragraphs, there are Received: April 10, 2013 Revised: July 12, 2013

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immersed in deionized water, which was replaced a number of times with fresh water to remove any unreacted monomer. Two UV intensities, 15 and 3 mW/cm2, were used for the photopolymerization reactions, and the radiation exposure times for each intensity was 10 min (dose = 9 J/cm2) and 9 h (dose = 97 J/cm2), respectively. The sample notation contains the information about the recipes used for the synthesis of the different networks. Each individual network is described by the name of the monomer used, followed by four numbers in parentheses that indicate (1) the molar concentration of monomer in deionized water, (2) the mol % of photoinitiator with respect to monomer, (3) the mol % of cross-linking agent with respect to monomer, and (4) UV dose used for the reaction (i.e., intensity × time of exposure). Thus, SAPS(1,4,2,9) corresponds to the polymerization of a 1 M SAPS solution using 4 mol % OXGA, 2 mol % MBAA, and a UV dose of 9 J/cm2. The first networks were prepared by keeping the concentration of the cross-linking agent constant (2 mol % MBAA with respect to the monomer) and varying the photoinitiator concentration (1 and 4 mol % OXGA with respect to the monomer) and photopolymerization conditions (UV intensity and radiation time). In refs 2−8 tough DN hydrogels were prepared by long radiation times (at least 17 h). In this study, the procedure for preparing tough gels was reduced to 9 h by increasing the dose rate for the synthesis of the first network. Polymer Characterization. Fourier transform infrared (FTIR) spectroscopy was used to determine if residual unsaturation remained in the first network after UV curing. A Nicolet 380 FTIR spectrometer was used with 32 scans and a resolution of 4 cm−1. Samples were washed at least five times with deionized water to remove any unreacted monomer and then dried before the FTIR measurements. Dilute solution viscosity (DSV) was used to estimate the molecular weight of the polymer chains in the second network. This was done by separately polymerizing neat poly(acrylamide), PAAm, using the same reaction conditions used to prepare the DNs and assuming that the presence of the SAPS network had negligible effect on the polymerization of AAm. The intrinsic viscosity, [η], of the neat PAAm solutions in water was measured at 30 °C using a Ubbelohde capillary viscometer, and the viscosity average molecular weight, Mv, was calculated using the Mark−Houwink equation

some inconsistencies among the various experimental observations. The objective of the work described in this paper was to better understand the physics of necking in DN hydrogels, specifically those where no cross-linking agent was used in the second polymerization step, and develop a physical picture to explain this phenomenon. The experiments indicate that the mechanical properties of DN hydrogels are controlled by the topological characteristics, e.g., cross-link density, of the first network and the molecular weight of the second, interpenetrating network. It is important to note that DN hydrogels that have already been damaged by a compressive load do not exhibit necking upon tension. That observation leads to a conclusion that a brittle network must be present for necking to occur in DN hydrogels. In fact, the necking phenomenon in DN hydrogels is a consequence of the damage to the first network during a tensile deformation, and necking occurs at the onset of the load transfer from the first network to the second one.

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EXPERIMENTAL SECTION

Materials. 3-Sulfopropyl acrylate potassium salt (SAPS) and AAm were purchased from Sigma-Aldrich Chemical Co. and used as received. The cross-linking agent N,N′-methylenebis(acrylamide) (MBAA) was purchased from Sigma-Aldrich Chemical Co. and was recrystallized from ethanol. A photoinitiator, 2-oxoglutaric acid (OXGA), was obtained from Fluka Chemical Co. and used as received. Synthesis of Polymeric Networks. DN hydrogels were synthesized by a two-step sequential free-radical polymerization. The first network was prepared by adding OXGA and MBAA to a 1 M solution of SAPS in deionized water. Dry nitrogen gas was bubbled through the reaction mixture for 5−10 min to remove oxygen, and the solution was injected into a glass mold made of two parallel glass slides, which was then exposed to a 365 nm ultraviolet (UV) light source (see Scheme 1). The resulting SAPS gel was then immersed

[η] = KM v a

Scheme 1. Synthesis of SAPS Network

(1) −2

where K = 0.65 × 10 and a = 0.82. Tensile Testing. Uniaxial tensile tests were performed with an Instron 5567 universal testing machine equipped with a 100 N load cell, using a constant crosshead speed of 50 mm/min at room temperature. Rectangular samples with length = 40 mm, width = 10 mm, thickness = 2−3 mm, and a gauge length of 30 mm were used. Sandpaper was used to prevent slippage of the samples in the grips. The tensile data are reported as engineering stress versus stretch ratio, where the engineering stress, σe, was obtained by dividing the force by the original cross-sectional area of the specimen and the stretch ratio, λ ≡ L(t)/Lo, where L(t) was the instantaneous sample length and Lo was the original sample length. Note that λ = εe + 1, where εe is the engineering tensile strain. 13

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RESULTS AND DISCUSSION The free-radical synthesis of cross-linked acrylic polymers, such as shown in Scheme 1, generally produces inhomogeneous networks as a consequence of undesirable side reactions, such as cyclization,14 which forms internally cross-linked structures that can trap some double bonds of the cross-linking species. As a result, the ability of the double bonds to react with other monomers is reduced or completely suppressed.15 Figure 1 shows the FTIR spectra of SAPS(1,4,2,9) and a DN of SAPS(1,4,2,9) and AAm prepared as described in the Experimental Section. The −CC− absorption band at ∼1650 cm−1 in the SAPS(1,4,2,9) spectrum (blue curve in Figure 1) is due to residual CC unsaturation, which is consistent with the

into a 2 M solution of AAm in deionized water containing the photoinitiator, which had already been deoxygenated with N2 gas, until an equilibrium swelling was achieved. The AAm-swollen SAPS gel was then placed between two parallel glass slides and exposed to 365 nm UV light (see Scheme 2). The resulting DN hydrogel sample was

Scheme 2. Synthesis of Poly(acrylamide) Network

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the subtraction, since the double bonds would comprise only a small amount of the absorption in the region of 1650 cm−1 for the difference spectrum. A more detailed study, preferably using a second monomer where there is no overlapping absorptions with the IR bands for the CC, is needed. The hydrogels made in this study used a procedure similar to that used by Na et al.5 and Tanaka et al.8 to prepare SIDNs, where linear PAAm was supposedly formed within a polyelectrolyte network. However, as shown by the infrared results, it is probable that during the free-radical polymerization of AAm, PAAm is grafted to the residual double bonds in the SAPS network, such that the some or all of the PAAm chains are actually chemical-bonded to the SAPS network and not simply unattached homopolymer. That possibility was recently evaluated by Nakajima et al.,12 who claimed that a “true” SIDN of PAMPS and PAAm, where the residual unsaturation of the PAMPS was eliminated prior to the polymerization of AAm, had poor mechanical properties compared with the materials that were previously reported as SIDNs.5,7,8 It should be noted, however, that no proof was offered by Nakajima et al.12 that they succeeded in eliminating all the double bonds in their first network in the preparation of their true SIDNs. During the synthesis of the linear PAAm chains in the previous work, PAAm grafts to the AMPS network, by either initiating the polymerization at the residual unsaturation in the latter or terminating the growing chain by reaction with the double bonds in the AMPS network. As a result, the product of the polymerization of the AAm is not exclusively free linear chains, but more probably a mixture of linear chains, grafted chains with free ends and grafted chains that are cross-links (i.e., both ends of the chain are bonded to the AMPS network). In fact, the concept of the strong, tough DN being an IPN is also brought into question by the paper by Nakajima et al.12 The properties of a true interpenetrating DN (t-DN) prepared in a way similar to that of the true SIDN described above, except that a multifunctional monomer was added in the second network synthesis, were very different from those of what the authors called a “connected double network” (c-DN). In a c-DN the second network is presumably attached to the first network through grafting reactions involving the residual unsaturation from the synthesis of the first network. When the concentration of the cross-linking monomer used in the second polymerization was below some critical value, the toughness of a c-DN was higher than that of a t-DN, but above some critical cross-linker concentration, the toughness of the t-DN improved remarkably. It is clear from the paper by Nakajima et al.12 that the c-DNs, i.e., the original DNs described by Gong et al.,4 have a more complicated microstructure than previously thought, and the mechanisms of toughening previously proposed11,16 need to be revisited and revised to account for the connectivity of the two networks. Actually, for the case where all the PAAm chains are cross-linked and attached to the PAMPs network, there is only one cross-linked network, though it has two types of network chains that differ in chemistry and probably molecular weight. Based on spectra in Figure 1, the hydrogels discussed in the current paper were assumed to have a microstructure similar to pseudo-SIDNs discussed above; so to be consistent with the nomenclature defined in ref 12, these materials will be denoted c-DNs. It is important to note, however, that ref 12 did not distinguish between a pseudo-SIDN and a pseudo-interpenetrating DN in the definition of c-DN, though they did describe the effect on fracture toughness of changing the cross-

Figure 1. FTIR spectra: (blue) SAPS(1,4,2,9); (green) SAPS/AAm DN prepared from SAPS(1,4,2,9); (red) difference spectrum of SAPS(1,4,2,9) minus DN.

hypothesis of Nakajima et al.12 that some double bonds remained after the polymerization of AMPS networks. Some unsaturation was observed for all the first SAPS networks used to prepare the DN hydrogels discussed in the current paper. This result indicates that all the previous DN’s prepared in the literature are most likely not the independent interpenetrating networks as was first proposed by Gong et al.4 and later questioned by Nakajima et al.12 Given that in preparing a DN the second network is synthesized in the presence of residual carbon−carbon double bonds, it is most likely that all of the DNs heretofore reported in the literature were single networks with two different chemistries of cross-links and, perhaps, some second network interpenetrating network. The single network with two cross-link chemistries arises from initiation at the residual unsaturation of the first network or termination of a second network at the unsaturation of the first network. The interpenetrating network would occur if chains of the second network did not react with the first network. Unfortunately, resolution of the structure of those networks is not likely to be easy. For the DN prepared in this study evidence for the grafting reaction would be the disappearance of the residual double bonds in the first network (SAPS) after the polymerization of the acrylamide. That, however, is not straightforward, since the PAAm that is produced by the second polymerization absorbs in the infrared in the same region as the unsaturation in the SAPS. An attempt at the determining if the double bonds persisted or disappeared following the second polymerization was made by subtracting the spectrum of the final DN from that for the first (SAPS) network with the residual double bonds. This is shown by the red curve in Figure 1. In performing the subtraction, the absorption at 1038 cm−1, which is due to the symmetric stretching of the S−O bond in the sulfonate anion and/or the C−O stretch of the ester, both of which are absent in PAAm, was normalized for the SAPS and DN spectra before the subtraction. That procedure should produce a negative absorption spectrum of only polyacrylamide and any remaining double bonds. The difference spectrum only shows IR absorption bands for PAAm. The unsaturation band at 1650 cm−1 appears to have disappeared, which is consistent with the double bonds participating in the second polymerization to produce grafted chains of PAAm. We hesitate to offer this as absolute proof of the hypothesis of grafted chains. One caveat is the precision of C

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chains (black circles) showed necking in tension (see inset figure) while the one made with the lower molecular weight PAAm (red circles) failed in a brittle fashion. For the lower stretch ratios, the tensile data for the two different c-DN hydrogels, SAPS(1,4,2,9)/AAm(2,0.1,0,97) and SAPS(1,4,2,9)/AAm(2,0.1,0,9), coincided. The common feature of the two c-DNs was that the first network of each was the same. Therefore, it is tempting to attribute the occurrence of necking to the higher molecular weight PAAm chains. The blue points in Figure 2 represent an experiment where the SAPS(1,4,2,9)/AAm(2,0.1,0,97) c-DN, i.e., the sample that showed necking in Figure 2, was first damaged by a compression load of 10 kN and then subjected to a tensile test. The disappearance of necking following the destruction of the first network prior to stretching indicates that the necking phenomenon is related to the brittle structure of the first network. Presumably, after damaging the first network by compression loading, the contribution of the broken brittle network to the mechanical behavior of the material becomes negligible, and the PAAm chains must carry the load. If one assumes that the mechanical contributions of the first and second networks of the c-DN hydrogel are additive, it is possible to estimate the brittle behavior of the first network by subtracting the tensile curve of the predamaged sample from that of the virgin c-DN. That amounts to calculating the tensile response of SAPS(1,4,2,9) by subtracting the blue data from the black data in Figure 2. The result is represented by the green curve in Figure 2, which agrees extraordinarily well with the tensile data for the SAPS(1,4,2,9)/AAm(2,0.1,0,9) c-DN hydrogel (the red points) that showed brittle behavior. That analysis leads to the conclusion that the lower molecular weight PAAm (AAm(2,0.1,0,9)) provided no mechanical contribution to the behavior of the SAPS(1,4,2,9)/AAm(2,0.1,0,9) c-DN hydrogel. Once the first network, SAPS(1,4,2,9), broke, the cDN hydrogel failed catastrophically. The results in Figure 2 indicate that both networks play a role in determining whether necking occurs, and this conclusion may explain some of the contradictions reported in the literature with regard to necking in c-DN hydrogels. A necessary, but insufficient, criterion for necking is that the first network be fragile. However, it is also critical that interpenetrating polymer chains, building blocks of the second network, have sufficient molecular weight to get highly entangled in the skeleton of the first network and therefore be able to maintain the integrity of the structure after necking. In effect, the highly entangled structure of the c-DN hydrogel due to high molecular weight of PAAm chains provides the ductility needed for necking. When a c-DN hydrogel is subjected to a tensile load, the first network that serves as the skeleton for the c-DN becomes the load-bearing component and is extended. Because of its brittle nature, however, it undergoes a damage process (first regime of deformation) during which a critical point is reached where the second network assumes the load-bearing role (Figure 3). At this point, a neck appears in the sample, and a second regime of deformation with a more complicated damage process occurs, including chain scission, disentanglement, and chain sliding. The extent of this second regime, i.e., the ultimate extension ratio, depends on the entanglement density of the second network chains into the first network. When the cross-link density of the first network is substantially increased, a tensile deformation produces catastrophic failure of the first network. If the second network is not able to maintain the integrity of

linker concentration of the second network, including no crosslinking (see discussion above). In the rest of this paper the term c-DN is used exclusively to describe a pseudo-SIDN, i.e., where no cross-linking agent was used in the synthesis of the second polymer. The SAPS gel used herein is a polyelectrolyte threedimensional network, and the second polymerization step produces PAAm homopolymer (no cross-linking agent was used) that is, at least partially, covalently bonded to the SAPS network. The key difference in the materials that are discussed herein was the formulation of the PAAm, where the UV dose was varied to produce polymers with different molecular weight. The PAAm chains appeared to be trapped within the SAPS network as a consequence of kinetic effects, e.g., molecular entanglements and/or grafting to the SAPS network. That assumption was supported by the fact that no PAAm was extracted by soaking the c-DN samples in distilled, deionized water for as long as 14 days, which indicates a high degree of connectivity of the two polymers. The characterization of the molecular weight of the PAAm in the c-DN was not possible with the facilities available, but ex situ polymerization of neat AAm using the same photopolymerization conditions was used to prepare the c-DN’s produced linear polymers with viscosity average molecular weights of 678 000 and 1 648 000 g mol−1 for UV doses of 9 and 97 J/cm2, respectively. Hereafter, we refer to the interpenetrated PAAm as the second network, though it may be a physical network formed strictly from molecular entanglements, of long PAAm chains grafted to the SAPS network. The SAPS single networks were brittle regardless of what recipe was used. The samples broke in the grips, and it was not possible to measure their tensile properties. As will be discussed later in this paper, the brittle character of the first network is important with regard to developing necking of the c-DN hydrogels in tension, and the properties of the brittle SAPS network can be extracted from the tensile data of the c-DN hydrogel. The mechanical behavior of c-DN hydrogels made using SAPS(1,4,2,9) as the first network and the two different AAm polymerizations for the c-DNs are compared in Figure 2. The cDN hydrogel prepared with the higher molecular weight PAAm

Figure 2. Engineering tensile stress versus stretch ratio for c-DN hydrogels made of SAPS(1,4,2,9) as the first network. Black circles: virgin SAPS(1,4,2,9)/AAm(2,0.1,0,97) c-DN hydrogel; blue circles: SAPS(1,4,2,9)/AAm(2,0.1,0,97) c-DN hydrogel predamaged with a compression load; red circles: virgin SAPS(1,4,2,9)/AAm(2,0.1,0,9) cDN hydrogel; green curve: subtraction of the blue data from the black data (see explanation in text). D

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Figure 3. Schematic representation of onset of necking in a c-DN hydrogel. The blue network represents the first network, and red polymer chains are the components of the second network. At the onset of necking, the first network fails to carry the load and the second one assumes the loadbearing role.

AAm(2,0.1,0,97) c-DN hydrogel are also shown in Figure 4. The hysteresis associated with this experiment represents the extent of damage in the first network during the first regime of deformation. The area between the red and green curves is much smaller than the hysteresis associated with the damage of the entire hydrogel, which indicates that the damage during the second regime of deformation is more extensive than that in the first regime, which is primarily responsible for the exceptional toughness of c-DN hydrogels. The low work of deformation in the first regime of deformation indicates that during this regime the first network is not completely damaged. It is sufficiently damaged, however, that it is no longer able to support the load. The remainder of the first network is damaged during the second regime of deformation. When a very low extension rate is used in a tensile test of a cDN hydrogel, a significant amount of water may evaporate from the sample during the experiment. If enough water evaporates, the sample may actually vitrify and freeze-in extended conformations of the network chains. However, the sample recovers when rehydrated and with very low residual strain from the extension of the PAAm chains at high strains. Vitrification may also occur if the extension rate is high if the sample is held in a highly extended state until all the water evaporates. The recovery of the dried damaged sample by rehydration is similar to the forced elasticity exhibited by semicrystalline polymers in that a necked semicrystalline polymer heated to a temperature above the glass transition, but below the melting point, exhibits nearly complete recovery.17 In fact, for c-DN hydrogels the role of water concentration is analogous to the effect of temperature in semicrystalline polymers.

the sample, the sample fails, which is what was observed for the c-DN hydrogels made from SAPS(1,4,2,97). Figure 4 shows the tensile behavior of the SAPS(1,1,2,9)/ AAm(2,0.1,0,97) c-DN hydrogel. The black points represent

Figure 4. Engineering tensile stress versus stretch ratio for SAPS(1,1,2,9)/AAm(2,0.1,0,97). Black circles: virgin SAPS(1,1,2,9)/ AAm(2,0.1,0,97); blue circles: reloading of damaged sample; red circles: loading up to onset of necking; green circles: unloading before onset of necking.

the result for the virgin sample, which clearly shows the yielding behavior associated with necking and the strain-hardening response of the c-DN hydrogel. The blue symbols represent the tensile behavior of a sample that was first deformed up to the failure point, but the deformation was halted prior to failure. The shape of this tensile curve is similar to that of an elastomer, and in fact, this was characteristic of the reloading of every cDN hydrogel that exhibited necking after it was damaged by stretching to the second regime of deformation. The same rubber-like stress−deformation curve can also be achieved by unloading the virgin sample prior to failure, which is approximated by the dashed blue curve shown in Figure 4. The results of these two experiments would be expected to coincide if the reloaded sample could sustain stress up to high stretch ratio originally used. The area between the black and blue curves is the amount of energy per unit volume that was dissipated by the damage to the virgin c-DN hydrogel. Hysteresis in the loading and unloading experiments of c-DN hydrogels is a consequence of damage to the internal structure of the c-DN. This was first reported by Webber et al.6 for compression and tensile testing of c-DN hydrogels made of PAMPS and PAAm, but they did not observe necking in their tensile experiments. Loading (red circles) and unloading (green circles) tensile data prior to necking for the SAPS(1,1,2,9)/

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CONCLUSION Most, if not all, interpenetrating polymer network (IPN) hydrogels, so-called double network hydrogels, are actually what ref 12 refers to as connected double network hydrogels, cDNs. c-DNs are prepared by two polymerizations of two distinct polymer networks, but rather than producing two unattached, but intertwined polymer networks, the two networks in a c-DN are connected by covalent bonds. Even when no cross-linking agent is used in the synthesis of the second network (i.e., to make a semi-interpenetrating doublenetwork (SIDN)), the homopolymer chains produced chemically attach to the first network by free-radical reaction involving residual double bonds that are present in product of the polymerization of the first network. The presence of a brittle network is necessary to observe necking in c-DN hydrogels. In effect, the necking phenomenon in c-DN hydrogels is triggered by the damage of the first E

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network, and necking occurs at the onset of load transfer from the first network to the second one. The ability of second network to assume the load bearing role which is necessary for neck propagation is highly dependent on the extent of molecular entanglements between the two networks. Therefore, the molecular weight of interpenetrating polymer chains of second network is a crucial factor for neck propagation. The onset of necking is also the demarcation of two regimes of deformation with different damage intensities. The first regime of deformation is related to the damage of the first network, and the second one is associated with the damage during neck propagation. At the end of second regime of deformation (end of strain hardening prior to failure), the sample shows rubberlike behavior which can be identified either by unloading a sample prior to failure or reloading a sample which has been damaged by a tensile deformation.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (R.A.W.); [email protected] (A.I.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by a grant from the Engineering Directorate of the National Science Foundation, CMI-1300212. REFERENCES

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