Nonlinear Viscoelastic Behavior and Chain Entanglement Network

Sep 10, 2013 - filler−polymer matrix is studied from the nonlinear viscoelastic behavior of an ..... which is important for potential injectable ela...
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Dynamics of Silica-Nanoparticle-Filled Hybrid Hydrogels: Nonlinear Viscoelastic Behavior and Chain Entanglement Network Jun Yang* and Chun-Rui Han College of Materials Science and Technology, Beijing Forestry University, Beijing, China S Supporting Information *

ABSTRACT: The understanding of nanoscale fillers in polymeric materials is of the utmost importance for the performance of elastomers. The dynamics of a filler−polymer matrix is studied from the nonlinear viscoelastic behavior of an entangled composite’s network by using silica nanoparticle (SNP)/poly(acrylamide) (PAM) as a model, which allows us to elucidate the nature of the filler association and its role in the nonlinear viscoelastic properties at large strain amplitudes, termed as the Payne effect. The systems show reduced elastic modulus and turn flowable behavior at sufficiently high strains, then partially recover upon switching to a small strain. The Payne effect seem to be timedependent and is affected by the filler network’s reversible breakdown and rearrangement. This nonlinear viscoelastic property, in particular the decrease of modulus at high strain amplitude, is interpreted to be a reason for the breakdown of the filler network. The greater reinforcement for nanocomposites indicates the filler association through chain immobilization on bridging. The concept of a layer of “glassy bridge” is used to demystify the interparticle connection and correlates it to the Payne effect. The SNP-filled nanocomposite’s reinforcement mechanisms include the plasticization of glassy-layer-bridging neighboring clusters, trapped entanglement at the filler−polymer interface, and polymer chains dynamic adsorption−desorption transformation. the filler’s surface, and polymer chain topological entanglement. Besides, the state of filler dispersion plays a critical role in determining the nonlinear viscoelastic behavior of nanocomposites, where the surface chemistry of filler particles and filler−polymer compatibility dominate filler distribution and the level of reinforcement.14,15 Recently, intensive experimental studies on the glassy transition of confined polymers have proposed that elastic modulus reinforcement stems from an interfacial layer around the filler surface, and the Payne effect is ascribed to the formation of the shear-induced melting of the glassy layer.16−18 By using the silica nanoparticle (SNP)/polymer-based cluster−cluster interconnection model, we have shown a facile fabrication platform for tough and stretchable nanocomposite hydrogels in the absence of chemical cross-linkers (e.g., N,N′methylenebisacrylamide).19−23 It was found that strong interactions between SNP and poly(acrylamide) (PAM) affected the modulus of nanocomposites, and the nature of the constrained polymer region in the SNP/polymer cluster correlated to the reinforcement mechanism.22,23 The mechanical reinforcement of SNP/polymer systems was attributed to the SNP surface-tethered polymer chains that were well mixed with the polymer matrix, leading to an extensive glassy boundary region. It is universally accepted that the filler−

1. INTRODUCTION The reinforcement of nanocomposites by inorganic particles, a widely applied technology to fabricate high-performance materials due to the presence of a partially aggregated filler network, has attracted increasing interest in the past decade.1−3 In particular, the reinforcement by the dispersion of solid fillers into an elastomer is a well-known method to enhance mechanical properties, which is attributed to the hydrodynamical interaction, as well as a modification of chain dynamics.4,5 The addition of filler particles would affect the polymer chain’s mobility in the vicinity of the filler surface; that is, the fillers would act as a solid core with a soft shell and would disperse in the even softer matrix. Upon incorporation of fillers, the nanocomposite’s reinforcement is often reflected by the increased elastic modulus beyond the pristine polymer.6−8 The phenomenon for the drop of storage modulus G′ with increasing oscillatory strain amplitude, termed as the Payne effect (strain softening), has long been recognized in polymer science and engineering.9,10 It has been reported that the dispersion of the filler affects the amplitude of the Payne effect, and the distance between particles is a critical parameter to alter the polymer chain’s dynamic and the mechanical properties of nanocomposites.11,12 The popular explanation of the filler reinforcement and strain softening is based on the filler−filler interaction during the preparation of nanocomposite and the breakdown of the filler network at high strain amplitudes.13 For polymeric nanocomposites, filler−filler interaction may arise from polymer chain bridging, adsorption of polymer chains on © 2013 American Chemical Society

Received: May 9, 2013 Revised: August 26, 2013 Published: September 10, 2013 20236

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polymer interactions dictate the filler’s surface coverage and the level of adsorption of polymer chains on the filler surface.18 The adsorption of PAM chains onto the filler surface promoted the formation of a monolayer of shell outside of the fillers, where the thickness of the layer was determined by the graft density, the molecular weight of polymer chains, and the state of adsorption.21−23 Additionally, it has been shown that the introduction of SNP into the PAM matrix could lead to the formation of a glassy layer, so-called interphase, in the vicinity of the filler surface, resulting in the enhanced Young’s modulus.23 In fact, there has been increasing evidence of the formation of a glassy polymer layer at the interface with the fillers.24,25 Since the thickness of this rigid layer shell can be the comparable order of magnitude of the filler particles, a local region of improved strength and a consequent retarding of growth of the craze is rationally expected.26 According to Gersappe’s molecular dynamics simulations on nanoscale particle-filled polymers, it has been proposed that the role of nanofiller is not only limited to its rigid properties but also to its ability to dissipate energy when stretching occurred,27 which was consistent with the viscoelastic behavior in our SNP-filled elastomers. While polymer nanocomposites have been widely explored in efforts to fabricate materials with mechanical properties superior to those of pristine polymers, the fundamental origins of the reinforcement mechanism have remained elusive. The SNPs were dispersed throughout the polymeric matrix, and immobilization of PAM on the SNP surface within the polymer matrix has been observed in our recent work through dielectric relaxation experiments,23 where the thickness of the immobilized interfacial layer was found to be 2−10 nm between fillers. We can make an assumption of the existence of an entanglement network that is supported by swelling behaviors of nanocomposites with water, which is a good solvent. It was noted that the materials swelled but did not dissolve after several weeks, even though the solvent was replaced every day, suggesting the existence of an elastic cross-linked network.19−21 In this perspective, the combined results from TEM observation giving access to morphological information on the filler’s dispersion, rheometry experiments enabling the examination of the Payne effect at strain and cyclic loading− unloading measurements providing the correlated energy dissipation, the aim of this paper is to delineate the correlation between the dispersion of particles and polymer chain’s dynamic modification, as well as to examine if the constrained chains on filler’s surface relates to the Payne effect. The results indicate that the presence of immobilized layer on filler surface acts as a “bridge” to dominate the elastic modulus, and the addition of nanoparticles affects the entanglement networks, where the particles act as entanglement attractors and change the topological constraint in the composites. Substantially, the SNP-filled elastomers here can be used as a model to shed some light regarding the origin of the nonlinear viscoelasticity and to demystify the filler−polymer interactions.

process. The surface coverage by organosilane was 9 wt% by thermogravimetric analysis. The elastomers containing grafted silica nanoparticles dispersed in a poly(acrylamide) matrix and all the samples applied here are the same as the samples used in our previous work.23 The synthesis process was similar to previous work,19−21 and the main characteristics of the nanocomposites are listed in Table 1. The dispersion state of Table 1. Compositions and Characteristics of SNP-Filled Nanocomposite Preparation sample code SNP SNP SNP SNP SNP CCa

0.05-a 0.05-b 0.05-c 0.1 0.15

SNP (mg)

AM (g)

water (g)

APS (mg)

Mw (10−4)

PDI

5 5 5 10 15

2.5 2.5 2.5 2.5 2.5 2.5

10 10 10 10 10 10

28 34 52 36 45 20

2.68 4.89 6.05 2.74 2.57

1.81 1.72 1.92 1.65 1.57

Vc (%) 0.86

1.65 3.32

a

Chemically cross-linked polymer matrix by N,N′-methylenebisacrylamide (50 mg) as control.

filler particles in the nanocomposites was examined using transmission electron microscopy (JEM 1010), and the ultrathin sections of the elastomers were prepared at −100 °C. The viscoelastic measurements were conducted on a dynamic mechanical analyzer (TA AR2000) in a tension mode. The Payne effect measurements were performed at a constant frequency of 10 Hz at 25 °C. Typically, three samples were analyzed, and the repeatability of the measurements of the storage and loss moduli were usually with a range of 5%.

3. RESULTS Nonlinear Viscoelasticity. The incorporation of the filler has been found to significantly enhance the mechanical properties of the polymer, where the dynamic mechanical properties of elastomeric materials are of enormous significance.1−5 For current SNP/PAM systems, the effects of strain amplitude on storage modulus and loss modulus as a function of SNP volume fraction are demonstrated in Figure 1. One can note that the storage modulus is at the highest (referred to as G′0) at small amplitude and gradually decreases to a lower value (referred as G′∞) at high amplitude, and the magnitude of the Payne effect (G′0−G′∞) rises with increasing SNP content. Besides, the degree of nonlinearity increases continually with increasing filler loading, without any jump or discontinuity in curves, implying that the filler percolation may be not a prerequisite for the observation of the Payne effect. In fact, the probability of formation of the connected filler network is small at low filler loading, whereas the filler particles tend to agglomerate into an interpenetrated network at higher loading due to the small particle size and high specific area.18 Thus, the state of dispersion of filler particles from isolation to aggregation dominates the thermodynamics of the materials. Additionally, the behavior of the loss moduli G″ with strain (Figure 1b) is basically similar to the behavior depicted in Figure 1a. Nevertheless, it is worthy of noting that the rate of loss modulus decreases, and the range of loss modulus at low amplitude strains is much less than that of the storage modulus. This difference is ascribed to the filler network structure, which is discussed later in this paper. Combined with the fact that filler network structure is clearly observed in TEM images (Figure 2), the filler network can be broken down into a large

2. EXPERIMENTAL SECTION Silica oxide powder was obtained by the well-known Stöber method28 and contained primary particles of size around 15 nm in diameter with an average surface area of 240 m2/g. The organosilane γ−methacryloxypropyl trimethoxy silane, which can react with the monomer (acrylamide, AM) under ammonium persulfate (APS) as an initiator to form covalent bonds with silica, was used to modify the fillers before the graft 20237

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Figure 1. Shear storage moduli (a) and loss moduli (b) versus strain amplitude as a function of SNP volume fraction.

Figure 3. Storage modulus at low strain amplitude (G0′) as a function of SNP content at 10 Hz, where the dotted line represents the predicted values of G0′ by the Guth−Gold model.

Figure 2. TEM image of SNP dispersion composites. The characteristic aggregate size is around 35 nm, and a typical distance between two neighboring aggregates is 45 nm (bar = 20 nm).

number of smaller particles, which is consistent with the theory that the Payne effect in filled elastomers is attributed to the breakdown of the filler network at high strains (Figure.S1). Gauthier et al. proposed a theoretical description of the physical mechanism associated with the Payne effect and speculated that the debonding of the polymeric chains from the filler surface was responsible for the nonlinear viscoelastic behavior and interfacial interactions played a key role in determining the amplitude of the Payne effect.29 Upon going to increasingly greater strains, the original connected network of filler particles become loosely broken up, where the open aggregates that tend to resist deformation due to the strong filler−filler interactions are no longer effective at this large strain. That is, there is a chance for the occurrence of multiple attachments for the initial large agglomerate size particles, whereas these multiple points may convert to a single-point attachment upon straining because of the reduced size of agglomerates.11,12 The effect of SNP volume fraction on the storage modulus at low strain amplitude (G0′) is shown in Figure 3. One can note that the G0′ rises linearly below a critical filler fraction (∼0.05% v/v), then it increases steeply at a higher filler content. The

Guth−Gold models is a well-known model to calculate the modulus for reinforcement of elastomers by fine particulate fillers. If we apply the Guth−Gold equation30 G0′ = Gp′(1 + 2.5ϕ + 14.1ϕ2)

(1)

where Gp′ and ϕ are the storage modulus of the pristine polymer and the filler volume fraction, respectively, one can note that the experimental values of G0′ are significantly higher than the predicted ones (given that ρSNP = 2.2 g/cm3 and ρPAM = 1.41 g/cm3, and the volume fraction ϕ ranging from 0.01 to 0.2% in the present study), indicating the existence of strong interactions between fillers and matrix. Besides, to parametrize the amplitude−sweep curves, the well-known Kraus model, which is based on the assumption of agglomeration/ deagglomeration mechanism of the filler network, can be employed to depict the strain-sweep measurements:31 G′(γ ) − G′∞ = G′0 − G′∞ 20238

1 1+

2m

() γ0 γc

(2)

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moduli finally recovered to more than 70% of their original values within 5 min. This result is attributed to the nature of dynamics of polymer entanglements because the temporary cross-links of such systems are transformable and recoverable within experimental time scales. When the external deformation displaces chains in opposing directions, the uncrossabilityinduced polymer entanglement produces intermolecular gripping forces, which in turn lead to the formation of an intrachain elastic retraction force.15,16 For the nanocomposites, since the filler network interactions are established through direct filler−filler contact as well as through polymer chain bridging, the systems could partially recover to solid-like behavior at small strains through chains readsorption. Since the breakdown of polymer-chain-mediated SNP/polymer systems involves polymer chain desorption and cluster breakdown under high strains, such rheological behavior of the SNP/ polymer clusters is attractive for potential drug or protein delivery as injectable hydrogels. Constrained Polymer. It is widely viewed that a layer of nanoscale-immobilized polymer chains forms near the surface of filler particles, where the mobility of polymer segments is pronouncedly hindered and leads to the formation of a thin layer of “glassy-like polymer”.32,33 This interlayer is supposed to possess different physical characteristics from the bulk matrix. Here, we elucidate how the Payne effect is related to the polymer chain’s dynamic modification in the vicinity of filler surface that is observed by rheology measurements. For SNP/ polymer systems, assuming the bridges between filler particles are generated by the immobilized polymer, multiple connections per particle are expected. The results are analyzed in terms of loss factor and a change in the peak height (Figure 6). In principle, the height of loss factor (H) is related to the fraction of polymer chains that participate at immobilization on the filler surface and is proportional to the number of internal degrees of freedom of molecular motion.25 For example, in terms of high SNP content, the thick boundary layer has strong bridging characteristics, and it is difficult to peel the host polymer from the surface at low strains, as indicated by the high reinforcement ability. It is shown that H systematically decreases with increasing filler content: as more SNP is incorporated into the polymer matrix, a higher fraction of polymer chains would be constrained among filler galleries. This high reinforcement capability is related to the extensive boundary zone that is well-mixed with the matrix polymer, leading to the volume fraction of constrained polymer chains to increase with increasing SNP content.23 In fact, similar results have been attained in other polymer nanocomposites, suggesting that the volume of the constrained polymer depends on the amount of SNP in the matrix, and this fact can be utilized to determine the interfacial interaction between the filler and polymer. The fraction of constrained polymer (Vc) can be determined by following equation:34

in which the critical strain γc denotes the point where the straindependent storage modulus G′(γ) reaches the half value of ΔG′ = G′(γ0)−G′∞. Consequently, γc corresponds to the breakage of half the number of filler−filler contacts: a small critical value γc reflects a weak filler network which is breakable at low strain amplitudes, whereas a high value indicates the strong filler− filler interaction that is stable up to a high dynamic load. The characteristics of individual primary clusters are further delineated by the loss factor (tan δ, G″/G′), where SNPs lead to similar loss factor changes (Figure 4) due to the similar

Figure 4. Loss factor versus shear strain at 10 Hz for SNP-filled nanocomposites.

nonlinear behavior of elastic and loss moduli. One can note that all the composites show nearly flat curves (until γ ≈ 0.398%), strains that are similar to the behavior of a pristine polymer. This appearance of a plateau in loss factor reflects the proportional decrease of storage moduli and loss moduli at strain levels below 0.398%. Whereas at high strains (>0.631%), the loss factor becomes nonlinear, and the loss modulus shows a greater effect than the storage modulus, where all nanocomposites show an upturn in the loss factor. In fact, this upturn is attributed to the disentanglement of chains and the simultaneous decrease of storage and loss moduli, but with a higher relative reduction in the storage modulus. The higher SNP content leads to a steeper slope of loss factor versus strain due to hydrogen bonds between the filler surface and matrix polymer providing more drag forces at a higher SNP loading, thereby lessening the rate of reduction in the loss modulus and leading to a viscous boundary layer at all strains. In fact, this viscous coupling of the filler to the matrix and the hydrodynamic boundary glassy layer lead to an increase in viscosity of the nanocomposites.22 To examine the recovering behavior of the nanocomposites, which is important for potential injectable elastomers, the response of the samples to a dynamic stepwise oscillatory strain amplitude test was performed on the selected samples (Figure 5). In this measurement, the initial G′ was found to be about 74.6 KPa for SNP 0.15. When a large strain amplitude (γ = 100%) was applied to the hydrogels, G′ gradually decreased to 40.3 KPa. Meanwhile, G′ decreased to less than G″, suggesting the breakdown of the filler network. When the strain amplitude was returned to the small value (γ = 1%) again, G′ of the systems recovered to above G″ as the gel re-formed, and the

Vc = 1 −

H H0(1 − ϕ)

(3)

where ϕ is volume fraction of SNP and H and H0 are the height of the tan δ peak of the nanocomposite and the pristine polymer, respectively (assuming Vc = 0 for the amorphous phase in the pristine PAM matrix). The values of Vc are summarized in Table 1, and Vc increases from 0.86 to 3.32% v/ v as the SNP volume fraction increases from 0.05 to 0.15%. Thus, an increase in filler content would constrain more 20239

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Figure 5. Dynamic stepwise strain amplitude tests of SNP-filled systems.

uncrossability, which is due to a combination of excluded volume and chain connectivity in term of strong and localized intermolecular coupling at chain junctions.15 As the molecular weight of polymer chains increases, the spatial domain segments that are spanned by a given chain increasingly overlap with neighboring entanglement points to form topological constrains. According to our earlier work, the molecular weight of PAM is up to 104 Da,22 which is much greater than the theoretical value of the average molecular weight between entanglements, Me, should be 3800 Da,35 supporting the theory of an entanglement network. Consequently, the mechanical reinforcement due to trapped entanglements at the filler−polymer interface and the subsequent release at strains represent a disproportionate perturbation to the glassy layer, which leads to the nonlinear viscoelastic behavior of SNP/polymer systems. For the pristine polymer, entanglements could only occur as the primitive paths of the chains cross each other, forming topological constrains through which a chain has to diffuse to undergo substantial conformational rearrangements. Whereas for the filled nanocomposites, the creation of topological constraints may occur in two ways: one way is similar to that as in the pristine polymer where chains can produce entanglement, and the other way is when the particles themselves contact and disturb the primitive

Figure 6. Constrained polymer chains in SNP-filled nanocomposites.

polymer chains on the filler surface and contribute to the stronger interfacial interaction and enhancement in modulus. Trapped Entanglement and Molecular Weight. It is widely held that the chain entanglement stems from the 20240

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paths of the chains.36 Thus, the nature of entanglement during deformation in nanocomposites is characterized by direct viscoelastic behaviors, which is different from the completely elastic features of the chemically cross-linked network. The fracture strength at the same polymer content is greater for the matrix with a higher molecular weight, which is further support that the thickness of the polymer shell depends on the molecular weight of the polymer matrix. The long-lived chain bridging is important in enhancing the strength of nanocomposites, where a large amount of small space among fillers is accessible to long chains and directs the filler−filler contact through a thick layer of polymer on the filler’s surface that allows contacts between fillers. In fact, under the same filler particle loading, a thicker shell allows stronger filler−filler association, leading to greater elastic modulus. Because chain bridging can lead to filler association by overlapping neighboring shells, the higher molecular weight always results in a denser filler network. For example, at a small loading of 0.025% v/v, the chain bridging effect is hardly effective due to an insufficient amount of space for polymer chains to reach. Nevertheless, the G′ for a higher loading at 0.075% v/v increased to 51.5 KPa. Similarly, upon grafting long chains with a molecular weight of 6.05 × 104 to replace 2.68 × 104 Da, while keeping the same filler loading, it is shown that these long chains make a huge boost over the level of fracture strength from 155 to 204 KPa (Figure.S2). Zhu et al. reported that the nanocomposites with high molecular weight showed a constant G′ at low frequencies where the pristine polymer showed terminal behavior, suggesting that the long chains are able to achieve an equilibrium between fillers of spacing on the order of the chain size where chain adsorption and layer bridging occur.12 In the current viscoelastic SNP/polymer cluster forming a filler network in an elastic medium, it has been found that elastic modulus increased linearly with ϕ at a low value, whereas a percolation transition was probed beyond a critical ϕ, indicating that the filler reinforcement occurs in the limit of the isolated filler cluster and is enhanced significantly due to the large scale filler network structure formation.

Figure 7. Schematic illustration of the SNP/polymer cluster’s breakdown and chain segments at the SNP surface, where the original aggregated clusters convert to isolated ones and lead to single points of adsorption on the filler surface on straining.

properties of elastomers, where the properties of composites are controlled by the themodynamic of the filler/polymer interface. For instance, the adhesion between filler particles and polymer molecules, dispersion of filler particles in the composite, and wettability of the solid filler by the polymer dominate the mechanical properties of materials. Even though the PAM chains are covalently tethered to the SNP surface, slippage still occurs due to a complex disentanglement process between the immobilized chains and the bulk matrix. At sufficiently high strain, the surface chains are effectively disentangled from the bulk matrix and become dynamically flexible. According to time-dependent loading−unloading cyclic tensile measurements (Figure.S3), the systems show partial recovery properties, indicating the dynamic mobility of polymer chains in networks. For example, after 5 min of waiting, the fracture strength can attain over 75% compared to that of the pristine polymer. In fact, our recent rheological measurements have also noted the desorption of polymer chains through a disentanglement process for SNP/polymer systems, implying the rearrangement of chains at the rigid filler’s surface. In general, the adsorption of polymer chains on the filler surface occurs when the filler is mixed with matrix. According to the Maier and Göritz model,37,38 the polymer segments have a high probability to attach to the neighboring particles after forming the first link and favor the formation of other links with neighboring interaction sites, resulting in close contact with the filler surface. Once these chains form a stable interaction on the filler surface, the remaining chains arriving later may have fewer chances to form stable bonds and will only form unstable bonds on the filler surface, leading to fragile and breakable interaction that can be easily removed at straining.17,18 For current SNP/ polymer systems, the interfacial interactions between SNPs and the matrix are labile, ranging from covalent bonds (saline coupling bridges) to noncovalent bonds (e.g., physical adsorption, hydrogen bonding, or van der Waals forces). These interactions lead to a layer of glassy immobilization of the matrix that acts as trapped entanglements. The polymer chains may contact the fillers at multiple points, and the possible looped chains are shorter than the overall chains. Besides, the incremental change in the modulus is ascribed to the appearance of a layer of bound polymer with finite thickness at the filler−matrix interface, where near-field effects are limited to the chains directly contact with the surface due to

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DISCUSSION As an alternative explanation of the Payne effect, the destruction and re-formation of filler aggregates should be considered, where the dynamics of adsorption/desorption of polymer chains on filler surface is responsible for the nonlinear behaviors.16−18 The interaction between the filler particles and the polymer matrix leads to the immobilization of polymer chains on the filler surface and may be dominated by the nature of polymer−filler interaction. In other words, the molecular interpretation of the Payne effect involves the existence of equilibrium between the breakdown and rearrangement of filler network and the polymer chain’s entanglement around the filler particles (Figure 7). The interaction zone argument,17 one of the proposed concepts to rationalize the reinforcement of polymeric materials loaded with nanoparticles, suggests that a layer polymer near the surface of the particles exhibits significantly different properties than those of the bulk matrix. Some researchers have speculated that the density of entanglements near the surface of nanoparticles is higher than in the bulk, where the entangled polymer chains on the filler surface bridge neighboring SNPs and dominate the large strain behavior of nanocomposites. The interaction between the polymer matrix and the solid surface of filler particles is of critical importance in tailoring the 20241

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the trapped entanglements. In fact, these trapped entanglements which have direct contact with the fillers may also affect the far-field mobility of the neighboring chains. For example, the high amplitude strains increase the kinetics of the chain mobility (debonding or slipping) at the interface and reduce the stiffness of the glassy layer and overall matrix phase. That is, the release of the trapped entanglement (a change in the boundary condition from adsorption to slippage at the interface) lowers the modulus of the composites.36 Taken together, the results in this paper indicate that the origins of reinforcement and nonlinearity may stem from the filler−polymer interactions-induced cluster entanglement state changes at strains. The breakdown of the primary interconnected cluster building blocks into isolated ones leads to the reduction of storage and loss moduli with increasing strains and partially recover to their original moduli following small strain perturbations due to the dynamic and transformable cross-links. Notwithstanding the complication of possible fillers’ agglomeration at high filler contents, the nanoscale particulates could alter the mobility and conformational freedom of both the nearand far-field polymer chains, leading to a trapped entanglement zone (glassy layer) at the filler surface, regardless of particle distribution. However, the homogeneously dispersed fillers do have a greater filler surface area, and consequently, a greater fraction of polymer encompasses on the filler surface. Besides, the space of interfacial spacing is small enough for the some chains having enough probability to form a “bridging effect” and “interpenetrated boundary layers” among neighboring fillers.13,14 It is speculated that this bridging effect is also responsible for the nonlinear viscoelasticity of the SNP/ polymer systems, and the specific behavior of the elastic and loss modulus at applied strains may be ascribed to the relative effect of the layer boundary and the bridging network. Thus, the trapped entanglements coming from filler−polymer interactions lead to significantly stiffer composites and higher loss moduli due to an increase in dynamic friction.

completely aggregated and form a very compact structure that has essentially no polymer chains. The second lesson from this study is that filler−polymer interactions may also be responsible for the increase in toughness compared to the pristine polymer. Since the PAM chains could produce intramolecular hydrogen bonding with silica particles that would act as temporary junctions or stickers, the SNP/PAM cluster entangled process could be facilitated. The elasticity of the network is viewed as having stemmed from the existence of the constrained polymer region around the filler surface, which has been proposed from both 1H NMR and rheological measurements.39 It suggests that this “glassy zone” increases the effective elastic modulus of the nanocomposite and shifts the volume of the filler fraction for the threshold percolation toward to a lower value. For current SNP/polymer systems, this region acts as a corona between the filler (hard silica core) and the polymer matrix, which adjusts the chains’ mobility for a given thickness and decreases the mobility as they percolate. The improved resistance of fractures is interpreted as a consequence of the presence of entanglement between surface grafted chains that give rise to energy dissipation during deformation through constrained region plastic deformation and craze formation. This result requires a need to reconsider the filler−polymer interaction, which appears to be stronger than expected. For SNP/polymer systems, the clusters form small primary aggregates of several particles, with a mean radius of 30 nm and separated by a rimto-rim distance of 70 nm. Therefore, the origin of this interaction could be partially attributed to the formation of primary aggregates, where the matrix chains bridge the neighboring primary aggregates and form a typical rim-to-rim distance equal to twice the polymer gyration radius. Due to the dynamic adsorption−desorption of the polymer on filler’s surface and the sensitivity to applied stress, the energy accumulated in the nanocomposites could be effectively released by this dynamic chain relative motion. In this regard, the nonlinear viscoelasticity behavior of the loaded elastomers is dependent on the dynamic strain due to the fact that the filler addition is viscously coupled to the strains, and the gradient of trapped entanglements’ density in the local region surrounding a filler surface is still an open question. Therefore, as for future studies, we plan to conduct molecular dynamics simulations of polymers reinforced with nanoscopic filler particles through a coarse-grained “dissipative particle dynamic” model to grasp the more fundamental physical characteristics of the nanocomposites. Furthermore, we intend to examine if the energy dissipation process during the deformation is related to the high flexibility of the hydrogel, especially when compared to the covalently cross-linked gels where the polymer chains’ micromotion and longer relaxation process in matrix are pronouncedly suppressed or eliminated.

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SUMMARY We are now in a position to attempt to elucidate the role of filler−filler interaction and nonlinear viscoelastic behavior of nanocomposites. The first lesson is that filler−filler interactions have a notable effect on the modulus, which can be divided into both direct and indirect sides. From a direct view, for a given adhesion at the interface and when the properties of each cluster are identical, increasing them could result in a certain increase in modulus. The indirect effect can be ascribed to a different filler−filler interaction, together with the formation of a glassy layer at the interface, which tends to produce clusters with different levels of agglomeration. In turn, it has been noted that the volume of the constrained polymer has a monotonic effect on the modulus reinforcement. In both cases, the presence of geometrical confinements around the filler’s surface enhances entanglement interactions through polymer-mediated adsorption, where either topological re-strains (including covalent bonds or temporary interactions to the fillers surface) or dynamic interactions (such as hydrogen bonding or van der Waals force) dominate the viscoelastic behavior. Therefore, assuming the particles form a connected structure that spans a large volume within the matrix (loosely while interpenetrated connecting filler network), the increase in the effective volume fraction of the filler leads to significant boosting in the modulus through chain bridging until a certain point where the fillers are

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ASSOCIATED CONTENT

* Supporting Information S

TEM images of SNP0.05-a under compressed and elongated state, tensile stress−strain curves, multiple repeat hysteresis of SNP 0.05-a, SNP 0.05-b, and SNP 0.05-c, and Huber−Vilgis model prediction of modulus. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 86-10-62338152. 20242

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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by Fundamental Research Funds for the Central Universities (TD2011-10), Beijing Forestry University Young Scientist Fund (BLX2011010), and Research Fund for the Doctoral Program of Higher Education of China (20120014120006).

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dx.doi.org/10.1021/jp404616s | J. Phys. Chem. C 2013, 117, 20236−20243