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Viscoelastic Behaviors of Carbon Black Gel Extracted from Highly Filled Natural Rubber Compounds: Insights into the Payne Effect Shunchang Gan, Zi Liang Wu,* Huilong Xu, Yihu Song,* and Qiang Zheng MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, China S Supporting Information *

ABSTRACT: Carbon black filled natural rubber (CB/NR) is a paradigm of nanocomposite materials with high performances. However, the mechanism for the nonlinear Payne effect is still not fully clear. CB gel (CBG) network embedded in the entanglement rubber matrix is supposed to be crucial for the reinforcement and viscoelastic nonlinearity. In this paper, we report for the first time the preparation of bulk CBGs by extracting the highly filled compounds in toluene and the systematic study of their viscoelastic behaviors. The CBG obtained from highly filled compounds with CB loadings from 40 to 70 phr has almost identical microstructure and composition, containing 40 wt % inextractable rubber fractions, among which ∼12 wt % is glassy. Dynamic rheological studies show that the Payne effect of the CBG network is frequencyindependent and highly resilient, exhibiting an unjamming characteristic. On the other hand, the Payne effect of highly filled compounds is determined by the coupling between the breakdown of CBG network and the frequency-dependent chain disentanglement of extractable rubber fractions. This work provides new insights into the Payne effect of CB filled NR and should merit designing other rubbery nanocomposites with high performances and functions. effect has been assigned to the breakdown of filler aggregates,11−13 desorption of (weakly absorbed14) bridging chain,15,16 and breakdown of filler network due to stressinduced variations in bound rubber17 or junction rubber.18 To be specific, the Payne model proposed in 1962 assumes that the particle network upon straining undergoes breaking down like colloidal thixotropicity.19 The van de Walle−Tricot−Gerspacher model assumes that the particle aggregates upon straining transform from the bound to unbound states.20 The links− nodes−blobs (LNB) model assumes that the rigid particles and their aggregates are interconnected by weak bonds to form LNB chains, of which yielding and destroying processes are responsible for the Payne effect and the mechanical hysteresis.21,22 The chain slippage models assume a two-phase (naked particle dispersed in rubbery matrix) structure of filled compounds; the Payne effect is involved in the slippage of rubbery chains along the surface of nanoparticles.23,24 The bound rubber/entanglement network model25 and the localized glassy layer model,26,27 on the other hand, assume a three-phase (dispersed particle−interfacial layer−continuous matrix) structure; the former model relates the Payne effect to the dynamic destroy−formation of the entanglements in the transition region of the bound and the free rubbers, and the latter one relates it to the crazing of the glassy interfacial layer. While all

1. INTRODUCTION Nanofilled rubbers are an important industrial material with excellent mechanical performances and broad applications. In rubber industry, carbon black (CB) is widely used as a reinforcing filler due to the low price and capacity to form hierarchical structures embedded in soft rubbery matrix.1 Although the reinforcement mechanism is not fully clear, it is recognized for more than 90 years that highly filled rubber compounds have two interpenetrating networks, i.e., a CB gel (CBG, consisting of CB particles and absorbed rubber chains) network and a matrix entanglement network.2 Another feature introduced by CB is the striking nonlinear viscoelasticity characterizing the dynamic moduli as a function of strain amplitude at a fixed frequency,3 commonly known as strain softening or the Payne effect, i.e., the enormous drop of storage modulus of the filled compounds with increasing strain amplitude during the dynamically shearing.4−7 Many efforts have been made to investigate the Payne effect due to both practical and theoretical importance.8−10 Diminishing the Payne effect is beneficial to reduce hysteresis loss in tread rubber, thus cutting the gas mileage of vehicles. On the other hand, this effect associated with strain-induced microstructure changes is crucial for understanding the mechanisms of reinforcement and mechanical hysteresis. A number of theories and models have been proposed to interpret the Payne effect by emphasizing the rubber−particle interfacial interaction, which is essentially important for the filler clustering and networking. In such a framework, the Payne © XXXX American Chemical Society

Received: December 14, 2015 Revised: January 27, 2016

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The antioxidant N-(1,3-dimethylbutyl)-N′-phenyl-p-phenylenediamine was obtained from Changzhou Xince Polymer Materials Co. Ltd., China. All the materials and solvents were used as received. 2.2. Sample Preparation. The CB/NR compounds containing 1.7 phr (parts per hundred rubber) antioxidant were prepared by using a laboratory two-roll open mill (XK-160, Zhanjiang Rubber & Plastic Machinery Co. Ltd., China) through a standard mixing procedure elaborated in ASTM-D3192. All the compounds were compressed into sheets on a press vulcanizer (XL-25, Huzhou Xinli Rubber Machinery Co. Ltd., China) at 100 ± 5 °C under 14.5 MPa for 10 min. Samples of 1.5 and 4 mm in thickness were prepared for rheological test and solvent extraction experiments, respectively. The sheet samples were stored at room temperature in brown desiccators for at least one month to achieve complete evolution of rubber−filler interaction.50 Then the samples were cut into discs with diameter of 25 mm for rheological tests. Bulk carbon black gel (CBG) samples were obtained from highly filled compounds by solvent extraction, as shown in Figure S1. A specially designed glass device equipped with a stainless-steel mesh container was used in the extraction experiment to ensure the integrity of the swollen specimen. The disc-shaped CB/NR compound (diameter of 25 mm, thickness of 4 mm) was extracted in 800 mL of fresh toluene at 30 °C for 10 days; the solvent was renewed every day. The extracted rubber in the solvent was collected by rotary evaporation. For the remained bulk sample, anhydrous alcohol was used to replace the residual toluene. After drying under vacuum at 60 °C for 48 h, the obtained bulk CBG was compression molded at 100 °C under 14.5 MPa for 10 min. The molded CBG was cut into discs with diameter of 25 mm for rheological tests. The samples of CB/NR and CBG are coded as NRx and CBGx, in which x denotes the CB loading in phr (parts per hundred rubber) of the original compounds. 2.3. Characterizations. The respective amount of NR and CB in the compounds and CBG samples was determined by thermogravimetric analysis (TGA, Q1000, TA Instruments, USA). The samples were first heated from 50 to 625 °C under a continuous nitrogen flow (50 mL/min). Then the atmosphere was switched to air flow (50 mL/ min); the samples were heated to 900 °C. The heating rate was 10 °C/ min. The bound rubber fraction was calculated by the weight of NR in the CBG relative to that in the compound. The molecular weight of extracted rubber was measured by gel permeation chromatography (GPC, Waters 2690, Waters Co., USA) using tetrahydrofuran as mobile phase and polystyrene as standard calibration. Temperature-modulated differential scanning calorimetry (MDSC, Q100, TA Instruments, USA) was used to study glass transition temperature (Tg) and heat capacity of CB/NR compounds and CBG samples. Measurements were performed by using an underlying heating rate of 1 °C/min and a superimposed temperature modulation procedure with an amplitude of 1 °C and a period of 100 s. Before measurement, the heat capacity signal of the instrument was calibrated by using standard sapphire sample. The jump of reversing heat capacity of the samples (ΔCp,sample) during the glass transition was obtained by analyzing the reversing heat capacity signals between −80 and −30 °C. The jump of reversing heat capacity of the rubber fraction (ΔCp,rubber) in the sample is calculated by ΔCp,rubber = ΔCp,sample/(1 − XCB), in which XCB is the mass fraction of CB in the sample. Scanning electron microscopy (SEM, S-4800, Hitachi, Japan) was adopted to investigate the morphology of the compounds and CBG. The samples were cryogenic fractured in liquid nitrogen and were then dried under vacuum. The fractured surfaces were coated with gold− palladium by using a Denton Desk-1 vacuum sputter coater for SEM observation. A strain-controlled rheometer (ARES-G2, TA Instruments, USA) was used to measure the linear and nonlinear dynamic rheological responses of the compounds and CBG samples at 100 °C. The plate− plate geometry was equipped with serrated surface texture to prevent slipping; thus, obtained rheological results are almost the same as those by using plates with smooth surface (Figure S2). All the specimens were equilibrated for 5 min before performing frequency (ω) sweeps from 100 to 0.01 rad/s and strain (γ) sweeps from 0.01%

these models focus on the destroy mechanism involved in the filler structure or the interfacial region, they have ignored the contribution of the free rubber phases in general. By creating nonlinear rheology master curves of filled compounds with a reference of the matrix, Sun et al.28 argue that the Payne effect is related to the molecular disentanglement while the nanoparticles accelerate this process via strain amplification effect.29−33 Meera et al.34 argue that the molecular disentanglement could occur in both the bound and the free rubber fractions, accounting for the Payne effect. The theories and models are still in debate because they cannot independently interpret various experimental results. The complexity of the Payne effect lies in the discrimination of filler−filler and polymer−filler interactions; the modification of filler status inevitably impacts both of them.35 How to distinguish the different physical processes, i.e., the breakdown of filler structure, the molecular desorption and its resultant effects, and the molecular disentanglement is a long-standing problem. According to the interpenetrating network picture of highly filled rubber, the CBG network swells but does not disintegrate in a good solvent,36,37 whereas the matrix entanglement network is soluble. The CBG should provide a simplified system for clarifying the relationship between polymer−filler interactions and mechanical properties.38 The inextractable rubber in CBG (i.e., the rubber fraction remains attached to the filler after lengthy extraction with a good solvent39−41), called bound rubber,42 and often used as an indirect measure to estimate the filler−rubber interaction,43 is considered as an important factor that influences the processing, rheology, and storage stability of compounds, and mechanical properties of vulcanizates.41,44−49 However, there are no reports on the viscoelastic behaviors of bound rubber and bulk CBG. In this article, we obtain bulk CBG by solvent extraction of highly filled natural rubber (NR) compounds in toluene and investigate the composition, microstructure, and rheological behaviors of CBG samples to give insights into the Payne effect. Temperature-modulated differential scanning calorimetry was used to examine the existence of glassy rubber layer. The dynamic viscoelastic behaviors of CB/NR compound, CBG, and masticated NR were studied and compared. We found that the CBG obtained from different highly filled compounds has the same composition, microstructure, and viscoelastic behaviors; the Payne effect of bulk CBG is analogous to a frequency-independent unjamming process, mainly involving the strain-induced irreversible rearrangement of CB particles. For the highly filled compounds, both the breakdown of the CBG network and the frequency-dependent chain disentanglements are responsible for the Payne effect; the latter delays this effect, which depends on CB loading. Another feature of CBG is the rapid recovery of storage modulus, which is mainly due to the bound rubber mediated quick healing of interparticle association, while in the compounds, the recovery is driven by a diffusion process of CB aggregates and dominated by the viscoelasticity of the matrix rubber.

2. EXPERIMENTAL SECTION 2.1. Materials. Carbon black (CB, N330; primary particle size ∼30 nm, density 1.86 g cm−3, dibutyl phthalate absorption 1.002 cm3 g−1) was purchased from Longxin Chem. Stock Co. Ltd., China. Natural rubber (NR, SVR3L grade; density 0.92 g cm−3, weight-averaged molecular weight Mw = 1120 kg mol−1, polydispersity Mw/Mn = 3.57) was purchased from Shanghai Duokang Industrial Co. Ltd., China. B

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Macromolecules to 100%. The shear strain changes following a sine function during a period of oscillatory test, and γ is used to refer to strain amplitude value for simplicity. Additionally, it is worth noting that that the storage and loss moduli (G′ and G″) directly obtained from the rheometer software in the nonlinear regime are actually the firstharmonic viscoelastic moduli.

agglomerates. On the other hand, CBGs show a densely compacted granule morphology, reflecting the three-dimensional filler network structure.52 There are small pores ∼100 nm in CBGs, which could not be eliminated even after compression molding the CBG samples at elevated temperatures; these pores should correspond to the space of extracted rubber. Weight-average molecular weight (Mw) and polydispersity (Mw/Mn) of the extracted rubber were analyzed by GPC (Table 1). Mw and Mw/Mn of the extracted rubbers from NR40-NR70 are similar to those of masticated NR processed at the same condition, indicating that there are no preferential adsorptions of high molecular weight fractions on the surface of CB in our system. We should note that the mixing procedure reduces Mw and Mw/Mn of rubber chains, from 1.1 × 106 and 3.6 of original NR to 2.8 × 105 and 2.3 of masticated or extractable rubbers, respectively. To determine the percolation threshold of CB in the filled compounds, small-amplitude oscillatory ω-sweep experiments were carried out in the linear regime of the samples. Figure 2a shows dynamic storage modulus (G′) as a function of ω for the unfilled masticated rubber, the filled compounds, and the CBG samples. The introduction of CB strongly influences the dynamics of rubber in the compounds. With increasing CB volume fraction (ϕ), the ω-dependence of G′ in the terminal regime weakens and the G′ plateau in the low-ω region becomes evident due to the retarded long-term relaxations of rubber chains in the compounds. Especially, the CBG samples with ϕ ≈ 0.42 show gel-like behavior; G′ is nearly independent of ω. By plotting G′ at different frequencies as a function of ϕ (Figure 2b), critical CB volume fraction (ϕc) for the onset of percolation is determined as 0.15, corresponding to ∼40 phr of CB in the compounds. Furthermore, G′ of CBG is lower than the value extrapolated according to the G′ ∼ ϕ relationship of the compounds at ϕ > ϕc (Figure 2b), which will be discussed in detail later. MDSC was used to investigate the glass transition temperature (Tg) and the jump of reversing heat capacity (ΔCp) of the samples;53 the results are presented in Figure 3 and Table 2. For the compounds, increasing CB loading does not influence Tg (Tg = −66.5 °C)54,55 except for a decrease in ΔCp following the mass balance law. In fact, ΔCp of the composite samples (ΔCp,sample) is mainly contributed by the rubber because of the

3. RESULTS 3.1. Composition and Structural Features. It is widely acknowledged that a CBG network penetrates throughout the entanglement rubbery matrix in the highly filled compounds. This complicated structure often results in the difficulties for deeply understanding the reinforcement mechanism and nonlinear viscoelasticity. To simplify this system, we separate the CBG network and the rubbery entanglement network (unbound rubber) by solvent extraction and investigate the composition, structural feature, and rheological behavior of the CBG sample. Bulk CBG samples could be obtained from the compounds with CB loadings above 40 phr. Otherwise, the CB particles leak out and the compounds break into small pieces during extraction. The composition and microstructure of the compounds and CBG were studied by TGA and SEM. Table 1 lists the Table 1. Compositions of CB/NR Compounds and Their CBGs bound rubber content (%) samples NR00 NR40 NR50 NR60 NR70

in compds 28.0 32.6 40.7 45.2

± ± ± ±

1.4 3.4 0.9 4.2

extractable rubber

in CBG

Mw (105 g/mol)

Mw/Mn

± ± ± ±

2.81 2.63 2.76 2.62 3.50

2.30 2.23 2.19 2.05 2.61

40.8 38.9 40.1 39.7

1.1 2.6 0.7 2.2

composition characteristics for the highly filled compounds and corresponding CBGs. As expected, the content of bound rubber increases with CB loading.51 It is interesting that the CBG samples obtained from NR40-NR70 have the same rubber content, around 40 wt %. The microstructures of the compounds and CBGs are shown in Figure 1. The primary CB particles fuse into aggregates of several tens of nanometers and disperse well in the compounds; there are no distinct large-scale

Figure 1. SEM images of cryogenic fracture surfaces of the samples (a) NR40, (b) NR50, (c) NR60, (d) NR70; (e) CBG40, (f) CBG50, (g) CBG60, and (h) CBG70. Arrows show the pores in CBGs. C

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rational to conclude that the contribution of constrained rubber to the glass transition of the compounds is marginally small.56 In contrast, the CBG samples have rubber chains tightly bounded on the CB surface with a larger proportion, providing enhanced MDSC signal of constrained rubber. The CBG samples show much smaller values of ΔCp,rubber than those of the compounds. The fraction of tightly bound rubber is determined as ∼12 wt % based on the ΔCp values per rubber mass; this fraction is unable to undergo α relaxation.57−62 Similar results have been observed in 50 phr CB filled polybutylene system.63 Furthermore, Tg of the CBG is 1−2 °C lower than that of unfilled masticated rubber and compounds (Table 2), which could probably be assigned to the geometrical confinement effect, quantitatively equivalent to decreasing thickness of planar polymer films.64 In addition, the presence of long bridging chains interconnecting nanoparticles may result in small variation of Tg of the inextractable rubber in CBGs. In the compounds, the presence of a large amount of free rubbers shields the calorimetric signals from the constrained rubber and bridging chains. 3.2. Payne Effect. Bulk CBG has excluded the matrix entanglement network and provides a simplified picture of highly filled compounds, which should be helpful for elucidating the underlying mechanism of the Payne effect. The dynamic γ-response of the CBGs is shown in Figure 4.

Figure 2. (a) G′ as a function of ω for the unfilled masticated rubber, the filled compounds, and the CBGs at γ = 0.1% and T = 100 °C. (b) G′ as a function of ϕ for the filled compounds at three diffeent frequencies.

Figure 4. Variations of (a) G′, (b) G″, and (c) tan δ as a function of γ for CBGs at 100 °C and 1 rad/s. Figure 3. Reversing heat capacity per mass of samples as a function of temperaure.

Here we focus on a direct comparison of complex modulus due to its simple and intuitive advantage in understanding the Payne effect. According to normalized Lissajous map (stress vs strain) generated from oscillatory shears at different γ for the highly filled compounds and CBG at 100 °C and 1 rad/s (Figure S3), the compounds (NR40, NR50, and NR70) and CBG70 are viscoelastic at γ ≤ 50% and γ ≤ 0.2%, respectively, and the high-order harmonics are negligibly small compared to the first-order, which allows direct comparing G′ and G″ of the filled compounds and CBGs.65−67 After extracting the free rubbery fraction, the nonlinearity emerges in CBG at γ as low as 10%. The departure in the nonlinear regime due to the contribution of higher order harmonics,68 where the filler network goes through a significant structural breakdown/ rearrangement,69 causes softening of the material during one cycle.70 This is recognized as a simple but useful way to characterize and classify complex fluids in both experiments and simulations.71,72 As aforementioned, the CBG samples obtained from NR40 to NR70 have similar composition and microstructure; as expected, they also display similar dynamic γ response. G′

Table 2. Calorimetric Results from Modulated DSC samples NR00 NR10 NR40 NR70 CBG40 CBG70

Tg (oC) −66.7 −66.5 −66.5 −66.4 −67.9 −68.5

± ± ± ± ± ±

0.1 0.2 0.2 0.1 0.2 0.3

ΔCp,samplea (J g−1 K−1) 0.425 0.398 0.301 0.254 0.154 0.138

± ± ± ± ± ±

0.010 0.010 0.012 0.011 0.014 0.015

ΔCp,rubberb (J g−1 K−1) 0.425 0.438 0.421 0.431 0.375 0.350

± ± ± ± ± ±

0.010 0.011 0.015 0.013 0.015 0.038

a

Jump of reversing heat capacity of the samples during the glass transition. bJump of reversing heat capacity of the rubber fraction of samples during the glass transition.

sufficiently small ΔCp value of CB. Thus, we can calculate the reversing heat capacity of the rubber fraction (ΔCp,rubber) in the samples by ΔCp,rubber = ΔCp,sample/(1 − XCB), in which XCB is the mass fraction of CB in the sample. The identical values of ΔCp,rubber suggest that the rubber fraction in the compounds behaves like the unfilled rubber (Table 2). Therefore, it is D

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Macromolecules initially keeps constant at γ < 0.1% and hereafter falls sharply, following a power law of G′(γ) ∼ γ−1.2. At the same time, G″ passes a maximum at a critical strain (γm) of 0.2% and then decreases according to G″(γ) ∼ γ−0.9. The G′(γ)-dominant linear viscoelasticity accompanying with a weak but evidenced G″(γ) maximum prior to the onset of strain softening suggests that CBG behaves as a jammed system and could be categorized into the soft glasses.73−78 The G″(γ) maximum is absent in the filled compounds, which only show strain thinning behavior.3 It means that the CB nanoparticles in CBG are in the jammed state only after extracting the sol fractions. In the jamming systems with strong interaction such as CBG, the peak of G″ appears as the materials yield. The origin of the nonlinearity is thus attributed to irreversible rearrangement of the particles under oscillatory shear.79−81 Because the CBG samples have the similar composition, microstructure, and viscoelastic behaviors, in the following sections we use CBG70 as a representative sample to compare its viscoelastic behaviors with those of the compounds. To explore the detailed response of CBG network under oscillatory shearing, dynamic time sweeps were performed after shearing CBGs to prescribed strains below, equal to or above γm = 0.2%. The results are shown in Figure 5. At γ < γm, both

Figure 6. Normalized storage moduli (G′/G0′) and loss moduli (G″/ G0″) as a function of γ for the filled compounds and CBG70 at 100 °C and 0.1 rad/s. G0′ and G0″ denote the γ-independent storage modulus and loss modulus, respectively, in the oscillatory γ-sweep measurement.

filled compounds and is usually assigned to the breakdown of clusters and even the filler network.83 It is worth noting the similar slope during the softening stage of the compounds, reflecting the relaxation through the disruption of filler interconnection.84−86 CBG70 exhibits much smaller γc and more rapid decrease in G′ at γ > γc than those of compounds, suggesting that the extractable rubber delays the strain softening. The G′(γ) and G″(γ) are measured at different ω to reveal the differences of the Payne effect among the unfilled masticated rubber, filled compounds, and CBGs. The curves are vertically and horizontally shifted to superimpose the data measured at ω = 1 rad/s (Figure 7). Respective master curves

Figure 5. G′ as a function of γ during oscillatory γ-sweeps for CBG70 at 100 °C and 1 rad/s. The insets show the subsequent time sweeps after dynamic γ-sweep to (I) γ = 0.05% < γm, (II) γ = 0.2% = γm, and (III) γ = 5% > γm.

G′ and G″ are independent of time. At γ = γm, G′ declines and G″ increases very slightly with time; they cross each other after 4000 s. Similar to the filled compounds, at γ > γm, CBG70 shows liquid-like behavior (G′ < G″); G′ and G″ drop continuously with time. Thus, the modulus variation is sensitive to both γ and time. γm is the threshold of the strain-induced viscoelastic nonlinearity of CBG; above γm, yielding of CBG occurs like other jamming materials. In such a case, the interactive CB particles will experience irregular motion; the growing disturbance at γ > γm leads to the evident γ- and timedependent nonlinear responses. In the highly filled compounds, it is well accepted that the oscillatory γ-sweep at low ω could detect the viscoelastic response of CBG network.82 To compare the γ-response of CBG network between the compounds and bulk CBGs, dynamic γ-sweeps were performed at ω = 0.1 rad/s. The normalized G′ and G″ as a function of γ are shown in Figure 6. As expected, the critical strain for the onset of nonlinearity, γc, deceases with increasing CB loading, which is common for

Figure 7. Master curves of normalized G′ (a) and G″ (b) at ω = 1 rad/ s as a function of Aγγ for the unfilled masticated rubber (NR00), the filled compounds (NR40 and NR70), and CBG70 at prescribed test ω. The inset in (b) shows ω-dependence of horizental shift factor Aγ for constructing the master curves. The solid and dotted lines in (a) and (b) show the slopes of G′ and G″ for CBG70 and unfilled rubber, respectively.

could be obtained for the three categories of samples, indicating that the underlying mechanism of the Payne effect is independent of ω. However, the horizontal shift factor Aγ increases with ω for the unfilled rubber, while it is independent of ω for CBG70 (inset in Figure 7b), revealing the different nonlinearity mechanisms for the entanglement network and the CBG network. It is easy to understand that the molecular disentanglement involved in reptation is time- and γ-dependent and accounts for the ω-dependent Aγ. However, the viscoelastic nonlinearity of bulk CBGs should originate from the straininduced microstructural variation of CBG network, which is E

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(Figure 8b); this slow variation of G′ is due to the migration and clustering of CB particles under long-time thermal treatment (Figure S4), similar to the physical aging process often observed in polymer glass88 and the CB-filled styrene− butadiene rubber system.89 To further confirm the role of CBG network played in the structure rebuilding process, we performed loading−unloading cyclic measurements for NR00, NR70, and CBG70 up to a maximum strain amplitude of 100% (Figure 9). NR00

formed through bound rubber mediated interaction between CB particles.79 With increasing CB loading, Aγ of the compounds decreases and gradually becomes ω-independent (inset in Figure 7b); Aγ of NR70 is almost the same as that of CBG. These results reflect the mechanical coupling of the CBG network and the entanglement network. Although the two physical processes may proceed independently in the two interpenetrating networks, the entanglement between the chains of extractable fraction and those of CBG network brings synergistic effect, leading to the slopes of G′(γ) and G″(γ) of NR 40 and NR70 smaller than those of CBG70. It means that the interplay between the two networks delays the microscopic processes responsible for the viscoelastic nonlinearity. 3.3. Modulus Recovery. The modulus recovery process can give a complementary insight into the time-dependent behavior of the Payne effect. The masticated NR, compounds, and CBG70 were sheared stepwise to γ = 0.03% and γ = 50% in succession and then sheared back to γ = 0.03%. The corresponding variations of G′ are presented in Figure 8a. G′

Figure 9. Dynamic γ-sweep curves for NR00, NR70, and CBG70 during a loading−unloading cycle at 100 °C and 1 rad/s. The arrows indicate the loading and unloading processes.

subjected to a sequent loading−unloading cycle shows marked recovery hysteresis; the shearing causes significant reduction of G′. The recovery hysteresis of NR70 is smaller than that of NR00, indicating that the presence of CB particle restrains the molecular disentanglement. In contrast, the hysteresis of CBG is negligible, although it shows a remarkable Payne effect. These results indicate that the CBG network facilitates the instant structural reconstruction of highly filled compounds upon unloading.

Figure 8. (a) G′ at ω = 1 rad/s for the compounds and CBG70 in response to a first straining to an amplitude of 0.03% for 300 s, followed by 50% strain perturbation for 600 s and then shearing back to a strain amplitude of 0.03%. (b) Normalized G′ recovery kinetics of the masticated NR, compounds, and CBG70 after a perturbation at 50% strain amplitude.

4. DISCUSSION The CBG network embedded in the rubbery matrix is considered to be crucial for the mechanical reinforcement and Payne effect of the filled compounds. Investigating the viscoelasticity of bulk CBG is thus helpful for revealing the underlying mechanism of the Payne effect. The present study is still incapable of distinguishing all the debates about the proposed mechanisms of the Payne effect. Nevertheless, the results should provide insights into the effect of CB networking on the mechanical responses. The reinforcement of filled polymers is usually assigned to the percolation mechanism.90,91 In CB/NR compounds, a continuous filler network contributing largely to the mechanical enhancement is formed when ϕ ≥ ϕc = 0.15 (∼40 phr CB).56 Bulk CBG could be obtained after extraction of the sol fraction. However, G′ of CBG is lower than the expected value of the compound at given ϕ (Figure 2b), which can be ascribed to the presence of small pores in CBGs (Figure 1e−h), the absence of an additional contribution from matrix entanglement,92 and the imperfect interfacial interaction. The CBG network penetrates through the rubbery entanglement network in highly filled compounds; the bridging chains connecting CB aggregates should entangle with the chains of rubber matrix (i.e., the sol fractions), partially accounting for the extrapolated G′ of filled compounds higher than that of CBG at the same ϕ (Figure 2b).92

remains constant at γ = 0.03%, yet the samples after shearing to γ = 50% exhibit a rapid G′ decay and undergo a solid- to liquidlike transition.84 G′ of CBG70 decays with 3 orders of magnitude, much higher than that of the masticated NR and compounds. After the materials are sheared back to γ = 0.03%, they become solid-like with a rapid recovery of G′. The normalized storage modulus, G′/G′0, is plotted as a function of the elapsed time after shearing back (Figure 8b); G′0 is the initial storage modulus of samples before shearing to γ = 50%. The recovery of G′ is partially instant, followed by a gradual recovery process. The masticated NR exhibits a multistep G′ recovery to a constant value of G′/G′0 = 0.8 after about 1 h. The viscoelastic nonlinearity and its recovery of the masticated NR are mainly related to the molecular disentanglement and reentanglement; the shearing thus causes some “permanent” changes in entanglement density. The instant recovery of CBG70 at short elapsed time is more rapid than that of masticated NR and compounds. This result indicates that the CBG network rather than the entanglement network dominates the instant recovery of the highly filled compounds, supporting the deduction of Satoh et al. about the quick healing behavior of filler network.87 Note that during the recover process G′ of both compounds and CBG after 4000 s slightly exceeds G′0 F

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filler interaction could be readily excluded because such processes should not produce the time-dependent Payne effect and its recovery.35,85 A conceivable route of the time-dependent G′ recovery of the unjammed CBG network should involve the network re-formation due to nanoparticle reorganization,94,95 accompanied by chains diffusion to absorb on CB particles and to uniformly fill the interparticle space.73,96,97 Furthermore, the recovery process shown in Figure 8b might also be able to explain by analogy to the aging of soft glassy materials;87,89 it is driven by the diffusion and rearrangements of CB aggregates and their rebuilding interactions mediated by the viscoelasticity of bound rubbers. In highly filled compounds, the rapid unjamming of CBG network couples with the slow disentanglement of the rubbery network, leading to the Payne effect of compounds slower than that of CBGs (Figures 7 and 9). On the other hand, with increasing ϕ, the onset of nonlinearity shifts to low strain, and the ω-dependence of the Payne effect weakens (Figure 7), which should be related to the strain amplification effect.28 Besides the Payne effect, the appearance of G″ maximum, sometimes observed in nanoparticle-filled polymer with suitable filler−polymer interaction,98 is not observed here in the CB/ NR compounds. Robertson and Wang argue that even though the G″ maximum does not appear, the nanoparticles jam at ϕ > ϕc while the straining causes a jamming−unjamming transition; a conceptual fictive dynamic strain is proposed by drawing an analogy to fictive temperature in nonequilibrium glasses.99,100 They find that critical strain energy for onset of the Payne effect, i.e., unjamming, increases linearly with increasing CB loading prior to ϕc, yet it becomes constant above ϕc.66 The critical energies of the isoenergetic unjamming is determined as 2.1 and 3.0 kJ m−3 respectively for CB-filled polybutadiene and NR vulcanizates.100 Richter et al. find that the sheared composite melts exhibit a modulus recovery pointing to the jamming kinetics, whereas the isoenergetic criterion is not transferable to CB-filled ethylene propylene diene rubber.101,102 In the highly filled compounds investigated here, the isoenergetic unjamming transition is excluded as a possible mechanism of the Payne effect on the basis of critical strain energy (Figure 7b). The critical strain energy for the onset of the Payne effect in the filled compounds is located between those of unfilled rubber and CBG and decreases with increasing ϕ.

To account for the reinforcement effect, Satoh et al.87 formulated storage modulus of filled compounds, G′compound = (1 − ϕ)G′rubber + ϕG′BFN + G′CFN, after considering the presence of three networks, the rubber entanglement network, the filler network joined by bridging polymers (BFN), and the contact filler network (CFN). The idea is inspirational, and the results disclose dominative contributions of CFN to both the reinforcement and the Payne effect above ϕc. In our work, the modulus contributions from both BFN and CFN are included in the storage modulus of CBG. There are no leaked CB particles during extended extraction experiment. We thus reconstruct the storage modulus of filled compounds, G′compound, with the measured G′(γ) data of CBG, G′CBG, and masticated NR, G′rubber, by using a simple mixture rule, G′compound = (1 − ϕCBG)G′rubber+ϕCBGG′CBG, in which the volume fraction of CBG, ϕCBG, is calculated by ϕCBG = ϕ/0.42 after taking account of the bound rubber fraction (Table 1). The simple reconstruction should be applicable at ϕ > 0.15 where CB forms network structure. Nevertheless, it is unable to reproduce the Payne effect of the filled compounds (Figure S2a) because the mixing law does not consider the entanglement interaction between the chains of rubber matrix and the bridging chains in CBG. The Payne effect of CBGs (Figure 4) is possibly related to unjamming66 arising from oscillatory shear-induced fluctuation, migration, and rearrangement of CB aggregates at γ > γm.81,89 In CBGs, the caging or self-constraining effects resulting from bound chains mediated multibody attractions between CB aggregates lead to reversibly thermodynamic localization with severely reduced particle diffusion inside the cage;93 therefore, the aggregates jam into a random, rigid network. Under oscillatory shear, the strain induces fluctuation of CB particles, forcing the system to explore different configurations. The CB particles would experience rearrangement once γ surpasses γm; as a consequence, the CBG exhibits yielding and resultant nonlinear viscoelastic response. The unjamming upon shearing is well demonstrated by the appearance of the G″(γ) peak (Figure 4b), which reflects the enhanced energy dissipation produced by constrain motion of individual particles when the cages break apart under shear action.78 In addition, we found that the recovery of G′ of CBG is rapid and reversible upon unloading, whereas the masticated NR (related to the rubber matrix of the compounds) demonstrates slow and irreversible changes of G′ (Figure 8). The strongly bound chains bridging different CB aggregates make CBGs maintain the network structure, which is resistant to high swelling degree during solvent extraction and mechanical disintegration during straining. On the other hand, the reversible unjamming−rejamming during loading− unloading via structural variation of CBG network should proceed with the help of desorption−absorption of some weakly bonded rubber chains with activation energy of absorption in the range of van der Waals interaction.14 The shearing at γ > γm undoubtedly produces smaller aggregates; however, molecular absorption and redistribution of bridging chains should occur after unloading or shearing back to γ < γm, resulting in the recovery of G′ with value slightly higher than the initial one, G′0, after long elapsed time (>4000 s) (Figure 8b). These rheological behaviors cannot be properly explained by the chain slippage model,23,24 bound rubber/entanglement model, or the localized glassy layer model.26 The breakdown and re-formation of CB aggregates generated by direct filler−

5. CONCLUSIONS Bulk CBGs are prepared by solvent extraction of CB highly filled NR compounds. The viscoelastic behaviors of CBG have been systematically studied for the first time. The CBGs obtained from the compounds with CB loadings from 40 to 70 phr are in a jammed state and have a similar composition (ϕ = 0.42), microstructure, and viscoelastic behaviors. The CBG shows more significant Payne effect under oscillatory shearing, characterized by the G′(γ)-dominant linear viscoelasticity accompanied by a weak but evidenced G″(γ) maximum prior to the onset of strain softening, which is ascribed to the unjamming associated with strain-induced rearrangement of CB particles. The Payne effect of CBGs is ω-independent and does not exhibit hysteresis during loading−unloading cycle. Furthermore, the CBG samples sheared to the nonlinearity regime demonstrate rapid modulus recovery immediately after unloading. In comparison, the Payne effect of the compounds is ω-dependent and exhibits evident hysteresis and relatively slow G

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Macromolecules modulus recovery. In the filled compounds, the coexistence of CBG network and rubbery entanglement gives rise to the strong reinforcement effect and the weakened Payne effect. The rapid unjamming of CBG network in combination with the slow disentanglement of the rubbery network results in the decelerated and ω-dependent Payne effect of the highly filled compounds. These results provide a general understanding of viscoelastic behavior of the filler network and will be helpful in clarifying the debates about the proposed mechanisms of the Payne effect for rubbery nanocomposites.

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A Detailed Molecular Dynamics Simulation Study. Soft Matter 2014, 10, 5099−5113. (9) Kreiselmaier, R. Mullins and Payne Effect. Kautsch. Gummi Kunstst. 2014, 67, 16−19. (10) Yang, J.; Han, C. R. Dynamics of Silica-Nanoparticle-Filled Hybrid Hydrogels: Nonlinear Viscoelastic Behavior and Chain Entanglement Network. J. Phys. Chem. C 2013, 117, 20236−20243. (11) Payne, A. R. A Note on the Existence of A Yield Point in the Dynamic Modulus of Loaded Vulcanizates. J. Appl. Polym. Sci. 1960, 3, 127−127. (12) Rharbi, Y.; Cabane, B.; Vacher, A.; Joanicot, M.; Boue, F. Modes of Deformation in A Soft Hard Nanocomposite: A SANS Study. Europhys. Lett. 1999, 46, 472−478. (13) Leblanc, J. L. Simplified Modeling Calculations to Enlighten the Mechanical Properties (Modulus) of Carbon Black Filled Diene Rubber Compounds. J. Appl. Polym. Sci. 2011, 122, 599−607. (14) Sternstein, S. S.; Zhu, A. J. Reinforcement Mechanism of Nanofilled Polymer Melts as Elucidated by Nonlinear Viscoelastic Behavior. Macromolecules 2002, 35, 7262−7273. (15) Kraus, G. Mechanical Losses in Carbon-Black-Filled Rubbers. Appl. Polym. Symp. 1984, 39, 75−92. (16) Maier, P. G.; Goritz, D. Molecular Interpretation of the Payne Effect. Kautsch. Gummi Kunstst. 1996, 49, 18−21. (17) Drozdov, A. D.; Dorfmann, A. The Payne Effect for ParticleReinforced Elastomers. Polym. Eng. Sci. 2002, 42, 591−604. (18) Ouyang, G. B. Modulus, Hysteresis and the Payne Effect. Kautsch. Gummi Kunstst. 2006, 59, 332−343. (19) Payne, A. R. The Dynamic Properties of Carbon Black-Loaded Natural Rubber Vulcanizates. Part I. J. Appl. Polym. Sci. 1962, 6, 57− 63. (20) van de Walle, A.; Tricot, C.; Gerspacher, M. Modeling Carbon Black Reinforcement in Rubber Compounds. Kautsch. Gummi Kunstst. 1996, 49, 172−179. (21) Lin, C. R.; Lee, Y. D. Strain-dependent Dynamic Properties of Filled Rubber Network Systems. Macromol. Theory Simul. 1996, 5, 1075−1104. (22) Lin, C. R.; Lee, Y. D. Strain-dependent Dynamic Properties of Filled Rubber Network Systems, 2. The Physical Meaning of Parameters in the L-N-B Model and Their Applicability. Macromol. Theory Simul. 1997, 6, 339−350. (23) Houwink, R. Slipping of Molecules during the Deformation of Reinforced Rubber. Rubber Chem. Technol. 1956, 29, 888−893. (24) Dannenberg, E. M. Molecular Slippage Mechanism of Reinforcement. Trans. Inst. Rubber Ind. 1966, 42, 26−32. (25) Funt, J. M. Dynamic Testing and Reinforcement of Rubber. Rubber Chem. Technol. 1988, 61, 842−865. (26) Merabia, S.; Sotta, P.; Long, D. R. A Microscopic Model for the Reinforcement and the Nonlinear Behavior of Filled Elastomers and Thermoplastic Elastomers (Payne and Mullins Effects). Macromolecules 2008, 41, 8252−8266. (27) Fukahori, Y. The Mechanics and Mechanism of the Carbon Black Reinforcement of Elastomers. Rubber Chem. Technol. 2003, 76, 548−566. (28) Sun, J.; Song, Y. H.; Zheng, Q.; Tan, H.; Yu, J.; Li, H. Nonlinear Rheological Behavior of Silica Filled Solution-Polymerized Styrene Butadiene Rubber. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 2594− 2602. (29) Rault, J.; Marchal, J.; Judeinstein, P.; Albouy, P. Stress-Induced Crystallization and Reinforcement in Filled Natural Rubbers: 2H NMR Study. Macromolecules 2006, 39, 8356−8368. (30) Medalia, A. I. Effective Degree of Immobilization of Rubber Occluded within Carbon Black Aggregates. Rubber Chem. Technol. 1972, 45, 1171−1194. (31) Song, Y. H.; Zheng, Q. Linear Viscoelasticity of Polymer Melts Filled with Nano-Sized Fillers. Polymer 2010, 51, 3262−3268. (32) Song, Y. H.; Zheng, Q. Application of Two Phase Model to Linear Dynamic Rheology of Filled Polymer Melts. Polymer 2011, 52, 6173−6179.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b02701. Experimental setup for solvent extraction, strain sweep of the compound and CBG by using plates with serrated or flat surface, Lissajous map, and time sweep of the compounds (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (Z.L.W.). *E-mail [email protected] (Y.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the National Nature Science Foundation of China (No. 51573157, 51373149, and 51333004), the Major Projects of Science and Technology Plan of Guizhou Province of China (Grant No. (2013)6016), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, is gratefully appreciated.

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REFERENCES

(1) Koga, T.; Hashimoto, T.; Takenaka, M.; Aizawa, K.; Amino, N.; Nakamura, M.; Yamaguchi, D.; Koizumi, S. New Insight into Hierarchical Structures of Carbon Black Dispersed in Polymer Matrices: A Combined Small-Angle Scattering Study. Macromolecules 2008, 41, 453−464. (2) Wolff, S.; Wang, M. J.; Tan, E. H. Filler Elastomer Interactions 0.7. Study on Bound Rubber. Rubber Chem. Technol. 1993, 66, 163− 177. (3) Hyun, K.; Wilhelm, M.; Klein, C. O.; Cho, K. S.; Nam, J. G.; Ahn, K. H.; Lee, S. J.; Ewoldt, R. H.; McKinley, G. H. A Review of Nonlinear Oscillatory Shear Tests: Analysis and Application of Large Amplitude Oscillatory Shear (LAOS). Prog. Polym. Sci. 2011, 36, 1697−1753. (4) Harwood, J. A. C.; Payne, A. R.; Whittake, R. E. Stress Softening and Reinforcement of Rubber. J. Macromol. Sci., Part B: Phys. 1971, 5, 473−486. (5) Harwood, J. A. C.; Mullins, L.; Payne, A. R. Stress Softening in Natural Rubber Vulcanizates. Part II. Stress Softening Effects in Pure Gum and Filler Loaded Rubbers. J. Appl. Polym. Sci. 1965, 9, 3011− 3021. (6) Medalia, A. I. Electrical-Conduction in Carbon-Black Composites. Rubber Chem. Technol. 1986, 59, 432−454. (7) Heinrich, G.; Vilgis, T. A. A Statistical Mechanical Approach to the Payne Effect in Filled Rubbers. eXPRESS Polym. Lett. 2015, 9, 291−299. (8) Shen, J.; Liu, J.; Gao, Y.; Li, X.; Zhang, L. Elucidating and Tuning the Strain-Induced Non-linear Behavior of Polymer Nanocomposites: H

DOI: 10.1021/acs.macromol.5b02701 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

Dynamics in Poly(vinyl acetate). Macromolecules 2008, 41, 1289− 1296. (57) Kaufman, S.; Slichter, W. P.; Davis, D. D. Nuclear Magnetic Resonance Study of Rubber-Carbon Black Interactions. J. Polym. Sci., Part A-2: Polym. Phys. 1971, 9, 829−839. (58) Kenny, J. C.; McBrierty, V. J.; Rigbi, Z.; Douglass, D. C. CarbonBlack Filled Natural-Rubber. 1. Structural Investigations. Macromolecules 1991, 24, 436−443. (59) Obrien, J.; Cashell, E.; Wardell, G. E.; McBrierty, V. J. NMR Investigation of Interaction between Carbon-Black and Cis-Polybutadiene. Macromolecules 1976, 9, 653−660. (60) Litvinov, V. M.; Steeman, P. A. M. EPDM-Carbon Black Interactions and the Reinforcement Mechanisms, As Studied by LowResolution 1H NMR. Macromolecules 1999, 32, 8476−8490. (61) Luchow, H.; Breier, E.; Gronski, W. Characterization of Polymer Adsorption on Disordered Filler Surfaces by Transversal 1H NMR Relaxation. Rubber Chem. Technol. 1997, 70, 747−758. (62) Svensson, L. G.; Svanson, S. E. An NMR Investigation of the Interaction between Carbon-Black and Cis-Polyisoprene. Rubber Chem. Technol. 1980, 53, 975−981. (63) Mansencal, R.; Haidar, B.; Vidal, A.; Delmotte, L.; Chezeau, J. M. High-Resolution Solid-State NMR Investigation of the FillerRubber Interaction: 2. High-Speed 1H Magic-Angle Spinning NMR Spectroscopy in Carbon-Black-Filled Polybutadiene. Polym. Int. 2001, 50, 387−394. (64) Bansal, A.; Yang, H. C.; Li, C. Z.; Cho, K. W.; Benicewicz, B. C.; Kumar, S. K.; Schadler, L. S. Quantitative Equivalence between Polymer Nanocomposites and Thin Polymer Films. Nat. Mater. 2005, 4, 693−698. (65) Petekidis, G.; Moussaid, A.; Pusey, P. N. Rearrangements in Hard-Sphere Glasses under Oscillatory Shear Strain. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2002, 66, 051402. (66) Wang, X. R.; Robertson, C. G. Strain-Induced Nonlinearity of Filled Rubbers. Phys. Rev. E 2005, 72, 031406. (67) Koumakis, N.; Pamvouxoglou, A.; Poulos, A. S.; Petekidis, G. Direct Comparison of the Rheology of Model Hard and Soft Particle Glasses. Soft Matter 2012, 8, 4271−4284. (68) Khandavalli, S.; Rothstein, J. P. Large Amplitude Oscillatory Shear Rheology of Three Different Shear-Thickening Particle Dispersions. Rheol. Acta 2015, 54, 601−618. (69) Randall, A. M.; Robertson, C. G. Linear-Nonlinear Dichotomy of the Rheological Response of Particle-Filled Polymers. J. Appl. Polym. Sci. 2014, 131, 5829−5836. (70) Papon, A.; Montes, H.; Lequeux, F.; Guy, L. Nonlinear Rheology of Model Filled Elastomers. J. Polym. Sci., Part B: Polym. Phys. 2010, 48, 2490−2496. (71) Hyun, K.; Kim, S. H.; Ahn, K. H.; Lee, S. J. Large Amplitude Oscillatory Shear as a Way to Classify the Complex Fluids. J. NonNewtonian Fluid Mech. 2002, 107, 51−65. (72) Sim, H. G.; Ahn, K. H.; Lee, S. J. Large Amplitude Oscillatory Shear Behavior of Complex Fluids Investigated by a Network Model: A Guideline for Classification. J. Non-Newtonian Fluid Mech. 2003, 112, 237−250. (73) Agarwal, P.; Archer, L. A. Strain-Accelerated Dynamics of Soft Colloidal Glasses. Phys. Rev. E 2011, 83, 041402. (74) Mason, T. G.; Weitz, D. A. Linear Viscoelasticity of Colloidal Hard Sphere Suspensions near the Glass Transition. Phys. Rev. Lett. 1995, 75, 2770−2773. (75) Fielding, S. M.; Sollich, P.; Cates, M. E. Aging and Rheology in Soft Materials. J. Rheol. 2000, 44, 323−369. (76) Sollich, P. Rheological Constitutive Equation for a Model of Soft Glassy Materials. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1998, 58, 738−759. (77) Pham, K. N.; Petekidis, G.; Vlassopoulos, D.; Egelhaaf, S. U.; Poon, W. C. K.; Pusey, P. N. Yielding Behavior of Repulsion- and Attraction-Dominated Colloidal Glasses. J. Rheol. 2008, 52, 649−676. (78) Nugent, J. L.; Moganty, S. S.; Archer, L. A. Nanoscale Organic Hybrid Electrolytes. Adv. Mater. 2010, 22, 3677−3680.

(33) Song, Y. H.; Zheng, Q. Application of Two Phase Model to Linear Viscoelasticity of Reinforced Rubbers. Polymer 2011, 52, 593− 596. (34) Meera, A. P.; Said, S.; Grohens, Y.; Thomas, S. Nonlinear Viscoelastic Behavior of Silica-Filled Natural Rubber Nanocomposites. J. Phys. Chem. C 2009, 113, 17997−18002. (35) Allegra, G.; Raos, G.; Vacatello, M. Theories and Simulations of Polymer-Based Nanocomposites: From Chain Statistics to Reinforcement. Prog. Polym. Sci. 2008, 33, 683−731. (36) Stickney, P. B.; Falb, R. D. Carbon Black-Rubber Interactions and Bound Rubber. Rubber Chem. Technol. 1964, 37, 1299−1340. (37) Kraus, G.; Gruver, J. T. Molecular Weight Effects in Adsorption of Rubbers on Carbon Black. Rubber Chem. Technol. 1968, 41, 1256− 1270. (38) Song, Y. H.; Du, M.; Yang, H. M.; Zheng, Q. Structure and Viscoelasticity of Rubber Materials. Acta Polym. Sin. 2013, 13, 1115− 1129. (39) Leblanc, J. L. Rubber-Filler Interactions and Rheological Properties in Filled Compounds. Prog. Polym. Sci. 2002, 27, 627−687. (40) Hamed, G. R.; Hatfield, S. On the Role of Bound Rubber in Carbon-Black Reinforcement. Rubber Chem. Technol. 1989, 62, 143− 156. (41) Pliskin, I.; Tokita, N. Bound Rubber in Elastomers-Analysis of Elastomer-Filler Interaction and Its Effect on Viscosity and Modulus of Composite Systems. J. Appl. Polym. Sci. 1972, 16, 473−492. (42) Sodhani, D.; Reese, S. Finite Element-Based Micromechanical Modeling of Microstructure Morphology in Filler-Reinforced Elastomer. Macromolecules 2014, 47, 3161−3169. (43) Wang, M. J. Effect of Polymer-Filler and Filler-Filler Interactions on Dynamic Properties of Filled Vulcanizates. Rubber Chem. Technol. 1998, 71, 520−589. (44) Dannenberg, E. M. Bound Rubber and Carbon-Black Reinforcement. Rubber Chem. Technol. 1986, 59, 512−524. (45) Leblanc, J. L.; Staelraeve, A. Studying the Storage Maturation of Freshly Mixed Rubber Compounds and Its Effects on Processing Properties. J. Appl. Polym. Sci. 1994, 53, 1025−1035. (46) Schaal, S.; Coran, A. Y. The Rheology and Processability of Tire Compounds. Rubber Chem. Technol. 2000, 73, 225−239. (47) Choi, S. S. Effect of Bound Rubber on Characteristics of Highly Filled Styrene-Butadiene Rubber Compounds with Different Types of Carbon Black. J. Appl. Polym. Sci. 2004, 93, 1001−1006. (48) Leblanc, J. L. A Molecular Explanation for the Origin of Bound Rubber in Carbon Black Filled Rubber Compounds. J. Appl. Polym. Sci. 1997, 66, 2257−2268. (49) Fang, X.; Huang, X.; Lu, Z.; Chen, L.; Chen, S. Synthesis of New Superhydrophobic Nanosilica and Investigation of Their Performance in Reinforcement of Polysiloxane. Polym. Compos. 2010, 31, 1628−1636. (50) Leblanc, J. L.; Hardy, P. Evolution of Bound Rubber during the Storage of Uncured Compounds. Kautsch. Gummi Kunstst. 1991, 44, 1119−1124. (51) Villars, D. S. Studies on Carbon Black. III. Theory of Bound Rubber. J. Polym. Sci. 1956, 21, 257−271. (52) Ban, L. L.; Hess, W. M.; Papazian, L. A. New Studies of CarbonRubber Gel. Rubber Chem. Technol. 1974, 47, 858−894. (53) Ruggerone, R.; Geiser, V. r.; Dalle Vacche, S.; Leterrier, Y.; Manson, J. A. E. Immobilized Polymer Fraction in Hyperbranched Polymer/Silica Nanocomposite Suspensions. Macromolecules 2010, 43, 10490−10497. (54) Robertson, C. G.; Roland, C. M. Glass Transition and Interfacial Segmental Dynamics in Polymer-Particle Composites. Rubber Chem. Technol. 2008, 81, 506−522. (55) Leyva, M. E.; Barra, G. M. O.; Moreira, A. C. F.; Soares, B. G.; Khastgir, D. Electric, Dielectric, and Dynamic Mechanical Behavior of Carbon Black/Styrene-Butadiene-Styrene Composites. J. Polym. Sci., Part B: Polym. Phys. 2003, 41, 2983−2997. (56) Bogoslovov, R. B.; Roland, C. M.; Ellis, A. R.; Randall, A. M.; Robertson, C. G. Effect of Silica Nanoparticles on the Local Segmental I

DOI: 10.1021/acs.macromol.5b02701 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules (79) Pine, D. J.; Gollub, J. P.; Brady, J. F.; Leshansky, A. M. Chaos and Threshold for Irreversibility in Sheared Suspensions. Nature 2005, 438, 997−1000. (80) Corte, L.; Chaikin, P. M.; Gollub, J. P.; Pine, D. J. Random Organization in Periodically Driven Systems. Nat. Phys. 2008, 4, 420− 424. (81) Nagamanasa, K. H.; Gokhale, S.; Sood, A. K.; Ganapathy, R. Experimental Signatures of a Nonequilibrium Phase Transition Governing the Yielding of A Soft Glass. Phys. Rev. E 2014, 90, 049904. (82) Hobbie, E. K. Shear Rheology of Carbon Nanotube Suspensions. Rheol. Acta 2010, 49, 323−334. (83) Kluppel, M. The Role of Disorder in Filler Reinforcement of Elastomers on Various Length Scales. Adv. Polym. Sci. 2003, 164, 1− 86. (84) Vermant, J.; Ceccia, S.; Dolgovskij, M. K.; Maffettone, P. L.; Macosko, C. W. Quantifying Dispersion of Layered Nanocomposites via Melt Rheology. J. Rheol. 2007, 51, 429−450. (85) Zhu, Z. Y.; Thompson, T.; Wang, S. Q.; von Meerwall, E. D.; Halasa, A. Investigating Linear and Nonlinear Viscoelastic Behavior Using Model Silica-Particle-Filled Polybutadiene. Macromolecules 2005, 38, 8816−8824. (86) Song, Y. H.; Zheng, Q. Linear Rheology of Nanofilled Polymers. J. Rheol. 2015, 59, 155−191. (87) Satoh, Y.; Fujii, S.; Kawahara, S.; Isono, Y.; Kagami, S. Differential Dynamic Modulus of Carbon Black Filled, Uncured SBR in Single-Step Large Shearing Deformations. e-J. Soft Mater. 2007, 3, 29−40. (88) Cavaille, J. Y.; Etienne, S.; Perez, J.; Monnerie, L.; Johari, G. P. Dynamic Shear Measurements of Physical Aging and the Memory Effect in a Polymer Glass. Polymer 1986, 27, 686−692. (89) Satoh, Y.; Suda, K.; Fujii, S.; Kawahara, S.; Isono, Y.; Kagami, S. Novel Characterization of Filler Network in Rubber Materials Using Differential Dynamic Modulus in Large Compression and Recovery. eJ. Soft Mater. 2007, 3, 14−20. (90) Prasad, V.; Trappe, V.; Dinsmore, A. D.; Segre, P. N.; Cipelletti, L.; Weitz, D. A. Universal Features of the Fluid to Solid Transition for Attractive Colloidal Particles. Faraday Discuss. 2003, 123, 1−12. (91) Trappe, V.; Weitz, D. A. Scaling of the Viscoelasticity of Weakly Attractive Particles. Phys. Rev. Lett. 2000, 85, 449−452. (92) Zhang, X.; Yang, H.; Song, Y.; Zheng, Q. Rheological Behaviors of Randomly Crosslinked Low Density Polyethylene and Its Gel Network. Polymer 2012, 53, 3035−3042. (93) Maiti, M.; Heussinger, C. Rheology Near Jamming: The Influence of Lubrication Forces. Phys. Rev. E 2014, 89, 052308. (94) Treece, M. A.; Oberhauser, J. P. Soft Glassy Dynamics in Polypropylene-Clay Nanocomposites. Macromolecules 2007, 40, 571− 582. (95) Treece, M. A.; Oberhauser, J. P. Ubiquity of Soft Glassy Dynamics in Polypropylene-Clay Nanocomposites. Polymer 2007, 48, 1083−1095. (96) Agarwal, P.; Qi, H.; Archer, L. A. The Ages in a Self-Suspended Nanoparticle Liquid. Nano Lett. 2010, 10, 111−115. (97) Agarwal, P.; Srivastava, S.; Archer, L. A. Thermal Jamming of a Colloidal Glass. Phys. Rev. Lett. 2011, 107, 268302. (98) Majesté, J. C.; Vincent, F. A Kinetic Model for Silica-Filled Rubber Reinforcement. J. Rheol. 2015, 59, 405−427. (99) Robertson, C. G.; Wang, X. R. Isoenergetic Jamming Transition in Particle-Filled Systems. Phys. Rev. Lett. 2005, 95, 075703. (100) Robertson, C. G. Flocculation in Elastomeric Polymers Containing Nanoparticles: Jamming and the New Concept of Fictive Dynamic Strain. Rubber Chem. Technol. 2015, 88, 463−474. (101) Richter, S.; Saphiannikova, M.; Stöckelhuber, K. W.; Heinrich, G. Jamming in Filled Polymer Systems. Macromol. Symp. 2010, 291− 292, 193−201. (102) Richter, S.; Kreyenschulte, H.; Saphiannikova, M.; Götze, T.; Heinrich, G. Studies of the So-Called Jamming Phenomenon in Filled Rubbers Using Dynamical-Mechanical Experiments. Macromol. Symp. 2011, 306−307, 141−149.

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DOI: 10.1021/acs.macromol.5b02701 Macromolecules XXXX, XXX, XXX−XXX