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Nonlinear Viscoelastic Behavior of Silica-Filled Natural Rubber Nanocomposites A. P. Meera,† Sylvere Said,‡ Yves Grohens,‡ and Sabu Thomas*,† School of Chemical Sciences, Mahatma Gandhi UniVersity, Priyadarshini Hills P.O., Kottayam, Kerala, India 686 560, Laboratoire Polyme`res, Proprie´te´s aux Interfaces et Composites, Centre de Recherche, UniVersite de Bretagne Sud, Rue Saint Maude´, Lorient Cedex, France ReceiVed: March 5, 2009; ReVised Manuscript ReceiVed: August 25, 2009
The nonlinear viscoelastic behavior of the composites of natural rubber filled with surface-modified nanosilica was studied with reference to silica loading. The effect of temperature on the nonlinear viscoelastic behavior has been investigated. It was observed that Payne effect becomes more pronounced at higher silica loading. The filler characteristics such as particle size, specific surface area, and the surface structural features were found to be the key parameters influencing the Payne effect. A nonlinear decrease in storage modulus with increasing strain was observed for unfilled compounds also. The results reveal that the mechanism includes the breakdown of different networks namely the filler-filler network, the weak polymer-filler network, the chemical network, and the entanglement network. The model of variable network density proposed by Maier and Goritz has been applied to explain the nonlinear behavior. The activation energy of desorption was calculated and found to be within the range of Van der Waal’s interaction energy. The model fits well with the experimental results. Introduction The dynamic properties of filled elastomers have been a subject of active research because they affect the performance of tires such as skid, traction, and rolling resistance to cite but a few.1-6 In particular, the effect of the strain amplitude on the viscoelastic properties of filled rubbers, known as the “Payne effect”7 has been extensively investigated because it directly impacts the fuel consumption. From a phenomenological point of view, beyond a strain higher than a few 0.1%, the storage modulus of filled rubber departs from a plateau value G′0 and collapse to a minimum value G∞′ . The decrease in the storage modulus is accompanied by a maximum of the loss modulus, G′′. The amplitude of the Payne effect, ∆G ) G′0 - G′∞ increases with the filler content,7 the specific surface of the filler8 and strongly depends on the surface properties of the fillers and its dispersion9 within the matrix. On the contrary it decreases with temperature.10 A number of different local mechanisms have been proposed so far to explain this phenomenon, but no consensus has emerged yet. In the widely accepted physical interpretation of the strain dependence of the elastic modulus first proposed by Payne,7 the contribution from the pure polymer matrix is assumed to be totally independent of the strain amplitude. According to Payne, the three-dimensional structure network constructed by the aggregation of carbon black filler significantly influences the dynamic viscoelastic properties of carbon black filled rubbers. Kraus8 proposed a model based on the agglomeration/ deagglomeration kinetics of filler aggregates by assuming a Van der waal’s type interaction between the particles. This model was further developed by Huber and Vilgis,11-13 who relate G′ and G′′ to the fractal dimension and the connectivity of the network, and by Kluppel, who introduces the idea of cluster.14 * Corresponding author. E-mail:
[email protected]; sabut@ sancharnet.in. Tel.: 91-481-2730003; Fax: 91-481-2731002. † Mahatma Gandhi University. ‡ Universite de Bretagne Sud.
The fact that the temperature and the frequency dependence of the amplitude of the Payne effect are not taken into consideration is certainly the most accepted criticism of this approach. However, one of the major drawbacks comes from the evidence brought by Funt,15 who shows from electrical conductivity measurements that the Payne effect might occur although a continuous filler network does not exist through the sample. As an alternative to the destruction and reformation of a filler network, it has also been proposed that the dynamics of adsorption/desorption of the polymer chains at the particle surface may be responsible for various linear and nonlinear effects.16,17 Zhu and Sternstein have suggested that the reduction of the storage modulus with the applied strain could be related to polymer-filler interactions including the aspects of trapped topological entanglements.18 The interaction between the filler particles and the rubber matrix, which leads to the adsorption of polymer chains on the particle surface, can be controlled by varying the nature of the polymer-filler interface.19-24 Maier and Goritz16,25-27 take into consideration the adsorption/ desorption mechanism by considering the filler particles as multifunctional cross-link with chains which are either loosely or strongly anchor to the surface. The molecular interpretation of the Payne effect is then based on a variable network density when the loosely tied chains are desorbed with the increase of the strain. A compromise is also suggested, considering that the primary mechanism for the Payne effect certainly involves the existence of cooperation between the breakdown and reformation of the filler network and the molecular disentanglement of the bound and free rubber.15,28-30 Another explanation first proposed by Yatsuyanagi et al.31 considers the existence of a percolation network through the rigid amorphous layer formed around the particles. Their interpretation of the Payne effect equally relies on the competition between desorption and adsorption of this rigid amorphous layer. The importance of glassy layers in filled polymer has received considerable attention very recently, when it was recognized
10.1021/jp9020118 CCC: $40.75 2009 American Chemical Society Published on Web 09/24/2009
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TABLE 1: Characteristics of Nanosilica properties
values
specific surface area (BET) average particle diameter carbon content moisture pH SiO2 content
160 ( 25 m2/g 12-13 nm 2.0-4.0 wt % e0.5 wt % g5.0 >99.8 wt %
TABLE 2: Formulation of Mixes ingredient
recipe, phr
rubber zinc oxide stearic acid TMQa CBSb sulfur silica
100 5 1.5 1 0.6 2.5 variable
a 2,2,4-Trimethyl-1,2-dihydroquinoline, polymerized. 2-benzothiazyl-sulphenamide.
b
Figure 1. TEM micrographs of silica.
N-Cyclohexyl-
that a glass transition gradient exist near the surface and that the dynamics could be either enhanced or slowed down according to the interaction of the chains with the surface. In a body of work,32-35 Montes et al. among others36 have clearly shown in filled elastomers that a maximum of reinforcement is obtained when this rigid or slow dynamics layer forms a continuous path through the filler aggregates. In their work, Merabia et al.37 model the Payne effect by considering that the stress is supported mainly by the cross section of glassy bridges in a direction normal to the stress. They explain the strain dependence of the elastic modulus by the local lowering of the glass transition due to the amplification of the stress in the vicinity of the aggregates. This plasticizing effect induces the yielding of the glassy bridges and the collapse of the storage modulus. To the best of our knowledge, not much work has been devoted to the studies of the nonlinear viscoelastic behavior of natural rubber filled with nanofillers. The objective of the present study is to investigate the effect of nanosilica on the nonlinear viscoelastic properties of rubbers and to understand the mechanism of nonlinearity in such systems. Experimental Section Materials. The natural rubber, NR, used for the study was procured from Rubber Research Institute of India, Kottayam, Kerala. The molecular weight of NR obtained by light scattering is Mn )2.68 × 105 g/mol, Mw ) 8.38 × 105 g/mol and Mw/Mn )3.1. The surface modified nanosilica used for the study (AEROSIL R 8200) was obtained from Degussa, Germany. The characteristics of silica are given in Table 1. All other ingredients used were of commercial grade and were kindly supplied by LANXESS, Germany. Preparation of Composites. The composite materials were prepared via melt mixing technique on a laboratory two-roll mill. Formulation of mixes is shown in Table 2. NR was masticated on the two-roll mill for about two to three minutes followed by addition of the ingredients. Cure characteristics were studied using an Oscillating Disc Rheometer (Monsanto R-100), at a temperature of 150 °C. The compounds were cured at their respective cure times using a hydraulic press under a pressure of about 120 bar at 150 °C. Viscoelastic Measurements. The viscoelastic measurements were performed on a dynamic mechanical analyzer (TA Instru-
Figure 2. Strain dependence of the storage modulus for NR filled with nanosilica: (O) 0 phr, (4) 5 phr, (3) 10 phr, (]) 15 phr, (*) 20 phr. The dotted lines represent the curve fits according to the model.
ments) in tension mode. Payne effect measurements were carried out at a constant frequency of 0.5 Hz at 303 K. To study the effect of temperature on the Payne effect, we tested the samples at various temperatures ranging from 248 to 373 K with 10 K steps. Morphology Characterization. The size of the elementary particles was characterized by transmission electron microscopy (TEM) with a C M 12 PHILIPS HRTEM. The structure of pure silica was analyzed by TEM (Figure 1). The silica particles are aggregated and the mean aggregate diameter was found to be around 25 nm. The state of dispersion was analyzed by atomic force microscopy on ultra cryotomed surfaces cut at 153K in tapping mode with a cantilever having a stiffness of 48 N/m and a length of 250 µm. The images were carried out simultaneously in height, phase, and amplitude. Results and Discussion Viscoelastic Properties versus Strain. The viscoelastic behavior vs strain is investigated for silica filled natural rubber and the results show the qualitative features generally observed for the Payne effect. The effect of the strain amplitude on the storage modulus at various silica concentrations for the composites is shown in Figure 2. The storage modulus is the highest at small amplitude (referred to as E′0) and gradually decreases to a low value (referred to as E′∞). The magnitude of the Payne effect (E0′ - E′∞) increases with the silica content. At low silica loading, the observed variation in the amplitude of the Payne effect is weak. But as the silica concentration increases, significant and pronounced variation is observed. This is principally due to the breakdown of the filler networks at high strains. At low filler loading, the chances of forming agglomer-
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Figure 4. Strain dependence of loss modulus for silica-filled NR: (]) 0 phr, (b) 5 phr, (2) 15 phr, (*) 20 phr. Figure 3. AFM height images of natural rubber composites filled with 20 phr nanosilica.
ates are practically nil. But at higher loading, because of the small particle size (12-13 nm) and high specific surface area (160 ( 25 m2/g), silica particles tend to agglomerate to higher extent. The structure of filler particles within the rubber matrix, i.e., the state of dispersion and aggregation has a strong influence on the Payne effect. In the rubber matrix, the state of dispersion of spherical particles can vary from highly dispersed to totally aggregate depending on the thermodynamics of the system and kinetics of samples preparation. The clustering of filler particles is favored by strong van der Waals forces. The AFM picture of cryo microtomed silica nanocomposites with 20 phr is shown in Figure 3. Although it is not possible to derive an accurate characterization of 3D network from a 2D representation, we can have a rough estimate of the aggregates size and their separating distance. A typical aggregate size is 100 nm and a characteristic distance between two aggregates is a few tens of nanometers. Although it might be misleading in a 3D space, no continuous path was found in a 2D space, hinting that if a percolation network does exist, it is mediated through polymer bridges. Many experimental works come to this conclusion. The rheological properties can be used as a tool to assess the state of dispersion in the melt state38,39 and the existence of a network by analyzing the independence of the storage and loss modulus at low frequency.28,40 For instance Leblanc has estimated the so-called bound rubber41 from the unextractable polymer fraction and has related the effect of elastomer-filler interactions to the rheological properties. Zhang and Archer39 in poly(ethylene oxide) melt containing silica nanospheres show that the rheological properties are governed by the bridging of nanosized silica particles surrounded by an immobilized shell of PEO. A maximum in the loss modulus E′′ is observed for the composites as shown in Figure 4. At filler loading higher than 10 phr, a pronounced maximum is observed. It is thus very appealing to make the hypothesis that different contributions are at stake in the dissipated energy. One contribution comes from the rubbery matrix and is mainly independent from the filler content. A second one comes from the shearing of the glassy layers around the filler particles. Another contribution may be ascribed to the mechanism responsible for the collapse
of the storage modulus. Within the frame of the Kraus model, this extra contribution to the energy dissipation comes from the friction between the filler particles. For models involving bound rubber, it might be related to the friction of the chains, either on the surface of the filler particles or within the glassy layer during its softening under the effect of the applied stress. In those two former mechanisms, the amount of energy dissipated scales the total surface of the particles. The maximum comes from the competition between the breaking and the reformation of the network whatever the nature is (filler-filler, entanglement, glassy bridges, etc.). When the strain increases, the destruction of the network starts and increases the dissipated energy. For higher value of the strain, the rate of destruction is higher than the rate of the reconstruction of the network. As a consequence, the dissipation energy associated with the breaking of the network decreases and the loss modulus goes through a maximum with the strain. The drop of the storage modulus is attributed to the breakdown of this network. The structural breakdown of the silica agglomerates is shown schematically in Figure 5a. On applying strain to the filled vulcanizates, the breakdown of the filler network occurs, which results in a decrease in the agglomerate size and desorption of the rubber chains from the filler surface. In the initial stage, because of the large agglomerate size, there are chances for multiple points of attachment. But on straining, because of the reduced size of the agglomerates, multiple points get converted to single points of attachment as shown schematically in Figure 5b. An interesting finding is the observation of a Payne effect for the unfilled vulcanized rubber, which is contrary to what is reported so far in the literature. According to the generally accepted interpretation of the Payne effect, the contribution from the unfilled rubber is assumed to be independent of the strain amplitude. However, Pan and Kelley recently reported an enhanced Payne effect near the glass transition region for gum vulcanizates prepared from oil extended styrene-butadiene rubber (SRB).42 Although a consensus does not exist, the Payne effect is associated with the competing destruction/building process. Thus, we infer the existence of a secondary network in the unfilled vulcanized rubber. Considering the large polydispersity index of 3.1, we can make the assumption of the existence of an entanglement network. This assumption is backed up by swelling measurements of un-cross-linked rubber with toluene, a good solvent.
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Figure 6. Effect of temperature on the Payne effect for NR filled with 20 ph silica: (0) 248 K, (4) 263 K, (O) 303 K, (]) 373 K. The dotted lines represent the curve fits according to the model.
Figure 5. (a) Schematic representation of the breakdown of aggregates and desorption of rubber chain segments from the filler surface in silicafilled NR system (b) Schematic representation showing the multiple points of attachments of rubber chains at the silica surface converting to the single points of attachments on straining.
We notice that the raw rubber swells and does not dissolve completely after several weeks even when the solvent is renewed, proving the existence of an elasticity network. Besides, for this hypothesis to hold true, the mass between cross-links, Mc, should be larger than the entanglement mass of polyisoprene, which is 1850 g/mol.43 This last point has been checked from swelling measurements on vulcanized natural rubber and 20 phr silica vulcanized nanocomposites. The mass between cross-links has been computed from the polymer volume fraction in the swollen samples using the Flory Rhener44 model. Typical values of Mc of 6000 g/mol have been obtained, sustaining the idea of an entanglement network. Effect of Temperature on the Payne Effect. Figure 6 shows the effect of temperature on the Payne effect for natural rubber filled with 20 phr of nano silica. As previously reported,10 the amplitude of the Payne effect decreases dramatically with temperature. This is contrary to the theory of rubber elasticity, according to which the modulus should increase linearly with the temperature. In agreement with the former explanation given for the Payne effect, the temperature increases the rate of destruction of the network by weakening its cohesion. In the Kraus’ model, the temperature affects the strength of the van der Waals forces between the particles. In the Merabia’s vision, the thickness of the glassy layer decreases, diminishing as a consequence the number of glassy bridges forming the network. For Maier and Goritz, the rate of the chains desorption increases with temperature. Application of the Model of Variable Network Density. In the Maier and Go¨ritz model,25-27 it is assumed that the rubber molecules come in contact with the filler surface and get adsorbed. After forming the first link, the neighboring segments have a high probability to attach to the next interaction position. These chains form stable bonds to the filler surface, whereas the remaining chains coming afterward form unstable bonds
having very weak links to the particle. These can be easily removed by a tensile force or by raising the temperature. According to this model, the network density of a filled vulcanised elastomer (N) comes from the overall contribution of the chemical network density, Nc, the chains network density caused by stable bonds at the filler surface, Nst, and the density of unstable bonds between chains and filler, Nl
N ) Nc + Nst + Nl
(1)
Storage modulus E′ ) NkBT where N is the network density, kB is the Boltzmann constant, and T is the temperature in Kelvin. The strain dependent modulus can be described by means of the theory of entropy and elasticity with
E′(γ) ) (Nc + Nst + Nl(γ))kBT
(2)
By analogy with the Langmuir isotherm formation, it is assumed that the adsorption/desorption process reaches a balance after a certain time. On the assumption that the desorption rate is proportional to the strain amplitude, γ, the dependence of the modulus on γ can be written as
E′(γ) ) E′st + E′l /(1 + cγ)
(3)
E′st ) (Nc + Nst)kBT
(4)
E′l ) NlokBT
(5)
With
and
The experimental curves were fitted to eq 3. Figure 1 shows the curve fits for the storage modulus versus the strain amplitude. The fit parameters, E′st and E′l and the values of χ2/DOF and R2 to assess the quality of fit are given in Table 3. Both E′st and E′l increase with an increase in silica content. The values characterizing the unstable part of the network are strongly influenced by the filler content, as can be seen from the table. The model equally applies when no filler is added, suggesting
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TABLE 3: Fit Parameters of Eq 1 silica content (phr)
E′st (MPa)
E′l (MPa)
c
χ2/DOF
R2
0 10 15 20
0.17 0.32 0.43 0.57
1.56 1.82 1.75 2.22
0.03 0.06 0.11 0.15
0.001 0.002 0.002 0.003
0.992 0.993 0.993 0.994
TABLE 4: Fit Parameters As a Function of Temperature silica T Nc + Nst/1020 Nlo/1020 content (phr) (K) (1/cm3) (1/cm3) 15 20
303 323 343 248 263 303 343 373
0.82 0.63 0.45 1.88 1.17 0.90 0.83 0.37
3.86 3.53 3.09 10.87 7.07 4.98 2.99 2.73
c
χ2/DOF
R2
0.10 0.08 0.07 0.17 0.12 0.10 0.13 0.05
0.001 0.002 0.002 0.020 0.004 0.003 0.002 0.001
0.995 0.991 0.992 0.988 994 994 992 0.996
that part of the entanglement network has a longer relaxation time than the experimental time defined as the inverse of the frequency. Effect of Temperature. The experimental curves obtained for NR filled with 20 phr silica and fitted to eq 3 are shown in Figure 6. The dotted lines represent the curve fits according to the model. The fit parameters along with the values of Chıˆ2/ DoF and Rˆ2 are listed in Table 4. It is observed that both the number of the stable and unstable bonds of the network is identically reduced by roughly a factor 5 when the temperature goes from 248 to 373 K. The huge variation of the stable bonds with temperature questions the initial picture where stable bonds were depicted in terms of trains and tightly bounded chains at the vicinity of the surface.45-47 This image was mainly sustained by NMR results, which show that this layer with a typical thickness of 1 nm remains immobile to temperature up to Tg + 200 K.47,48 Unless the polymer filler interface is poorly cohesive, it seems unlikely to explain the sharp decrease in the stable bond contribution from the desorption of the tightly bounded chains when the temperature is around Tg + 150 °C. A plausible explanation to reconcile the Maier and Goritz model and the variation of the stable bonds with temperature is to consider that the stable bonds are materialized by glassy bridges as suggested by Merabia et al. It is thus straightforward to understand the dramatic effect of temperature when it goes higher than the glass transition temperature of the rigid amorphous layer. The unstable bonds would represent the population of chains whose Tg are very close to the experiment temperature. To further analyze the results, the temperature dependence of the density of unstable bonded chains is written as an Arrhenius law according to
Nlo(T) ) Nlooe-El/kBT
(6)
where Nloo is a constant characterizing the density of unstable bonds and is independent of temperature and the deformation amplitude; El is the activation energy of desorption. From the plot of the logarithm of the density of unstable chains against the inverse of temperature shown in Figure 7, the activation energy can be calculated and is found to be 0.09 eV for NR filled with 20 phr of silica. This value is within the range of Van der Waal’s interaction energy.49 The rate of desorption is directly proportional to the number of unstable chains at the filler surface. Hence it is concluded that the number
Figure 7. Arrhenius plot of the network density of unstable fixed chains for NR filled with 20 phr silica.
of unstable fixed chains adsorbed on the filler surface is also responsible for the reduction in modulus with increase in temperature. Conclusions This study focuses on the dynamic viscoelastic properties of nanosilica-filled natural rubber composites. The objective of the present study was to look at the nonlinear viscoelastic behavior of natural rubber filled with commercially used nanosilica. The Payne effect is assumed to arise from the elementary mechanism consisting of adsorption-desorption of macromolecular chains from the filler surface. It was found that because of the small particle size and high specific surface area, nanosilica forms stronger and more developed filler-filler network and the breakdown of these networks results in larger Payne effect. Also, the amount and morphology of the fillers played a major role on the Payne effect. At low loading, there is not much variation in storage modulus, loss modulus, and loss tangent compared to gum vulcanizates. But at higher loading, a pronounced effect has been observed. This is due to the breakage of weak polymer-filler linkages and filler-filler networks at higher strain amplitude. But surprisingly, enhanced Payne-like behavior has been observed for gum vulcanizates at room temperature where there are no filler-filler and no filler-polymer interactions, which are typically associated with filled vulcanizates. This is explained by the effect of chain disentanglements on straining. The model of variable network density has been applied and the calculated activation energy for NR filled with 20 phr silica is found to be within the range of Van der Waal’s interaction energy. Hence it is concluded that the number of unstable fixed chains adsorbed on the filler surface is also responsible for the reduction in modulus with increase in temperature. Finally, it is concluded that in addition to the contribution from filler-filler network, there are a lot of factors that affect the nonlinear viscoelastic behavior including the breakdown of different networks, namely, filler-filler networks, weak polymer-filler networks, chemical networks, and entanglement networks. Acknowledgment. We gratefully acknowledge Rubber Research Institute of India (RRII), Kerala, for providing natural
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rubber; LANXESS Deutschland GmbH, Germany, for supplying the rubber chemicals for the research work. Thanks are due to KSCSTE, Kerala, for the financial support. The authors are grateful to Prof. Dr. Dietmar Goeritz, Fakulty of Physics, University of Regensburg, for the fruitful discussion. References and Notes (1) Payne, A. R. J. Appl. Polym. Sci. 1962, VI, 57. (2) Payne, A. R. Reinforcement of Elastomers; Interscience: New York, 1965’ Chapter 3, p 69. (3) Payne, A. R. J. Appl. Polym. Sci. 1962, VI, 368. (4) Payne, A. R. J. Appl. Polym. Sci. 1965, 9, 1073. (5) Payne, A. R.; Whitaker, R. E. Rubber Chem. Technol. 1971, 44, 440. (6) Robertson, C. G.; Lin, C. J.; Rackaitis, M.; Roland, C. M. Macromolecules 2008, 41, 2727. (7) Payne, A. R. J. Appl. Polym. Sci. 1965, 8, 2661. (8) Kraus, G. J. Appl. Polym. Sci. 1984, 39, 75. (9) Medalia, A. I. Rubber World 1973, 168, 49. (10) Wang, M. Rubber Chem. Technol. 1998, 71, 520. (11) Huber, G.; Vilgis, T. A. Macromolecules 2002, 35, 9204. (12) Witten, T. A.; Rubinstein, M.; Colby, R. H. J. Phys. II 1993, 3, 367. (13) Heinrich, G.; Kluppel, M.; Vilgis, T. A. Curr. Opin. Solid State Mater. Sci. 2002, 6, 195. (14) Kluppel, M.; Schuster, R.; Heinrich, G. Rubber Chem. Technol. 1997, 70, 243. (15) Funt, J. M. Rubber Chem. Technol. 1999, 4, 657. (16) Maier, P. G.; Goritz, D. Kautsch. Gummi Kunst. 1996, 49, 18. (17) Sternstein, S. S.; Zhu, A. J. Macromolecules 2002, 35, 7262. (18) Zhu, A. J.; Sternstein, S. S. Compos. Sci. Technol. 2003, 63, 1113. (19) Marrone, M.; Montanari, T.; Busca, G.; Conzatti, L.; Costa, G.; Castellano, M.; Turturro, A. J. Phys. Chem. B 2004, 108, 3563. (20) Bokobza, L. Macromol. Mater. Eng. 2004, 289, 607. (21) Castellano, M.; Conzatti, L.; Turturro, A.; Costa, G.; Busca, G. J. Phys. Chem. B 2007, 111, 4495. (22) Paquien, J. N.; Galy, J.; Gerard, J. F.; Pouchelon, A. Colloids Surf., A 2005, 260, 165. (23) Clement, F.; Bokobza, L.; Monnerie, L. Rubber Chem. Technol. 2005, 78, 211. (24) Ramier, J.; Gauthier, C.; Chazeau, L.; Stelandre, L.; Guy, L. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 286.
Meera et al. (25) Maier, P. G.; Goritz D. Kautsch. Gummi Kunstst. 1993, 46, Jahrgang.Nr.11/93. (26) Maier, P. G.; Goritz D. Kautsch. Gummi Kunstst. 1996, 49, Jahrgang.Nr.1/96. (27) Maier, P. G.; Goritz D. Kautsch. Gummi Kunstst. 2000, 53, Jahrgang.Nr.12/2000. (28) Cassagnau, P. Polymer 2008, 49, 2183. (29) Cassagnau, P. Polymer 2003, 44, 2455. (30) Sun, J.; Song, Y.; Zheng, Q.; Tan, H.; Yu, J.; Li, H. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 2594. (31) Yatsuyanagi, F.; Kaidou, H.; Ito, M. Rubber Chem. Technol. 1999, 4, 657. (32) Berriot, J.; Lequeux, F.; Montes, H.; Monnerie, L.; Long, D.; Sotta, P. J. Non-Cryst. Solids 2002, 307, 719. (33) Berriot, J.; Montes, H.; Lequeux, F.; Long, D.; Sotta, P. Macromolecules 2002, 35, 9756. (34) Berriot, J.; Montes, H.; Lequeux, F.; Long, D.; Sotta, P. Europhys. Lett. 2003, 64, 50. (35) Montes, H.; Lequeux, F.; Berriot, J. Macromolecules 2003, 36, 8107. (36) Jouault, N.; Vallat, P.; Dalmas, F.; Said, S.; Jestin, J.; Boue, F. Macromolecules 2009, 42, 6–2031. (37) Merabia, S.; Sotta, P.; Long, D. R. Macromolecules 2008, 41, 8252. ¨ ttinger, H. C. J. Rheol. (38) Osman, M. A.; Atallah, A.; Schweizer, T.; O 2004, 48, 5–1167. (39) Zhang, Q.; Archer, L. A. Langmuir 2002, 18, 10435. (40) Leblanc, J. L. Prog. Polym. Sci. 2002, 27, 627. (41) Leblanc, J. L. J. Appl. Polym. Sci. 2000, 78, 8–1541. (42) Pan, X. D.; Kelley, E. D. Polym. Eng. Sci. 2003, 43 (8), 1512. (43) Bicerano, J. Prediction of Polymer Properties; Marcel Dekker: New York, 2002; p 396. (44) Flory, P. Principles of Polymer Chemistry; Cornell University Press; Ithaca, NY, 1971; Chapter 12. (45) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T. Polymers at Interfaces; Chapman & Hall: London, 1993. (46) Cohen Addad, J. P.; Frebourg, P. Polymer 1996, 17, 4235. (47) V. M. Litvinov, V. M.; Steeman, P. A. M. Macromolecules 1999, 32, 8476. (48) Haidar, B.; Vidal, A.; Papirer, E. Proceedings of the International Conference on Filled Polymers and Fillers (Eurofillers ’97); Manchester, U.K., Sept 8-11, 2007; British Plastics Federation: London, 1997; p 239. (49) Frisch, M. L.; Shima, R.; Eirich, F. E. J. Phys. Chem. 1953, 57, 584.
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