Rubbery Materials Research Articles

Novel percolation phenomena and mechanism of strengthening elastomers by nanofillers

Nano-strengthening by employing nanoparticles is necessary for high-efficiency strengthening of elastomers, which has already been validated by numerous researches and industrial applications, but the underlying mechanism is still an open challenge. In this work, we mainly focus our attention on studying the variation of the tensile strength of nanofilled elastomers by gradually increasing the filler content, within a low loading range. Interestingly, the percolation phenomenon is observed in the relationship between the tensile strength and the filler loading, which shares some similarities with the percolation phenomenon occurring in rubber toughened plastics. That is, as the loading of nanofillers (carbon black, zinc oxide) increases, the tensile strength of rubber nanocomposites (SBR, EPDM) increases slowly at first, then increases abruptly and finally levels off. Meanwhile, the bigger the particle size, the higher the filler content at the percolation point, and the lower the corresponding tensile strength of rubber nanocomposites. The concept of a critical particle-particle distance (CPD) is proposed to explain the observed percolation phenomenon. It is suggested that rubber strengthening through nanoparticles is attributed to the formation of stretched straight polymer chains between neighbor particles, induced by the slippage of adsorbed polymer chains on the filler surface during tension. Meanwhile, the factors to govern this CPD and the critical minimum particle size (CMPS) figured out in this work are both discussed and analyzed in detail. Within the framework of this percolation phenomenon, this paper also clearly answers two important and intriguing issues: (1) why is it necessary and essential to strengthen elastomers through nanofillers; (2) why does it need enough loading of nanofillers to effectively strengthen elastomers. Moreover, on the basis of the percolation phenomenon, we give out some guidance for reinforcement design of rubbery materials: the interfacial interactions between rubber and fillers cannot be complete chemical bonding, and partial physical absorption of macromolecular chains on the filler surface is necessary, otherwise the formation of stretched straight chains would be seriously hindered. There should exist such an optimum crosslinking density for a certain filler reinforced rubber system, and as well an optimum filler loading for rubber strengthening. Additionally, the different percolation behaviors of Young's modulus, the tensile strength and the electrical conductivity are compared and analyzed in our work. Lastly, molecular simulation indicates that it is not possible to strengthen glassy or hard polymer matrices by incorporating spherical nanoparticles. In general, by providing substantial experimental data and detailed analyses, this work is believed to promote the fundamental understanding of rubber reinforcement, as well provide better guidance for the design of high-performance and multi-functional rubber nanocomposites.

Problems in determining the elastic strain energy function for rubber

Abstract Lightly crosslinked natural rubber can be stretched by 600% or more, and recovers almost completely. It is often regarded as a model highly elastic material and characterized by a strain energy function to describe its stress–strain behavior under various types of deformation. A number of such functions have been proposed; some of them appear in current finite element programs. They are usually validated by comparison with measured stress–strain relations by Treloar [7] [L.R.G. Treloar, Stress–strain data for vulcanized rubber under various types of deformation, Trans. Faraday Soc. 40 (1944) 59–70] and Jones and Treloar [15] [D.F. Jones, L.R.G. Treloar, The properties of rubber in pure homogeneous strain, J. Phys. D Appl. Phys. 8 (1975) 1285–1304]. But Treloar pointed out that the relations at high strains became markedly irreversible, and he did not assign a strain energy function for strains greater than about 300%. Rivlin's universal relation between torsional stiffness and tensile stress [14] [R.S. Rivlin, Large elastic deformations of isotropic materials. Part V1: further results in the theory of torsion, shear and flexure, Philos. Trans. R. Soc. A 243 (1949) 251–288] is applied here to show that a typical elastic solid cannot be described by any strain energy function at strains greater than about 300%. Elastic strain energy functions for higher strains, or for other rubbery materials, are thus of doubtful value unless evidence for reversibility of stress–strain relations is adduced or the applicability of a strain energy function is demonstrated.

Field emission scanning electron microscopy combined with focused ion beam for rubbery material with nano-matrix structure

Nano-matrix structure of a graft-copolymer consisting of deproteinized natural rubber (DPNR) and polystyrene (PS) was observed through field-emission scanning microscopy combined with a focused gallium (Ga) ion beam (FIB-SEM). The graft-copolymer was carefully stained with osmium tetraoxide for more than a week to avoid a charge-up through FIB-SEM. Field emission SEM images of the graft-copolymer were taken after etching its surface with the Ga ion at each interval and they were reconstructed to obtain the three-dimensional image of the nano-matrix structure. The NR particles of about 0.5 μm in diameter were found to be dispersed into the nano-matrix of PS, which connected to each other on all directions. The dimensional feature of the NR particles was dependent upon an expression of orthogonal views of the 3D image.

The M-Integral Description for a Brittle Plane Strip With Two Cracks Before and After Coalescence

In this paper we extend the M-integral concept (Eshelby, J. D., 1956, The Continuum Theory of Lattice Defects, Solid State Physics, F. Seitz and D. Turnbull, eds., Academic, New York, pp. 79–141; Eshelby, J. D., 1970, The Energy Momentum Tensor in Continuum Mechanics, Inelastic Behavior of Solids, M. F. Kanninen, ed., McGraw-Hill, New York, pp. 77–115; Eshelby, J. D., 1975, “The Elastic Energy-Momentum Tensor,” J. Elast., 5, pp. 321–335; Knowles, J. K., and Sternberg, E., 1972, “On a Class of Conservation Laws in Linearized and Finite Elastostatics,” Arch. Ration. Mech. Anal., 44, pp. 187–211; Budiansky, B., and Rice, J. R., 1973, “Conservation Laws and Energy Release Rates,” ASME J. Appl. Mech., 40, pp. 201–203; Freund, L. B., 1978, “Stress Intensity Factor Calculations Based on a Conservation Integral,” Int. J. Solids Struct., 14, pp. 241–250; Herrmann, G. A., and Herrmann, G., 1981, “On Energy Release Rates for a Plane Cracks,” ASME J. Appl. Mech., 48, pp. 525–530; King, R. B., and Herrmann, G., 1981, “Nondestructive Evaluation of the J- and M-Integrals,” ASME J. Appl. Mech., 48, pp. 83–87) to study the degradation of a brittle plan strip caused by irreversible evolution: the cracks coalescence under monotonically increasing loading. Attention is focused on the change of the M-integral before and after coalescence of two neighborly located cracks inclined each other. The influences of different orientations of the two cracks and different coalescence paths connecting the two cracks on the M-integral are studied in detail. Finite element analyses reveal that different orientations of the two cracks lead to different critical values of the M-integral at which the coalescence occurs. It is concluded that the M-integral does play an important role in the description of the damage extent and damage evolution. However, it only provides some outside variable features. This means that the complete failure mechanism due to damage evolution cannot be governed by a single parameter MC as proposed by Chang and Peng, 2004, “Use of M integral for Rubbery Material Problems Containing Multiple Defects,” J. Eng. Mech., 130(5), pp. 589–598. It is found that there is an inherent relation between the M-integral and the reduction of the effective elastic moduli as the orientation of one crack varies, i.e., the larger the M-integral is, the larger the reduction is. Of great significance is that the M-integral is inherently related to the change of the total potential energy for a damaged brittle material regardless of the detailed damage features or damage evolution. Therefore, this provides a useful and convenient experimental technique to measure the values of M-integral for a damaged brittle material from initial damage to final failure without use of many stain gages (King, R. B., and Herrmann, G., 1981, “Nondestructive Evaluation of the J- and M-Integrals,” ASME J. Appl. Mech., 48, pp. 83–87).

Fingerprints are unlikely to increase the friction of primate fingerpads

It is generally assumed that fingerprints improve the grip of primates, but the efficiency of their ridging will depend on the type of frictional behaviour the skin exhibits. Ridges would be effective at increasing friction for hard materials, but in a rubbery material they would reduce friction because they would reduce contact area. In this study we investigated the frictional performance of human fingertips on dry acrylic glass using a modified universal mechanical testing machine, measuring friction at a range of normal loads while also measuring the contact area. Tests were carried out on different fingers, fingers at different angles and against different widths of acrylic sheet to separate the effects of normal force and contact area. The results showed that fingertips behaved more like rubbers than hard solids; their coefficients of friction fell at higher normal forces and friction was higher when fingers were held flatter against wider sheets and hence when contact area was greater. The shear stress was greater at higher pressures, suggesting the presence of a biofilm between the skin and the surface. Fingerprints reduced contact area by a factor of one-third compared with flat skin, however, which would have reduced the friction; this casts severe doubt on their supposed frictional function.

Rigidity of polyurethane in various loading conditions

A method is proposed for estimating the Poisson’s ratio of rubbery materials, on the basis of velocity measurements of plane longitudinal waves (ultrasound). Approximation of the relaxation curves by an exponential series is discussed, as well as the use of creep to take account of the viscoelastic characteristics. Sample calculations are presented, along with the error of the approximation.

Effect of an electric field on the deformation of incompressible rubbers: Bifurcation phenomena

Well above their glass transition temperatures, polymers behave like rubber materials. In the rubbery state, the elastic modulus is low enough to allow large deformations. Rubbery materials also deform under the application of an electric field. Rubbers can be referred as electromechanically active elastomers (EMAE) or lightweight materials that convert electrical into mechanical energy and vice versa [H. Xu, Z.-Y. Cheng, D. Olson, T. Mai, Q.M. Zang, G. Kavarnos, Ferroelectric and electromechanical properties of poly(vinylidene-fluoride-trifluoroethylene-chlrotrifluoroethylene) terpolymer, Appl. Phys. Lett. 78 (2001) 2360–2362]. Possible applications include biomedical prostheses, actuators, energy harvesters and robots [R.E. Pelrine, R.D. Kornbluh, J.P. Joseph, Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation, Sens. Actuators, A 64 (1998) 77–85; G. Kofod, W. Wirges, Energy minimization for self-organized structure formation and actuation, Appl. Phys. Lett., 90 (2007) 81916–81918; J.S. Plante, S. Dubowsky, Large-scale failure modes of dielectric elastomer actuators, Int. J. Solids Struct. 43 (2006) 7727–7751]. However, although the engineering applications of EMAE are quite recent, the theoretical foundations of continua under simultaneous electrical and mechanical force fields date back the 1960s. In this paper we present the basis of the nonlinear electroelasticity according to the formulation by Dorfmann and Ogden [A. Dorfmann, R.W. Ogden, Nonlinear Electroelastic Deformations, J. Elasticity 82 (2006) 99–127; A. Dorfmann, R.W. Ogden, Nonlinear electroelasticity, Acta Mechanica 174 (2005) 167–183] and discuss the influence of an electrical field on the bifurcation phenomena appearing in some cases of electromechanical deformation in rubber materials.

Multiscale Reinforcement of Polymers Combining Cellulosic Wood Pulp with Layered Silicate Nanoplatelets

Synergies resulting from the combination of discontinuous reinforcing elements at two different size scales are examined in two polymer types — rubbery matrices comprising acrylonitrile-co-butadiene (NBR) elastomer and a high density polyethylene plastic. The latter is derived from a recycled post-consumer waste stream that is upgraded by the reinforcement to compensate for any degradation experienced during prior use or impurities introduced during recycling. The two reinforcements are wood pulp at the microscale and exfoliating layered silicate clays at the nanoscale. Appropriate compatibilizing agents are employed to allow wetting of the reinforcement with the polymer matrix, promote dispersion and provide a strong interface. In general, the microscale elements provide mechanical strengthening in tension, while the nanoscale reinforcements enhance stiffening and reduce failure propagation by tearing. The use of natural reinforcements and recycled feedstocks imparts environmental acceptability to such formulations.

Sulfonation of metallocene‐based polyolefinic elastomers and its influence on physicomechanical properties: Effect of reaction parameters, styrene grafting, and pendant chain length

AbstractDirect sulfonation and styrene‐mediated sulfonation were carried out onto metallocene‐based poly(ethylene‐co‐octene) (POE) and poly(ethylene‐co‐butene) (PBE) elastomers to impart polarity on the completely nonpolar rubbery matrices and to prepare a new class of elastomer. The influence of styrene‐grafting and pendant chain length on the degree of sulfonation was also studied. The effects of sulfonation, styrene grafting and styrene‐mediated sulfonation at their optimized levels on various physicomechanical properties were thoroughly investigated, and the resultant properties were correlated with structures of the modified elastomers. Higher extent of sulfonic acid groups were introduced through direct sulfonation in comparison with the styrene‐mediated sulfonation, whereas better thermal and mechanical properties were obtained through styrene‐mediated sulfonation in comparison with the direct sulfonation process. PBE had shown higher degree of sulfonation and percentage grafting than POE. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 8023–8040, 2008

Fabrication and Properties of Ethylene Vinyl Acetate-Carbon Nanofiber Nanocomposites

Carbon nanofiber (CNF) is one of the stiffest materials produced commercially, having excellent mechanical, electrical, and thermal properties. The reinforcement of rubbery matrices by CNFs was studied in the case of ethylene vinyl acetate (EVA). The tensile strength was greatly (61%) increased, even for very low fiber content (i.e., 1.0 wt.%). The surface modification of the fiber by high energy electron beam and gamma irradiation led to better dispersion in the rubber matrix. This in turn gave rise to further improvements in mechanical and dynamic mechanical properties of EVA. The thermal conductivity also exhibited improvements from that of the neat elastomer, although thermal stability of the nanocomposites was not significantly altered by the functionalization of CNFs. Various results were well supported by the morphological analysis of the nanocomposites.

FIB-SEM and TEMT Observation of Highly Elastic Rubbery Material with Nanomatrix Structure

ADVERTISEMENT RETURN TO ISSUEPREVNoteNEXTFIB-SEM and TEMT Observation of Highly Elastic Rubbery Material with Nanomatrix StructureSeiichi Kawahara*†, Yoshimasa Yamamoto†, Shuji Fujii†, Yoshinobu Isono†, Ken-ichi Niihara‡, Hiroshi Jinnai‡, Hideo Nishioka§, and Akio Takaoka∥View Author Information Department of Materials Science and Technology, Faculty of Engineering, Nagaoka University of Technology, Nagaoka, Niigata 940-2188, Japan, Department of Macromolecular Science and Engineering, Graduate School of Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Kyoto 606-8585, Japan, JEOL Ltd., 1-2-3 Musashino, Akishima, Tokyo 196-8556, Japan, and Research Center for Ultra-High Voltage Electron Microscopy, Osaka University, 7-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan* To whom correspondence should be addressed at the Department of Materials Science and Technology, Faculty of Engineering, Nagaoka University of Technology, Nagaoka, Niigata 940-2188, Japan. Telephone: 81-258-47-9301 . Fax:81-258-47-9300. E-mail: [email protected]†Department of Materials Science and Technology, Faculty of Engineering, Nagaoka University of Technology.‡Department of Macromolecular Science and Engineering, Graduate School of Science and Engineering, Kyoto Institute of Technology.§JEOL Ltd.∥Research Center for Ultra-High Voltage Electron Microscopy, Osaka University.Cite this: Macromolecules 2008, 41, 12, 4510–4513Publication Date (Web):May 20, 2008Publication History Received22 December 2007Revised24 March 2008Published online20 May 2008Published inissue 1 June 2008https://doi.org/10.1021/ma7028538Copyright © 2008 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views889Altmetric-Citations34LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit Read OnlinePDF (753 KB) Get e-AlertsSUBJECTS:Aromatic compounds,Biopolymers,Chemical structure,Hydrocarbons,Nanoparticles Get e-Alerts

Iterative control approach to high-speed force-distance curve measurement using AFM: Time-dependent response of PDMS example

Force–distance curve measurements using atomic force microscope (AFM) has been widely used in a broad range of areas. However, currently force-curve measurements are hampered the its low speed of AFM. In this article, a novel inversion-based iterative control technique is proposed to dramatically increase the speed of force-curve measurements. Experimental results are presented to show that by using the proposed control technique, the speed of force-curve measurements can be increased by over 80 times—with no loss of spatial resolution—on a commercial AFM platform and with a standard cantilever. High-speed force curve measurements using this control technique are utilized to quantitatively study the time-dependent elastic modulus of poly(dimethylsiloxane) (PDMS). The force-curves employ a broad spectrum of push-in (load) rates, spanning two-order differences. The elastic modulus measured at low-speed compares well with the value obtained from dynamic mechanical analysis (DMA) test, and the value of the elastic modulus increases as the push-in rate increases, signifying that a faster external deformation rate transitions the viscoelastic response of PDMS from that of a rubbery material toward a glassy one.

High Strength - Low Hardness Thermoplastic Elastomers from Ethylene-Butene Copolymers and Low Density Polyethylene

Abstract A thermoplastic elastomer (TPE) is a rubbery material with final properties and functional performance similar to those of a conventional vulcanized rubber at ambient temperature, yet it can be processed as a thermoplastic at elevated temperature. The main objective of the present investigation was to prepare novel olefinic thermoplastic elastomers based on blends of a thermoplastic i.e. low density polyethylene (PE) and new ethylene-butene copolymers (PEB), which would have higher strength and lower hardness compared to the existing TPEs. The 70:30 PEB: PE blend exhibited the best properties. Ethylene vinyl acetate was found to work as compatibilizer at lower loadings in these blends. The resultant blends were of low hardness (60–80 Shore A) and high strength (26–33 MPa). The interaction parameter and the morphology of the blends were the key parameters, which governed the final properties of blends.

Networks and conetworks of PIB‐based cyanoacrylate‐telechelic prepolymers: Synthesis, characterization, and properties

AbstractNovel networks and conetworks were prepared by the instantaneous polymerization of cyanoacrylate‐telechelic three‐arm star polyisobutylene [Ø(PIB‐CA)3] and the copolymerization of Ø(PIB‐CA)3/2,4,4‐trimethylpentane cyanoacrylate (TMP‐CA) mixtures, respectively, by means of strong nucleophiles, such as NEt2‐telechleic linear or three‐arm star PIBs [Ø(PIB‐NEt2)2 or 3]. The reactants were combined in the bulk in double‐barrel syringes by reaction injection molding (RIM). The chemical and mechanical properties of products prepared in the bulk and by conventional solution techniques were characterized by various techniques (swelling, extractables, FTIR and NMR spectroscopies, Instron, microhardness, oxidative resistance, DSC, DMTA). Conditions for the preparation of rubbery materials for possible biomedical applications were developed. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2612–2623, 2008

A novel elastomer/liquid crystal polymer nanocomposite created in situ from controlled radical graft-polymerization.

We present the original design and properties of a novel, all-polymer hierarchical composite comprising an elastomer and a fluorinated liquid crystal polymer. The material follows from the phase separation between the two highly incompatible components, occuring in situ during the controlled radical graft-polymerization of the liquid crystal monomer onto functionalized elastomeric chains. We demonstrate that the composite remarkably combines the mechanical properties, static and dynamic, of both an elastomer and a semi-crystalline polymer. We thereby illustrate how the careful choice of a graft can provide a simple rubbery material with original and antonymic functionalities. Here, the temperature-sensitive liquid crystal polymeric domains act as hard particulate fillers under their fusion temperature and liquid softening inclusions above, with fast reversible transitions from one state to another. A variety of composites combining physico-chemical features difficult to marry otherwise may be designed following this simple method.

Reinforcing effect of organoclay in rubbery and glassy epoxy resins, part 1: Dispersion and properties

AbstractThe reinforcing effect of organoclay in two epoxy matrices, one rubbery and one glassy, was studied. The rubbery and glassy epoxy matrices were chosen to have a very similar chemistry to minimize its impact on the comparison of properties. The epoxy resin was EPON™ 828, and the two hardeners were amine‐terminated polyoxypropylene diols, having different average molecular weights (MW) of 2000 and 230 g/mol, namely Jeffamine® D‐2000 and Jeffamine® D‐230, respectively. The nanocomposites were prepared with the organoclay Cloisite® 30B from Southern Clay Products. The quality of dispersion and intercalation/exfoliation was analyzed by means of X‐ray diffraction (XRD), field emission gun scanning electron microscopy (FEGSEM), and transmission electron microscopy (TEM). Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) were used to study the curing reactivity and the thermal stability of the epoxy resin systems, respectively. Tensile properties and hardness of epoxy resin and epoxy nanocomposites were measured according to ASTM standards D638‐02 and D2240‐00, respectively. Fracture surfaces were also analyzed by FEGSEM. These two epoxy systems as well as their nanocomposites display totally different physical and mechanical behavior. It is found that the quality of clay dispersion and intercalation/exfoliation, and the mechanical behavior of the glassy and rubbery epoxy nanocomposites are distinct. The results also indicate that the presence of the clay does not significantly affect the Tg of either the rubbery or the glassy epoxy; however, the fracture surface and mechanical properties were found to be influenced by the presence of nanoclay. Finally, several different reinforcing mechanisms are proposed and discussed for the rubbery and glassy epoxy nanocomposites. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2008

Polymer Networks in Research and Application

AbstractSummary: The present review presents an attempt to trace common aspects in the research on networks of very different origin, directed to industrial or biochemical applications. One major feature is the preparation of thermal, pH or ionic sensitive core/ shell structures. These elements proved to be significant in the field of reinforcement of rubbery materials as well as for suitable design of scaffolds for tissue engineering. Striking properties are reveal with examples of thermo‐ and magneto‐sensitive core/shell microgels. Two other instances of oscillating systems are discussed. One was directed to the development of nano‐scaled motors, the other to broadcasting biochemical relevant signals via oscillating Ca++ and H+ ions in vesicle/cytosol systems. Finally problems and progress in scaffold preparation are discussed.

Transport and physicochemical parameters of polypentenamer

Physicochemical properties of a cis-polypentenamer—a hydrocarbon polymer with a low glass transition temperature (Tg = 168.8 K)—have been studied. Measurements of permeability coefficients P in rubbery material for a wide range of gases (He, H2, O2, N2, CO2, CH4, C2H6, C3H8, and n-C4H10) indicate a high permeability of this polymer for which the values of P are only slightly lower than those of the most permeable rubber—poly(dimethylsiloxane). The method of inverse gas chromatography has been employed to estimate solubility coefficients S for n alkanes C3–C10 and cycloalkanes in cis-polypentenamer in the range from 25 to 150°C. It has been shown that the solubility coefficients linearly increase in lnS-Tcr2 coordinates, where Tcr is the critical temperature of a solute. In terms of the above correlation, the solubility coefficients of light gases have been estimated and the diffusion coefficients D of gases in the same polymer have been calculated via the formula P=DS. The free volume in cis-polypentenamer has been studied by positron annihilation lifetime spectroscopy. The temperature dependence of the positronium lifetime τ3 that characterizes the size of the free volume element in a polymer demonstrates saturation at temperatures above 250 K. This effect is probably related to a rapid migration of fluctuation holes in the rubbery polymer at temperatures remote enough from its glass transition temperature.

Electrical Insulating and Heat-Resistive Properties of PDMS-TEOS Hybrid with Different Molar Ratio of TEOS to PDMS

The hybrids prepared from polydimethylsiloxane (PDMS) and tetraethoxysilane (TEOS) have been well known to be rubbery hybrid materials. In this report, the authors have investigated the electrical insulating and heat resistive properties of the hybrids by changing the molar ratio of TEOS to PDMS. The electrical insulating properties are evaluated by volume resistivity and AC breakdown strength at room temperature. The resistivity is about 1013 Ω · m and AC breakdown strength is about 25 kV/mm irrespective of the molar ratio. Heat-resistive properties are evaluated by the weight loss after keeping for 480 h at 200°C in air. The weight loss becomes smaller as the TEOS content increases, and it is less than 3%. It has been clarified that the hybrids have good electrical insulating and heat-resistive properties.

Thermal Fluctuations and Rubber Elasticity

The effects of thermal elastic fluctuations in rubbery materials are examined. It is shown that, due to their interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation and shows good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation.