A new attempt to reconcile the statistical and phenomenological theories of rubber elasticity

The statistical and phenomenological theories of rubber elasticity are reviewed briefly. Combining recent concepts proposed by Yeoh and Gent, a new theory is proposed. The proposed constitutive model for rubber vulcanizates invokes two mechanisms; one influences behavior at small strains while the other dominates behavior at large strains. Network flaws, such as entanglements, are suspected to be responsible for the first mechanism. Finite extensibility of network chains is identified as the cause of the second. Thus, macroscopic behavior is directly linked to molecular concepts. The proposed theory allows prediction of the stress–strain behavior of a family of four rubber vulcanizates in different modes of deformation (simple extension, compression, and simple shear) from regression analysis of tensile data alone from just one member. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1919–1931, 1997     

A non-Gaussian model for the chemo-mechanical coupling behavior of largely deformed hydrogels

A non-Gaussian model is developed to precisely describe the chemo-mechanical coupled large deformation of responsive hydrogels. In this model, the free-energy density is composed of two parts, including the elastic energy due to stretching of cross-linked polymer networks described by Gent hyperelastic model, and the mixture energy of polymer network and described by Flory–Huggins theory. The effects of junction functionality and chain entanglements are investigated by analyzing free swelling of a cubic hydrogel and constrained swelling of a blanket layer of the gel. The present model is found to exhibit obvious hardening characteristic during large deformation of the hydrogel, and the considerations of functionality of junctions and chain entanglements are essential in the coupled chemo-mechanical deformation analysis of hydrogels.     

Effect of large deformation and material nonlinearity on the JKR (Johnson–Kendall–Roberts) test of soft elastic materials

We study in detail the effect of large deformation and material nonlinearity on the JKR (Johnson–Kendall–Roberts) theory of adhesive contact for two systems. The first is a Neo‐Hookean hemisphere in adhesive contact with a smooth rigid substrate. The second is a smooth rigid spherical indenter in adhesive contact with a Neo‐Hookean half space. We show that our results are special cases of a general theory that models large deformation adhesive contact of spherical lenses. This theory shows that the solution of any large deformation JKR (LDJKR) problem can be obtained from the solution of a corresponding large deformation Hertz (LDH) problem. Using this theory, we extend the small strain JKR theory to the large deformation regime, the only restriction being that the materials are nonlinear elastic or hyperelastic. The adhesive contact problem for the two systems is solved using two methods. In method one, the LDJKR theory is obtained using finite element simulation results for a corresponding LDH problem; in method two, we solve the adhesive contact problems directly using a cohesive zone model to quantify adhesive interaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2912–2922, 2006     

Molecular structure and properties of click hydrogels with controlled dangling end defect

In this study, controlled amount of dangling ends is introduced to the two series of poly(ethylene glycol)‐based hydrogel networks with three and four crosslinking functionality by using click chemistry. The structure of the gels with regulated defect percentage is confirmed by comparing the results of low‐field NMR characterization and Monte Carlo simulation. The mechanical properties of these gels were characterized by tensile stress–strain behaviors of the gels, and the results are analyzed by Gent model and Mooney–Rivlin model. The shear modulus of the swollen gels is found to be dependent on the functionality of the network, and decreases with the defect percentage. Furthermore, the value of shear modulus well obeys the Phantom model for all the gels with varied percentage of the defects. The maximum extension ratio, obtained from the fitting of Gent model, is also found to be dependent on the functionality of the network, and does not change with the defect percentage, except at very high defect percentage. The value of the maximum extension ratio is between that predicted from Phantom model and the Affine model. This indicates that at the large deformation, the fluctuation of the crosslinking points is suppressed for some extend but still exists. Polymer volume fractions at various defect percentages obtained from prediction of Flory–Rehner model are found to be in well agreement with the swelling experiment. All these results indicate that click chemistry is a powerful method to regulate the network structure and mechanical properties of the gels. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1227–1236     

Strain‐induced crystallization and strength of elastomers. I. cis‐1,4‐polybutadiene

Crosslinked samples of cis‐1,4‐polybutadiene (BR) were crystallized at low temperatures and then slowly melted. From volume changes and differential scanning calorimetry measurements, the degree of crystallization in the unstrained state was estimated to be about 20%, much lower than for natural rubber (NR). Crystallization and melting were followed in stretched samples by corresponding changes in tensile stress. Crystallization was faster at higher strains, and the melting temperature was raised significantly on stretching but less than for NR, and the decrease in stress on crystallizing was smaller. Measurements of tensile strength were made over a wide temperature range and showed a marked drop with heating to temperatures of 40–60 °C, falling to values of only 1–2 MPa. A similar drop in strength occurred in NR vulcanizates at high temperatures and was attributed to failure to crystallize on stretching (A. G. Thomas & J. M. Whittle, Rubber Chem Technol 1970, 43, 222; A. N. Gent, S. Kawahara & J. Zhao, Rubber Chem Technol 1998, 71, 668). At ambient temperatures, where strain‐induced crystallization occurred, the strength of BR samples was only about one‐half of that of similar NR materials. This was attributed to less strain‐induced crystallinity in BR (verified by X‐ray studies), paralleling the lower amount developed at low temperatures. We speculate that the higher density of molecular entanglements in BR than in NR prevents BR from crystallizing to the same degree as NR. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 811–817, 2001     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007     

一种基于分子链统计理论的橡胶超弹性混合本构模型

橡胶材料因其独特的超弹性在实际中广泛应用,通过解析应力-应变关系可以为橡胶力学性能的工程应用提供理论指导.为了更准确地描述橡胶材料力学性能,提出一种适用于橡胶材料的超弹性混合本构模型.新模型基于Gaussian模型与八链模型,引入有关拉伸比的权重函数将二者耦合,在拉伸比较小的情况下,新模型退化成Gaussian形式,在...     

Thermodynamic model of gas permeability in polymer membranes

A new molecular thermodynamic model is developed of the gas permeability in polymer membranes on the basis of configurational entropy and Flory‐Huggins theory to predict permeability dependence on the concentration of penetrant. Three kinds of configurational entropy are taken into account by this model; that is, the disorientation entropy of polymer, the mixing entropy, and specific interaction entropy of polymer/gas. The validity of the mathematical model is examined against experimental gas permeability for polymer membranes. Agreement between experimental and predicted permeability is satisfactory. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 661–665, 2007     

Cavitation criterion for rubber materials: A review of void‐growth models

The principal criteria used to predict cavitation in rubber materials are reviewed, and experimental evidence is recalled for three different configurations: in the bulk, in the vicinity of a rigid particle, and in small rubber particles embedded in a rigid polymer matrix. Two major classes of cavitation criteria are defined, those based on an elastic instability (i.e., related to a stress state and finite strains) and those based on the energy balance (i.e., involving surface energies). The different criteria, in which various hyperelastic behavior laws are considered, are compared in numerical applications, and the tendencies are derived. The particular case of accounting for the surface tension of the rubber, a parameter common to the stress state and the energy balance, is treated in detail. It appears that the understanding of the genesis of a microcavity in a rubber material, when no pre‐existing flaw is assumed, still constitutes a difficulty for the analysis of mechanical damage in polymers containing a rubber phase. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2081–2096, 2001     

Structural characterization of vulcanized natural rubber by latex state 13C NMR spectroscopy

Structural characterization of vulcanized natural rubber was performed by high‐resolution latex‐state ¹³C NMR spectroscopy. The vulcanized natural rubber latex was prepared by vulcanization of high ammonia natural rubber latex with sulfur and sodium di‐n‐butyldithiocarbamate as vulcanizing agents. High resolution was attained for latex‐state ¹³C NMR spectroscopy even after vulcanization of the rubber latex, as is evident from no background in spectrum and narrow half width of signals, which were independent of vulcanization time. Small signals at 44 and 58 ppm in the carbon region were assigned by measurements of both distortionless enhancement by polarization transfer (DEPT) and attached proton test (APT) to secondary, tertiary, and quaternary carbons of crosslinking points. The assignment was proved by high‐resolution solution‐state NMR spectroscopy of vulcanized liquid cis‐1,4‐polyisoprene as a model, in which DEPT, APT, 2‐dimensional ¹H‐¹³C correlation (HETCOR), and 2‐dimensional heteronuclear multiple bond correlation (HMBC) measurements were applied. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1003–1009, 2007     

Molecular modeling of cellulose in amorphous state. III. An innovative elastomeric crosslink system

The flexibility of molecular structures of rubber materials was evaluated using molecular modeling techniques to develop new crosslink agents which improve deformation recovery of cellulose without significant loss of the mechanical strength. Among the studied structures Poly(propylene oxide) (PPO) pentamer appears to be the most flexible and coiled one. Our calculation results showed that, cellulose crosslinked with PPO pentamers had similar deformation recovery to that crosslinked with DMDHEU. No conformation transitions were observed in these crosslinks when cellulose models were extended to 15% strain, which is consistent with the previous result that conformation transitions in crosslinks should be avoided upon extension to achieve a good recovery on crosslinked cellulose. In addition, PPO crosslinks did not significantly affect the breaking strain of cellulose based upon the cavity volume calculations, and they helped to remove the stress concentration among cellulose chains as suggested by the results of hydrogen bonding analysis. Thus, breaking strength of cellulose might not be significantly affected by PPO crosslinks as well. The preliminary experimental results confirmed above observations. Therefore, PPO pentamer appears to be a promising elastomeric backbone structure of crosslinking agents. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1821–1833, 2007     

Constitutive modeling of polymers accounting for their hyperelasticity,plasticity, creep and viscoelastic relaxation

The hyperelastic Yeoh model has been generalized to account for creep, plasticity and viscoelasticity of polymers. The general tensorial model developed is applied to several rheometric situations: the tensile test used to measure the stress-strain curve in tension, as well as the creep and recovery tests. The resulting equations are compared to the experimental results acquired in the present work for several monolithic synthetic fibers used as specimens. The comparison revealed that the proposed phenomenological rheological constitutive equation is capable of reproducing the experimental data with a uniformly valid set of physical parameters. Moreover, it was possible to accurately predict the residual plastic deformation of the fibers.     

Basic studies on gas solubility in natural rubber–cellulose composites

This work reports sorption processes of oxygen, carbon dioxide, methane, ethylene, and propylene in films of both vulcanized natural rubber and vulcanized rubber–regenerated cellulose composites. The curves representing the pressure dependence of the concentration of carbon dioxide in the composites clearly exhibit a slight concavity with respect to the abscissa axis as a result of adsorption processes taking place in Langmuir sites located in the glassy cellulose component. Adsorption processes are also detected in the sorption curves of ethylene at low pressures. The concavity with respect to the ordinate axis of the curve concentration of propylene versus pressure at high pressure is pretty well described by the Flory‐Huggins formalism. The solubilities of the other gases mainly obey Henry's behavior, adsorption processes in the glassy component being in most cases negligible. Values of the interaction χ parameter for gas–natural rubber and gas–natural rubber composites are obtained from the comparison of the experimental solubility coefficients with those predicted by the Flory‐Huggins theory. The theory suggests that Henry's constant is a linear function of the boiling temperature of the gases. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2131–2140, 2005     

On the relevance of the 8‐chain model and the full‐network model for the deformation and failure of networks formed through photopolymerization of multifunctional monomers

Crosslinked networks were synthesized by copolymerization of mono‐functional tert‐butyl acrylate (tBA) with diethyleneglycol dimethacrylate (DEGDMA) or polyethylene glycol dimethacrylates (PEGDMA). By varying the chain length and concentration of the difunctional PEGDMA, we obtained tBA‐PEGDMA copolymer networks while by varying the concentration of difunctional DEGDMA, we obtained tBA‐DEGDMA crosslinked networks. The various materials were submitted to large deformations through uniaxial tension tests. For moderate weight percent of crosslinking agent, up to 20%, the networks showed standard S‐shape stress–strain curves, characteristic of rubber‐like elasticity. Two macromolecular models, the 8‐chain model and the full‐network model, were applied to fit the uniaxial tensile response of the materials. Both models provide good representations of the overall uniaxial stress–strain response of each material. After fitting to stress–strain data, the network models were employed to predict the shear modulus and the elongation at break. Neither the 8‐chain nor the full network model were capable of predicting the failure strain or shear modulus, indicating these models are best used to describe stress–strain relations rather than predict mechanical properties for the network polymers considered here. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1226–1234, 2008     

Élaboration de nouvelles lois de comportement pour les élastomères : principe et avantages

A phenomenological study of deformed rubber in uniaxial tension, pure shear and equi-biaxial tension, leads to a generalized strain energy density representation for hyperelastic elastomeric material behaviour. A strain energy density function family is built with a new process. It is particularly well adapted for representing experimental data of different types of loading, and so, for a wide class of elastomers. Besides, parameter identification of this family of strain energy density functions is simple and fast.     

Liquid–liquid equilibria of polymer solutions: Flory‐huggins with specific interaction

We have developed a new Flory‐Huggins model by adding a specific interaction parameter derived from a modified double‐lattice model for the Helmholtz energy of mixing for binary liquid mixtures. This model is very simple and could be easily integrated into engineering applications. Using this revised model, we can successfully describe the phase behavior of polymer solutions with an upper critical solution temperature (UCST), a lower critical solution temperature (LCST), both UCST and LCST, and a closed miscibility loop. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 162–167, 2010     

The influence of hard‐segments on two‐phase structure and shape memory properties of PCL‐based segmented polyurethanes

Poly(ε‐caprolactone)‐based segmented polyurethanes (PCLUs) were prepared from poly(ε‐caprolactone) diol, diisocyanates (DI), and 1,4‐butanediol. The DIs used were 4,4′‐diphenylmethane diisocyanate (MDI), 2,4‐toluenediisocyanate (TDI), isophorone diisocyanate (IPDI), and hexamethylene diisocyanate (HDI). Differential scanning calorimetry, small‐angle X‐ray scattering, and dynamic mechanical analysis were employed to characterize the two‐phase structures of all PCLUs. It was found that HDI‐ and MDI‐based PCLUs had higher degree of microphase separation than did IPDI‐ and TDI‐based PCLUs, which was primarily due to the crystallization of HDI‐ and MDI‐based hard‐segments. As a result, the HDI‐based PCLU exhibited the highest recovery force up to 6 MPa and slowest stress relaxation with increasing temperature. Besides, it was found that the partial damage in hard‐segment domains during the sample deformation was responsible for the incomplete shape‐recovery of PCLUs after the first deformation, but the damage did not develop during the subsequent deformation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 557–570, 2007     

Morphology development of main‐chain liquid crystalline polymer fibers during solvent evaporation

A nonequilibrium thermodynamic approach has been developed for describing the emergence of fiber morphologies from a liquid crystalline polymer solution undergoing solvent evaporation, including fibrillar structures, concentric rings, and spiral structures. We utilized Matsuyama–Kato free energy for main‐chain liquid crystalline polymer (MCLCP) solutions, which is an extension of Maier–Saupe theory for nematic ordering and incorporates a chain‐stiffening, combined with Flory‐Huggins free energy of mixing. Temporal evolution of the concentration and nematic order parameters pertaining to the above free energy density of liquid crystalline polymer solution was simulated in the context of time‐dependent Ginzburg–Landau theory coupled with the solvent evaporation rate equation under the quasi‐steady state assumption. The emerged morphological patterns are discussed in relation to the phase diagram of the MCLCP solution and the rate of solvent evaporation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 429–435, 2007     

Swelling behaviors of sub‐micron‐sized copolymer gel particles: The effect of physical crosslinking

The swelling equilibria model of copolymer gel particles is proposed. It accounts for physical crosslinking as a result of hydrogen bonding. The modified Flory–Erman model is used to describe the elastic contribution to swelling. The model considers hydrogen bonding as a physical crosslinker. A free‐energy‐of‐mixing term is represented using the extended Flory–Huggins theory. The interaction parameter χ in the model is a function of both composition and temperature. We then compare the proposed model with the swelling behaviors of copolymer gel particles. Our model offers fairly good agreement with the experimental data for given systems. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1928–1934, 2001