Establishment of Constitutive Model of Silicone Rubber Foams Based on Statistical Theory of Rubber Elasticity

In this study, a constitutive model based on microscopic physical mechanism of silicone rubber foams was established. A theoretical statistical model of rubber elasticity considering the effect of dangling chains was modified to build this model. When a strain amplification factor （X） was introduced, the theoretical model could fit the tensile stress-strain data of mono- and bi-modal foam matrix well （Adj. R-Square = 0.9989, 0.9983）. Parameters related to the polymer network, namely, average molecular weight （Me） and volume fraction （Ф） of chain segments between adjacent cross-linking points （network strands）, were calculated by probabilistic method from the number-average molecular weight （Mn）, vinyl content （wvi） of the primary polysiloxanes and percent conversion （q） of vinyl groups. The primary and infinite strain amplification factors （X0, X∞） and decay exponent （z）, introduced by X and related to the nanoparticles, were obtained by fitting. Inspired by the fact that the actual strain of matrix was lower than that of the foams＇, we introduced another item, strain hysteresis item （H, related with the foam porosity and cell structure）, into the statistical model as well. With the same above values of Mc, Ф, X0 and X∞, the model could also fit the compressive stress-strain data of mono- and bi-modal foams well （Adj. R-Square = 0.9948, 0.9985）. Interestingly, the strain hysteresis items of the mono- and bi-modal foams almost completely coincided under all experimental strains, which may be attributed to the almost equal porosity and similar cell structure of the two foams. This constitutive model may connect the macroscopic stress-strain behaviour to the parameters of microscopic molecular structures, promisingly providing a basis for the performance improvement and optimization of silicone rubber foams.

CONFORMATIONAL PROPERTIES OF STRETCHED POLYETHYLENE CHAIN

When polyethylene chains are stretched, the chains are regarded as being confined in an infinite cylinder with decreasing diameter. The conformational properties of polyethylene chains confined in an infinite cylinder are investigated by using rotational isomeric state model. Using the average conformational energy and entropy and the average length, we can determine the elastic force f, or the fraction of the energy term to the total force f(e)/f where f(e) = partial derivative /partial derivative < r > and f = partial derivative /partial derivative < r >. Comparisons with experimental data are also made. The results of these microscopic calculations are discussed in terms of the macroscopic phenomena of rubber elasticity.

A tree-growing graphic model for asymmetrical phantom networks in polymeric gels undergoing dynamic mechanochemical coupling

Network structures of various polymers have significant effects on their mechanical properties;therefore,numerous studies have investigated the constitutive relationship between symmetrical network structures and their rubber elasticity in polymers.However,few studies have focused on asymmetrical network structures in polymers that undergo bond exchange reactions,selfassembly,or mechanochemical coupling—all of which are induced by transition probabilities of chemical bonding processes.In this study,an extended constraint junction and phantom network model is formulated using the tree-growing theory to establish a constitutive relationship between asymmetrical network structures and their rubber elasticity in polymers.A free-energy equation is further developed to explore working principles of configurational transitions on the dynamic rubber elasticity of symmetrical and asymmetrical network structures.The constitutive relationship between dynamic rubber elasticity and symmetrical and asymmetrical network structures has also been proposed for the gels undergoing mechanochemical and hydromechanical coupling.Finally,the effectiveness of this newly proposed tree-growing model has been verified by comparing with the classical affine network model,finite element analysis,and the experimental results of gels reported in literature.