Concentration dependence polymer properties, matrix model

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

The investigations of model compositions, based on linear elastomers and various fillers, have shown that the yield stress also may be characterized by the value of the complex shear modulus measured at various frequencies. The dependence of the dynamic modulus on the filler concentration characterizes critical concentrations of the filler, above which the viscoelastic behavior of composition drastically changes. Dynamic modulus corresponding to the yield stress does not depend on the matrix viscosity or its nature. This fact indicates a predominant role of the structural frame for rheological properties of filled polymers. 

The effective carrier mobilities and their dependence on concentration for benztriazole derivatives embedded in polycarbonate were explained by the percolative aspects in photoconductivity [296]. The observed field dependence of the mobility for polycarbonate films doped with diethynylaminobenzaldehy-de-diphenyl hydrazone cannot be accounted for by any known hopping model [297]. The influence of the nature of the polymer matrix on photogeneration and transport properties of the molecule doped polymers was investigated in some papers [57, 58, 298, 299],... 

An examination of the experimental findings and the calculation model shows that the deformability of a syntactic foam depends mainly on the elastic properties of the polymer matrix, whereas the filler concentration mainly affects its compressibility. In fact, monolithic (unfilled) samples do deform elastically at the start of the compression curve, but when the material is deformed further, the forced elasticity limit is reached (Fig. 21). Thus, the nominal ultimate strength for non-brittle failure is determined by the fact that the forced elastic limit is reached, and not because the adhesive ties have lost their stability (as it is the case with light plastic foams) 8 10). 

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