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Abstract: We derived the analytical solution of the eigenvalue problem for stereo-regular vinyl chains, such as stereo-regular polypropylene chains. The solution is applicable to all stereo-regular polymers of the type (AB) x which do not have symmetry between gauche + and gauche − states, and to polymers, such as polyoxymethylene or polydimethylsiloxane, for which symmetry between the gauche + and gauche − states does exist. For symmetric chains, the general solution of the eigenvalue problem is reduced to the known solution for polyoxymethylene chains. To illustrate the method the calculations have been performed for the three rotational states (trans, gauche + and gauche −) model, but the general algebraic solution is applicable for any ν rotational states models of polymer chains. We used the analytical solution of the eigenvalue problem to calculate numerically elastic properties of stereo-regular polypropylene chains within the framework of Mark–Curro theory (J Chem Phys, 79, 5705, 1983). [Copyright &y& Elsevier]

Abstract: The elastomeric properties of networks of stereoregular polypropylenes (PP) filled with spherical nanoparticles have been modeled in an attempt to obtain better insights into elastomer reinforcement. The polymers were either isotactic or syndiotactic PP in the amorphous state, and the simulations were based on rotational isomeric state (RIS) theory combined with the largest eigenvalue method for deriving conditional bond probabilities. Monte Carlo simulations gave distributions of the end-to-end distance of these chains in the presence of the particles, and these were used in the Mark–Curro theoretical approach to calculate values of the normalized stress, and the reduced stress (shear modulus) under uniaxial stretching. The simulations were calculated for PP chains having 100–200 skeletal bonds, for several temperatures from 481 to 650K, and for varying filler particle sizes (up to 100Å). The presence of the filler nanoparticles was found to influence chain conformations, frequently leading to significant chain extensions, which significantly affect the elastomeric properties of the nanocomposites. [Copyright &y& Elsevier]