Configurational Statistics of Polyethylene Chains

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Abstract
A mathematical procedure is described to handle the configurational statistics of a chain placed on a rigid lattice, allowing for first-neighbor interaction between consecutive rotational states. Many statistics connected with chain bonds orientation with respect to a fixed reference frame are calculated easily. Assuming a diamond lattice, results are reported for polyethylene chains with different lengths: They include the W (r) end-to-end vector distribution, the principal mean-square radii of gyration of the polymer coils both under a fixed force applied to the chain ends and under a fixed end-to-end distance, the plots of 〈cos2Φ〉 and of fG vs r Φ=angle between a chain bond and the direction of the force, fG=fraction of gauche rotational states). The last two results allow derivation of the average optical polarizability and of the internal energy for different chain elongations. Both the calculated characteristic ratio C∞ and its derivative with temperature agree with the experimental data.