Moments of Chain Vectors for Models of Polymer Chains

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Abstract
Four model chains, namely, the freely jointed chain (1), the freely rotating chain (2), the Porod–Kratky wormlike chain (3), and the model with independent bond rotations hindered by a symmetrical potential (4), are compared with a realistic isomeric‐state representation (5) of the polymethylene chain through calculations of various properties of their distributions. Parameters used for Models 1–4 were adjusted to secure agreement with 5 at the infinite chain limit. Properties treated are the mean‐square end‐to‐end distance, its temperature derivative, the mean‐square radius of gyration, and higher even moments of the end‐to‐end distance. Convergences to asymptotic ratios with chain length are examined. None of the simpler models 1–4 adequately represents these properties of the realistic chain 5 at all chain lengths. The success of any one of the models 1–4 in accounting for the dependence of a given property on chain length varies considerably from one property to another.