Configurational distributions for finite chain molecules

Abstract

AbstractExact functions expressing the distribution of the end‐to‐end vector for real chains of finite length are unknown. Moments of the distribution can be calculated, however, for linear chains unperturbed by excluded‐volume effects. Thus, second and fourth moments for real chains with interdependent bond rotational potentials, in the rotational isomeric state approximation, can be computed as a function of chain length by methods developed recently. These moments are here compared with those calculated for hypothetical models, e.g., for the Gaussian distribution (to which all distributions converge in the limit of infinite chain length), for the freely jointed chain, for the distribution involving the inverted Langevin function, for the freely rotating chain, for the Porod “wormlike” chain, and for the chain with independent bond rotations that have a symmetrical hindrance potential. The convergence of the series expansion for the distribution function in terms of its even moments obtained by Nagai is investigated for the freely jointed chain (for which any number of moments may be readily calculated). Application of this series to the model with interdependent bond rotations is also considered.