Statistical mechanics of helical wormlike chains. VI. Approximations

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Abstract
Two methods of evaluating approximately the distribution functions and related averages for the helical wormlike chain are presented. One, called the weighting function method, is a modification of the Laguerre series approximations developed in Paper V and also a generalization of the procedure of Fixman and Skolnick. The other, called the ε method, is a simple one leading to expansions in terms of the relative deviation of the squared end‐to‐end distance near the rod limit. After an examination of the convergence of the two methods, they are applied to a derivation of approximate expressions for the mean reciprocal distance required in the calculation of the transport coefficients of helical wormlike cylinders, and also to a re‐evaluation of the scattering functions at large magnitudes of the scattering vector. Relations between the characteristics of the average chain configuration and the model parameters are also examined to serve as criteria for the selection of test codes.