Abstract
The characteristic function of the distribution function of S2 for a ring chain with interactions is obtained in closed form. The Fourier transformations of the characteristic function are performed numerically, in one-, two-, and three-dimensional spaces and analytically in two-dimensional space. The expressions for the perturbed distribution functions valid for small S2 values and large S2 values are given. A simple variational technique is introduced to obtain the perturbed mean square radius of gyration in a closed form. It should be noted that, in two-dimensional spcce, there exists the negative critical value of z, below which no Fourier transformation of the characteristic function may be permitted. Here, z is the usual excluded volume parameter.
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Minato, T. Distribution Function of Polymers with and without Interactions. II. The Distribution Function of the Square Radius of Gyration of a Ring Chain. Polym J 9, 479–488 (1977). https://doi.org/10.1295/polymj.9.479
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DOI: https://doi.org/10.1295/polymj.9.479