Abstract
The unperturbed distribution function of the distance between the i -th and j -th segments of a chain polymer molecule is assumed to be the distribution function of the | j - i | steps random flights. The expansion coefficient of the excluded volume effect of chain molecule is calculated with this distribution function by the method of cluster expansion. The number and types of clusters under consideration and the acquired asymptotic behavior of the expansion coefficient are identical with the previous report. The expansion coefficient is expressed in a closed from by the aid of the error function as \(\alpha^{2}{=}1+\frac{2+((1/c)-2)\mathrm{e}^{-\xi 2}\xi^{-2}\text{Erfc}^{-1}(\xi)}{1+\mathrm{e}^{-\zeta 2}Erfc^{-1}(\xi)/c}{=}3+O(\mathrm{e}^{-N}/N)\).
Published Version
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