A Monte Carlo numerical method has been employed for the computation of the meanhyphen;square separation between pairs of elementsiandj, lang;Rij2rang;, and the meanhyphen;square radius of gyration, lang;Sn2rang;, for annhyphen;segment coiling type polymer molecule. A restricted random walk was used as a model for the polymer, and the average dimensions in question were calculated for random samples of nonintersecting walks generated by means of a highhyphen;speed digital computer. lang;Rij2rang; has been found to be a rather complicated function ofi/nandj/n,depending upon the position in the chain as well as upon the contour length of the segment betweeniandj.The meanhyphen;square radius of gyration was found to be proportional to the average square endhyphen;tohyphen;end distance, as for simple unrestricted random walks, but the constant of proportionality differs from the value of frac16; which is applicable in the absence of the excluded volume effect. The exact value of the ratio of the two quantities depends upon whether the molecule is constrained to 2 or 3 dimensions.
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