Effect of Volume Exclusion on the Dimensions of Polymer Chains

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Abstract
The effect of volume exclusion on the mean-square radius of gyration s2 is treated by use of the empirical expression W0(s)=const s6exp[−(7/2)〈s2〉0−1s2] for the statistical distribution of s for a system of linear chain molecules unperturbed by volume exclusion. Segment interactions within the perturbed molecule are treated in the smoothed-density approximation. The result is α5—α3=Azh(z/α3), where α2=〈s2〉/〈s2〉0, A is a numerical constant, z is the usual parameter proportional to the excluded volume for a segment pair and to the square root of the chain length, and h(ζ) is a function which decreases by almost one-half as ζ increases from 0 to ∞. Asymptotic dependence of α2 on the ⅕th power of the chain length is thus confirmed. Extremely long chains, exceeding 106 bonds, would be required however for realization of this limiting behavior.

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