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• W2011489959 abstract "Fixman's integral for the distribution function P(S2) obeyed by S2 of the unperturbed polymer chain was evaluated analytically, and its asymptotic forms valid for t ≪ 1 and t ≫ 1 were derived. Here S is the radius of gyration of the chain and t is the ratio of S2 to its statistical average 〈S2〉. The values of P(S2) calculated from the analytic solution agreed with Koyama's computer values over the entire range of t. The leading term of the asymptotic form for t ≪ 1 confirmed the previous result of Fixman. The asymptotic form for t ≫ 1 agreed not with Fixman's but with that of Forsman. The Flory–Fisk theory for the excluded volume effect in polymer chains was reformulated with the exact form being substituted for P(S2) in their basic equation for αs2. Here αs is the linear expansion factor of a polymer molecule defined in terms of 〈S2〉. The calculated curve for αs3 as a function of the interaction parameter z differed markedly from that derived by Flory and Fisk who had employed an approximate expression for P(S2). Our curve followed quite closely the one recently deduced by Yamakawa and Tanaka from an entirely different treatment. However, both are different in the limiting behavior at indefinitely large z, our curve tending to the fifth power type as represented by αs5 = 1.668z, whereas Yamakawa–Tanaka's approaches αs4.35 = 1.11z." @default.
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• W2011489959 date "1970-02-01" @default.
• W2011489959 modified "2023-09-23" @default.
• W2011489959 title "Some Topics Concerning the Radius of Gyration of Linear Polymer Molecules in Solution" @default.
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• W2011489959 doi "https://doi.org/10.1063/1.1673106" @default.
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