The effect of excluded volume on chain dimensions

Abstract Excluded volume‐interactions are treated in terms of the Gaussian probabilities for intersegmental contacts, as obtaining in equivalent chains consisting of links expanded by the interactions but otherwise obeying the random‐flight statistics. The linear development of the interaction energy exponent into the contact probabilities is (a) conducted sequentially segment by segment, so that the “chain connectivity” is duly preserved (difference from Flory), and (b) cast into a formula that uses Gaussian expressions only for the contact probabilities; the use of the Gaussian expression for the distribution of the end‐to‐end distance, which is known to be non‐Gaussian, is, however, avoided (difference from Fixman). An integral equation is derived, describing α(z) by a line which initially, up to α2 < 4, closely resembles the line derived by Fixman but thereafter diverges increasingly, the asymptotic result being α ≈︁ z5½−2 = z0.236….