Long-Range Correlations in a Polymer Chain Due to Its Connectivity

Abstract

The analysis of intrachain monomeric interactions reveals a new effect in the description of polymer conformations in dilute θ-solutions, semidilute solutions, and melts. The chain connectivity modifies the effective monomeric interaction, which results in the long range correlations between orientations of polymer bonds, that decay as a power law. A major modification of the standard polymer models was made to describe this effect. We predict the power-law decay of the bond-vector correlation function of a polymer in the θ-solvent, 〈aiaj〉 ∼ |i − j|-3/2, (ai is the ith bond vector) instead of commonly assumed exponential decay. We calculated the length dependence of the ratio of the mean squared size of a chain segment to its length s. Our theory predicts that this ratio has a maximum below the θ-point due to the balance of the new effective interaction and the two-body attraction. The Flory characteristic ratio Cn of a chain with n main chain bonds is found to approach its asymptotic value C∞ as n-1/2 and not as n-1, predicted by the classical polymer models. We show that the necessary conditions for the existence of new effective interactions is the chain connectivity and nonzero range of monomeric interactions.