Configurational Correlations in Chain Molecules

Abstract

Although the potentials affecting the rotation about a skeletal bond in a chain molecule such as polymethylene (PM) usually depend only on rotations of immediately adjoining bonds, the interdependence of rotational states may be transmitted over greater distances. In the case of PM or of polyoxymethylene(POM) the effective range of correlation is only four or five bonds. This has been established by calculating a priori probabilities for rotational states of a bond as a function of its location relative to the chain termini and of the total chain length. The range of directional correlations between bonds is much greater owing to the further effects of the geometrical constraints imposed by bond angles and hindrance potentials. The correlation between bond directions is reflected in the average sum of the projection on bond i of all bonds i to n . Convergence of this quantity calculated for PM occurs for sequences exceeding about 25 bonds in length. Effects of chain ends are perceptible only for i < 4 . In confirmation of these observations, the characteristic ratio 〈r pq 2 〉 0 / | p − q |l 2 of the mean‐square distance between chain atoms p and q converges only for sequences | q − p | > 100 bonds , but for | q − p | > 3 it differs inappreciably from the value for a finite chain of length | q − p | , i.e., for p = 0 and q = n .