Kinematics of Polymer Chains with Freely Rotating Bonds in a Restrictive Environment. 2. Conformational and Orientational Correlations

The mathematical formulation developed in the preceding paper is used to study the kinematics of polymer chains in a restrictive environment. Conformational and orientational correlations along the chain are analyzed. Calculations are performed by generating an initial configuration for a 25-bond freely rotating chain, changing the dihedral angle for the middle bond, and studying the resulting changes in all of the degrees of freedom, internal and external. Results from Monte Carlo chains generated in this manner are averaged over a sufficient number of initial configurations. The following conclusions are reached: (i) A change in the dihedral angle of a given internal bond in small steps up to ±120° is accommodated by the spatial readjustments of about three neighboring bonds on each of its sides. Spatial configurations of more distant neighbors are negligibly affected. Thus, the conformational correlation length along the freely rotating chain extends over 6-8 bonds, (ii) In general, the rotational motion of a given bond is accompanied by counterrotations of its first neighbors, (iii) The response of second neighbors is lightly stronger than that of the first neighbors on the average, though occurring randomly in the positive or negative sense, (iv) The kinematics of motion imply the potential occurrence of transitions of the form g^±tt ↔ ttg^± and ttt ↔ g^±tg^∓, in agreement with previous predictions of Helfand. (v) Bonds in the close neighborhood of the rotating bond exhibit a broad distribution of angular displacements in space as a result of the compensating effect of the cooperative motions.