Local Steric Hindrances and Configurations of Linear Macromolecules in Solutions. I. Formulation

Abstract

The previous theory treating the analogous problem is developed to include rigorously the interactions between the atomic groups whose relative spatial configurations are determined by the rotational angles of two neighboring skeletal bonds. The mean-square end-to-end distances and/or the electric moments are calculated for isotactic- and syndyotactic-vinylic macromolecules as well as a few other macromolecules with similar structures. As a model for linear macromolecules is adopted, the discrete one whose each C–C bond is assumed to take only three rotational configurations (e.g., trans, gauche, and another gauche). In such a model the problem of taking all of the interactions between neighboring bonds into account is equivalent to that of a one-dimensional cooperative system. While the partition function of this system can be obtained easily, some techniques are required to find the mean quantities under consideration. Results obtained involve the task of evaluating the trace of a certain matrix of nine degrees. Numerical calculations by a computer and discussions of the results will be given in part II of this series.