Structural Symmetry Consideration in the Calculation of Unperturbed Dimensions of Polymer Chains

The possibility has been examined that structural symmetry may be utilized to reduce the order of matrices to be treated in the calculation of unperturbed mean-square end-to-end distances of polymer chains. It is found that this is the case for a class of polymers possessing such a symmetry that when all the skeletal bonds are forced to be in the trans conformation the chemical structure is symmetric with respect to the plane involving skeletal bonds. For this class of polymers, the order of matrices is shown to be reduced from 3s to 32s when the cis and trans states are forbidden to occur, and from 3s to 32(s+1) when the cis state is forbidden but the trans state is allowed. Here s is the number of rotational isomeric states of skeletal bonds. It is suggested that the method is equally effective in the calculation of higher even moments of end-to-end distances and optical anisotropies of polymer chains.