APPLICATION OF PROJECTION MATRICES TO THE CALCULATION OF UNPERTURBED DIMENSIONS OF CHAIN POLYMERS

The projection operator method of matrix algebra is applied to calculate the unperturbed dimensions of an independently hindered rotating bond model for linear chain molecules. It does not require eigenvectors of a given transformation matrix in order to evaluate products of that matrix. This is an advantage to usual matrix diagonalization methods. As a result, we obtained four different types of conformations depending upon the values of parameters adopted. One of them shows a typical dependence on the number of bonds N, which has also been given by the usual matrix diagonalization method. Two further conformations are rather extended compared with the first one. In addition, as the fourth one we obtained also a helix-like conformation. These conformation types correspond to those previously obtained by continuous models for stiff-chain polymers.