Statistical Computation of Mean Dimensions of Macromolecules. I

The configurations of flexible coiling type polymer molecules have been investigated statistically with a high-speed electronic digital computer by generation of large numbers of ``random walks.'' These walks were carried out subject to the excluded volume effect in simple cubic and tetrahedral lattices. It was found that the walk attrition obeys an exponential decay law with a half-walk of 6.7 steps in the cubic lattice and 17.3 steps for the tetrahedral. Mean square end-to-end separations, 〈rn2〉Av, were also obtained, and two distinct kinds of empirical formulas have been fitted to the data. So far, the statistical data are insufficient to establish unequivocally the nature of the functional dependence of 〈rn2〉Av for large values of n, the number of steps. A study was also made on the probabilities of ring closures for restricted random walks in the cubic system. It was found that for rings greater than 6 steps, the probability of formation varies inversely as the square of the ring size.