chapter
22 Pages

3. The Number of Configurations of Polymeric Chain in the Self-Avoiding Random Walks Statistics

Summary ................................................................................................. 56 3.1 Introduction .................................................................................... 56 3.2 An Average Variance of Trajectories Step of Sarw and their

Number .......................................................................................... 58 3.3 An Avarage Variance of the Step in the Sarw Statistics ................. 61 3.4 Conclusion ..................................................................................... 73 Keywords ................................................................................................ 74 References ............................................................................................... 75

SUMMARY

The number of configurations L of the linear polymeric chain accurate within the constant multiplier neared to unit is unambiguously determined via the average variance z of the step of SARW trajectory: L ≈ zN. Probabilistic analysis of the SARW trajectories leads to the expression z = (2d - 1) (1 - p), in which p is the average upon the all SARW trajectories probability to discover the neighboring cell by occupied. The SARW statistics

occupancy cell upon the conformational volume. From the comparison of these expressions the next relationship follows:

The three last expressions are retained for the linear chains and polymeric stars into diluted and concentrated solutions, ideal and real ones. The number of configurations L2N for any pair of rays of the polymeric star with the s rays by the N length is determined by the expression L2N = z

2N, and for the whole star LsN = z

s(s-1)N.