Optional Project 1B  (Total of 2 Quizzes possible)

This project involves an alternative method to that of Project 1 (Flory Method) of calculating a random walk using two random angles between 0 and pi and 0 and 2pi for the bond direction.  The intent is to compare the speed of calculation with the method of project 1, compare the persistence length and compare the mean end-to-end distance and RMS end-to-end distance with the results of Project 1.  (1 Quiz)  Do this for a chain of 100,000 steps and averaging 100 of such chains.

Wignall reported in 1985 that the radius of gyration and chain scaling for polyethylene in the melt and in the semi-crystalline state does not vary.  This seemingly unusual result can be verified in a simulation by first simulating a chain of 100,000 steps averaging 100 of such chains (part 1 above) and then considering a random condition where A) the chain does not change position for a number of steps equal to the lamellar thickness in step units (30 or so) followed by further chain steps.  B)  A more realistic approach is to make the chain display a directed growth for the lamellar thickness (30 steps) with random onset associated with the degree of crystallinity.  C)  Finally, a fixed probability of adjacent re-entry can be incorporated in the simulation of the chain using a reversed persistence of 30 steps (returning to 0 propagation) for cases where adjacent re-entry occurs.  (1 Quiz)