Stochastics of rotational isomeric transitions in polymer chains

The stochastic process of conformational transitions between isomeric states in polymer chains is considered. In analogy with the conventional treatments of chain statistics where equilibrium configurations are assigned statistical weights based on near neighbor intramolecular potential, stochastic weights are defined for the configurational transitions undergone by chains of pairwise interdependent bonds. The stochastic weights are expressed by v ^N × v^N matrices for N mobile bonds with v isomeric states accessible to each bond. For a given time, serial multiplication of stochastic weight matrices yields the configurational transition partition function corresponding to the space of time-delayed probabilities of occurrence of two distinct configurations for a mobile segment. A matrix multiplication scheme is devised to determine the fraction of bonds and/or segments that undergo specific isomeric transitions in a given time interval.