Stochastic Treatment of Conformational Transitions of Polymer Chains in the Sub-Rouse Regime

Orientational autocorrelations and cross-correlations are considered for vectors rigidly affixed to bonds subject to configurational transitions in a long polymer chain. Transitions of bonds from one rotational isomeric state to the other are assumed to be dependent on the state of the neighboring bonds. Bond transition rates are obtained from Kramers' expression in the high-friction limit. The friction coefficient affecting a transition is assumed to depend on the location of the bond along the moving sequence in the chain, The joint probability of having a sequence of bonds in one configuration at time zero and in another at time z and the orientational correlation functions are obtained by an efficient matrix multiplication scheme analogous to the matrix generator formalism of the rotational isomeric theory of chain statistics. A sequence of bonds whose length is prescribed by the time window of the experimental technique used is defined as an independent kinetic unit. The stochastic behavior of the latter is assumed to be uncorrelated with the remaining parta of the chain. Calculations are performed for different lengths of independent units, ranging from a few skeletal bonds to segments of the size of a Rouse subchain. Frequency distribution of relaxational modes obtained in this manner agree closely with previous calculations of Fixman by Langevin dynamics. Thus, unlike the Rouse dynamics predictions, the fastest modes of the investigated sub-Rouse regime scale linearly with inverse chain length and the distribution of relaxational frequencies for a given sequence exhibits a pronounced plateau.