Distributions of the unperturbed dimensions of Markov-chain copolymers

This investigation shows that Markov-chain copolymers can be regarded as random copolymers the segment lengths of which depend on the copolymerization parameters. It was possible to derive simple analytical formulae for the mean-square end-to-end distance (〈r²〉), the Kuhn length, and the distribution of r² under theta-conditions. The results of these equations are in excellent agreement with data from simulations. It is shown that 〈r²〉 as well as the non-uniformity of r² increase strongly with increasing probabilities of homopropagation, i.e., with increasing mean homosequence lengths. Furthermore it is demonstrated by simulation that even chains of identical length and composition show a distribution of r² because of different arrangements of the sequences inside the chains. For chains or chain segments shorter than the average homosequences, a double-peak distribution of r² is found. The equations derived in this paper can be applied to real copolymers as well as to chains the curvature of which is altered locally by the association of ligands.