Computer simulation of the steady state in reversible polymer‐analogous reactions, 3. Flows and statistics in detailed balance

Abstract

The steady state of reversible polymer-analogous reactions was simulated by Monte Carlo calculations. The length of the simulated copolymer chains was chosen large enough to yield data with an acceptable degree of statistical fluctuation. Two types of sets of relative rate constants K were investigated, first K , = K , = K , , and second K, # K 2 , K , # K , , K2 # K , , with K, . K, = K i . The relative rate constants K are defined as K, = k(AAA)/k(ABA), K , = k(AAB+)/k(ABB+), and K, = k(BAB)/k(BBB), where k is the ordinary rate constant pertaining to the reaction of the central monomeric unit in the triad given in parentheses, with two different types of monomeric units A and B in the binary copolymer. For both types of sets of relative rate constants the simulation showed a detailed balance to prevail for the kinetics in the steady state. It was also shown that the same kinetics and statistics were obtained in the steady state when starting the simulation first from a homopolymer consisting of A-monomeric units, and then from a homopolymer of B-monomeric units. Based on the finding of a detailed balance and on the definition of K, it could be shown by analysis that the first type of the sets of K leads to a Bernoullian statistics of the copolymers in the steady state, while the second type leads to a first-order Markov statistics. Correspondingly, equations are given which allow to calculate the relative rate constants from statistics and vice versa.