Statistical Thermodynamics and Kinetics of Polycondensation: 1. Ensembles with Randomly Arranged Bonds between Monomers

Polycondensation is presented as a process of irreversible growth in time t of the number of randomly located bonds B ( t ) with the same energy E 0 in an ensemble of M monomers at t = 0. It is shown that MB ensembles are isomorphic to classes of the permutation group composed of n -mers, being their irreducible representations with fixed M and BE 0 values. Representation of MB ensembles as eigenstates makes it possible to find the number of elements in them and their molecular mass distributions . The distributions include the ascending ( B M /2) and descending ( M − B M /2) branches of deterministic transitions ∆ B = 1 separated by a region of stochasticity caused by mixing elements of different classes.