Multistate reversible copolymerization of non-Markovian chains under low conversion conditions

Abstract

The reversible kinetics of copolymerization is solved analytically for the multistate mechanism proposed by B. D. T. G. Fox [J. Chem. Phys. 38, 1065 (1963)] under low conversion conditions where the concentrations of monomeric species are chemostatted and stay constant in time. Although the rates of this mechanism only depends on the currently attached or detached monomer, the growing macromolecular chain forms a nonMarkovian sequence that is characterized by matrices associated with every monomeric unit composing the sequence. These matrices are obtained by solving the kinetic equations and they determine the growth velocity of the copolymers, the statistical properties of its possible sequences, as well as the thermodynamics of the copolymerization process.

Template-directed growth of copolymers

“…In the case of a uniform template (i.e., of period L = 1), we recover the expression previously obtained in Ref. 24 for multistate templatefree copolymerization.…”

“…Moreover, the assumptions (26), (27),... are substituted into Eqs. (24), (25),... Since all of them have the same structure, they are satisfied at once if the matrices Y m l ,l obey the following relation,…”

“…23 With this aim, the matrix product method developed in Ref. 24 for multistate template-free copolymerization is here extended to multistate template-directed copolymerization, generalizing results previously obtained for single-state template-directed copolymerization in Refs. 25-28. In this context, the use of matrix products finds its origin in pioneering work by Coleman and Fox on the multistate mechanism for irreversible polymerization processes.…”

“…(43) and can be evaluated as well. 24 Thermodynamic equilibrium can be identified with the detailed balance conditions as explained in Appendix A.…”

“…[29][30][31] As shown in Ref. 24, the matrix product method can be extended to reversible processes without template. Here, the matrix product method is combined with iterated function systems to consider template-directed processes.…”