Use of Markov Chains in Treating Depropagation in Copolymerization. I. Composition of Copolymers

Equations for the composition of the copolymers in binary, ternary, and K-component copolymerization with depropagation developed by means of Markov chains. The mole fractions of the different monomers in the copolymers are determined as components of the limit vector α = (a1, …, an), the latter being obtained as an eigenvector of the transition matrix P. The elements of this matrix are so defined that they reflect the possibility of slipping one, two, or K types of monomer units off the growing chain in the K-component copolymerization (K = 2, 3, …, n). We take the case in which the monomer units slip off if they are attached to a chain, ending with one or more monomer units of the same type. Calculated and experimental data for the composition of the copolymers of o-methylstyrene and methyl methacrylate obtained by radical copolymerization are given. These data agree very well. It is shown that after small simplifications, the equations developed can also be used for common copolymerization (without depropagation).