Use of Markov Chains in Treating Depropagation in Copolymerization. II. Distribution of Monomer Units in Copolymers

A regular Markov chain is set equivalent to n-component copolymerization (n ≥ 2) with depropagation. It is shown that the elements of the matrix of the average times for first approach M (m_ij), represent the average number of units m_k (k = 1, 2, …, n; k ± j), occupying places between the units m_i and m_j in the macromolecules. These are the average lengths of the blocks, beginning with any monomer unit m_i and ending with any unit m_j, which however do not meet further in the block. For n = 2, the composition of these blocks is fully determined, because they are composed only of one type of units. When, however, n ≥ 3, two or more types of monomer units are included in these blocks. By means of the absorbing Markov chains, expressions for the composition of these blocks when n ≥ 3 are also obtained. In binary copolymerization the diagonal elements of the matrix M (m_ij) give the average lengths of the homoblocks ～ m_i-m_i-…-m_i ～ in the macromolecules. For the n-component copolymerizatior. (n ≥ 3), the elements m_ii do not give this information. Expressions for these lengths in this case may be obtained by additional probability analysis.