Matrix Formulation of Copolymerization Statistics

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Abstract
The molecular distribution statistics of a binary linear copolymer are developed by the application of matrix methods appropriate to the treatment of the statistical thermodynamics of one‐dimensional systems. Through the definition of a matrix of sequential probabilities, the character of the copolymerization, the various average degrees of polymerization, and the relative probabilities of certain kinds of sequences can be readily obtained. The results are applied to a number of ``most probable'' copolymerizations: For example systems in thermodynamic equilibrium and radical copolymerizations in the steady‐state approximation. The question of stereoregularity in the latter case is also examined. Some generalizations of the approach are discussed.