Enzymatic generation of binary block-copolymeric structures: mathematical analysis based on triad frequencies...

A mathematical model is derived for describing a multiple-attack pathway for enzymatic generation of block structure in binary linear copolymers having initially a randomized sequential structure. The model is based on sequential information in terms of copolymer monads, diads, and triads estimated by nmr spectroscopy, and is applicable to enzymes attacking next to a reacted unit in the polymer chains. Then the block distribution of unreacted units remains constant and explicit relationships are provided. The probability of triad frequencies as a function of monads, i.e., progress curve of enzyme copolymer sequential structure, allows us to characterize the enzymatic mode of attack independently of enzyme kinetics. The produced fractions of heterogeneous triads centered by reacted units are shown to be affected, to a large extent, by the degree of multiple attack (d) entering into the formula as a variable parameter. The single-chain, d = infinity, and multiple-chain mechanisms, d = 1, representing the two extremes of the treated mechanism, are very clearly discriminated.