Markovian approach to nonlinear polymer formation: Free-radical polymerization with chain transfer to polymer

Molecular Weight Development during Simultaneous Chain Scission, Long‐Chain Branching and Crosslinking, 2

“…However, the use of larger‐sized matrix requires larger amount of computational time. It was found previously12–14 that the extrapolation, $N \to \infty$ could be conducted satisfactorily by using rather small values of N s, for example, with N = 30, 40, 60.…”

“…When this concept is applied to Monte Carlo simulation method based on the random sampling technique,7–11 one can observe the structure of each polymer molecule formed in the complex molecular buildup processes directly on the computer screen and very detailed structural information can be obtained in a straightforward manner, such as the full molecular weight distribution, the gel point, and the spatial conformation of polymer molecules in solution including the elution curve of size exclusion chromatography. On the other hand, the matrix formula for the weight‐average molecular weight can be applied to free‐radical polymerization by extrapolating the number of chain types, N to infinity 12–14. This method is free from the statistical error inevitable in the Monte Carlo simulation method.…”

Simultaneous long‐chain branching and random scission. II. Analytic expression for the weight‐average molecular weights

“…In this article, I use the random sampling technique to obtain a matrix formula for the weight-average molecular weights, as was done to solve the heterochain branching/crosslinking problems. [15][16][17][18][19][20][21] In the illustrative calculations, the calculated results are compared with those from the MC simulation method developed in the first part of this series, 1 and the validity of the obtained results is confirmed.…”

Molecular Weight Development during Simultaneous Chain Scission, Long‐Chain Branching and Crosslinking, 1

“…To account for the non‐random nature of chain connection statistics, the heterochain connection model was proposed 16–20. The heterochain model is designed to consider nonlinear polymer architecture formed by connecting N types of different chains whose connection statistics are Markovian.…”

“…The primary chain connection statistics are different depending on the birth time; therefore, by considering the primary chains formed at different times as different types of chains, the heterochain model can describe the molecular architecture formed in free‐radical polymerization as a limiting condition, N → ∞ . In the heterochain theory, the analytical expression of the weight‐average molecular weights are usually given in a matrix formula 16–20. The use of matrix equations may remind one of the cascade theory when applied to multicomponent systems 4,21.…”