On the molecular weight distribution in condensation polymerization

Development of a quantitative theory of polycondensation

“…Various modifications of the statistical method have been employed for calculation of the most probable Flory distribution (1). In particular, they proceed from consideration of a one-dimensional process of a random walk [22] and a convolution integral [23]. The kinetic method has also been extensively applied when calculating the polymer MWD.…”

“…(25). To get the gf of a polymer weight MWD, it is necessary first to find the solution of the set of the integral equation (23) for functions u 0 ðtÞ; …; u f21 ðtÞ; and to subsequently substitute this solution into the expression for functional F ð0Þ ½u in Eq. ( 24).…”

“…Such a treatment leads to a reduced branching process with particles of a single kind. Expressions (23) describe this process of the development of the populations of passive particles. It was found that there is no need to distinguish them by types, provided the simplified FSSE model is used.…”

“…Review[13] comprises integral equations(23) written down erroneously due to an unfortunate misprint at the stage of the manuscript preparation. The results of the calculations reported in this review are certainly correct since these were obtained from the solution of the undistorted set of Eqs (23)…”

Theoretical Size Distribution in Linear Step-Growth Polymerization for a Small Number of Reacting Species

“…Equations and represent the most probable distributions of Flory, which are also related to the distributions of reaction products obtained in the Fischer–Tropsch synthesis, which are known as the Anderson–Schulz–Flory distribution . The Flory distribution functions are well-accepted, and several independent derivations have appeared. − Alternatively, modifications of the original distributions of Flory to include the considerable formation of cyclic polymers have also been proposed. , However, as was pointed out by Kricheldorf and co-workers, eq contains inconsistency because in the case of p = 1, eq predicts the infinite number-average degree of polymerization. The case p = 1 means that all functional end groups have been reacted and the final reaction product should be a giant cyclic polymer with a degree of polymerization equal to the initial number of monomers.…”