Controllable Power‐Law Distribution in Free‐Radical Vinyl/Divinyl Copolymerization by Using a Continuous Stirred Tank Reactor

Abstract

AbstractIt has been believed that the power‐law molecular weight distribution is formed at the gel point, and the power exponent falls in a category of universality in critical phenomena, and therefore, it cannot be changed. It is found that the power‐law weight fraction distribution W(P) ∝ P−α, capable of controlling the exponent α, can be synthesized by using a continuous stirred tank reactor (CSTR). The exponent is governed by a single non‐dimensional parameter, ξ that is equivalent to the Damköhler number, representing the ratio of timescales between the mean residence time and the crosslinking reaction. For small ξ’s, the non‐critical transition of the weight‐average molecular weight to infinity is observed, and the exponent approaches α = 2. For large ξ’s, the system shows similar behavior to that in a closed system and the exponent is the same as for the batch polymerization, with α = 1.5. At the gel point, the product of the average crosslinking density and the weight‐average primary chain length satisfies the relationship, . The crosslinking density of the gel molecule at the gel point is found to be .