Hyperbranched Polymers Formed Through Self‐Condensing Vinyl Polymerization in a Continuous Stirred‐Tank Reactor (CSTR): 1. Molecular Weight Distribution

Abstract

A new Monte Carlo simulation algorithm, based on the random sampling technique, is proposed for the self-condensing vinyl polymerization conducted in a continuous stirred-tank reactor. In order to highlight the most fundamental aspects of the reaction system, the kinetic rate constants are assumed to be constant, and the size and structure dependence is neglected. With this ideal model, the high molecular weight (MW) tail of the weight fraction distribution W(P) is shown to follow the power law, W(P) ∝ P −α . The power exponent is represented by α = 1/(ηξ) for ξ < 1/(2η), where ξ and η are defined in the text. For ξ ≥ 1/(2η), the weight-average MW cannot reach the steady state because of the power exponent with α ≤ 2.The reactivity ratio, r, is defined by(3)

Universal Relationships in Hyperbranched Polymer Architecture for Batch and Continuous Step Growth Polymerization of AB2-Type Monomers

“…To set the value of ξ corresponds to fixing the steady state conversion level, x A . For a CSTR, it was found that the weight-average molecular weight cannot reach the steady state for large t cases [8,9], and similar behavior was also reported for the SCVP [20,21] which is another route to synthesize HB polymers. The upper limit ξ-values above which the weight-average molecular weight cannot reach the steady state for a given reactivity ratio r was shown graphically in the earlier publication [9].…”

Detailed Structural Analysis of the Hyperbranched Polymers Formed in Self‐Condensing Vinyl Polymerization

“…For the present ideal polymerization systems, it was found that the weight-average molecular weight (MW) cannot reach the steady state for large residence time cases. [9,16] The critical ξ-value, ξ c above which the weight-average MW cannot reach the steady state for a given reactivity ratio r is shown in Figure 6. [9] The MC simulation was conducted mainly for ξ < ξ c .…”

“…[9,16] The critical ξ-value, ξ c above which the weight-average MW cannot reach the steady state for a given reactivity ratio r is shown in Figure 6. [9] The MC simulation was conducted mainly for ξ < ξ c . Figure 7 shows how the number of units incorporated into the largest cluster of tri-branched dendritic units, P LC changes with the degree of polymerization, P. In the case of a CSTR, P LC is larger for large polymers.…”

“…When a CSTR is employed for SCVP, the polymerization behavior at steady state is fully controlled by the reactivity ratio r , and the following dimensionless number ξ, sometimes referred to as the Damköhler number for the second order reaction. where is the mean residence time.…”

“…Critical ξ-value above which a CSTR cannot reach the steady state for the weight-average MW, ξ c as a function of the reactivity ratio, r. The data were taken from ref [9]…”