Autoacceleration in Free Radical Polymerization. 2. Molecular Weight Distributions

Abstract

Molecular weight distributions during autoacceleration in free radical polymerization are calculated within the framework developed in part 1. Most macroradicals (living chains) are so immobilized by entanglements that they terminate with short mobile unentangled chains with rate constants independent of their own lengths. In some respects, Flory's "equal reactivity" hypothesis is recovered, leading to a Flory (exponential) distribution of the living population for most chain lengths N. The instantaneous distribution of the polymer product, $& is a copy of the living one. Its mean length is Nd -1/Ri where & is the initiation rate. For the shortest chains, $d exhibits power law behavior with exponents determined by short chain termination kinetics and vanishes at N = 0. It follows that $d is peaked at N = z, the characteristic short chain length.

Kinetic modeling of free radical polymerization of styrene initiated by the bifunctional initiator 2,5-dimethyl-2,5-bis(2-ethyl hexanoyl peroxy)hexane

“…A constant k t dependent on the chain length would give a better result. For long chains, the termination would be smaller than for small active chains due to a restricted mobility [37][38][39][40][41][42], which leads to an increase of the mass molecular weight and the polydispersity.…”

Co-polymerization of Acrylates

“…Since the 1970s several scientists have investigated the polymer behaviors of crosslinked PMMA [14,[22][23][24][25][26]. Cross-linked PMMA is used in a variety of commercial materials such as membranes [27], dental fillings [28], dentures, latex coatings [29], computer-to-sensor data transmission links [30], composites [31], optically clear sheeting, limb prostheses, bathtubs, bathroom sinks and shower surrounds where cross-linking plays a vital role in both processing and ultimate properties.…”

Photocopying Living Chains. 1. Steady-State

“…We will see below how the predictions of the Flory-Schulz theory are modified 27 when one considers the dependence of k t on chain length at low conversions. At higher conversions, the Flory approximation becomes completely inadequate [33][34][35] as dead polymer accumulates in the polymerization mixture, slowing down the dynamics of reacting chains, and causing the famous autoacceleration phenomenon. 1 According to theory, the success of the Flory theory during low conversion FRP stems from a weak power law dependence of termination rate constant on chain lengths at low polymer concentrations.…”

“…Now, to obtain the steady-state living MWD, let us consider the dynamics of living chains, which obey: 9,34,35 where ψ(N, t) is the number of living chains of length N units at time t, and H(N, t) is the "reaction field", i.e., the total reaction rate per chain of length N due to all other living chains in the system, given by…”

“…The termination mechanism in FRP involves either coupling or disproportionation as shown in Figure 11. In the extreme case of 100% coupling, the mean dead chain length is twice the mean living chain length, 3,35 Therefore, in the photocopy experiment it is, in principle, possible to infer the relative roles of coupling vs disproportionation in termination events, since the dead and living populations are measured simultaneously.…”