No abstract

A computer program has been written which employs an implicit Euler method to solve directly the complete set of coupled differential equations which result from an analysis of polymerization kinetics. The program was written to make full use of the speed and power of modern supercomputers, and is suited to the solution of very large stiff systems of differential equations. The benefit of treating each propagation step as a discrete reaction is that information on the evolution of the molecular weight distribution is obtained directly without the need to make perhaps unjustified assumptions such as the steady-state approximation. For illustrative purposes, the method has been applied in the kinetic simulation of 'quasi-living' radical polymerization to assess the effect of experimental variables on the molecular weight, molecular weight distribution, and rate of polymerization. The calculations show that 'quasi-living' radical polymerization can produce polymers with polydispersities approaching those obtained with anionic 'living' polymerizations. Some necessary conditions for the formation of polymers with narrow molecular weight distribution are defined.' Moad, G., and Solomon, D. H., Aust. J. Chem., 1990, 43, 215.

No abstract

We describe a method of partial moments devised for accurate simulation of the time/conversion evolution of polymer composition and molar mass. Expressions were derived that enable rigorous evaluation of the complete molar mass and composition distribution for shorter chain lengths (e.g., degree of polymerization, Xn = N < 200 units) while longer chains (Xn ≥ 200 units) are not neglected, rather they are explicitly considered in terms of partial moments of the molar mass distribution, μxN(P)=∑n=N+1∞nx[Pn] (where P is a polymeric species and n is its’ chain length). The methodology provides the exact molar mass distribution for chains Xn < N, allows accurate calculation of the overall molar mass averages, the molar mass dispersity and standard deviations of the distributions, provides closure to what would otherwise be an infinite series of differential equations, and reduces the stiffness of the system. The method also allows for the inclusion of the chain length dependence of the rate coefficients associated with the various reaction steps (in particular, termination and propagation) and the various side reactions that may complicate initiation or initialization. The method is particularly suited for the detailed analysis of the low molar mass portion of molar mass distributions of polymers formed by radical polymerization with reversible addition-fragmentation chain transfer (RAFT) and is relevant to designing the RAFT-synthesis of sequence-defined polymers. In this paper, we successfully apply the method to compare the behavior of thermally initiated (with an added dialkyldiazene initiator) and photo-initiated (with a RAFT agent as a direct photo-iniferter) RAFT-single-unit monomer insertion (RAFT-SUMI) and oligomerization of N,N-dimethylacrylamide (DMAm).

Numerical integration has been used as a means of simulating the title polymerization so that the variation of molecular weight and molecular weight distribution with reaction time (conversion) can be evaluated. The time/conversion dependence of the polydispersity (R) has been evaluated as a function of the relative magnitude of the rate constants associated with the initiation/termination equilibria . It is shown that the short term behaviour of R and the rate of approach to the value (R = 4/3) predicted by the steady state treatment have a marked dependence on the choice of rate constants.