Development and Experimental Validation of a Dispersity Model for In Silico RAFT Polymerization

Abstract

The exploitation of computational techniques to predict the outcome of chemical reactions is becoming commonplace, enabling a reduction in the number of physical experiments required to optimize a reaction. Here, we adapt and combine models for polymerization kinetics and molar mass dispersity as a function of conversion for reversible addition fragmentation chain transfer (RAFT) solution polymerization, including the introduction of a novel expression accounting for termination. A flow reactor operating under isothermal conditions was used to experimentally validate the models for the RAFT polymerization of dimethyl acrylamide with an additional term to accommodate the effect of residence time distribution. Further validation is conducted in a batch reactor, where a previously recorded in situ temperature monitoring provides the ability to model the system under more representative batch conditions, accounting for slow heat transfer and the observed exotherm. The model also shows agreement with several literature examples of the RAFT polymerization of acrylamide and acrylate monomers in batch reactors. In principle, the model not only provides a tool for polymer chemists to estimate ideal conditions for a polymerization, but it can also automatically define the initial parameter space for exploration by computationally controlled reactor platforms provided a reliable estimation of rate constants is available. The model is compiled into an easily accessible application to enable simulation of RAFT polymerization of several monomers.

Beauty of Explicit Dispersity (Đ) Equations in Controlled Polymerizations

“…It should be mentioned that to approximate the integral regarding the dead chain contribution the Gaussian quadrature at a single node was used in both ATRP and NMP systems, resulting in p /4 in a single-term Taylor expansion of the fourth term, while Warren et al mentioned that analytically solving the integral of the fourth term could give p /3 in the fourth term, further increasing the predicted value of Đ . However, eq 35 derived from the treatment of Gaussian quadrature agrees more with experimental data …”

“…In contrast, the conventional Đ equation (eq 20) provides a monotonically declining curve, leading to a deviation from the experimental data. Similarly, comparisons of predication results between classical and updated equations for NMP and RAFT polymerization systems are shown in Figure (a2) and Figure (a3), respectively. , Besides, the results of explicit Đ equations can be used as a benchmark for evaluating the performance of numerical simulations, which has been demonstrated by the Zhou group in the mechanoATRP system . More recently, Warren et al proposed that the Đ equation can be programmed to predict the results of the flow RAFT polymerization system by accounting for residence time distribution in MMD …”

“…systems are shown in Figure 4(a2) and Figure 4(a3), respectively. 47,48 Besides, the results of explicit Đ equations can be used as a benchmark for evaluating the performance of numerical simulations, which has been demonstrated by the Zhou group in the mechanoATRP system. 88 More recently, Warren et al proposed that the Đ equation can be programmed to predict the results of the flow RAFT polymerization system by accounting for residence time distribution in MMD.…”

“…46 Subsequently, Zhou and co-workers derived a set of state-of-the-art Đ expressions for NMP based on both power-law and first-order kinetic behaviors in 2020 (eq 31 and eq 32). 47 Very recently, the latest Đ equation for RAFT polymerization was reported by Warren and co-workers (eq 35), 48 completing the updates for the four-term Đ expressions for the three most popular RDRP techniques. The four-term explicit Đ equations are summarized in Table 4, in which the fourth terms represent the contribution of dead chains to the overall Đ, and the predicted Đ displays the trend that first decreases and then gradually increases as polymerization proceeds.…”

“…(a3) Comparison of experimental data and the predictions from explicit equations for RAFT polymerization. Reproduced with permission from ref . Copyright 2023 American Chemical Society.…”