Modeling of Atom Transfer Radical Polymerization with Bifunctional Initiators: Diffusion Effects and Case Studies

Abstract

Summary: A mathematical model for atom transfer radical polymerization (ATRP) with bifunctional initiators was developed. The model was validated with three case studies in bulk and solution polymerization. We used only polymer yield data to estimate some of the model parameters, while others were obtained from the literature. The model fits the polymer yield data and also predicts weight‐average molecular weights and polydispersities very well. The free volume theory was also incorporated to the model to study the effect of diffusion‐controlled reactions. The adjustable parameters in the free volume theory for the termination, propagation, activation, and deactivation reactions were varied to show the effect on monomer conversion, polymer chain length, and polydispersity. The model shows that diffusion‐limited termination reactions produce polymer with smaller polydispersities, while diffusion‐limited propagation reactions have the opposite effect. Both models, considering and neglecting diffusion effects on the kinetic rate constants, were compared with experimental data. Even though the model predictions for monomer conversion, number‐average molecular weight, and polydispersity are good in both cases, the simulations indicate that diffusion‐controlled reactions can be ignored for the cases studied in the three case studies described in this paper.Comparison between model predictions and experimental data for BA polymerization of number‐average molecular weight in bulk at 90 °C.magnified imageComparison between model predictions and experimental data for BA polymerization of number‐average molecular weight in bulk at 90 °C.

A Review of Modeling of Diffusion Controlled Polymerization Reactions

“…Chain-length dependence of reactions among large macromolecules was considered by using a number and a weight average kinetic rate coefficient for such reactions. Exactly the same modeling approach was later used by Al-Harthi et al [165] and some case studies were investigated. Their model showed that diffusion-limited termination reactions produce polymers with smaller polydispersities, while diffusion-limited propagation reactions have the opposite effect.…”

Dynamic Monte Carlo Simulation of Atom‐Transfer Radical Polymerization

“…A large literature is available on the chemistry of LFRP and several of LFRP features have been elucidated with the help of mathematical models. For instance, the method of moments was used to describe NMP,8,9 ATRP10–13 and RAFT14 in batch reactors, and NMP, ATRP15,16 and RAFT17 in semi‐batch and continuous reactors; Predici was also used to study NMP,18 ATRP19–21 and RAFT22 in batch reactors.…”

Predicting the Limit of Control in the ATRP Process: Results from Kinetic Simulations

“…Figure 3A shows the logarithm of the initial apparent rate constants plotted against log(K ATRP ) for an ATRP system with four different propagation rate constants (representing four different monomers) and k t calculated from the composite model (Equation [14][15][16][17]. As expected, the apparent rate constant increases with K ATRP , but a …”

“…in the case of a static equilibrium (i.e., constant activation and deactivation rates), even in cases where the equilibrium is strongly shifted toward the dormant species due to very low equilibrium constants. Figure 3A, with k t calculated with the composite model (Equation [14][15][16][17]. The ''original k a '' series is the same as the simulated ATRP system with MMA in Figure 3A.…”

“…The propagation rate constant for the monomer of interest can be used to find the limiting equilibrium constant (K ATRP lim) from Figure 7 by employing the equations for the linear regression lines in Figure 7, i.e. for the constant k t we have log(K ATRP lim) ¼ 1.01 Â log(k p ) -10.05 and for k t from the composite model (Equation [14][15][16][17], log(K ATRP lim) ¼ 1.01 Â log(k p ) -10.30. Controlled ATRP will be achieved for systems with K ATRP lower than this limiting value.…”