Modeling of RAFT Polymerization Processes Using an Efficient Monte Carlo Algorithm in Julia

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

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.

Sequence Design of Random Heteropolymers as Protein Mimics

Random heteropolymers (RHPs) have been computationally designed and experimentally shown to recapitulate protein-like phase behavior and function. However, unlike proteins, RHP sequences are only statistically defined and cannot be sequenced. Recent developments in reversible-deactivation radical polymerization allowed simulated polymer sequences based on the well-established Mayo-Lewis equation to more accurately reflect ground-truth sequences that are experimentally synthesized. This led to opportunities to perform bioinformatics-inspired analysis on simulated sequences to guide the design, synthesis, and interpretation of RHPs. We compared batches on the order of 10000 simulated RHP sequences that vary by synthetically controllable and measurable RHP characteristics such as chemical heterogeneity and average degree of polymerization. Our analysis spans across 3 levels: segments along a single chain, sequences within a batch, and batch-averaged statistics. We discuss simulator fidelity and highlight the importance of robust segment definition. Examples are presented that demonstrate the use of simulated sequence analysis for in-silico iterative design to mimic protein hydrophobic/hydrophilic segment distributions in RHPs and compare RHP and protein sequence segments to explain experimental results of RHPs that mimic protein function. To facilitate the community use of this workflow, the simulator and analysis modules have been made available through an open source toolkit, the RHPapp.

Evolution of Molar Mass Distributions Using a Method of Partial Moments: Initiation of RAFT Polymerization

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).

Initiator Feeding Policies in Semi-Batch Free Radical Polymerization: A Monte Carlo Study

A Monte Carlo simulation algorithm is developed to visualize the impact of various initiator feeding policies on the kinetics of free radical polymerization. Three cases are studied: (1) general free radical polymerization using typical rate constants; (2) diffusion-controlled styrene free radical polymerization in a relatively small amount of solvent; and (3) methyl methacrylate free radical polymerization in solution. The number- and weight-average chain lengths, molecular weight distribution (MWD), and polymerization time were computed for each initiator feeding policy. The results show that a higher number of initiator shots throughout polymerization at a fixed amount of initiator significantly increases average molecular weight and broadens MWD. Similar results are also observed when most of the initiator is added at higher conversions. It is demonstrated that one can double the molecular weight of polystyrene and increase its dispersity by 50% through a four-shot instead of a single shot feeding policy. Similar behavior occurs in the case of methyl methacrylate, while the total time drops by about 5%. In addition, policies injecting initiator at high monomer conversions result in a higher unreacted initiator content in the final product. Lastly, simulation conversion-time profiles are in agreement with benchmark literature information for methyl methacrylate, which essentially validates the highly effective and flexible Monte Carlo algorithm developed in this work.

Kinetic Monte Carlo Simulation Based Detailed Understanding of the Transfer Processes in Semi-Batch Iodine Transfer Emulsion Polymerizations of Vinylidene Fluoride

Semi-batch emulsion polymerizations of vinylidene fluoride (VDF) are reported. The molar mass control is achieved via iodine transfer polymerization (ITP) using IC₄F₈I as chain transfer agent. Polymerizations carried out at 75 °C and pressures ranging from 10 to 30 bar result in low dispersity polymers with respect to the molar mass distribution (MMD). At higher pressures a significant deviation from the ideal behavior expected for a reversible deactivation transfer polymerization occurs. As identified by kinetic Monte Carlo (kMC) simulations of the activation⁻deactivation equilibrium, during the initialization period of the chain transfer agent already significant propagation occurs due to the higher pressure, and thus, the higher monomer concentration available. Based on the kMC modeling results, semi-batch emulsion polymerizations were carried out as a two pressure process, which resulted in very good control of the MMD associated with a comparably high polymerization rate.

Deterministic Approaches for Simulation of Nitroxide-Mediated Radical Polymerization

Since its development in the last decades, controlled radical polymerization (CRP) has become a very promising option for the synthesis of polymers with controlled structure. The design and production of tailor-made materials can be significantly improved by developing models capable of predicting the polymer properties from the operating conditions. Nitroxide-mediated polymerization (NMP) was the first of the three main variants of CRP to be discovered. Although it has lost preference over the years against other CRP alternatives, NMP is still an attractive synthesis method because of its simple experimental implementation and environmental friendliness. This review focuses on deterministic methods employed in mathematical models of NMP. It presents an overview of the different techniques that have been reported for modelling NMP processes in homogeneous and heterogeneous media, covering from the prediction of average properties to the latest techniques for modelling univariate and multivariate distributions of polymer properties. Finally, an outlook of model-based design studies of NMP processes is given.

Analytical and advanced kinetic models for characterization of chain-growth copolymerization: the state-of-the-art

A detailed overview is given on the currently developed analytical and advanced kinetic models to calculate the main bulk/solution chain-growth copolymerization characteristics.