Numerical Techniques for the Solution of the Molecular Weight Distribution in Polymerization Mechanisms, State of the Art

Reverse Engineering of Radical Polymerizations by Multi-Objective Optimization

Reverse engineering is applied to identify optimum polymerization conditions for the synthesis of polymers with pre-defined properties. The proposed approach uses multi-objective optimization (MOO) and provides multiple candidate polymerization procedures to achieve the targeted polymer property. The objectives for optimization include the maximal similarity of molar mass distributions (MMDs) compared to the target MMDs, a minimal reaction time, and maximal monomer conversion. The method is tested for vinyl acetate radical polymerizations and can be adopted to other monomers. The data for the optimization procedure are generated by an in-house-developed kinetic Monte-Carlo (kMC) simulator for a selected recipe search space. The proposed reverse engineering algorithm comprises several steps: kMC simulations for the selected recipe search space to derive initial data, performing MOO for a targeted MMD, and the identification of the Pareto optimal space. The last step uses a weighted sum optimization function to calculate the weighted score of each candidate polymerization condition. To decrease the execution time, clustering of the search space based on MMDs is applied. The performance of the proposed approach is tested for various target MMDs. The suggested MOO-based reverse engineering provides multiple recipe candidates depending on competing objectives.

Beauty of Explicit Dispersity (Đ) Equations in Controlled Polymerizations

Dispersity (Đ) as a critical parameter indicates the level of uniformity of the polymer molar mass or chain length. In the past several decades, the development of explicit equations for calculating Đ experiences a continual revolution. This viewpoint tracks the historical evolution of the explicit equations from living to reversible-deactivation polymerization systems. Emphasis is laid on displaying the charm of explicit Đ equations in batch reversible-deactivation radical polymerization (RDRP), with highlights of the relevant elegant mathematical manipulations. Some representative emerging applications enabled by the existing explicit equations are shown, involving nitroxide-mediated polymerization (NMP), atom transfer radical polymerization (ATRP), and reversible addition-fragmentation chain transfer (RAFT) polymerization systems. Stemming from the several outlined challenges and outlooks, sustained concerns about the explicit Đ equations are still highly deserved. It is expected that these equations will continue to play an important role not only in traditional polymerization kinetic simulation and design of experiments but also in modern intelligent manufacturing of precision polymers and classroom education.

Precise Modeling of the Particle Size Distribution in Emulsion Polymerization: Numerical and Experimental Studies for Model Validation under Ab Initio Conditions

The particle size distribution (PSD) in emulsion polymerization (EP) has been modeled in the past using either the pseudo bulk (PB) or the 0-1/0-1-2 approaches. There is some controversy on the proper type of model to be used to simulate the experimental PSDs, which are apparently broader than the theoretical ones. Additionally, the numerical technique employed to solve the model equations, involving hyperbolic partial differential equations (PDEs) with moving and possibly steep fronts, has to be precise and robust, which is not a trivial matter. A deterministic kinetic model for the PSD evolution of ab initio EP of vinyl monomers was developed to investigate these issues. The model considers three phases, micellar nucleation, and particles that can contain n≥0 radicals. Finite volume (FV) and weighted-residual methods are used to solve the system of PDEs and compared; their limitations are also identified. The model was validated by comparing predictions with data of monomer conversion and PSD for the batch emulsion homopolymerization of styrene (Sty) and methyl methacrylate (MMA) using sodium dodecyl sulfate (SDS)/potassium persulfate (KPS) at 60 °C, as well as the copolymerization of Sty-MMA (50/50; mol/mol) at 50 and 60 °C. It is concluded that the PB model has a structural problem when attempting to adequately represent PSDs with steep fronts, so its use is discouraged. On the other hand, there is no generalized evidence of the need to add a stochastic term to enhance the PSD prediction of EP deterministic models.

Theoretical and computational methodologies for understanding coordination self-assembly complexes

This perspective highlights three theoretical and computational methods to capture the coordination self-assembly processes at the molecular level: quantum chemical modeling, molecular dynamics, and reaction network analysis. These methods cover the different scales from the metal-ligand bond to a more global aspect, and approaches that are best suited to understand the coordination self-assembly from different perspectives are introduced. Theoretical and numerical researches based on these methods are not merely ways of interpreting the experimental studies but complementary to them.

A Novel Method for Dynamic Molecular Weight Distribution Determination in Organometallic Catalyzed Olefin Polymerizations

In this study, a mathematical model for the time evolution of molecular weight distribution (MWD) was developed. This temporal model is based on the well-known Ziegler–Natta polymerization mechanism and reaction kinetics by the parametric solving of related differential equations. However, due to the generality of the reactions involved, the model can be extended to the other type of catalysts, such as metallocenes, Phillips, etc. The superiority of this model lies in providing the possibility of a more precise prediction over the active sites and kinetic parameters using a simple mathematical equation, which leads to improved reactor design in large-scale production. The model uses a function to develop a methodology for MWD calculations. In this way, the transient response is limited to the first few minutes of the reaction; however, it is important as it demonstrates the establishment of the final MWD. According to the results, almost for practical conditions with negligible transfer resistances, the time dependency of the MWD has a transient interval, depending on the kinetic constants of polymerization reactions. Increasing the time to infinity results in an increase in MW and a widening in MWD, which confirms the experimental plots well. In short, the main advantage of our proposed model over the previous ones is its ability to predict the MWD even before the completion of the polymerization reaction. The results of the present model match well with those of the well-known Schulz–Flory distribution, which only predicts the final molecular weight distribution, thus confirming that the model is reliable and generalizable.

Coupled matrix kinetic Monte Carlo simulations applied for advanced understanding of polymer grafting kinetics

An innovative coupled matrix-based Monte Carlo (CMMC) concept has been applied to successfully assess the detailed description of the molecular build-up of linear and non-linear chains in the free-radical induced grafting of linear precursors chains.