Gillespie-Driven kinetic Monte Carlo Algorithms to Model Events for Bulk or Solution (Bio)Chemical Systems Containing Elemental and Distributed Species

A multi-scale framework for predicting α-cyclodextrin assembly on polyethylene glycol axles

Controlling the distribution of rings on polymer axles, such as α-cyclodextrin (αCD) on polyethylene glycol (PEG), is paramount in imparting robust mechanical properties to slide-ring gels and polyrotaxane-based networks. Previous experiments demonstrated that the functionalization of polymer ends could modulate the coverage of αCDs on PEG. To explore the design rule, we propose a multi-scale framework for predicting αCD assembly on bare and functionalized PEG. Our approach combines all-atom molecular dynamics with two-dimensional (2D) umbrella sampling to compute the free energy landscapes of threading αCDs onto PEG with ends functionalized by various moieties. Together with the predicted free energy landscapes and a lattice treatment for αCD and polymer diffusion in dilute solutions, we construct a kinetic Monte Carlo (kMC) model to predict the number and intra-chain distribution of αCDs along the polymer axle. Our model predicts the effects of chain length, concentration, and threading barrier on the supramolecular structure of end-functionalized polypseudorotaxane. With simple modifications, our approach can be extended to explore the design rule of polyrotaxane-based materials with advanced network architectures.

AI-Based Forecasting of Polymer Properties for High-Temperature Butyl Acrylate Polymerizations

High-temperature polymerizations involving self-initiation of the monomer are attractive because of high reaction rate, comparable lower viscosities, and no need for an additional initiator. However, the polymers obtained show a more complex microstructure, e.g., with specific branching levels or significant amounts of macromonomer. Simulations of the polymerization processes are powerful tools to gain a deeper understanding of the processes and the elemental reactions at the molecular level. However, simulations can be computationally demanding, requiring significant time and memory resources. Therefore, this study aims at applying AI-based forecasting of tailored polymer properties and using a kinetic Monte Carlo simulator for the generation of training and test data. The applied machine learning (ML) models (random forest and kernel density (KD) regression) predict monomer concentration, macromonomer content, and full molar mass distributions as a function of time, as well as the average branching level with an excellent performance (R 2 (coefficient of determination) > 0.99, MAE (mean absolute error) < 1% for kernel density regression). This study explores the number of training data needed for reliable and accurate predictions in ML models. Explainability methods reveal that the importance of input variables in ML models aligns with expert knowledge.

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.

Microporous Structure Formation of Poly(methyl methacrylate) via Polymerization-Induced Phase Separation in the Presence of Poly(ethylene glycol)

It has been demonstrated that nano- or micro-structured polymeric materials have huge potential as advanced materials. However, most of the current fabricating methods have limitations either in cost or in size. Here, we investigate the bulk polymerization of methyl methacrylate in the presence of poly(ethylene glycol) (PEG). We found that phase separation occurs during bulk polymerization. After removal of PEG via sonication, microscopic structures of poly(methyl methacrylate), including porous structures, co-continuous monolith structures, or particle aggregation structures, are formed. These structures can be controlled by the amount of PEG added and the reaction temperature. The results are summarized in phase diagrams. The addition of PEG significantly affects the reaction kinetics. Phase separation is coupled with the reaction acceleration known as the Trommsdorff effect. As a result, the reaction completes in a shorter time when the PEG amount is higher. We demonstrate surface coating to fabricate an amphiphobic surface, repelling both water and oil. The methods presented here have the potential to fabricate microscopic structures in large areas cost-effectively.

Differences and similarities between mono-, bi- or tetrafunctional initiated cationic ring-opening polymerization of 2-oxazolines

Cationic ring-opening polymerization (CROP) is an interesting synthesis technique to obtain well-defined polymers with narrow molar mass distribution (MMD).

A unified kinetic Monte Carlo approach to evaluate (a)symmetric block and gradient copolymers with linear and branched chains illustrated for poly(2-oxazoline)s

The synthesis of well-defined gradient, block-gradient and di-block copolymers with both asymmetric and symmetric compositions considering hydrophilic and hydrophobic monomer units is relevant for application fields, such as drug/gene delivery...

Coupling Kinetic Modelling with SAOS and LAOS Rheology of Poly(n-Butyl Acrylate)

A kinetic model based on fundamentals of radical polymerization and literature known rate parameters for the polymerization of n-butyl acrylate is validated against molecular analysis and rheological data. The model is used to predict conversion, molar mass distribution, and branching densities in form of short and long chain branching. Rheological measurements of synthesized model polymers are evaluated along the Carreau-Yasuda and Van Gurp-Palmen presentations, allowing to detect small differences in the degree of long chain branching. Contributions of anharmonics to viscoelastic response in large amplitude oscillations are small and differences between the products are dominated by the differences in molar mass.

Going Beyond the Carothers, Flory and Stockmayer Equation by Including Cyclization Reactions and Mobility Constraints

A challenge in the field of polymer network synthesis by a step-growth mechanism is the quantification of the relative importance of inter- vs. intramolecular reactions. Here we use a matrix-based kinetic Monte Carlo (kMC) framework to demonstrate that the variation of the chain length distribution and its averages (e.g., number average chain length x_n), are largely affected by intramolecular reactions, as mostly ignored in theoretical studies. We showcase that a conventional approach based on equations derived by Carothers, Flory and Stockmayer, assuming constant reactivities and ignoring intramolecular reactions, is very approximate, and the use of asymptotic limits is biased. Intramolecular reactions stretch the functional group (FG) conversion range and reduce the average chain lengths. In the likely case of restricted mobilities due to diffusional limitations because of a viscosity increase during polymerization, a complex x_n profile with possible plateau formation may arise. The joint consideration of stoichiometric and non-stoichiometric conditions allows the validation of hypotheses for both the intrinsic and apparent reactivities of inter- and intramolecular reactions. The kMC framework is also utilized for reverse engineering purposes, aiming at the identification of advanced (pseudo-)analytical equations, dimensionless numbers and mechanistic insights. We highlight that assuming average molecules by equally distributing A and B FGs is unsuited, and the number of AB intramolecular combinations is affected by the number of monomer units in the molecules, specifically at high FG conversions. In the absence of mobility constraints, dimensionless numbers can be considered to map the time variation of the fraction of intramolecular reactions, but still, a complex solution results, making a kMC approach overall most elegant.

Jacket temperature regulation allowing well-defined non-adiabatic lab-scale solution free radical polymerization of acrylates

Conventional batch solution free radical polymerization of n-butyl acrylate with thermal initiators such as AIBN is known to be strongly exothermic and influenced by highly activated side reactions such as backbiting and β-scission.

Impact of side reactions on molar mass distribution, unsaturation level and branching density in solution free radical polymerization of n-butyl acrylate under well-defined lab-scale reactor conditions

The paper describes the influence of side reactions in isothermal solution free-radical polymerization of n-butyl acrylate accounting for chain-length dependent diffusional limitations on termination.

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.