Alberto Cingolani, Danilo Cuccato, Giuseppe Storti and Massimo Morbidelli* ––––––––– A. Cingolani, Prof. G. Storti, Prof. M. Morbidelli. Institute for Chemical and Bioengineering, Department of Chemistry and Applied Bioscience ETH Zurich, Vladimir-Prelog-Weg 1-5/10, 8093 Zürich, Switzerland E-mail: massimo.morbidelli@chem.ethz.ch Dr. D. Cuccato Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom –––––––––

This chapter describes the potential of density functional theory (DFT)-based computational chemistry methods for investigating the kinetics of reactions involved in free-radical polymerization (FRP). The knowledge of reaction mechanisms and rate coefficients is crucial for the prediction of polymer properties and consequently for the production of desired polymer products. Additionally, this chapter provides the reader with an overview of all previous studies that have used computational methods based on quantum mechanics to determine the rate coefficients of reactions in FRP, covering the wide range of polymer systems and reactions that can be studied using DFT.

Reliable control of pore size distribution in porous materials is a key feature for addressing specific applications. The reactive gelation process represents a robust and efficient method to obtain mechanically stable monoliths with tunable pore size distribution. Primary polymer nanoparticles are destabilized and aggregated in a controlled way, forming a percolating gel. Afterward, this structure is hardened by a postpolymerization, carried out through heating. Different parameters play a major role in determining the final morphology of the monolith. In this work, the effect of primary particle architecture (i.e., core-to-shell ratio) and initial solid content of the latex is investigated, using two different sizes of nanoparticles. Actually, the first parameter affects the pores in the small range (0.01-1 mu m) whereas the latter those in the larger one (1 mu m to several micrometers), independently of the primary particle size. As a result, monoliths with very well-defined pore size distributions are obtained.

Acrylamide and sodium acrylate are copolymerized in aqueous solution to study the influence of monomer concentration and ionic strength onto the reactivity ratios using in-situ H-1 NMR. Increasing the monomer content leads to larger reactivity of the ionized monomer. At low monomer concentration, this effect was reproduced by adding NaCl to increase the ionic strength, indicating that the reaction kinetics is largely governed by charge interactions. On the contrary, this was not observed at higher monomer content, suggesting that non electrostatic effects are mainly responsible of the monomer concentration dependence at these conditions. A comprehensive mathematical model was developed to predict copolymer composition as a function of monomer concentration and ionic strength. It is based on a previously-proposed rate law of propagation for ionized monomers, which has been expanded to cover any ionization degree of acrylic acid. The model is capable to reproduce composition data from different sources obtained in a wide range of reaction conditions.

Water-soluble, carboxylic acid monomers are known to exhibit peculiar kinetics when polymerized in aqueous solution. Namely, their free-radical polymerization rate is affected by several parameters such as monomer concentration, ionic strength, and pH. Focusing on methacrylic acid (MAA), even though this monomer has been largely addressed, a systematic investigation of the effects of the above-mentioned parameters on its polymerization rate is missing, in particular in the fully ionized case. In this work, the kinetics of non-ionized and fully ionized MAA are characterized by in-situ nuclear magnetic resonance (NMR). Such accurate monitoring of the reaction rate enables the identification of relevant but substantially different effects of the monomer and electrolyte concentration on polymerization rate in the two ionization cases. For non-ionized MAA, the development of a kinetic model based on literature rate coefficients allows us to nicely simulate the experimental data of conversion versus time at a high monomer concentration. For fully ionized MAA, a novel propagation rate law accounting for the electrostatic interactions is proposed: the corresponding model is capable of predicting reasonably well the electrolyte concentration effect on polymerization rate. Nevertheless, further kinetic information in a wider range of monomer concentrations would be welcome to increase the reliability of the model predictions.

ABSTRACTIn this work, ring‐opening polymerization and reversible addition‐fragmentation chain transfer polymerization (RAFT) have been employed for the production of block copolymers where the backbone is brushed with poly(ethylene glycol) (PEG) and polyester chains. Because of their amphiphilic properties, they are able to self‐assemble in water, forming micelles. Molecular dynamics simulations have been accomplished to study the behavior of the copolymer single chain in water, and the self‐assembly properties have been characterized and correlated to the copolymer structure in terms of critical micellar concentration and particle size. As a proof of their flexibility, these materials have been employed for the production of polymer–lipid hybrid nanoparticles with tunable dimensions (from 120 to 260 nm) adopted for the controlled release of anticancer compounds (paclitaxel and curcumin). © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43084.

The reversible addition-fragmentation chain transfer (RAFT) copolymerization of non-ionized acrylic acid with acrylamide in dimethyl sulfoxide is investigated and compared with the conventional free radical process carried out at the same conditions. The effect of the living nature of the RAFT process on overall polymerization rate and on copolymer composition is studied by in situ H-1 NMR. The same values of reactivity ratios (r(AA) = 1.55 +/- 0.02 and r(Am) = 0.75 +/- 0.02) are estimated for both the processes, living and non-living. The copolymers prepared by RAFT polymerization exhibit well-controlled composition, with narrow distribution. This approach can be applied to the synthesis of copolymer standards at specific composition for direct calibration of size-exclusion chromatography. (C) 2016 Elsevier Ltd. All rights reserved.

The free-radical copolymerization of acrylamide with the cationic monomer DMAEA-Q in aqueous medium is investigated with special attention to its composition behavior, which reveals to be affected by the electrostatic interactions between the charges in the system. The reaction kinetics is determined by in situ H-1 NMR experiments, showing a peculiar dependence of the copolymer composition upon initial monomer and electrolyte concentrations. A kinetic model simulating the evolution of copolymer composition as a function of conversion is developed, accounting for the nonconventional features of the system. Namely, a description of the electrostatic interactions based on the DLVO theory is introduced to define a functional dependence of the rate coefficients on the ionic strength. Secondary reactions are also included due to the acrylic nature of both monomers. The proposed model is applied to estimate the corresponding reactivity ratios and proves to exhibit the correct functionality with respect to monomer concentration and ionic strength.

Throughout the last 25 years, computational chemistry based on quantum mechanics has been applied to the investigation of reaction kinetics in free radical polymerization (FRP) with growing interest. Nowadays, quantum chemistry (QC) can be considered a powerful and cost-effective tool for the kinetic characterization of many individual reactions in FRP, especially those that cannot yet be fully analyzed through experiments. The recent focus on copolymers and systems where secondary reactions play a major role has emphasized this feature due to the increased complexity of these kinetic schemes. QC calculations are well-suited to support and guide the experimental investigation of FRP kinetics as well as to deepen the understanding of polymerization mechanisms. This paper is intended to provide an overview of the most relevant QC results obtained so far from the investigation of FRP. A comparison between computational results and experimental data is given, whenever possible, to emphasize the performances of the two approaches in the prediction of kinetic data. This work provides a comprehensive database of reaction rate parameters of FRP to assist in the development of advanced models of polymerization and experimental studies on the topic.

The present computational study focuses on the investigation of bimolecular hydrogen abstractions that can occur during free radical polymerization (FRP) processes. In particular, several hydrogen abstractions from four monomers (butyl acrylate, BA; styrene, ST; butyl methacrylate, BMA; vinyl acetate, VA) and three different backbone chains (poly-BA, poly-BA-co-VA, and poly-BA-co-ST) have been studied. The aim is to provide an overview of the kinetics for all possible intermolecular hydrogen abstraction reactions from all chemical species present in a bulk FRP as well as to support the understanding of the influence of chemical environment on hydrogen abstractions. All simulations were performed using density functional theory (DFT) with quantum tunneling factors estimated using the Eckart model. This study provides proof that the presence of an electron donating group in the chemical environment of the abstracted hydrogen atoms can lead to lower activation energies and higher rate coefficients for abstraction whereas the presence of an electron withdrawing group leads to opposite effects.

Radical desorption from polymer particles is a kinetic event peculiar to the emulsion polymerization process. A careful modeling of this phenomenon is highly valuable in order to achieve accurate predictions of polymerization rate and average properties of molecular weight. In this work, radical desorption is described accounting for an aspect fully neglected in previous modeling literature. Specifically, particle state dependent desorption coefficients are used instead of a single average coefficient, and the corresponding rate expressions are developed and applied to the solution of the well-known Smith-Ewart equations. Parametric model simulations show that the higher level of detail introduced in the description of radical desorption improves the accuracy of the predicted values of the average number of radicals per particle, especially in the cases of high desorption rate and slow reactions in the aqueous phase.

In this work, the free-radical polymerization (FRP) of widely used fluorinated monomers was investigated. Computational studies were conducted to assess the FRP kinetics of each binary copolymerization between vinylidene fluoride (VDF), hexafluoropropylene (HFP), and tetrafluoroethylene (TFE). More specifically, all calculations were performed using density functional theory (DFT), and the B3LYP level of theory was used to optimize structures and determine absolute minimum energy geometries, whereas the electronic energies were estimated using B3LYP/6-31G(d,p) as well as a higher level of theory, MPWB1K/6-31G(d,p). Transition state theory was employed to determine kinetic parameters according to the terminal model of copolymerization. The homopolymerization of VDF and all of its corresponding copolymerizations were investigated by taking into account every possible propagation reaction (head to head, head to tail, tail to tail, head to monomer, tail to monomer, etc.) to estimate the Arrhenius parameters for each system. This study provides the estimation of a large set of rate coefficients, which gives detailed pictures of the specific copolymerization systems examined and is highly valuable to generate a comprehensive overview of the polymerization kinetics of relevant fluorinated monomers.

Recently, a growing amount of attention has been focused on the influence of secondary reactions on the free radical polymerization features and the properties and microstructure of the final polymer, particularly in the context of acrylate copolymers. One of the most challenging aspects of this research is the accurate determination of the corresponding reaction kinetics. In this paper, this problem is addressed using quantum chemistry. The reaction rate coefficients of various backbiting, propagation, and β-scission steps are estimated considering different chain configurations of a terpolymer system composed of methyl acrylate, styrene, and methyl methacrylate. The replacement of methyl acrylate radical units with styrene and methyl methacrylate globally decreases the backbiting probability and shifts the equilibrium toward the reactants, while the effect of replacing adjacent units is weaker and more dependent upon the specific substituting monomer. Propagation kinetics is affected primarily by the replacement of the radical units, while this effect appears to be particularly effective on midchain radical reactivity. The overall results clarify the different physicochemical behavior of chain-end, midchain, and short-branch radicals as a function of copolymer composition, providing new insights into free radical polymerization kinetics.

In this work, secondary reactions involved in the free radical polymerization of butyl acrylate are investigated using quantum chemistry. First, various backbiting reactions are studied by adopting a simplified molecular model suitable for treating long polymer chains. The predicted reaction kinetics suggest the possibility of a radical migration along the poly(butyl acrylate) (PBA) chain as a consequence of subsequent j:j+4 hydrogen abstractions, which are characterized by a low activation energy. Moreover, branching propagation and -scission reactions originating from mid-chain radicals are investigated using a complete PBA model composed of five monomer units. The reaction kinetics involving short-branch radicals are also examined, and a novel backbiting step leading to the formation of short branches is proposed.

Reactions of chain transfer to agent (CTA) are conventionally used to regulate the polymer molecular weight during radical polymerization processes, due to the interaction between CTAs and chain-end growing radicals. In acrylate polymerization, the presence of a relatively large amount of midchain radicals (MCRs) opens the way for alternative kinetic pathways involving CTAs, which can result in a modification of the overall kinetics as well as the final polymer properties. In this work, chain transfer reactions from butyl acrylate (BA) radicals of various size and nature to a set of selected CTAs are investigated using quantum chemistry. The different reactivity of chain-end and midchain radicals is emphasized, with particular focus on the kinetic effect of the radical chain length. Eventually, the mechanism of MCR patching and its relevance in decreasing the branching density are critically examined, with reference to the estimated kinetic parameters and experimental evidence about BA polymerization.

Free-radical polymerization of vinyl chloride is investigated computationally with special attention to the secondary reactions involving mid-chain radicals (MCRs). Namely, the rate constants of backbiting, chain scission, chain transfer, and propagation reactions are evaluated using a density functional theory method. The rate coefficients of such reactions are estimated taking into account the position of the radical along the chain as well as its distance from the chain-end. In particular 1:5, 5:1, and 5:9 backbiting are the most relevant secondary reactions, followed by the slower propagation of MCRs. Finally, a kinetic model of suspension polymerization including the investigated reactions is developed, in order to determine their impact on the quality of the final polymer.

Quantum tunneling in hydrogen transfer reactions active in FRP is investigated theoretically. Three systems are examined: polyethylene, polystyrene, and poly(vinyl chloride). Kinetic parameters of backbiting reactions are evaluated adopting quantum chemistry. Tunneling corrections are estimated adopting the one-dimensional Eckart model, which provides a reasonable accuracy along with a limited computational effort. The relevance of quantum tunneling in the investigated systems is highlighted, with focus on the temperature dependence of the tunneling correction in the typical polymerization conditions of the investigated monomers. Obtained results clearly show that tunneling plays an important role in the kinetics estimation of hydrogen abstractions in FRP.

Quantum chemistry was applied to the free radical polymerization of Vinyl Chloride with the aim of elucidating the reaction kinetics and especially the formation of structural defects and low molecular weight polymer. The radical reactions were studied using the Density Functional Theory. All calculations were performed with B3LYP functionals and in particular the 6-31G(d,p) basis set was selected to evaluate the exchange and correlation energies. The computational method was first validated by predicting the rate constant of the propagation step and comparing the calculated values to experimental ones. Then intramolecular chain transfer, beta-scission and branching reactions were also investigated, due to their direct connection with the production of defects in the growing chains. A comparison of the evaluated kinetic constants of such secondary reactions with other computational evaluations and experimental data was finally made.