Monte Carlo: A versatile tool for modeling complex polymerization processes
May 10-15, 2015
Monte Carlo is a stochastic simulation tool which reaches the molecular level to predict both microscopic and macroscopic properties which are of profound interest to the polymer industry and science. Selection of a modeling technique in polymerization systems should be a compromise between complexity of the system, complexity of the model ,stability, the level of the output that is needed and, of course, the time of the simulation. Comparing to other techniques, Monte Carlo is usually more time consuming, but it should be kept in mind that nowadays intensive numerical calculations are cheap and fast due to the current available computational power. On the other hand, Monte Carlo simulation usually needs less simplification than other methods and very detailed information on microscopic properties of very complex systems can be obtained that is elusive (if not impossible) to obtain by deterministic models as details are too complex as to be modeled by material and population balances. This is the place where Monte Carlo enlists as a unique tool for describing complex polymerization systems. In this work we exploit the advantages of the Monte Carlo approach to analyze two complex polymerization processes. The first example analyzed is the network formation in free-radical crosslinking copolymerization. The architecture of such a system is complex and not completely understood yet i.e., presence of the multiradicals, cycles and in some cases heterogeneous density of crosslinking. A kinetic Monte Carlo (KMC) approach has been applied to study the development of polymer network formation. The proposed modelling approach is able to provide detailed information beyond the gel point that can lead to an enhanced characterization of the gel fraction. The KMC simulation intrinsically considers the primary and secondary cyclization reactions and the existence of multiradicals, avoiding the use of further assumptions. The model gave very detailed information on the microstructure of a crosslinked system after gelation like conversion evolution of the entire molecular weight distribution, the primary and secondary cyclization, the molecular weight distribution between crosslinking points and the evolution of multiradicals along the polymerization. Furthermore, 3D distributions can also be obtained like the distribution of chains with a given chain length and crosslinking density. The KMC model was used to show the detailed characterization of the gel fraction with conversion and differences observed in the distributions before and after the gel point. The second example analyzed is the synthesis of hybrid polyurethane/acrylic polymer particles by batch miniemulsion polymerization. This is a very complex system in which polyaddition of the polyurethane prepolymer with the hydroxyl group of HEMA and the free radical polymerization of the acrylic monomers occur simultaneously. Furthermore, the fact that the process is heterogeneous should be considered. A detailed kinetic Monte Carlo simulation algorithm was developed to describe this system. The simulation considers both, the polymerization in the aqueous phase and in the polymer particles, and also simultaneous polyaddition and the free radical polymerization. The model has been assessed by batch miniemulsion polymerizations carried out using an aliphatic isocyanate prepolymer, n-butyl acrylate and 2-hydroxyethyl methacrylate monomers. Detailed information on gel microstructure such as distribution of molecular weight between crosslinking points in acrylic chains, level of incorporation of PU chains (dangling or crosslinked) in the polymer network, and chain length distribution of crosslinked PU prepolymers has been derived from the model. Furthermore, fitting of the experimental kinetics and microstructure evolutions (gel fraction) suggested that the presence of the water in polymer particles cannot be ignored in the presence of isocyanate groups in the polymer particles and that the terminal pendent double bond of the HEMA in polymer chains have significantly lower reactivity than that of the HEMA free monomer.
Shaghayegh Hamzehlou, Yuri Reyes Mercado, and Jose Ramon Leiza, "Monte Carlo: A versatile tool for modeling complex polymerization processes" in "Polymer Reaction Engineering IX", E. Vivaldo-Lima, UNAM; J. Debling, BASF; F. Zaldo-Garcia, CP-COMEX; J. Tsavalas, Univ. of New Hampshire Eds, ECI Symposium Series, (2015). http://dc.engconfintl.org/polymer_rx_eng_IX/26