Monte Carlo methods are heuristic algorithms that use probabilities to select an outcome among several possible events in a given process. Monte Carlo methods are useful in polymer reaction engineering because they can predict the molecular architecture of polymers with details that cannot be easily captured by any other modeling technique. One of the advantages of Monte Carlo simulation is that one does not need to solve differential or algebraic equations to predict the microstructures of polymers. This article reviews the literature on steady‐state and dynamic Monte Carlo methods in polymer reaction engineering. We hope to convince the readers that playing dice regularly can be a great asset to polymer reactors engineers.

The production of polymers from renewable materials has arisen increasing interest because of the environmental impacts caused by conventional processes. In this context, the present manuscript investigates the step-growth polymerization of poly(ethylene 2,5-furandicarboxylate), PEF, a furanic polyester with structural similarity to poly(ethylene terephthalate), PET, using ethylene glycol (EG), and 2,5-furandicarboxylic acid (FDCA) as monomers. The polymerization is performed in two steps: direct esterification of EG and FDCA under continuous nitrogen flow, followed by the transesterification of produced diesters and oligomers under reduced pressure. In order to do that, experiments were performed at distinct reaction temperatures and using different nitrogen flow rates. Based on the obtained experimental data, a mathematical model was built and model parameters were estimated to allow for appropriate description of available data. The obtained results indicate that the rates of polymerization are highly limited by mass transfer and removal of reaction byproducts. POLYM. ENG. SCI.,

The control of polymerization conditions and final properties of polybutadiene produced through solution polymerizations constitute an important industrial challenge, which can be tackled with help of mathematical models. For this reason, the present work focus on the development of a phenomenological mathematical model, and estimation of the respective model parameters, in order to describe the kinetics of 1,3‐butadiene solution polymerizations catalyzed by neodymium versatate. The proposed model can be used to predict some important final properties of polybutadiene resins, including the cis‐content and average molecular weights, and the evolution of operation conditions that are used at plant site to monitor the course of the reaction, including the reaction temperature and pressure. Given the low required computation times, the proposed model can be used for purposes of monitoring and control in actual industrial sites. POLYM. ENG. SCI., 59:2290–2300, 2019. © 2019 Society of Plastics Engineers

Kinetic Monte Carlo (MC) is the main stochastic strategy used to simulate polymerization systems, as it gives good results with simple formulation. Normally, the algorithm used in this method presents high computational times, being necessary to choose suitable control volume sizes, which gives reliable results in moderate simulation times. The use of high-level languages (Python, MATLAB) over low-level languages (C, Fortran) usually aggravates this scenario, as it is slower despite being easier to use. The current study presents a simple method for speeding up the MC simulation of polymerization reactions. First, the code itself is optimized to reduce by half the computational time required compared with the original code, and then a benchmark of pure Python and Python with Numba is made. The results show a drop in the computational times above 99% when using Numba instead of pure Python codes.

The present work analyzes whether discrimination of chain branching models is possible in addition diene polymerizations, based solely on average molecular weights and monomer conversions monitored during the reaction course, as usually performed in most quality control labs of industrial plants. In addition, it is verified whether the analyzed models present enough flexibility to fit data generated with the other rival models. Three kinetic models are considered, and kinetic parameters are varied in order to represent average molecular weights and monomer conversions that are typically found in addition diene polymerizations. The results show that model discrimination is indeed feasible with few experiments, even when only average molecular weights measured through GPC analyses are available, which can be of significant practical importance at plant site for critical characterization of product properties and process performance.