A Parallelised High Performance Monte Carlo Simulation Approach for Complex Polymerisation Kinetics

Abstract

A novel, parallelised approach to Monte Carlo simulations for the computation of full molecular weight distributions (MWDs) arising from complex polymerisation reactions is presented. The parallel Monte Carlo method constitutes perhaps the most comprehensive route to the simulation of full MWDs of multiple chain length polymer entities and can also provide detailed microstructural information. New fundamental insights have been developed with regard to the Monte Carlo process in at least three key areas: (i) an insufficient system size is demonstrated to create inaccuracies via poor representation of the most improbable events and least numerous species; (ii) advanced algorithmic principles and compiler technology known to computer science have been used to provide speed improvements and (iii) the parallelisability of the algorithm has been explored and excellent scalability demonstrated. At present, the parallel Monte Carlo method presented herein compares very favourably in speed with the latest developments in the h-p Galerkin methodbased PREDICI software package while providing significantly more detailed microstructural information. It seems viable to fuse parallel Monte Carlo methods with those based on the h-p Galerkin methods to achieve an optimum of information depths for the modelling of complex macromolecular kinetics and the resulting microstructural information.

Simulating Controlled Radical Polymerizations with mcPolymer—A Monte Carlo Approach

“…For the kinetic model, we recommend formulating the reaction with the highest reaction probabilities first to achieve a good hit rate. Barner-Kowollik et al [18] proposed an improved algorithm that reduces the complexity of reaction choice by using a special data structure (binary tree). This algorithm might have advantages when a large number of reactions in the kinetic model are included, which have widely scattered reaction probabilities.…”

“…We introduced this performance parameter with the first application of mcPolymer [17]. Later on, it was used by Barmer Kowollik et al [18] for benchmarking parallelized Monte Carlo simulations and by Broadbelt et al [32] for performance analysis of nitroxide-controlled copolymerization.…”

“…Barner-Kowollik et al presented a parallel high performance Monte Carlo simulation approach for complex polymerization using the example of RAFT polymerization [18]. In this paper, the simulation was compared to PREDICI regarding the influence of the following simulation parameters: the system size (n sx range between 1 × 10 9 and 1 × 10 10 particles), the number of parallel processes (4 to 16), and the reaction time between synchronization (2 to 500 s).…”

“…If a number is chosen which is too small, the simulation will lead to incorrect results, while a large model will increase the computation time and memory consumption. The ATRP polymerization [14], optionally with a bifunctional ATRP initator [15], ATRP copolymerization [16], RAFT polymerization [17,18], NMP homopolymerization [19], NMP copolymerization [20], and gradient copolymerization with tracking the sequence distribution [21,22] are examples of the application of the Monte Carlo simulation.…”

Specialising Simulator Generators for High-Performance Monte-Carlo Methods

“…This is of high practical relevance, as Monte-Carlo simulations can provide detailed microscopic information about generated polymeric species. Such microscopic information-which is not available from deterministic simulators, specifically those using the h-p-Galerkin method [6,7]-includes (yet is not limited to) information on polymer species with more than one chain length index (i.e., star polymer systems often applied in polymeric drug, gene, and vaccine delivery systems [8]), cross-linking densities, and branching in complex polymer networks as well as detailed information on copolymer compositions. Finally, we demonstrate good parallel speedups for our Monte-Carlo method, whereas no parallel h-p-Galerkin solvers for polymerisation exist to the best of our knowledge.…”