|author:||Peter van Dijk|
|title:||An efficient simulation of crosslinked RAFT copolymerization|
|keywords:||Polymerization, Monte-Carlo Simulation, Graph Transformation|
|topics:||Algorithms and Data Structures , Case studies and Applications , Graphs|
Crosslinked RAFT copolymerization, a process with which nanometer-sized polymer networks are created, is relatively new and as such many experiments are needed to further develop this technique. These experiments are both resource and time consuming, making this an expensive undertaking. The aim of this project was the simulation of this polymerization process in order to make predictions about the effects of the monomer concentration, the crosslinker/monomer ratio and the RAFT agent/monomers ratio on the size, weight distribution and crosslink density of the resulting polymers. Predictions of crosslink density are especially interesting, since this parameter is difficult to quantify experimentally. Such a simulation can thus not only save time and money, but also give
more insight into the polymerization process.
We chose to create a Kinetic Monte Carlo (KMC) simulation. Normally, a KMC simulation keeps track of the reaction rates of all possible reactions in the simulation. However, the number of possible reactions scales almost quadratically with the number of different molecules when simulating crosslinked polymerization, making the regular KMC algorithm unfit for large simulations. To overcome this problem, the tracking of the reaction rates was replaced by the tracking of the reactivity of the molecules in the simulation. The efficiency of the simulation was further improved by tracking these reactivities using Binary Indexed Trees (BITs), which provide both efficient time and memory scaling. The KMC algorithm was further extended with the tracking of polymer structures, which was
used for providing visual feedback.
The results of the simulation predicted increases in weight differences and polymer size for increases in monomer concentration, decreases in the ratio of RAFT agent to monomer and increases of the ratio of crosslinker to monomer. These predictions are in good correspondence to lab data. Additionally, higher crosslink density was predicted for higher ratios of crosslinker to monomer.
The created simulation scales almost linearly in time with the number of initial molecules in the simulation. Furthermore, the memory usage scales linearly with the number of different molecule species in the simulation. The techniques used in the simulation algorithm are not limited to crosslinked RAFT copolymerization and can also be applied to speed up other simulations of (networked) polymerization. Overall, the created simulation is useful in efficiently predicting a wide range of polymer properties and can be used to support or even replace lab experiments.
- A Software Package for Chemically Inspired Graph Transformation (Digital version available here)