Simulated Annealing Polymerization: A General Algorithm for Preparing Atomistic Model Structures of Amorphous Polymers

The quest for new polymers with specialized properties surges onward to fill the inherent industrial demand for materials with novel applications. The combinatorial approach of experimentally synthesizing and characterizing new polymers becomes increasingly expensive and time consuming for any project requiring an appreciable library of polymer systems. However, molecular modeling can provide insights into the relationship between the structure and properties of polymeric systems, issuing guidance for further investigation. Such an approach, for example, can be used to design polyacrylate copolymer membranes for efficient separation of alcohol-water mixtures for biofuels production. Previously, molecular models of linear chains and fully cured cross-linked epoxy have been created through polymerizing a mixture of monomers in simulations. For copolymer systems of interest here, however, each type of reacting monomer pair has a different reaction probability, thus rendering usage of simple polymerization algorithms based on uniform reaction probabilities inappropriate. The long term goal of this work is to create a general algorithm that accounts for specific chemical reactivity considerations while preparing model structures of amorphous polymers.
The process of forming a model polymer structure is accomplished in three stages: mixing specified ratios of the monomers, creating new bonds between potentially reacting monomer pairs, and relaxing the resulting model structure to relieve the strain generated during bond creation. Of these,
the process of bond formation in the second step plays a crucial role in creating well relaxed model structures, as realistic structures are obtained only by forming bonds between spatially close monomers. For an equilibrated reaction mixture, the interatomic distance between the reactive sites will be larger than the ideal bond length in all cases. The energy and hence the strain in a newly created model increases with an increase in the bond length. To predict the lowest energy solution, i.e. polymerization sequence, an algorithm based on the simulated annealing optimization technique has been developed
to minimize the total length of new bonds. In this simulated annealing approach, which is similar to the
Monte Carlo technique, stochastic changes are proposed to the current solution which are then
accepted or rejected according to the Metropolis criterion. The Metropolis criterion always accepts moves which lower the objective function, i.e. bond length, but occasionally also accepts moves which increase the objective function. The probability with which uphill moves are accepted is decreased over the course of the optimization, until the system is â??frozen.â?
The implementation of this algorithm developed here allows for addition type reactions, such as those occurring in polyacrylates, polystyrene, and polyethylene. Further, input specifications enable the user to allow or deny interspecies and intraspecies reactions. The method has been used to generate model structures of linear homopolymers such as polybutyl acrylate and poly-2-hydroxy ethyl acrylate, copolymers of butyl acrylate and 2-hydroxy ethyl acrylate, as well as cross-linked polyacrylates.
Currently the method is being extended to allow for the specification of the conversion for an individual
species or for user defined sets of monomers.