Analysis of Vinylidene Fluoride – Hexafluoropropene Copolymerization Propagation Kinetics Via Genetic Algorithms

The propagation kinetics of vinylidene fluoride – hexafluoropropene copolymerizations were determined via the PLP-SEC method, which combines pulsed laser initiated polymerization with polymer characterization via size-exclusion chromatography. To obtain reliable copolymerization propagation rate coefficients, k_p,copo, the knowledge of absolute molecular weights is required. These data were derived employing the principle of universal calibration after determination of the Mark-Houwink parameters for each copolymer composition.^[1] The kinetic data are provided for a wide range of temperatures, pressures, and comonomer feed compositions. The goal was to derive a single equation that describes simultaneously the variation with all three variables. To describe the kinetic data the explicit penultimate unit model was applied. Since hexafluoropropene homopropagation does not occur five propagation rate coefficients have to be accounted for.

Optimization of the kinetic parameters via manual fitting of the simulation results to the experimental data and repeated adjustment of the input fit parameters was not successful. The systematic variation of all five fit parameters in a sufficiently large search space using a relatively narrow grid would have required an unacceptably large number of individual model calculations. Alternately genetic algorithms (GA) were used.

The GA applied belongs to the class of stochastic search methods. These algorithms are based on a population of individuals with genes, in our case on the binary representation of the kinetic parameters. The deviations of simulated values for k_p,copo as a function of temperature, pressure, and monomer composition from the experimental data were subsequently automatically assessed via the sum of errors. This objective function quantifies the fitness of each individual. During the optimization process the genes are modified by application of genetic operators (e.g. mutation, crossover). To accomplish a good coverage of the parameter space a large population is required. The goal of the optimization is achieved by selection of individuals with high fitness over many generations of populations. A couple of individual optimization runs with successive reduction of the parameter window size around the optimum results were performed. The evaluations of the fitness are time-consuming, and thus, in the simulations the parallel genetic algorithm library (PGAPack) was applied.^[2]

[1] R. Siegmann, E. Möller, S. Beuermann, Macromol. Rapid Commun. 33, 1208 (2012)

[2] PGAPack Parallel genetic algorithm library: http://code.google.com/p/pgapack/