(370c) Analysis of Vinylidene Fluoride – Hexafluoropropene Copolymerization Propagation Kinetics Via Genetic Algorithms | AIChE

(370c) Analysis of Vinylidene Fluoride – Hexafluoropropene Copolymerization Propagation Kinetics Via Genetic Algorithms

Authors 

Beuermann, S. - Presenter, Clausthal University of Technology
Drache, M., Clausthal University of Technology



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, kp,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 kp,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/