Investigations into the simulation of free-radical polymerization

A suite of simulation strategies has been developed that is well suited to the simulation of free-radical polymerization in general and pulse initiated polymerization (PIP) in particular. It has been shown that the appropriate use of these techniques can accurately yield the solution of the population-balance differential equations that characterize PIP, and can do so in a short period of time. During this study it became clear that many of truths elucidated about the solution of the differential equations for PIP, also hold true for the solution of the differential equations for free-radical polymerization in general. Although this study focussed entirely on PIP systems, this assertion is based on the many similarities in the mathematics of these two systems of differential equations. A detailed analysis of the error incurred by these solution methods has been performed. Using this analysis as a basis several recommendations have been made concerning steps that can be taken to reduce the effect of this error upon the final molecular weight distribution. Two case studies have been undertaken where this suite of techniques has been used to test kinetic models and to extract rate parameters from experimental data. In the presented study, both analytic and numerical strategies have been used to solve the population-balance differential equations that give a microscopic description of PIP. Analytic solution strategies proved to be too computationally expensive to implement, as well as too difficult to change to reflect changes to the kinetic model being used. In contrast to this, finite difference based numerical methods produced solutions rapidly, ones that contained minimal error. Moreover, it has been shown that these methods can be used to model a wide range of PIP systems. This investigation confirmed that the population-balance differential equations for dead chains and living radicals have different mathematical characteristics. Of particular relevance to this study was the fact that population-balance differential equations for the living radicals are more complicated and more prone to error, when solved numerically, than the differential equations for dead chain species. This means that a simpler, less computationally expensive method can be used to solve the differential equations for dead chain species than that which is used to solve the differential equations for living radical species. The first of the two modeling studies performed in this thesis probed the mechanism of termination in the free-radical polymerization of methyl methacrylate. A method for extracting this information from a molecular weight distribution measured by Matrix-Assisted-Laser Desorption- Ionization Mass Spectrometry was developed. This analysis provided strong evidence that the termination mechanism of methyl methacrylate is dominated by the disproportionation mechanism at O°C. The second modeling study explored the kinetics of a PIP where radicals are created by an initiator which is bifunctional and which is sensitive to light in the visible region of the spectrum. This series of simulations confirmed that this initiator can be used to carry out meaningful PIPs