| A mathematical model which describes the kinetics of emulsion polymerization is presented and discussed in detail. The model is capable of predicting, according to the assumed mechanisms, the transient behavior of the monomer-to-polymer conversion and the particle size distribution for a wide range of polymerization recipes and reactor types, i.e. batch, semi-batch and continuous stirred-tank reactors. The major mechanisms included in the present model are: (a) particle generation from radicals entering micelles and from the precipitation of oligomeric radicals in the aqueous phase, i.e. homogeneous nucleation, (b) particle size dependence of the equilibrium monomer concentration and that of the average number of radicals per particle, n, (c) the gel or auto-acceleration effect at high conversion, (d) the desorption and re-absorption of free radicals from and into the particles, and (e) particle shrinkage during the monomer-starved period and the desorption of the adsorbed surfactant molecules due to overcrowding on the diminishing particle surface area, which is partly responsible for, (f) the re-appearance of micelles during the monomer-starved period.; Strict material balances used in developing the model incorporate not only the integro-partial differential equations (PDE's) which represent the particle population balance, but also the general form of the Smith-Ewart recursion equation which describes the quasi-steady state free radical balance in the particle population. The simulations for a wide variation of recipes and reactor types have been made possible by using a Crank-Nicholson integration technique to obtain the numerical solution to the population balance PDE's. The finite-difference method which can automatically adjust the integration step-size in time, as employed in the present model, appears most suitable for further modifications of the existing kinetic assumptions, or for the addition of new ones. A general equation for the steady-state free radical balance in the emulsion polymerization system has been proposed and used to calculate the theoretical values for n as a function of particle diameter, D, and/or particle number concentration, N.; Reasonable agreements have been found between the model prediction and experimental data for the emulsion polymerization of styrene in batch, semi-batch, and continuous reactors. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI... |
