Population Balance Model for Miniemulsion Polymerization, 2

Abstract

Summary: The predictions of the model developed in Part 1 of this series are compared with experimental values taken from literature. Initially, the method of solution of the population balance equation and the simulation algorithm are given. Various radical entry mechanisms are discussed in adequate detail. Plausible arguments are given to identify the correct radical entry mechanism. An expression to evaluate the radical exit coefficient is given. Model predictions of a number of variables are discussed. These include average number of radicals per particle, particle phase monomer volume fraction, average number of radicals averaged over all particles, monomer volume fraction averaged over all particles, variation of nucleation rate, variation of fraction of droplets nucleated, variation of average diameter, variation of standard deviation, variation of polydispersity index, and development of particle size distribution with time. Finally, model predictions for the variation of conversion with time for five different initiator concentrations, number average diameter, standard deviation and full distribution are compared with experimental values.

In situ bimodal or broad particle size distribution using miniemulsion polymerization

“…In this work, the potential of miniemulsion polymerization as a means to produce in situ bimodal or very broad particle size distribution is explored. This is based on our previous works 7–10. In the first of these works,7 we had found that the experimentally reported instability by Miller et al11, 12 is due to a broad initial droplet size distribution in which, depending on the nonideality of the costabilizer‐monomer system, the smaller fractions of the distribution may not be stable, leading to a bimodal droplet size distribution.…”

“…A low initial initiator amount or a high emulsifier amount or low reaction temperature or addition of monomer in batch mode rather than semi‐batch mode and faster addition of monomer in semi‐batch mode leads to broader distributions, as found through modeling studies 39, 40. However, compared with the broadness of the distribution obtained using miniemulsion polymerization as characterized in terms of the standard deviation and the polydispersity index, the breadth of the distribution in emulsion polymerization is low 8–11, 39, 40. Thus, the miniemulsion polymerization process offers a greater advantage over conventional emulsion polymerization process in obtaining very broad particle size distributions.…”

“…The stability criterion is based on the phenomenon of molecular diffusion or Ostwald Ripening and thermodynamics. In the works on the modeling of particle size distribution in miniemulsion polymerization,8–10 we found that due to the slow and continuous nucleation period in this process, the final particle size distribution is broad as characterized by a large standard deviation and polydispersity index. The model was validated against the data of Choi et al13 and Miller et al11, 14…”

Modeling evidence in support of coagulative nucleation theory

“…In this article, the rate of radical entry into the micelles ( R em ; s −1 ) is given as follows: where k mm is the mass‐transfer coefficient of radical entry into the micelles (cm −2 s −1 ), A m is the total surface area of the micelles (cm 2 ), and R tot is the total aqueous‐phase radical concentration (mol/cm 3 ). Here, we use the collisional radical entry model, as we have done in our previous studies 1, 16–19…”

“…Here, we use the collisional radical entry model, as we have done in our previous studies. 1,[16][17][18][19] According to the propagational entry model, only radicals derived from water-soluble initiators with a chain length above a critical degree of polymerization (2-3 for styrene) can enter the particles. However, there now exists experimental evidence provided by Tauer et al 20 that persulfate radicals also enter the particles.…”