Particle size dispersion during latex growth

Abstract

SynopsisThe evolution of the latex particle diameter distribution during batch emulsion polymerization is investigated, with emphasis on changes in the breadth of the size distribution. A model utilizing a surface area-dependent volumetric growth rate of a single particle results in a time-invariant standard deviation of the size distribution during periods of particle growth only. This behavior is reconciled with some experimental observations by considering the occurrence of particle nucleation during some part of the growth interval. Conclusions based on the results of the model suggest that higher inhibitor and low emulsifier concentrations favor narrow particle size distributions. INTRODUCTIONIt is well known that the polymer particles produced by emulsion polymerization are not of uniform size. The appearance of a distribution in particle sizes is primarily due to the fact that nucleation occurs over a period of time during which existing particles gr0w.l The particle size distribution, therefore, is coupled interdependently to the behavior of the polymerization system. Consequently, the particle size distribution can provide information about the colloid growth, e.g., particle nucleation, the size dependence of growth, or agglomeration of particles. The average growth rate can be related to the mean of the size distribution. The standard deviation, a measure of the breadth of the distribution, is indicative of the dependence of growth on particle size.If the volumetric growth rate of an individual particle were written in a power law form, du dt -= krb the kinetic order b would be important in dictating the dynamics of the particle size distribution. When b > 2, for example, the larger particles grow at a higher relative rate than the smaller particles and the size distribution broadens with time. When b = 2, the particles grow at a uniform relative rate, yielding in a distribution having a time-invariant standard deviation. If b < 2, the particle size distribution would exhibit self-sharpening behavior, that is, the size distribution would become narrower with time. By experimentally measuring the particle size distribution as it evolves during the course of a batch emulsion polymerization, the dependence of particle growth on particle size can be determined (in the absence of subsequent nucleation). Vanderhoff and coworkers24 have reported on the values of b obtained from competitive growth experiments for several polymers grown in emulsion.

Dynamic modeling of emulsion polymerization reactors

“…Of course, decisions must be made on the relative importance of the various phenomena occurring in a particular system. Other, more recent efforts on the modeling of emulsion reactors include: the dynamic modeling of a continuous stirred tank reactor (CSTR) for a general polymer system using a population balance approach (Thompson and Stevens, 1977); the dynamic and steady state modeling of a methyl methacrylate (MMA) CSTR using a population balance (Kirillov and Ray, 1978); the study of a general continuous emulsion system using population balances (Cauley et al, 1978); the modeling of a batch MMA reactor (Min and Ray, 1978); the population balance approach to a general continuous polymer system (Sundberg, 1979); the age distribution analysis approach to a continuous vinyl acetate (VAc) system (Kiparissides et al, 1979;Chiang and Thompson, 1979); the population balance modeling of a semibatch poly(viny1 chloride) (PVC) reactor (Min and Gostin, 1979); the dynamic modeling of a MMA CSTR using monodispersed approximation models (Schork et al, 1980); the simulation of a batch styrene (STY) reactor (Kiparissides and Ponnuswamy, 1981), and of a STY and a MMA reactor (Cauley and Thompson, 1982), and the discussion of PSD evolution (Lichti et al, 1981(Lichti et al, , 1983Gilbert and Napper, 1983;Gilbert et al, 1984); the description of a typical emulsion copolymerization system (Ballard et al, 1981); the study of batch and continuous VAc latex reactors (Penlidis et al, 1984;Pollock et al, 1981, respectively); the simulation of a STY emulsion reactor (Bataille et al, 1982); the dynamic modeling of the batch and continuous emulsion polymerization of vinyl chloride (Penlidis et al, 1984); and the steady state and dynamic modeling of both batch and continuous reactors for styrene-butadiene rubber (SBR) using both "monodispersed approximation" and population balance models (Hoffman, 1981;Hamielec et al, 1983;Broadhead, 1984;Broadhead et al, 1984).…”

Emulsion polymerization: Theory of particle size distribution in copolymerization system

“…Thus, for eqs. (11) and (12), we get Applying the steady state condition to eq. (lo), we get the recursion relation between q i -l ) A ( j + l ) B , NiAjB, and N(i+l)A(j-l)B as Ballard et d. 12 defined that Pi, is the probability of a particle containing i A-type and j B-type free radicals out of a total of (i + j) free radicals.…”