Monomer Concentration in Polymer Particles

One of the assumptions in the Smith and Ewart theory is that no new polymer particles are generated in the second stage of emulsion polymerization. The rate of polymerization per particle has been experimentally measured in the 

Comparison of Eqs. (7.4.9) and (7.3.28) reveals that the rate of polymerization in stage II of emulsion polymerization is proportional to This 

Finally, according to Eq. (7.4.9), the total number of particles, N, should be proportional to [S]o . This proportionality has been confirmed for styrene, but for other monomers, deviations have been found. Table 7.1 gives empirical correlations for different emulsifiers and monomers [4]. 

It is clear from Eq. 1 that the monomer concentration in a polymer particle is one of the three key factors that control the particle growth rate, and accordingly, the rate of polymerization. In emulsion polymerization, the course of emulsion polymerization is usually divided into three stages, namely. Intervals I, II and III. In Intervals I and II of emulsion homopolymerization, the monomer concentration in the polymer particles is assumed to be approximately constant. In Interval III, it decreases with reaction time. Two methods are now used to predict the monomer concentration in the polymer particles in emulsion homopolymerization empirical and thermodynamic methods. 

According to the empirical method [ 14,20,163], the monomer concentration in Intervals I and II can be expressed as 

Interval III begins when the monomer droplets disappear from the system at the monomer conversion Xmc. The monomer concentration in this interval (Xivi Xiyic) is approximately given by 

On the other hand, several researchers [164-167] have tried to thermodynamically describe the swelling behavior of polymer particles by one monomer. The thermodynamic approach now used is based on the so-called Morton equation given by 

In an emulsion copolymerization, monomer partitioning between the monomer droplet, polymer particle and aqueous phases plays a key role in determining the rate of copolymerization and the copolymer composition. Two approaches (empirical and thermodynamic) have been proposed to predict the monomer concentrations in the polymer particles in an emulsion copolymerization system. In the emulsion copolymerization of St and MMA, Nomura et al. [45,122,140] first proposed an empirical approach for predicting the saturated concentration of each monomer in the polymer particles as a function of the monomer composition in the monomer droplets, as shown by 

---

The Rp curves of miniemulsion and conventional emulsion polymerization obtained by calorimetry show the same general behavior [219]. In contrast to conventional emulsion polymerization, in miniemulsion polymerization, the monomer concentration in polymer particles diminishes throughout the polymerization. At the beginning, the nucleation rate overcompensates the decrease of monomer concentration leading to the first rise in the Rp. The number of droplets decreases and the remaining droplets shrink in size due to monomer loss by molecular diffusion to the polymer particles. As a consequence, the nucleation rate diminishes and eventually it may not be fast enough to compensate the decrease of the monomer concentration. Thus, Rp may reach a maximum and decrease before the end of the nucleation period [219], In conventional emulsion polymerization, the nucleation period ends before the first maximum in Rp, which is ascribed to the disappearance of monomer droplets [125]. 

Emulsion polymerization of vinyl chloride is initiated by a water-soluble initiator such as potassium persulfate. Initially in the reactor, monomer droplets are dispersed in the aqueous phase (continuous phase) containing initiator and surfactant (emulsifier). As the reactor content is heated, the initiator decomposes into free radicals. When the surfactant concentration exceeds the critical micelle concentration (CMC), micelles are formed. Free radicals or oligomers formed in the aqueous phase are then captured by these micelles. Vinyl chloride monomer is slightly soluble in water. As the monomer dissolved in water diffuses into micelles containing radicals, polymerization occurs. With an increase in monomer conversion in the polymer particles, separate monomer droplets become smaller and eventually they disappear. The monomer concentration in polymer particles is constant as long as liquid monomer droplets exist. The rate of emulsion polymerization is represented by... 

Polymerization proceeds in the polymer particles as the monomer concentration in the particles is maintained at the equilibrium (saturation) level by diffusion of monomer from solution, which in turn is maintained at the saturation level by dissolution of monomer... 

When the polymerization has proceeded to such an extent that all of the monomer droplets have vanished, which occurs after 60-80% conversion, all of the residual monomer is located in the latex particles. The monomer concentration in the particles now declines as polymerization proceeds further, i.e., in this final period the reaction is first order. At the end of the polymerization, the emulsion consists of polymer particles with a size distribution between 50 and 150 pm, which is larger than the original micelles, but smaller than the original monomer droplets. The changes of surface tension and overall rate of polymerization with conversion are schematically shown in Fig. 2.2. 

Shape of the Polymerization Curves. Since polymerization takes place within the polymer particle, the rate depends on monomer concentration in the particles this concentration remains relatively constant as long as free monomer phase is present. At some point during the polymerization, the amount of polymer present is sufficient to absorb essentially all of the unreacted monomer. After this point in the polymerization, the monomer consumed by the radicals cannot be replaced and monomer concentration in the particle must decrease. It then follows that the rate must also decrease. 

Equation (58) indicates that an increase in initiatior concentration will not enhance the rate of polymerization. It can be used for estimating the molecular mass of the polymer assuming, of course, the absence of transfer. The ratio N/q corresponds to the mean time of polymer growth and molecular mass is equal to the product of the number of additions per unit time and the length of the active life time of the radical, kpN/e. An increase in [I] also means a higher value of q, and thus a shortening of the chains. As in Phase II, the polymerized monomer in the particles is supplemented by monomer diffusion from the droplets across the aqueous phase a stationary state is rapidly established with constant monomer concentration in the particle. The rate of polymerization is then independent of conversion (see, for example the conversion curves in Fig. 7). We assume that the Smith-Ewart theory does not hold for those polymerizations where the mentioned dependence is not linear [132], The valdity of the Smith-Ewart theory is limited by many other factors. 

The idea of particle inhomogeneity was supported experimentally by Williams [149], However, his representation of growth is more complicated. In phase II, the monomer concentration in the particle decreases with conversion, while the rate remains constant. The particle has a core with a relatively high polymer content surrounded by a monomer-rich layer (see Fig. 16). Polymerization occurs at the polymer—monomer interface. Under these conditions, monomer concentration at the interface remains constant, even when its amount in the particle decreases. Napper presented the idea of an exactly opposite composition of the monomer—polymer particle [150], The core should be enriched in monomer and surrounded by a layer with a higher polymer content. Van den Hul and van der Hoff found most growing ends of macromolecules at the particle surface [151], which supports Napper s model. 

Equations, which are also applicable to suspension, solution, and bulk polymerization, form an extension of the Smith-Ewart rate theory. They contain an auxiliary parameter which is determined by the rate of initiation, rate constant of termination, and volume of the porticles. The influence of each variable on the kinetics of emulsion polymerization is illustrated. Two other variables are the number of particles formed and monomer concentration in the particles. Modifications of the treatment of emulsion polymerization are required by oil solubility of the initiator, water solubility of the monomer, and insolubility of the polymer in the monomer. 

With these assumptions two different conversion-time curves are associated. It is easily derived that for the case of assumption 1, the number of particles and therefore the rate increase in proportion to the square of the reaction time, provided [M] is constant (3). At the conversion. C, where the micelles have just disappeared, all particles contain a growing polymer radical and the rate is double the equilibrium rate given by Equation 9. The rate after Cj decays exponentially to the equilibrium value. If assumption 2 holds, the rate increases according to a complex function of reaction time. In Figure 3, examples are given of conversion-time curves which seem to correspond to the theoretical relations derived on the basis of either assumption. The usual course of the reaction is probably intermediate between the two types and may in addition be modified by changes in the monomer concentration in the particles during this period of transition from micelle to particle. 

The fourth factor determining polymerization rate is the monomer concentration in the particles. For some monomers the ratio of monomer to polymer in the particles is about constant during part of the polymerization. Smith (57) suggested that this results from a balance between the eflFect on the monomer activity of the dissolved polymer and the eflFect of interfacial tension of the very small particles. This equilibrium was put in a quantitative form by Morton, Kaizerman, and Altier (44), who derived the following equation by combining an expression for the interfacial free energy of the particle with the Flory-Huggins equation for the activity of the solvent (monomer) in the monomer-polymer particle. 

When a water-soluble initiator is added to a microemul-sion, polymer particles are nucleated mainly by the micellar mechanism. The role of the monomer-swollen micelles in microemulsion polymerization is not only to act as nucle-ation loci and surfactant reservoir but also as monomer reservoir. The fast nucleation rate leads to the initial increment of Rp. As the monomer is polymerized, its concentration in micelles diminishes and eventually monomer concentration within polymer particles decreases as well [205]. As a consequence, the nucleation and polymerization rates tend to decrease, explaining in this way the maximum in the Rp evolution curve experimentally observed. The final latex consists of surfactant-stabilized polymer particles that typically contain only polymer and empty micelles formed by excess surfactant. 

The initiation process, similar to other free-radical vinyl polymerizations, involves the chemical decomposition of unstable peroxides - azocompounds, or persulfates - into free radicals which can react rapidly with monomer to begin the propagation of polymer chains [4]. In the case of a water-soluble initiator, the radical concentration in polymer particles is related to the initiator concentration in water and the radical capture efficiency of latex particles. The radical capture efficiency of monomer droplets is very small and, therefore, their contribution to overall polymerization process is negligible. Thus, the small surface area of monomer droplets and/or high concentration of radicals in monomer droplets disfavor the growth events. Using an oil-soluble initiator, the radical concentration in particles and monomer droplets is related to the initiator concentrations in both phases. The initiator concentration between these phases is usually expressed in terms of an initiator partition coefficient. 

Figure 7.5 Representation of physical processes in emulsion polymerization in stage 2. Monomer concentration within polymer particles is maintained constant through...

Figure 8. Overall conversion vs. time, and polymer composition, styrene concentration in the particles, and MMA concentration in the particles vs. overall conversion for the data of Nomura and Fujita (12.). Initial weight ratio (MMA/Total monomer) = 0.5.

Models for emulsion polymerization reactors vary greatly in their complexity. The level of sophistication needed depends upon the intended use of the model. One could distinguish between two levels of complexity. The first type of model simply involves reactor material and energy balances, and is used to predict the temperature, pressure and monomer concentrations in the reactor. Second level models cannot only predict the above quantities but also polymer properties such as particle size, molecular weight distribution (MWD) and branching frequency. In latex reactor systems, the level one balances are strongly coupled with the particle population balances, thereby making approximate level one models of limited value (1). 

---