Equilibrium monomer concentration particles

If the monomer is a good solvent for the polymer, the latex particles might be assumed to expand indefinitely beeause of inhibition of monomer. An equilibrium monomer concentration and swelling equilibrium is reached, however, because the free energy decrease due to mixing of polymer and monomer is eventually balanced by the increase in surface free energy which accompanies expansion of the particle volume. 

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... 

The monomer concentration is usually quite high since in many cases the equilibrium swelling of the particle by monomer is of the order 50-85% by volume. Values of [M] as high a 5 M are common. [M] varies only weakly with the size of the polymer particles. 

Fig. 11. Estimate of variation of monomer concentration c1 of salt (Pbl2) in quasi-equilibrium with ions and colloid particle containing n monomers versus progress variable A.

It is usual to consider the course of emulsion polymerization to proceed through three intervals [16,17]. The particle number increases with time in Interval I, where latex particles are being formed, and then remains constant during Intervals II and II. The monomer concentration in particles is in equilibrium with a monomer saturated aqueous solution. Swelling is limited only by the opposite force of the particle surface/water tension. Hence, the concentration of monomer in the particles is usually taken as constant up to the point where free monomer droplets disappear. In Intervals I and II, the monomer concentration... 

Based on experimental results the loci of polymerization are assumed to be the micelles and latex particles. The 3rd power with respect to monomer concentration in Eq. (9) results from the 2nd order polymerization reaction in aqueous solution as well as from the influence of the monomer concentration on the partition equilibrium of the monomer between micelles and monomer/water droplets [13]. This influence is shown in Fig. 11. 

Tognacci et al. [ 183] discussed various methods for measuring the monomer concentration in the polymer particles. The method proposed by the authors is a direct estimation of the solvent activity by the GC (gas chromatography) measurement of its partial pressure in the gas phase at equilibrium with the polymer particle, monomer droplet (if any) and aqueous phase in the latex. They proposed an original measuring technique and carried out measurements for different monomers (St, MMA, and VAc) and polymeric matrices (PSt and MMA-VAc copolymer), both above and below saturation conditions (corresponding to Intervals II and III). They compared the experimental data with that predicted by the monomer partitioning relationships derived by Maxwell et al. [166,170] and Noel et al. [172]. 

In the above-mentioned cases of polymerization of lower alkyf acrylates, because of the high rate of the process = 1260 dm mol sec for MA (Bagdasar yan, 1966) and the high monomer concentration in particles (Gerrens, 1964), the surface of the monomer-polymer phase increases at a rate that may exceed the rate of attainment of equilibrium adsoiption. 

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. 

Equation 11 refers to equilibrium swelling conditions. Now, Flory (24) concludes from theoretical considerations that monomer is easily supplied to the polymer particles at the required rate even in the case of monomers which are little soluble in water, such as styrene. That equilibrium swelling is maintained during emulsion polymerization is supported by a comparison of values of the monomer concentrations determined in equilibrium swelling measurements with those found to prevail during polymerization and determined by analysis of reaction kinetics (see below). The results obtained by both methods are plotted in Figure 10. 

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