Monomer partitioning in emulsion polymerisation

Because an emulsion polymerisation comprises several phases (water, monomer droplets, particles) it is important to know what the local concentrations are at the locus of 

The monomer concentration in the latex particles directly determines the rate of polymerisation while the monomer ratio in the latex particles determines the chemical composition of the copolymer formed. The monomer concentrations can be accessed both experimentally and through models. These models can be useful in the design of polymerisation reactors, process control and product characteristics, such as molar mass and chemical 

At equilibrium the partial molar free energies of the monomer will have the same value in each of the phases present, that is, the monomer-swollen colloid (micelles, vesicles and/or latex particles), the monomer droplets and the aqueous phase (Morton et al, 1954 Gardon, 1968)  

Equation 3.10 can describe the swelling behaviour of a latex particle with one monomer below and at saturation. In the case of saturation swelling with two monomers, substituting the appropriate expression for the partial molar free energy of the different phases into Equation 3.10 leads to Equation 3.11 (for an exact derivation see. Maxwell et al, 1992a,b and Noel et al, 1993) which is quite similar to Equation 3.10, except that it is assumed that 

Here Vp,- and Vpj are the volume fractions of monomers i and j in the latex particles, respectively, Xi,j is Flory-Huggins interaction parameter between monomers i and j, while Xi,p and Xj,p are the Flory-Huggins interaction parameters between monomers i and j and the polymer, respectively ntij is the ratio of the molar volume of monomer i over monomer j, and, and represent the volume fraction of monomers i and j, respectively, 

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