Vanzo equation

Equation 25.21 suggests that [Mjp does not depend on the monomer concentration in the continuous phase. In the Vanzo equation [26], this shortcoming is corrected by adding In (7 ), that is the natural logarithm of the ratio of the actual monomer concentration to the saturation concentration of the monomer in the continuous phase, to the right-hand side of Equation 25.21. 

Here Vp is the volume fraction of polymer (related to the conversion), X is the number average degree of polymerisation of the polymer, x is the Flory-Huggins interaction parameter between the monomer and the polymer, R is the gas constant and T the temperature. Um is the molar volume of the monomer, y is the particle-water interfacial tension and To is the radius of the unswollen micelles, vesicles and/or latex particles. [M]a is the concentration of monomer in the aqueous phase and [M]a,sat the saturation concentration of monomer in aqueous phase. Figure 3.3 shows the contributions of the different terms of Equation 3.10 to the Vanzo equation. For a more detailed discussion see also Section 4.2 and Figure 4.5. 

Figure 3.3 Comparison of theoretical predictions and experimental measurements of methyl acrylate partitioning at 45°C for a poly(methyl acrylate) seed latex with an unswollen radius of 91 nm (closed squares). Theoretical predictions different terms of Equation 3.10 are depicted, for the Vanzo equation X = 0.2 and y = 45 mN m were taken from literature (Maxwell et al., 1992a).

In the absence of monomer droplets the monomer concentrations in the particles are directly related to the concentrations of monomers 1 and 2 in the aqueous phase. Equation 4.15, known as the Vanzo equation (Vanzo et ai, 1965) describes the partitioning of monomer between the aqueous phase and the latex particles in the absence of monomer droplets for homopolymerisation of monomer 1 ... 

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