Some theoretical aspects on morphology development in seeded composite latexes. I. Batch conditions below monomer saturation

In seeded emulsion polymerization, during the second stage, new interfaces appear and the surface area changes. A thermodynamic equilibrium approach is presented which predicts particle morphology of a whole range of non-spherical particles upon polymer conversion. Simulation takes into account swelling ratio, molar volumes and interfacial tension. As the particle geometry is complex, a new mathematical procedure is detailed.The computed data are useful to discuss either the stability or the instability of the particles morphology. These results must be compared with actual experimental structures.Abreviations and symbols G Gibbs' free energy - reduced Gibbs' free energy - _i interfacial tension - ₁₂ interfacial tension between polymer 1 and polymer 2 - _1w interfacial tension between polymer 1 and water - _2w interfacial tension between polymer 2 and water - r₁ polymer 1 swollen by monomer 2 sphere radius - r₂ polymer 2 swollen by monomer 2 sphere radius - r_i interfacial radius - h₁ sphere 1 distance to minimal section - h₂ sphere 2 distance to minimal section - h_i interfacial sphere distance to minimal section - sign ofh_i, positive when the interface sphere is on the side of the sphere 2, negative when the interface sphere is on the side of the sphere 1 - A₁₂ surface between polymer 1 and polymer 2 - A_1w surface between polymer 1 and water - A_1w⁰ surface between polymer 1 and water before polymerization - A_2w surface between polymer 2 and water - v₁ volume of the polymer 1 swollen by monomer 2 - v_i volume of the polymer 1 swollen by monomer 2 before polymerization - v₂ volume of the polymer 2 swollen by monomer 2 - V_p1 polymer 1 molar volume - V_p2 polymer 2 molar volume - V_m2 monomer 2 molar volume - n_p2 polymer 2 number of mole - n_p1 polymer 1 number of moles - n_m21 monomer 2 number of mole in the swollen polymer 1 - n_m22 monomer 2 number of mole in the swollen polymer 2 - n_m2 monomer 2 total number of mole - n_m2 monomer 2 number of mole before polymerization - TGn₁ polymer 1 swelling rate - TGn₂ polymer 2 swelling rate - TGn_i maximum number of mole of monomer 2 in polymeri by mole of polymeri - x polymer 2 conversion rate - K, p, q mathematical variables - D, r, a mathematical variables