Acousto-spinodal decomposition of compressible polymer solutions: early stage analysis

The structure and dynamics of early stage kinetics of pressure-induced phase separation of compressible polymer solutions via spinodal decomposition is analyzed using a linear Euler-Cahn-Hilliard model and the modified Sanchez Lacombe equation of state. The integrated density wave and Cahn-Hilliard equations combine the kinetic and structural characteristics of spinodal decomposition with density waves arising from pressure-induced couplings. When mass transfer rate is slower that acoustic waves, concentration gradients generate density waves that cycle back into the spinodal decomposition dynamics, resulting in oscillatory demixing. The wave attenuation increases with increasing mass transfer rates eventually leading to nonoscillatory spinodal demixing. The novel aspects of acousto-spinodal decomposition arise from the coexistence of stable oscillatory density dynamics and the unstable monotonic concentration dynamics. Scaling laws for structure and dynamics indicate deviations from incompressible behavior, with a significant slowing down of demixing due to couplings with density waves. Partial structure factors for density and density-concentration reflect the oscillatory nature of acousto-spinodal modes at lower wave vectors, while the single maximum at a constant wave vector reflects the presence of a dominant mode in the linear regime. The computed total structure factor is in qualitative agreement with experimental data for a similar polymer solution.