Coarsening Dynamics of True Morphological Phase Separation in Unstable Thin Films

Unstable thin films can spontaneously phase separate into two equilibrium flat-film morphologies of different thicknesses under the influence of gravity or favorable combinations of apolar and polar excess intermolecular forces. Two distinct pathways and associated dynamics of this morphological phase separation are presented based on numerical simulations of the 2-D thin film equation. The two pathways are (1) the "direct pathway" whereby the thicker phase forms directly and concurrently with the thinner phase and (2) the "defect pathway" whereby the thicker phase forms by the coarsening of defects of intermediate thickness and appears much later than the thinner phase. The defect pathway is favored by films whose initial thickness lies closer to the thickness of the thinner phase. Both pathways show an initial power law decay with exponent -1/4 in time followed by a plateau in the number density of domains/defects. Thereafter, the defect pathway shows another universal power law decay with exponent -1/3 and ends with a logarithmic decay, which is specific to the d = 2 case as there is no interfacial curvature in d = 2. The direct pathway skips the second power law decay and goes directly to the logarithmic decay.