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.