Coarsening and solidification via solvent-annealing in thin liquid films

Abstract

We examine solidification in thin liquid films produced by annealing amorphous Alq[subscript 3] (tris-(8-hydroxyquinoline) aluminium) in methanol vapour. Micrographs acquired during annealing capture the evolution of the film: the initially-uniform film breaks up into drops that coarsen, and single crystals of Alq[subscript 3] nucleate randomly on the substrate and grow as slender ‘needles’. The growth of these needles appears to follow power-law behaviour, where the growth exponent, γ, depends on the thickness of the deposited Alq[subscript 3] film. The evolution of the thin film is modelled by a lubrication equation, and an advection–diffusion equation captures the transport of Alq[subscript 3] and methanol within the film. We define a dimensionless transport parameter, α, which is analogous to an inverse Sherwood number and quantifies the relative effects of diffusion- and coarsening-driven advection. For large α-values, the model recovers the theory of one-dimensional, diffusion-driven solidification, such that γ→1/2. For low α-values, the collapse of drops, i.e. coarsening, drives flow and regulates the growth of needles. Within this regime, we identify two relevant limits: needles that are small compared to the typical drop size, and those that are large. Both scaling analysis and simulations of the full model reveal that γ→2/5 for small needles and γ→0.29 for large needles.