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Coarsening and solidification via solvent-annealing in thin liquid films
Published online by Cambridge University Press: 16 April 2013
Abstract
We examine solidification in thin liquid films produced by annealing amorphous ${\mathrm{Alq} }_{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
${\mathrm{Alq} }_{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,
$\gamma $, depends on the thickness of the deposited
${\mathrm{Alq} }_{3} $ film. The evolution of the thin film is modelled by a lubrication equation, and an advection–diffusion equation captures the transport of
${\mathrm{Alq} }_{3} $ and methanol within the film. We define a dimensionless transport parameter,
$\alpha $, which is analogous to an inverse Sherwood number and quantifies the relative effects of diffusion- and coarsening-driven advection. For large
$\alpha $-values, the model recovers the theory of one-dimensional, diffusion-driven solidification, such that
$\gamma \rightarrow 1/ 2$. For low
$\alpha $-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
$\gamma \rightarrow 2/ 5$ for small needles and
$\gamma \rightarrow 0. 29$ for large needles.
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- ©2013 Cambridge University Press
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