Formation of Shear Bands in Drying Colloidal Dispersions

In directionally dried colloidal dispersions regular bands can appear behind the drying front, inclined at $\pm 45°$ to the drying line. Although these features have been noted to share visual similarities with shear bands in metal, no physical mechanism for their formation has ever been suggested, until very recently. Here, through microscopy of silica and polystyrene dispersions, dried in Hele-Shaw cells, we demonstrate that the bands are indeed associated with local shear strains. We further show how the bands form, that they scale with the thickness of the drying layer, and that they are eliminated by the addition of salt to the drying dispersions. Finally, we reveal the origins of these bands in the compressive forces associated with drying, and show how they affect the optical properties (birefringence) of colloidal films and coatings.

Figure 1

Drying colloidal polystyrene in a freestanding film. The drying front is a bright horizontal line, with liquid film above it, and solid film below. The shear bands in the solid are angled away from the drying front. Domains of left-leaning and right-leaning bands can meet in two ways: junctions that open towards the drying front (black arrows) are sources of new bands, while those that open away from the front (white arrows) are where growing bands end.

Figure 2

Drying cells were made in a Hele-Shaw geometry. A dispersion was drawn into a cell and then dried naturally from one edge. As drying proceeded, a solid region slowly grew into the still-liquid dispersion. On close inspection the solidification front is a narrow transition region with strong gradients in particle concentration, over which the dispersion’s properties rapidly change.

Figure 3

The relative band spacing $\overline{\lambda }$ (squares, left axis) and band intersection angle (blue crosses, right axis) were measured in Hele-Shaw cells. Bars show the standard deviation of each measurement, while inset panels demonstrate how the measurements are made. (a) shows results in $150\text{−}\mu \mathrm{m}$-thick cells, for colloidal latex (filled squares) and silica (open squares) at low ionic strength ($1–5\mu \mathrm{M}$), while (b) shows data for particles with $d\simeq 100\mathrm{nm}$, in cells of different thickness. Neither measurement depends on particle size or thickness; the band spacing is always simply proportional to $h$.

Figure 4

Shear bands may be eliminated ($\overline{\lambda }=0$ indicates no banding) by the addition of salt, with a critical level depending on particle size and composition. Arrows mark where the strongest interactions between neighboring particles [Eq. (1)] drop below $5kT$. Above, images show how the dry films change with salt concentration, for 105 nm polystyrene.

Figure 5

Shear deformation. (a) A later band will displace any earlier bands to either side of it like a fault. (b) Dry films are birefringent. Under cross-polarized light a homogenous film should appear purple here. A clockwise rotation of the optical axis shifts the color towards blue, while the opposite motion shifts it to red. (c) The optical axis of a film (Levasil) shifts by $\pm 5°$ around the bands, showing how the entire bulk structure of the film is twisted by band formation.