Generation of strength in a drying film: How fracture toughness depends on dispersion properties

The fracture toughness of colloidal films is measured by characterizing cracks which form during directional drying. Images from a confocal microscope are processed to measure the crack width as a function of distance from the crack tip. Applying theory for thin elastic films the fracture toughness is extracted. It is found that the fracture toughness scales with the particle size to the $-0.8$ power and that the critical energy release rate scales with the particle size to the $-1.3$ power. In addition, the fracture toughness is found to increase at lower evaporation rates, but the film thickness does not have a significant effect.

Figure 1

Picture of 3D printed drying chamber. The entire device is 75 mm long, so that it fits within the confocal microscope. There are connections at either end to allow air of known humidity to be blown over the sample.

Figure 2

(a,b) show the fracture formation in colloidal dispersions containing silica particles and polystyrene particles recorded with a confocal microscope at 20 °C for an air humidity of 1.3% and a volume of colloidal dispersion of $4\mathrm{m}{\mathrm{m}}^3$. (c) shows the image of the colloidal dispersion based on silica particles processed with a matlab script. (d) presents one single crack of panel (c) used for measurements of the crack opening, δ, and the distance, $r$, from the crack tip. The crack geometry is the same as defined by Goehring et al. [3].

Figure 3

Average crack opening as a function of square root of distance from crack tip for 7-nm colloidal silica [red (dark gray)] and 300-nm polystyrene beads [green (light gray)] for an air humidity of 1.3% at 20 °C and a volume of colloidal dispersion of $4\mathrm{m}{\mathrm{m}}^3$.

Figure 4

Measured influence on the ratio of fracture toughness over Young's modulus, $K_c/E$, of colloidal dispersions containing silica particles (red diamond) and polystyrene particles (green circle) of (a) volume of colloidal dispersion of 7-nm silica particles and 300-nm polystyrene particles for an air humidity of 1.3% at 20 °C, (b) evaporation rate of 7-nm silica dispersion and 300-nm polystyrene dispersion with a volume of colloidal dispersion of $8\mathrm{m}{\mathrm{m}}^3$ at 20 °C, (c) silica particle size for an air humidity of 1.3% at 20 °C and a volume of colloidal dispersion of $8\mathrm{m}{\mathrm{m}}^3$, and (d) polystyrene particle size for an air humidity of 1.3% at 20 °C and a volume of colloidal dispersion of $8\mathrm{m}{\mathrm{m}}^3$.

Figure 5

(a) Measured influence of particle size on fracture toughness of colloidal dispersions containing silica particles (red diamond) and polystyrene particles (green circle) for an air humidity of 1.3% at 20 °C and a volume of colloidal dispersion of $8\mathrm{m}{\mathrm{m}}^3$. The best fit line has a slope of −0.8. (b) Measured influence of evaporation rate on fracture toughness of 7-nm colloidal silica (red diamond) and 300-nm polystyrene (green circle) for a volume of colloidal dispersion of $8\mathrm{m}{\mathrm{m}}^3$ at 20 °C.