Effects of substrate constraint on crack pattern formation in thin films of colloidal polystyrene particles

Crack formation and the evolution of stress in drying films of colloidal particles were studied using optical microscopy and a modified cantilever deflection technique, respectively. Drying experiments were performed using polystyrene particles with diameters of 47 ± 10 nm, 100 ± 16 nm, and 274 ± 44 nm that were suspended in water. As the films dried, cracks with a well-defined spacing were observed to form. The crack spacing was found to be independent of the particle size used, but to increase with the film thickness. The characteristic crack spacing was found to vary between 20 and 300 μm for films with thickness values in the range 3-70 μm. Cantilever deflection measurements revealed that the stresses that develop in the film increase with decreasing film thickness (increasing surface-to-volume ratio). The latter observation was interpreted in terms of the effects of a substrate constraint which causes the build up of stresses in the films. This interpretation was confirmed by crack formation experiments that were performed on liquid mercury surfaces in which removal of the substrate constraint prevented crack formation. Experiments were also performed on compliant elastomer surfaces in which the level of constraint was varied by changing the substrate modulus. The cracking length scale was found to increase with decreasing substrate modulus. A simple theory was also developed to describe the substrate modulus dependence of the cracking length scale. These combined experiments and theory provide convincing evidence that substrate constraints are an important factor in driving crack formation in thin colloidal films.