Critical cracking thickness of drying polymer films

Polymer coatings are used for a number of applications such as for decorative purposes, to protect surfaces and as functional parts of devices. The mechanical integrity of the coatings is critical to their function and hence it is important that the coatings do not fail during their lifetime. Here, we present a simple model to determine conditions under which drying films of polymer solutions can crack. The model accounts for the properties of the polymer film and substrate and predicts the tensile stress developed in the drying film. As the tensile stress increases and exceeds a critical value, the film relaxes by nucleating a crack. The model predicts a critical thickness below which the film does not crack. The predicted critical cracking thickness is compared with experiments performed on drying films of silicone resin on six different substrates with the value of Young's modulus spanning over six decades. The predicted trend matches the measurements.