Mathematical model to predict cracking in drying polymer film*

Thin films of polymer coatings find applications in several areas such as pharmaceutical products, personal care products, paints, etc. for functional and protection purposes. These coatings are initially cast as polymer solution where the concentration of the polymer increases as the solvent evaporates leading to the solidified film. During this process, the film can freely shrink from the thickness direction, however, the shrinkage is contained in the plane of coating as it strongly adheres with the substrate. Due to constraint shrinkage, the film comes under tension and it may lead to crack if tension exceeds a critical value. The formation of cracks makes the drying process very complex, and it is important to understand the mechanism to obtain the crack-free films. A model has been developed to predict the critical stress and the critical thickness for cracking in polymer films by equating the elastic energy to the surface energy. The model predictions show that cracking can be avoided if the initial film thickness is low, films are soft and the substrate is stiffer. In other words, for a film to crack on stiff substrates, the initial film thickness should be made large. The model predictions show good agreement with measurements.