Photochemically Induced Marangoni Patterning of Polymer Bilayers

Surface-tension gradients created along a polymer film by patterned photochemical reactions are a powerful tool for creating surface topography. Here, we use mathematical modeling to explore a strategy for patterning photochemically inactive polymers by coupling a light-sensitive and light-insensitive polymer to form a polymer bilayer. The light-sensitive polymer forms the top layer, and the most dominant surface-tension gradients are introduced at the interface between this layer and air. Lubrication theory is used to derive nonlinear partial differential equations describing the heights of each layer, and linear analysis and nonlinear simulations are performed to characterize interface dynamics. Patterns form at both the polymer-air and polymer-polymer interfaces at early thermal annealing times as a result of Marangoni stresses but decay on prolonged thermal annealing as a result of the dissipative mechanisms of capillary leveling and photoproduct diffusion, thus setting a limit to the maximum individual layer deformation. Simulations also show that the bottom-layer features can remain "trapped", i.e., exhibit no significant decay, even while the top layer topography has dissipated. We study the effects of two key parameters, the initial thickness ratio and the viscosity ratio of the two polymers, on the maximum deformation attained in the bottom layer and the time taken to attain this deformation. We identify regions of parameter space where the maximum bottom-layer deformation is enhanced and the attainment time is reduced. Overall, our study provides guidelines for designing processes to pattern photochemically inactive polymers and create interfacial topography in polymer bilayers.