Thickness of the Ice-Shedding Lubricant Layer in Equilibrium with an Underlying Cross-Linked Polymer Film

A thin lubricant oil layer in equilibrium with an underlying cross-linked polymer film is ideal for ice shedding and smudge repellency. While the oil film renders the desired repellency, the polymer layer bestows the mechanical strength and serves as a reservoir for the lubricant. Despite this knowledge, there have been no theoretical studies on factors that affect the equilibrium thickness h(s) of the lubricant layer. In this work, we treat the substrate-bound polymer as a rubber film that can only expand or contract along the vertical direction. The Flory-Rehner theory for treating the 1D swelling of a rubber by a solvent is then used to derive the system's free energy, which is further used to construct the phase diagrams of such systems. From these phase diagrams and the known feed volume ratios between the lubricant and the polymer, we calculate h(s) and plot h(s) as a function of the Flory-Huggins parameter for the polymer and the lubricant, the cross-linking density of the polymer, and the molecular volume and amount of lubricant. Aside from using these plots for regulating h(s) and for justifying prior experimental observations, we also propose methods to tune the different variables to sustain the release of the lubricant until it is essentially exhausted. Additionally, we draw attention to possible measures that can be used to design thermoresponsive ice-shedding coatings that store the lubricant in the polymer matrix during the warm seasons to minimize lubricant loss but release the lubricant during winter to enable ice shedding. While the current theory involves approximations, the predicted trends will be of guidance value for designing and preparing robust and long-lasting ice-shedding coatings.