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

Abstract

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.

Transparent Organogel Films Showing Extremely Efficient and Durable Anti-Icing Performance

“…A theoretical interpretation of the equilibrium state between the matrix of swollen cross-linked polymers and the top liquid layer has recently been proposed by Liu's group. 59 Although this theory partially and qualitatively fit our results, such as the influence of fraction of oil, cross-linking density, MW of infusing oils on syneresis, it is still difficult to explain quantitatively because of the gaps between the theory and the actual materials. Further development of this theory taking into account real conditions should be useful for both the theoretical interpretation and the practical design of SLIPS and other related analogues.…”

“…Based on these results, we concluded that both the MWs (∝ S ) of the infusing oils and their contents in the organogels (α pre %) primarily dominated the critical condition for determining the syneresis or nonsyneresis behavior of the samples. A theoretical interpretation of the equilibrium state between the matrix of swollen cross-linked polymers and the top liquid layer has recently been proposed by Liu’s group . Although this theory partially and qualitatively fit our results, such as the influence of fraction of oil, cross-linking density, MW of infusing oils on syneresis, it is still difficult to explain quantitatively because of the gaps between the theory and the actual materials.…”

Phase Equilibria of a Brush-Bearing Coating Swollen with a Lubricant and Regulation of Its Composition to Facilitate Ice Shedding

“…In a previous paper we discussed the equilibrium between a swollen coating matrix and a lubricant. 6 When a lubricant layer coexisted with the swollen underlying layer, the chemical potential of the lubricant in the matrix layer matched that of the neat lubricant and eq 18 held. Rearranging eq 18 yielded…”

“…1−5 We have discussed the derivation of ΔF c in a prior paper for the 1d swelling of a tethered cross-linked polymer layer. 6 The partial derivative of ΔF c with respect to the number of moles (n s,c ) of lubricant molecules in this layer yields the molar excess of the Helmholtz free energy as defined by eq 7a and the ln a s,c term…”

“…Statistical thermodynamic treatment of the swelling equilibrium of a cross-linked polymer by a solvent has been discussed in numerous polymer textbooks and journal articles. − There have also been reports on the one-dimensional vertical swelling of cross-linked thin films tethered to rigid substrates. , Furthermore, studies exist on solvent swelling of a polymer end-grafted to an impermeable plane. − However, we are unaware of statistical thermodynamic investigations regarding the partition of a solvent (or lubricant) into a cross-linked coating that resides on a rigid substrate and bears a dense end-tethered polymer monolayer on its upper surface. We report in this paper such a study.…”