Theoretical Investigation of Factors Governing the Ice-Shedding Performance of Hygroscopic Polymer Monolayers

The adhesion strength (τ) of ice to hygroscopic polymer monolayers can be minimized by optimizing parameters such as chain length and grafting density. However, a theoretical understanding of the effect of these factors on τ remains elusive. To clarify this, we model the ice adhesion using the Couette law (τ = <i>ηv</i>/<i>h</i>), where the apparent viscosity (η) and thickness (<i>h</i>) of the swollen layer are governed by the polymer volume fraction (ϕ₂). We derive η from unentangled semidilute polymer solution theory and calculate <i>h</i> from <i>h</i>₀/ϕ₂, where <i>h</i>₀ is the dry thickness. A key postulate is that the layer dehydrates under subzero cooling (-Δ<i>T</i>_m), compressing so that water stays in equilibrium with bulk ice and its activity (<i>a</i>₁) satisfies the classical freezing point depression relation. We employ a mean-field thermodynamic model to link ln<i>a</i>₁ to ϕ₂ and the monolayer's structural parameters. This integrated theory reveals how grafting density, chain length, polymer-water interaction, and monomer size collectively dictate ice adhesion, thereby providing a mechanistic basis for experimental observations and a rational design strategy for high-performance anti-icing coatings.