A general thermodynamic law for adsorption geometry at polymer/oxide interfaces: Lewis acid–base energetics and interfacial cooperativity

A general thermodynamic framework is established to describe adsorption at hybrid PMMA/silica interfaces. In this work, it was shown that the adsorbed molecular surface area aS/X(T,θ) follows a universal two-variable law,aX/S(T,θ)=aX/S(298,θ)+λX/S(θ)(T-298),with linear dependence on temperature and linear–quadratic dependence on PMMA recovery fraction (R2 > 0.98). An intrinsic temperature, TX/S(θ)=a(298,θ)/λ(θ), decreases linearly with the recovery fraction θ, revealing ideal mixing of adsorption robustness between silica and PMMA. The London dispersive energy γsd(T,θ) obeys a bilinear form:γsd(T,θ)=γsd(0,0)-mT-βθ+αθT,characteristic of a planar energetic surface. In contrast, the Lewis acid–base surface energy components γ+, γ-, and γAB vary non-linearly with θ, with γ+ and γAB maximized and γ- minimized at θ=0.31. Lewis acid-base parameters KA, KD, K, and K2A exhibit parallel cooperativity and correlate quadratically with the surface-energy components, identifying θ=0.31 as the universal amphoteric optimum of the PMMA/silica interface.