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 aspx(T, 6) follows a universal two-variable law, a(X/S)(T,theta) =a(X/S)(298,theta) +lambda(X/S)(theta)(T298) with linear dependence on temperature and linear-quadratic dependence on PMMA recovery fraction (R> 0.96). An intrinsic temperature, Txa(6) (298,6)/1(4), decreases linearly with the recovery fraction revealing ideal mixing of adsorption robustness between silica and PMMA. The London dispersive energy (T.6) obeys a bilinear forth:
gamma(d)(s)(T,theta) =gamma(d)(s)(0,0)mT beta theta+alpha theta T,
characteristic of aplanar energetic surface. In contrast, the Lewis acid-base surface energy components yy. and y vary non-linearly with 6, with y and yA maximized and y minimized at theta = 0.31 Lewis acidbase-parameters KA. Kp,IK, and Kaa exhibit parallel cooperativity and correlate quadratically with the surface-energy components, identifying theta = 0.31 as the universal amphoteric optimum of the PMMA/silica interface.