Chapter 10 - Adsorption at Solid Surfaces

Abstract

In this chapter we use our GvdW theory to rederive and extend traditional semiempirical theories of adsorption isotherms, i.e., the excess adsorption per unit surface area Γ of a bulk gas (or liquid) in contact with a solid wall. We represent the wall, assumed to be uniform to translations parallel to the surface, by an external wall potential with an attractive well and a steep repulsion. The first and simplest adsorption isotherm, Henry's law, takes the fluid molecules to be ideal both in the bulk and at the surface. This means that there are no molecule–molecule, only molecule–wall, interactions to account for. The particle density n(x) and adsorption excess Γ(T;P) can then be found analytically and quantization of the vibrations of adsorbed particles against the surface can be accounted for. The increased particle density at the surface will often give rise to the formation of an adsorbed monolayer in which interactions are important. The Langmuir isotherm accounts semiempirically for the steric interactions bringing in a concept of monolayer coverage θ which satisfies 0⩽θ⩽1 with the upper limit corresponding to a “full” (close packed) monolayer. The GvdW theory, with an additional assumption of separable translations and vibrations in the monolayer, allows adsorption isotherms to be derived either for a hard sphere (or disc) or Lennard-Jones interactions among adsorbed molecules. Then we consider the semiempirical BET theory of multilayer adsorption which accounts for “secondary adsorption” on top of already adsorbed molecules. The BET theory can account for the “wetting” (accumulation of liquid phase) of the solid surface as the bulk gas pressure approaches the vapor pressure of the bulk gas. While it is possible to use the GvdW density functional theory to predict secondary adsorption, layer by layer, we show in comparison with Monte Carlo simulation results that iterative minimization of the free energy in the 3D GvdW density functional theory can reproduce both density profiles and adsorption excess in general multilayer adsorption. We close by briefly considering adsorption at nonuniform solid surfaces with patches or sites of variable adsorption characteristics.