A General-Purpose Model Adsorption Isotherm and Whole Isotherm Surface Area Measurement Method

A popular way to measure the surface areas of porous solids involves fitting a small section of the experimentally measured liquid nitrogen, liquid argon, or moisture adsorption isotherm to the Brunauer-Emmett-Teller (BET) model. A small section is used, because the BET isotherm's shape differs dramatically from the experimental isotherm's shape. Several studies proposed consistency criteria to automate choosing the small isotherm portion fitted during BET analysis. In this article, we follow a different approach that constructs a general-purpose model adsorption isotherm with enough flexibility to fit the experimental adsorption isotherm across its entire pressure range. This enables the whole adsorption isotherm to be used to extract surface areas of porous materials. Our MD model isotherm is formulated to apply to fluids both below and above the critical temperature and critical pressure. Mathematical derivations revealed this isotherm is non-negative, monotonically increasing with x_A, and has correct limiting behaviors. We explain relationships between the MD model isotherm and many model isotherms described in prior literature. When using a single sitegroup, the MD model has five fitted parameters. We introduce a bootstrapping algorithm that computes 95% confidence intervals on the optimized model parameters and whole isotherm surface area. We present a detailed derivation of this new model isotherm and illustrate its utility with diverse examples: (a) liquid N₂ adsorption onto several porous nickel alloy sponges and metal-organic frameworks (MOFs), (b) diverse examples of gas adsorption in MOFs, (c) moisture adsorption onto various hydrophilic and hydrophobic materials, (d) adsorption of several proteins onto hydrophobic interaction chromatography resins, (e) CO₂ adsorption on Zeolite 13X, (f) butylamine adsorption from methanol-water solution onto sponge nickel catalysts, (g) aqueous red dye adsorption onto beechwood, (h) step-like layer-by-layer adsorption of methane onto a MgO surface at 87 K. These examples spanned: (i) each of the six IUPAC physisorption isotherm types, (ii) positive cooperative, negative cooperative, and noncooperative adsorption, (iii) single-layer and multilayer adsorption, (iv) adsorption with and without capillary condensation, and (v) adsorption modeled by a single sitegroup and by multiple sitegroups. Results showed the MD isotherm is a good general-purpose model for physical adsorption under diverse conditions on diverse materials.