(676e) Modeling Water Content and Solute Activities of Complex Fluids and Mixtures: Extension of the Brunauer-Emmett-Teller (BET) Adsorption Isotherm Equation

Multilayer adsorption isotherm models describe a wide range of sorption phenomena, from charcoal adsorption of natural gas to electrolyte uptake of water molecules in solution.  The seminal adsorption model, Brunauer-Emmett-Teller (BET), successfully reproduces solute concentrations of solutions at water activities (a_w, which ranges from a value of 0 in pure solute to a value of 1 in pure solvent solutions) of < 0.4 to 0.5 using only two parameters: (i) the number of adsorption sites and (ii) the energy of adsorption of the solvent directly on to the solute.  The Guggenhein-Anderson-deBoer (GAB) model applies to solutions of a_w < 0.7 to 0.8 by adding a single additional energy of adsorption to approximately account for the extended hydration shell surrounding the solute molecule. 

In this work, statistical mechanics is used to modify the BET and GAB model to include distinct energies of adsorption of the solvent on to n layers in the hydration shell.  Equations for the excess Gibbs energy, solvent and solute activity, and solute concentration are derived.  The inclusion of additional hydration layers of distinct energies, which closely follows hydration shell theory in solutions, results in remarkable agreement of the solute concentration and osmotic coefficients for solutions of a_w as high as 0.9 to 0.95.   Even further extension of the isotherm to the a_w = 1 limit can be achieved through incorporating electrostatic limiting law behavior.  New insights into solute and water activity for single and multicomponent systems are presented.  Any field that includes sorption (absorption or adsorption), including solution, environmental, and catalytic chemistry, regardless of phase state, may benefit from the models developed in this work.