Surprising Use of the Business Innovation Bass Diffusion Model To Accurately Describe Adsorption Isotherm Types I, III, and V

Abstract

Using adsorption isotherm data to determine heats of adsorption or predict mixture adsorption using the ideal adsorbed solution theory (IAST) relies on accurate fits of the data with continuous, mathematical models. Here, we derive an empirical two-parameter model to fit isotherm data of IUPAC types I, III, and V in a descriptive way based on the Bass model for innovation diffusion. We report 31 isotherm fits to existing literature data covering all six types of isotherms, various adsorbents, such as carbons, zeolites, and metal-organic frameworks (MOFs), as well as different adsorbing gases (water, carbon dioxide, methane, and nitrogen). We find several cases, especially for flexible MOFs, where previously reported isotherm models reached their limits and either failed to fit the data or could not sufficiently be fitted due to stepped type V isotherms. Moreover, in two instances, models specifically developed for distinct systems are fitted with a higher R2 value compared to the models in the original reports. Using these fits, it is demonstrated how the new Bingel-Walton isotherm can be used to qualitatively assess the hydrophilic or hydrophobic behavior of porous materials from the relative magnitude of the two fitting parameters. The model can also be employed to find matching heats of adsorption values for systems with isotherm steps using one, continuous fit instead of partial, stepwise fits or interpolation. Additionally, using our single, continuous fit to model stepped isotherms in IAST mixture adsorption predictions leads to good agreement with the results from the osmotic framework adsorbed solution theory that was specifically developed for these systems using a stepwise, approximate fitting, which is yet far more complex. Our new isotherm equation accomplishes all of these tasks with only two fitted parameters, providing a simple, accurate method for modeling a variety of adsorption behavior.