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 R
2 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.