An explicit dual-site BET isotherm model for the prediction of nonideal competitive and cooperative adsorption equilibrium

A dual-site extension is proposed to the previously derived ideal adsorbed solution theory analytical solution for two coadsorbing single-site BET isotherms. The proposed dual-site BET (DSBET) isotherm model is described in detail, along with multiple possible simplifications for real systems, including modeling humid carbon capture (CO2/H2O mixtures) using amine-functionalized chemisorbents and activated alumina. These simplifications allow nonideal binary equilibrium predictions of single-site Langmuir or dual-site Langmuir isotherm models (type-1 isotherms) coadsorbing with type-2 or type-3 isotherms as either a single-site BET or a dual-site BET isotherm model. The GAB isotherm could also be utilized in the proposed model via a change of variables. Many of the same advantages seen by the extended dual-site Langmuir isotherm are found for the dual-site BET isotherm. These include at least two distinct multicomponent equilibrium predictions per binary gas pairing and the ability to predict nonideal coadsorption. The choice of nonlinearity parameters (and their corresponding adsorption-site) is discussed along with their implications in coadsorption equilibrium prediction. A generalized single-site and dual-site BET isotherm model was also derived to extend multicomponent loading predictions to any number of components in a coadsorbing mixture. The DSBET isotherm model is able to predict nonideal adsorption equilibrium for both competitive and cooperative systems. This is demonstrated using hypothetical binary mixtures of DSBET isotherms and their IAST solutions, as well as loading deviation plots quantifying their difference from the unary DSBET prediction. Multiple DSBET isotherm model examples are shown for both hypothetical and experimental systems. Experimental examples include CO2/H2O mixtures on an amine-functionalized polymer (Lewatit VP OC 1065) and F-200 activated alumina.