Break

Adsorption systems exhibiting stepped isotherms are of practical interest for a number of reasons. A potential advantage is that the steps allow for a large working capacity over small temperature and pressure ranges, which can be exploited in pressure or temperature swing adsorption processes. The steps can also be used to aid selectivity during separation of a multicomponent system. Although the causes underlying the emergence of non Type I isotherms are understood qualitatively, such isotherms are usually modelled by empirical functions for the purpose of process simulation. Such functions rely heavily on experimental data, may require many fitting parameters and are not predictive. Molecular simulations on the other hand, have become a powerful quantitative tool in describing such systems, but are computationally demanding and therefore not suitable in process modelling.

Here we present the prediction of stepped isotherms using a lattice fluid based model, the Rigid Adsorbent Lattice Fluid (RALF) model. The RALF model is a relatively simple model, with few parameters, which all have a physical meaning, such as interaction energies and densities. These are fixed for any given molecule and the number of adjustable parameters is therefore kept to a minimum.

For non-flexible adsorbents, the RALF model is able to predict type V inflections in isotherms based on the pore volume of the solid and the strength of the intermolecular interaction of the guest molecules. As observed experimentally, the model predicts that highly coordinating molecules such as water or ethanol show this behaviour more readily than weakly interacting aliphatic organics in frameworks with the same porosity. It is remarkable that a relatively simple model is capable of reproducing both type I and type V shapes.

Stepped isotherms may also originate from flexibility in the adsorbent, for instance resulting from host-guest interactions, thermal or mechanical stimuli. A typical example is the breathing behaviour of the MIL-53 family of metal organic frameworks (MOFs), whereby the material reversibly swaps between two phases with open and closed porosity, respectively. This structural transition leads to a step akin to a double type I isotherm. We show that the RALF model is also able to capture this effect, simply by treating the two solid phases as identical but with different densities. Some variation of the density with respect to amount adsorbed is allowed within the phases to reflect the material’s large flexibility. Phase stability is determined by evaluating the total Gibbs energy of the two phases during adsorption. Structural transitions occur under those conditions at which the Gibbs energy profiles cross-over due to differences in the amount adsorbed for the two phases. Due to the difference in densities of the two solid phases, the RALF model reproduces a step in the isotherm upon the structural transition. Predictions for breathing of MIL-53 in CO₂, CH₄ and xenon are in good agreement with experimental results, but currently do not include hysteresis effects.