General Theory of Absorption in Porous Materials: The Restricted Multilayer Theory

In this paper we present an approach for the generalization of adsorption of light gases in porous materials. This new theory goes beyond the Langmuir and BET theories, which are the standard approaches that have limited application to crystalline porous materials by their unphysical assumptions on the amount of possible adsorption layers. The derivation of the more general equation for any crystalline porous framework is presented; the Restricted Multilayer Theory (RMT). Our approach allows the determination of gas uptake considering only geometrical constraints of the porous framework and the interaction energy of the guest molecule with the framework. Based on this theory, we calculated optimal values for the adsorption enthalpy at different temperatures and pressures. We also present the use of this theory to determine the optimal linker length for a topological equivalent framework series. We validate this theoretical approach by applying it to Metal-Organic Frameworks (MOF) and show that it reproduces the experimental results for 7 different reported materials. We obtained the universal equation for optimal linker length given the topology of a porous framework. This work applied the general equation to MOFs and H$_2$ to create energy storage materials, however this theory can be applied to other crystalline porous materials and light gases, which opens the possibility of designing the next generations of energy storage materials by first considering only the geometrical constraints of the porous materials.