Effect of Entropic Constraints on the Thermodynamics of Molecular Adsorption in Nano-Porous Materials

Gas separation is a critical industrial process that consumes a significant amount of energy due to the widely used techniques that are currently employed. Adsorptive materials-such as metal-organic frameworks (MOFs)-show promise as an energy-efficient alternative. Of particular current interest are novel, temperature-dependent separation processes in MOFs, such as the recently reported separation of ternary isomeric hydrocarbon mixtures within one and the same material. However, the mechanisms of these highly desirable separations remain poorly understood. Herein, through a combination of ab initio simulations and statistical mechanics, it is shown that the temperature dependence is the result of a constraint on the guest molecule's entropic degrees of freedom when loaded into the MOF, caused by the fortuitous tight fitting of the guest inside the pore. While the framework applies to all molecular adsorption in porous media, it is essential for the description of large molecules in small pores, which is demonstrated here using the separation of C6 isomers in Ca(H₂tcpb) as a test case. The developed framework and analysis not only reveal the reason why separation occurs but also predict the temperatures at which it takes place, thus opening the door to newly designed MOFs with tailor-made precision.