Isosteric enthalpies for hydrogen adsorbed on nanoporous materials at high pressures

A sound understanding of any sorption system requires an accurate determination of the enthalpy of adsorption. This is a fundamental thermodynamic quantity that can be determined from experimental sorption data and its correct calculation is extremely important for heat management in adsorptive gas storage applications. It is especially relevant for hydrogen storage, where porous adsorptive storage is regarded as a competing alternative to more mature storage methods such as liquid hydrogen and compressed gas. Among the most common methods to calculate isosteric enthalpies in the literature are the virial equation and the Clausius-Clapeyron equation. Both methods have drawbacks, for example, the arbitrary number of terms in the virial equation and the assumption of ideal gas behaviour in the Clausius-Clapeyron equation. Although some researchers have calculated isosteric enthalpies of adsorption using excess amounts adsorbed, it is arguably more relevant to applications and may also be more thermodynamically consistent to use absolute amounts adsorbed, since the Gibbs excess is a partition, not a thermodynamic phase. In this paper the isosteric enthalpies of adsorption are calculated using the virial, Clausius-Clapeyron and Clapeyron equations from hydrogen sorption data for two materials-activated carbon AX-21 and metal-organic framework MIL-101. It is shown for these two example materials that the Clausius-Clapeyron equation can only be used at low coverage, since hydrogen's behaviour deviates from ideal at high pressures. The use of the virial equation for isosteric enthalpies is shown to require care, since it is highly dependent on selecting an appropriate number of parameters. A systematic study on the use of different parameters for the virial was performed and it was shown that, for the AX-21 case, the Clausius-Clapeyron seems to give better approximations to the exact isosteric enthalpies calculated using the Clapeyron equation than the virial equation with 10 variable parameters.