Isosteric enthalpies for hydrogen adsorbed on nanoporous materials at high pressures

Abstract

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 materialsactivated 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.

Application of the modified Dubinin-Astakhov equation for a better understanding of high-pressure hydrogen adsorption on activated carbons

“…Q st,exc was found to be almost constant in the range of n exc considered, which corresponds to a relatively low fractional filling. Nevertheless, it increases dramatically for n exc values above 3.5 mmol g -1 (see Figure S5 in the Supplementary Information), which could be due in part to both the increased uncertainty and the accumulation of errors in the measurements, as concluded in previous studies [88][89][90]. However, lateral interactions between hydrogen molecules and cooperative adsorption could also play an important role.…”

High volumetric and energy densities of methane stored in nanoporous materials at ambient temperatures and moderate pressures

“…The methane isotherms were modelled using a methodology our group reported in the past, of using excess adsorption data and converting these into an absolute isotherm 36 . More recently, we adapted a model where a distinction is made between excess, absolute and total 28,37,38 . The absolute corresponds to the high-density adsorbed phase, with the total corresponding to the total quantity present in the pore, including the gas in the pore space which resembles a bulk gas.…”

Direct Determination of Enthalpies of Sorption Using Pressure‐Gradient Differential Scanning Calorimetry: CO2 Sorption by Cu‐HKUST

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Enthalpyo fs orption (DH)i sa ni mportantp arameter for the design of separation processes using adsorptive materials. [2] Indeed, Chang and Ta lu demonstrated the importanceo fm anaging thermale ffects during sorptions ince temperature changes affect the working capacity of the material( see the Supporting Information, Figure S4). Combining ah eatflow thermogram with as ingle sorptioni sotherm enables the determination of DH as af unctiono fl oading.

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“…Bimbo et al stated that an accurate determination of the enthalpy of adsorption is essential to at horough understanding of any sorption-based system and that its reliable measurement is particularly critical for heat management. [2] The isosterica pproach is therefore an approximation of the differential enthalpy of sorption (also known as D ads ḣ), [12] which is most reliable at lowc overage where guest-guest interactions makeanegligible contributioni nc omparison to host-guest interactions. [3] Correct accounting for thermal affects can lead to the developmento farange of sorption-based technologies, which may include heat pumps and cooling systems.…”

“…The enthalpy of sorption encompasses both host-guest and guest-guest interaction energies. [2] The isosterica pproach is therefore an approximation of the differential enthalpy of sorption (also known as D ads ḣ), [12] which is most reliable at lowc overage where guest-guest interactions makeanegligible contributioni nc omparison to host-guest interactions. [8] The two most commonm ethods of determining enthalpies of sorption are (i)the indirect isosteric methodb yu sing the Clausius-Clapeyron approximation and (ii)direct measurementb yu sing calorimetry.…”