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Isosteric enthalpies for hydrogen adsorbed on nanoporous materials at high pressures

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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 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.

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Abbreviations

bdc:

Benzene-1,4-dicarboxylate

BET:

Brunauer–Emmett–Teller

DA:

Dubinin–Astakhov

DR:

Dubinin–Radushkevich

EOS:

Equation of state

H–K:

Horváth–Kawazoe

IUPAC:

International Union of Pure and Applied Chemistry

MOF:

Metal-organic framework

MIL:

Matérial Institut Lavoisier

TPD:

Temperature programmed desorption

RMSR:

Root mean squared residual

a :

Adjustable first term parameters for the virial equation

b :

Adjustable second term parameters for the virial equation

b T :

Affinity parameter for the Tóth equation

c T :

Heterogeneity parameter for the Tóth equation

g(n):

Polynomial function for the isosteres

h :

Enthalpy

l :

Number of parameters for a in the virial

m :

Number of parameters for b in the virial

m E :

Excess mass uptake

m A :

Absolute mass uptake

m T :

Total mass uptake

n :

Mass amount adsorbed

n a :

Constant mass amount adsorbed

P :

Absolute pressure

Q st :

Differential isosteric enthalpy of adsorption

\(\overline{{Q_{st} }}\) :

Average differential isosteric enthalpy of adsorption

R :

Molar gas constant

R 2 :

Coefficient of determination

s :

Entropy

T :

Temperature

T f :

Final temperature

T i :

Initial temperature

v :

Molar volume

V A :

Volume occupied by the constant density adsorbate

V P :

Total volume in the pore

v A :

Molar volume of the adsorbate

v B :

Molar volume of the bulk adsorptive

wt%:

Units for hydrogen uptake as a percentage of sample specific dry mass

Δh :

Change in enthalpy

Δs :

Change in entropy

θA :

Fractional filling

ρA :

Adsorbate mass density

ρB :

Bulk adsorptive mass density

χ 2red :

Reduced Chi squared

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Acknowledgments

NB, AND and TJM thank the Engineering and Physical Science Research Council (EPSRC) for funding via the SUPERGEN Hydrogen and Fuel Cells Hub (EP/E040071/1). JES thanks the UK EPSRC Doctoral Training Centre in Sustainable Chemical Technologies at the University of Bath and EADS Innovation Works, Munich, Germany for financial support. VPT thanks the University of Bath for funding via a Prize Research Fellowship. The authors also thank the organisers of the Fundamentals of Adsorption 11 conference for the opportunity to present this work orally.

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  1. Department of Chemical Engineering, University of Bath, Claverton Down, Bath, BA2 7AY, UK

    Nuno Bimbo, Jessica E. Sharpe, Valeska P. Ting, Antonio Noguera-Díaz & Timothy J. Mays

  2. EPSRC Doctoral Training Centre in Sustainable Chemical Technologies, University of Bath, Claverton Down, Bath, BA2 7AY, UK

    Jessica E. Sharpe

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  1. Nuno Bimbo
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Correspondence to Timothy J. Mays.

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Bimbo, N., Sharpe, J.E., Ting, V.P. et al. Isosteric enthalpies for hydrogen adsorbed on nanoporous materials at high pressures. Adsorption 20, 373–384 (2014). https://doi.org/10.1007/s10450-013-9575-7

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