**The most frequently quoted hydrogen content quantity, in terms of storage applications, is wt.%: the weight percent capacity or the gravimetric storage density of a material. The calculation or definition of this quantity differs between hydrogen absorbers and adsorbents; although it is more clearly defined in the former case, there is some uncertainty associated with both quantities due to the definition of either the sample volume or density, and the effect of hydrogen sorption on this quantity.**

In both cases, there are sorption measurement-related issues associated with the choice of hydrogen capacity definition that are important to consider. This brief article summarizes some of the definitions, and the associated problems.

## Hydrogen Absorption

The gravimetric storage capacity of a hydrogen-absorbing material, in which the hydrogen is stored within the bulk of the material, is typically calculated from the ratio of the mass of hydrogen stored within the metal or compound to the mass of the host material including the hydrogen^{[1]}, so that the capacity in wt.%, C_{wt.%}, is given by,

Equation 1 |

where H/M = the hydrogen-to-metal or material host atom ratio, M_{H} = the molar mass of hydrogen, and M_{Host} = the molar mass of the host material or metal.

Note that M_{Host} should be calculated for a mole of host atoms, rather than a mole of molecular formula units of the host, by dividing the total molecular weight by the number of atoms in a formula unit, if and where appropriate. The alternative is to use the ratio of hydrogen atoms to formula units for H/M.

Two alternative ways of defining the capacity are relative to the empty (unhydrided) material and to the fully hydrided state. The first is essentially a conversion of the H/M value to a percentage figure,

Equation 2 |

And the second can either be treated as the equivalent to a percentage mass loss figure obtained during a thermal decomposition measurement, or by using an assumption of the hydrogen stoichiometry in the fully hydrided state. Unless the sample is a known stoichiometric compound this adds an additional uncertainty to the calculated hydrogen content of the material as a function of pressure or time.

In each case, the calculation of an accurate storage content should take account of the expansion or contraction of the material as a result of hydrogen absorption or desorption. In gravimetric measurements the corresponding sample volume and density change could potentially affect the buoyancy effect corrections. In volumetric (Sieverts' Method) measurements this will affect the dead volume of the system or sample cell.

The measured quantity in a hydrogen adsorption measurement is the excess adsorption, also known variously as the surface excess, the Gibbs excess or the Gibbsian surface excess. This quantity is the difference between the actual amount of adsorbate present in the adsorbed layer and that which would be present in the layer if it had the same density as the bulk gas phase, at the particular measurement temperature and pressure.

The conversion from the experimentally-determined excess adsorption to the total adsorption requires an assumption regarding the nature of the adsorbed layer. In sub-critical adsorbates it is typically assumed that the adsorbate layer has the same density as the bulk liquid phase of the adsorbate species; however, this is not necessarily applicable to supercritical adsorbates, such as hydrogen at the measurement temperatures of interest for hydrogen storage.

So, it can be seen that a calculation analogous to Eq. (1) is not possible for a hydrogen adsorbent because of the difficulty in defining the total adsorbed quantity of hydrogen, and therefore the problem of knowing exactly how much hydrogen can be attributed to the adsorbed layer.

A typical unit for the excess adsorption in adsorption measurement is the number of moles of adsorbate per unit mass of adsorbent; for example, mol g^{-1}, mmol g^{- 1}, or µmol g^{-1}. As the molar mass of the adsorbate is known, this can easily be converted into a wt.% uptake but this is not the same as the wt.% uptake definition for hydride materials given in Eq. (1). The gravimetric uptake can also be seen expressed in terms of the adsorbate mass (mg g^{- 1}) and adsorbate volume (cm^{3} (STP) g^{-1}), although these units are interchangeable*.

A calculation equivalent to Eq. (1) can be made in which the excess adsorption is included in the denominator^{[2]},

Equation 3 |

where n_{a} = the excess adsorption in moles and n_{Host} = the number of moles of host material in the sample. However, this still does not account for the total amount of adsorbed hydrogen, which is given by the following expression,

Equation 4 |

where n_{tot} is the total adsorbed mass, ρ_{H}is the density of bulk gas phase hydrogen at the measurement temperature and pressure, and ρ_{a} is the adsorbed phase density.

Expression of the absolute adsorbed quantity, as defined in Eq. (4), requires an assumption about the nature of the adsorbed hydrogen layer. Possible assumptions for this calculation include the adsorbed layer having the same density as hydrogen in its liquid state, the layer density being equal to the critical density of hydrogen, and the adsorbed layer volume being equal to the sample's total pore volume^{[3]}.

Figure 1 shows gravimetrically-determined hydrogen adsorption data for an activated carbon at 77 K. The graph shows the raw data uncorrected for buoyancy effects, the corrected excess adsorbed quantity and a total adsorbed quantity calculated using the assumption that the adsorbed layer has the same density as liquid hydrogen.

It can be seen that the conversion of the data from the excess to the total adsorption in this case adds approximately 0.5 wt.% to the measured uptake. The equivalent calculation is of course also necessary for volumetrically-determined hydrogen adsorption data as the measured quantity using the Sieverts Method is also the surface excess.

**Figure 1. **Hydrogen uptake for an activated carbon sample measured at 77 K using a Hiden Isochema Intelligent Gravimetric Analyzer (IGA-001), showing the uncorrected weight measurement, as a weight percentage, the corrected excess adsorbed quantity and the total adsorption, calculated assuming the density of the adsorbed phase is equal to that of liquid hydrogen.

## Summary

Different definitions for the hydrogen storage capacity of hydrogen absorbers and adsorbents have been discussed in this article. The definitions for hydrogen absorption are easier to define as the assumption of the nature of an adsorbed layer does not need to be considered. However, the contraction and expansion of the material during the measurement, if significant, should be taken into account.

In the case of hydrogen adsorption, the experimentally-measured quantity is the excess adsorption. In order to calculate the total adsorption an assumption must be made regarding the adsorbed layer volume or density. An example dataset measured using a Hiden Isochema Intelligent Gravimetric Analyzer (IGA-001) has been presented.

**References**

[1] Sandrock G., Journal of Alloys and Compounds 293-295 (1999) 877-888

[2] Garberoglio G., Skoulidas A. I., Johnson J. K., Journal of Physical Chemistry B 109 (2005) 13094-13103

[3] Murata K., El-Merraoui M., Kaneko K., Journal of Chemical Physics 114(9) (2001) 4196-4205

This information has been sourced, reviewed and adapted from materials provided by Hiden Isochema.

For more information on this source, please visit Hiden Isochema.

* Note that the expression of the gravimetric storage density/capacity in terms of adsorbate volume at STP is not a volumetric uptake, but just an alternative unit for a mole of adsorbate (for example, the volume of 1 mole of an ideal gas at STP = 22.4 l).