The volumetric technique determines the amount of hydrogen ad- or absorbed by a sample by monitoring the drop in hydrogen pressure in a fixed volume in direct contact with the sample. During the desorption process, the quantity of hydrogen released is determined by the increase in the hydrogen pressure, following evacuation of some or all of the hydrogen in the gas phase. To illustrate the principle, Figure 1 shows a schematic diagram of a basic volumetric set-up. V1 and V2 are known volumes, of volume V₁ and V₂, and valves A and B control the hydrogen gas inlet and vacuum outlet, respectively, allowing the control of the hydrogen pressure in V1. Valve C allows the introduction or removal of gas to or from V2, and the pressure in V1 is measured using the manometer. The sample sits at the bottom of V2, with a temperature sensor (not indicated in the diagram) either near or in contact with it. As with all of the measurements described in this report, the sample should be secured appropriately, although this will depend on the form of the sample (for example, a fine or coarse powder, foil, single crystal, and so on). The thermostat or thermal bath can be any temperature-controlling system, including a liquid N2 dewar, a cryostat, a low temperature fluid bath or a furnace. The temperature of the system should be controlled and monitored, with temperature sensors in more than one position, preferably including the measurement of the gas temperature away from the sample. The manometer represents one or more pressure measuring devices, depending on the hydrogen pressure ranges required. In a system designed for both low and high pressures, this is likely to include separate gauges for different ranges. The generic vacuum pump can be of any type, although an oil-free system with a ultra-high vacuum (UHV) compatible pump (for example, turbomolecular) would be preferable, particularly if samples are to be degassed (in the case of porous adsorbents) or if measurements are to be made at low pressures (< 10² Pa, for example). An oil-free system is favourable because oil vapour can backstream into the system causing contamination; although oil vapour filters can reduce this, they are unlikely to eliminate it entirely. The hydrogen supply should be of very high purity (> 99.999 %) and/or filtered adequately.

Figure 1: A schematic diagram of volumetric sorption apparatus

To perform a simple, single step absorption experiment on an activated sample in the apparatus shown in Figure 1, valves B and C are first opened to evacuate V1 and V2. After sufficient time, valves B and C are then closed. Valve A is opened, allowing V1 to fill with hydrogen to an initial pressure Pi. Valve C is then opened thus filling V2. Any drop in pressure beyond that which is expected from the volume difference between V₁ and (V₁ + V₂) is then assumed to have resulted from the absorption of hydrogen. So, assuming the experiment is performed at a constant temperature, T, and that the final measured pressure is P_f, the number of moles sorbed is given by,

   ......eq (1)

where R is the universal gas constant.

To extend this measurement to a full isotherm, the subsequent step would then use the values of △n and P_f as a starting point. The repetition of the above procedure will result in the measurement of a complete absorption isotherm. This description of the principle ignores both the compressibility of the gas and the expansion of the hydride (and subsequent reduction in the dead space volume) during the absorption process, and any consideration of temperature difference between the system and the sample. The compressibility, Z_P,T, appears in both the terms on the right hand side of Eq. (1). In each case the value of Z corresponds to the particular pressure, P, and temperature, T, of the hydrogen at the time of the measurement. The difference in temperature can be accounted for by assuming that there is a fixed dividing line between the two temperature regions. Although this will not practically be the case, the effective dividing line for a particular sample cell temperature can be determined during calibration measurement.

An adsorption experiment follows the same principle, although in this case the quantity determined by the drop in pressure is the excess adsorption. In the case of an adsorption measurement, the determination of the dead space volume (V2, where this equals the volume of the sample cell minus the volume occupied by the sample) is crucial. This can be performed in one of two general ways: using the direct or indirect method, where the former involves the measurement of the volume using a gas that is assumed to be noninteracting (typically helium), and the latter involves the subtraction of an estimated sample volume from the measured volume of the empty sample cell. The excess adsorption, also known variously as the surface excess, Gibbs’ excess or Gibbsian Surface Excess, is defined as the amount of hydrogen adsorbed beyond that which would be present in the absence of enhanced adsorption (or surface interaction); the surface excess can also be negative, indicating the presence of a lower density of hydrogen near the surface than would be present in the bulk phase at that particular temperature and pressure.

In the case of the direct measurement of dead space volume, it is assumed that there is no interaction between the helium and the adsorbent surface; however, this is not necessarily the case in micropores and so the measurement must be made at a temperature for which this assumption is valid to an acceptable degree. For the measured molar uptake or hydrogen content, △n, to be converted into a wt.% (or mol g^-1), the sample mass must be determined accurately. In the case of metallic absorbers this is straightforward, as the sample can simply be weighed before the absorption measurement. In the case of porous adsorbents, it is the degassed sample mass that is required and the presence of atmospheric adsorbates will affect the accuracy of the sample mass measurement. Therefore, a suitable method must be used to determine the value without significant error.

This technique has come to be known generally as volumetric, but it is also known as the manometric technique, or manometry, as the sorbed quantity is actually determined from the measurement of a change in pressure, not volume. Early nitrogen adsorption measurements were performed with a mercury burette and manometer, whereby the adsorbed quantity was measured by the change in volume rather than a change in the pressure, and so the technique has become known as volumetric. In both hydride and adsorption research it is more common to use manometric systems, although there are exceptions. For example, in the hydride field, some presented a system that measures the sorbed quantity of hydrogen by measuring variations in the volume of a system at a fixed pressure, although it was designed for the performance of kinetic measurements. However, manometric systems are more common. In the hydride field, volumetric apparatus is also known as Sieverts’ apparatus.

Reilly and Wiswall presented a relatively early high pressure system, including their reactor design, which was used for absorption measurements on various binary and ternary hydrides. This system was used up to 21.50 atm (2.178 MPa), with the lowest isotherm point around 0.1 atm (10.13 kPa). Early examples of both low pressure and high pressure systems were also described by Blackledge. Bowman et al presented an automated volumetric system that they used for both thermal cycling of AB5 intermetallics and for isotherm determination. The system is designed for use at ambient temperature and above, and is used up to 500 K. It operates up to 35 atm (3.546 MPa) and is equipped with a pump of base pressure <10-4 torr (13.33 mPa). The lowest pressure point in the presented data is around 0.05 atm (5.066 kPa).

In the field of gas adsorption, a volumetric system designed for the determination of adsorption isotherms was presented by Borghard and co-workers. The system operates in the pressure range 10-5 - 1000 torr (1.333 mPa - 133.3 kPa) and at both high temperatures (< 300 ºC) and low temperatures (77 K) . Data are presented for nitrogen adsorption on a porous glass and argon adsorption on faujasite (zeolite). The authors state that their apparatus could be used for hydrogen sorption measurement, although it is only for low pressures. Maglara et al presented a volumetric system designed specifically for the measurement of the adsorption of probe gases on microporous materials at low relative pressures (P/P0) at low temperatures. Their system was used to perform measurements with nitrogen at 77 K and argon at 77 and 87 K on four types of zeolites, and is again for low pressure measurement. High pressure volumetric adsorption instrumentation was presented recently by Kiyobayashi et al. It operates at a sample temperature of 35 °C and up to pressures of 10 MPa, although the system operates only with a rotary pump. Poirier et al recently presented a volumetric system, alongside gravimetric apparatus, which operates using mass flow controllers (MFCs) to determine the amount of gas sorbed by a sample. However, they do not show isotherms produced with either of their systems.

Recent examples of the use of the volumetric technique in hydrogen storage material research include investigations into hydrogen storage on metal-organic frameworks (MOFs), conducting polymers and Si-destabilized LiH and MgH2. One of the practical advantages of volumetric measurement is its versatility with regard to upper sample size. An example of the use of volumetric instrumentation with a scaled-up reactor bed (in this case, catalysed NaAlH4) is given by Sandrock et al and Gross et al.