With respect to characterizing a material’s hydrogen storage performance there are two principal types of measurements, kinetics measurements and pressure-composition-temperature (PCT) measurements. Kinetics measurements can be considered the fundamental measurement of hydrogen storage because other types of measurement, including PCTs, are collections of several individual kinetics measurements. The relationship between kinetics and PCT measurements will be discussed further. Beyond these two main characterization measurements, there is a host of other measurements such as scanning temperature measurements that have value in rough screening for potential new hydrogen storage materials.

• Measurement Type: Kinetics

Kinetics measurements track the rate of change of hydrogen concentration in a sample after the sample has been perturbed from quasi-equilibrium. Because hydrogen storage measurements can only approximate thermodynamic equilibrium due to experimental limitations, equilibrium will be used synonymously with quasi-equilibrium throughout the rest of this manuscript. Perturbation from equilibrium is accomplished by changing the thermodynamic state of the sample’s environment, which causes the sample to sorb/desorb hydrogen in the attempt to restore equilibrium. For the gravimetric and volumetric methods, kinetics measurements are generally conducted under isothermal conditions, with changes in pressure used to perturb equilibrium. This is done partly for compatibility with PCTs and partly because of the profound effect of temperature on the kinetics character of almost all materials.

It is instructive to introduce a few fundamental features common to almost all kinetics measurements for reversible systems. The degree of perturbation from equilibrium is the driving force behind sorption/desorption in hydrogen storage materials: large perturbations cause relatively large rates of change in concentration while smaller perturbations cause relatively small rates of change. The rate of change of hydrogen concentration in a sample is largest at the beginning of a kinetics measurement, when the sample is furthest from equilibrium with its environment. The distance from equilibrium diminishes as hydrogen is sorbed by the sample, slowing the sorption rate as the sample reaches a time independent equilibrium concentration. These effects are illustrated in the sorption kinetics measurement in Figure 1. At the beginning of the experiment, the concentration changes quickly because the sample is furthest from equilibrium and with time the rate of change of concentration decreases until it becomes effectively zero.

Figure 1: representative kinetics measurement of an individual hydrogen dose to a porous material

• Measurement Type: Pressure-Composition Isotherm

Pressure-composition-temperature measurements (PCTs) are the most reported hydrogen storage measurement type in academic literature (composition in this context is synonymous with the concentration of hydrogen in a sample). A PCT measurement is a collection of data points that represents the pressure, concentration and temperature of a sample in equilibrium and relates the influence of the thermodynamic variables on concentration. PCTs are also commonly referred to as PCI (Pressure-Composition Isotherms) because they are taken at isothermal conditions. This minimizes the number of free variables and allows the relationship between concentration and pressure to be presented via two-dimensional graphics. The effect of temperature on hydrogen storage properties can be determined by comparing PCT isotherms at various temperatures. Because PCTs represent a sample in equilibrium, they can also be used to determine the thermodynamic properties of a hydrogen storage material. Unfortunately, the absolute interpretation of PCT data must be kept in perspective because it is difficult to make true equilibrium measurements. This is because as the pressure approaches the true equilibrium pressure, the driving force (or potential) becomes diminishingly small and therefore, kinetics becomes increasingly slower. In other words, it would take an infinitely long time to reach equilibrium. 

It is instructive to conceptualize the relationship between PCT measurements and kinetics measurements in the volumetric method as follows: a sample is perturbed from equilibrium by a change in the pressure of the system and is allowed to reach equilibrium through the dynamic process represented by a kinetics measurement. The last data point of each kinetics measurement, which most closely represents equilibrium, provides a single point of hydrogen concentration, pressure and temperature at equilibrium. In the volumetric method, this dosing process is performed repeatedly at one temperature until there are enough equilibrium data points are collected to construct a full PCT diagram. In this sense the PCT measurement can be thought of as a cumulative series of mini-kinetics measurements. Figure 2 demonstrates the PCT diagram of a porous material using the volumetric method by conducting a series of small dose kinetics measurements. In each kinetics measurement (separated by recharging the dosing volume which appears as discontinuities), the final pressure at the last data point represents the equilibrium pressure at a given concentration. In the volumetric method, the concentration is determined from the change in pressure with each dose. Therefore the equilibrium pressure of the sample corresponding to each equilibrium concentration point is also known and a full PCT can be constructed from the series of kinetics measurements.

Figure 2: Representative measurement of a porous material. The last point in each ‘row’ of points is taken as representative of the equilibrium concentration of hydrogen in the sample at the pressure and temperature of experimentation.

This is shown in Figure 3 where the Pressure / Time data is translated to Pressure / Concentration data to form a PCT diagram. The relationship between pressure drop due to absorption (rise on desorption) and concentration is depicted in Figure 4.

Figure 3: Representative pressure  time measurement and the resulting PCT plot of hydrogen absorption to form a metal hydride. The last point of each gas sorption dose provides the concentration of hydrogen in the sample at the equilibrium pressure and temperature of each dose.

Figure 4: The relationship between pressure drop on absorption and the concentration associated with this pressure drop that is used to create each point on the equilibrium PCT diagram