A key aspect of being able to measure “excess adsorption capacity” through either gravimetric or volumetric measurements is to be able to determine the skeletal density of the physisorption material. This is typically done by helium pycnometetry. That is helium at a measured pressure and temperature in a calibrated volume is released into a sample vessel of a known empty volume and the pressure re-measured. The volume of the sample vessel with the sample inside is determined from the resulting pressure. The difference between the empty sample vessel volume and the measured volume gives the skeletal volume of the sample and together with the samples mass, the skeletal density of the porous material.

These measurements involve a few important assumptions: 

1. that helium is accessible to all the pores of the adsorbent, 

2. that there is no significant helium adsorption under the measuring conditions, 

3. the equation of state and temperature distribution is adequately accounted for in the gas mass balance determination and, 

4. that there are no impurities in the helium gas before or after exposure to the sample.

With respect to these assumptions it is generally held that pores which have a diameter of less than 2.25 Å (the Lennard-Jones kinetic diameter) are not accessible to helium will also not be accessible to hydrogen. It is also generally assumed in the literature that helium at ambient conditions (near or below 1 bar and room temperature) will not be adsorbed to the materials surface in any significant quantity.

As shown in below image, the adsorption capacity is generally proportional to the pore volume or more exactly the specific surface area of the material. Thus, measuring the specific surface area of a sample material can provide much insight into the physical chemical interpretation of hydrogen physisorption. Such measurements are also made through gas adsorption studies.

It is useful when discussing the surface properties of solids having large specific surfaces, to distinguish between the external and the internal surfaces. The external surface includes all the protrusions and all cracks that are wider than they are deep. The internal surface consists of the walls of all cracks, pores and cavities which are deeper than they are wide. Despite being somewhat arbitrary, the distinction between an external and an internal surface is useful in practice. A wide range of porous solids have an internal surface greater by several orders of magnitude than the external surface. The total surface of a solid thus being predominantly internal and for a given mass of solid, the surface area is inversely proportional to the size of the constituent particles.

It is useful to have a good knowledge of the range of pore sizes in a porous solid. The pore sizes in a porous solid must be of a suitable size to admit, hold, and discharge individual gas molecules. If the pores are too small, the gas molecules can not enter. If they are too large, most of the molecules of gas in the pore behave as a gas under pressure with rapid movement and molecular collisions. They are not packed as tightly and bound to the surface in the adsorbent structure. The individual pores may vary greatly both in size and in shape within a given solid and between materials. The conventional classification for pore size has been defined by the International Union of Pure and Applied Chemistry (IUPAC) and is summarized below. The classification is arbitrary and was developed on the basis of the adsorption of nitrogen at 77K on a wide range of porous solids. The basis of the classification is that each of the size ranges corresponds to characteristic adsorption effects.

Porous materials may contain pores made up of highly regular structures or cracks, crevices, and tortuous passageways. For all of these materials three distinctly different types of density measurements are possible, one that includes and one that excludes these pores. And a third definition that defines sample volume in terms of the volume of a container into which a known quantity of material (powder or pieces) can be filled or packed. This last density includes not only the pore spaces within the material but also the spaces among the particles or pieces. The following is a summary of these three different density definitions:

1. Skeletal density: also termed the absolute or true density, excludes both the intraparticle spaces that may be in the particles and the interparticle spaces.

2. Apparent density: also termed as the envelop density, includes the intraparticle but excludes interparticle spaces.

3. Packing density: also referred to as bulk density includes both intra- and interparticle spaces.

Note that the term “bulk density” causes some confusion because it is variously used for both apparent density and packing density. For example, the density obtained from filling a container with the sample material and vibrating it to obtain near optimum packing is also called “bulk density”. This would be what is referred to here as the packing density. Similarly, X-ray density may be equivalent to skeletal density for porous solid materials and apparent density for crystalline open framework materials.

Reference List:

• Sircar, S., “Gibbsian Surface Excess for Gas AdsorptionRevisited”, Industrial & Engineering Chemistry Research, 38 (1999) p. 3670-3682.

• Malbrunot, P., Vidal, D., Vermesse, J., “Adsorbent Helium Density Measurement and Its Effect on Adsorption Isotherms at High Pressure”, Langmuir, 13 (1997) p. 539-544

• Ridha F.N., “A study on high-pressure adsorption and desorption of methane, ethane, propane and their mixtures on porous adsorbents”, Ph.D. Thesis 2006 Faculty of Chemical and Natural Resources Engineering, Universiti Teknologi Malaysia.

• Adamson, A.W., “Physical Chemistry of Surfaces”, 5th ed. New York. (1990), John Wiley and Sons, Inc.

• Ross, S., and Morrison, L.D., “Colloidal Systems and Interfaces”, New York (1988), John Wiley and Sons, Inc.