# Gas pycnometer

A gas pycnometer is a laboratory device used for measuring the density — or more accurately the volume — of solids, be they regularly shaped, porous or non-porous, monolithic, powdered, granular or in some way comminuted, employing some method of gas displacement[1][2][3] and the volume:pressure relationship known as Boyle's Law. A gas pycnometer is also sometimes referred to as a helium pycnometer.

## Types of gas pycnometer

### Gas expansion pycnometer

Gas expansion pycnometer is also known as constant volume gas pycnometer. The simplest type of gas pycnometer (due to its relative lack of moving parts) consists of two chambers, one (with a removable gas-tight lid) to hold the sample and a second chamber of fixed, known (via calibration) internal volume – referred to as the reference volume or added volume. The device additionally comprises a valve to admit a gas under pressure to one of the chambers, a pressure measuring device – usually a transducer – connected to the first chamber, a valved pathway connecting the two chambers, and a valved vent from the second of the chambers. In practice the sample may occupy either chamber, that is gas pycnometers can be constructed such that the sample chamber is pressurized first, or such that it is the reference chamber that starts at the higher pressure. Various design parameters have been analyzed by Tamari.[4] The working equation of a gas pycnometer wherein the sample chamber is pressurized first is as follows:

$V_{s} = V_{c} + \frac{ V_{r}} {1-\frac{P_{1}}{P_{2}}}$

where Vs is the sample volume, Vc is the volume of the empty sample chamber (known from a prior calibration step), Vr is the volume of the reference volume (again known from a prior calibration step), P1 is the first pressure (i.e. in the sample chamber only) and P2 is the second (lower) pressure after expansion of the gas into the combined volumes of sample chamber and reference chamber.

Derivation of the "working equation" and a schematic illustration of such a gas expansion pycnometer is given by Lowell et al..[5]

### Variable volume pycnometer

Variable volume pycnometer (or gas comparison pycnometer) consists of either a single or two variable volume chambers. The volume of the chamber(s) can be varied by either a fixed amount by a simple mechanical piston of fixed travel, or continuously and gradually by means of a graduated piston. Resulting changes in pressure can be read by means of a transducer, or nullified by adjustment of a third ancillary, graduated variable-volume chamber. This type of pycnometer is commercially obsolete; in 2006 ASTM withdrew its standard test method D2856[6] for the open-cell content of rigid cellular plastics by the air pycnometer, which relied upon the use of a variable volume pycnometer, and was replaced by test method D6226[7] which describes a gas expansion pycnometer.

## Practical use

### Volume vs density

While pycnometers (of any type) are recognized as density measuring devices they are in fact devices for measuring volume only. Density is merely calculated as the ratio of mass to volume; mass being invariably measured on a discrete device, usually by weighing. The volume measured in a gas pycnometer is that amount of three-dimensional space which is inaccessible to the gas used, i.e. that volume within the sample chamber from which the gas is excluded. Therefore the volume measured considering the finest scale of surface roughness will depend on the atomic or molecular size of the gas. Helium therefore is most often prescribed as the measurement gas, not only is it of small size, it is also inert and the most ideal gas.

Closed pores, i.e. those that do not communicate with the surface of the solid, are included in the measured volume. Helium may however demonstrate some measurable permeability through low density solids (polymers and cellulosic materials predominantly) thus interfering with the measurement of solid volume. In such cases larger molecule gases such as nitrogen or sulfur hexafluoride are beneficial.

Adsorption of the measuring gas should be avoided, as should excessive vapor pressure from moisture or other liquids present in the otherwise solid sample.

### Applications

Gas pycnometers are used extensively for characterizing a wide variety of solids such as heterogeneous catalysts, carbons,[8] metal powders,[9][10] soils,[11] ceramics,[12] active pharmaceutical ingredients (API's) and excipients,[13] petroleum coke,[14] cement and other construction materials,[15] cenospheres/glass microballoons and solid foams.[7]

## Notes

• Pycnometer is the preferred spelling in modern American English usage. Pyknometer is to be found in older texts, and is used interchangeably with pycnometer in British English. Pyknometer is preferred in European English. The term has its origins in the Greek word πυκνός, meaning "dense".
• The density calculated from the volume measured by a gas pycnometer is often referred to as skeletal density,[16][17] true density [18][19] or helium density[19] and sometimes as particle density for non-porous solids.[17]
• One of the most extreme examples of the gas displacement principle for volume measurement is described in U.S. Patent 5,231,873 (Lindberg, 1993) wherein a chamber large enough to hold a flatbed truck full of timber is described for the purpose of measuring the volume of the load.

## References

1. ^ U.S. Patent 2,667,782 Shea, "Apparatus for measuring volumes of solid materials".
2. ^ U.S. Patent 4,083,228 Turner et al., "Gas comparison pycnometer".
3. ^ U.S. Patent 4,888,718 Furuse, "Volume measuring apparatus and method"
4. ^ S. Tamari (2004) Meas. Sci. Technol. 15 549–558 "Optimum design of the constant-volume gas pycnometer for determining the volume of solid particles" doi:10.1088/0957-0233/15/3/007
5. ^ S. Lowell, J.E. Shields, M.A. Thomas and M. Thommes "Characterization of Porous Solids and Powders: Surface Area, Pore Size and Density", Springer (originally by Kluwer Academic Publishers), 2004 ISBN 978-1-4020-2302-6 p. 327
6. ^ ASTM D2856-94(1998) Standard Test Method for Open-Cell Content of Rigid Cellular Plastics by the Air Pycnometer (withdrawn in 2006).
7. ^ a b ASTM D6226-05 Standard Test Method for Open Cell Content of Rigid Cellular Plastics.
8. ^ DIN 51913 Testing of carbon materials – Determination of density by gas pycnometer (volumetric) using helium as the measuring gas
9. ^ ASTM B923-02(2008)Standard Test Method for Metal Powder Skeletal Density by Helium or Nitrogen Pycnometry
10. ^ MPIF Standard 63: Method for Determination of MIM Components (Gas Pycnometer)
11. ^ ASTM D5550 -06 Standard Test Method for Specific Gravity of Soil Solids by Gas Pycnometer
12. ^ ASTM C604 Standard Test Method for True Specific Gravity of Refractory Materials by Gas-Comparison Pycnometer
13. ^ USP<699> "Density of Solids"
14. ^ ASTM D2638 – 06 Standard Test Method for Real Density of Calcined Petroleum Coke by Helium Pycnometer
15. ^ C. Hall "Water Transport in Brick, Stone and Concrete", Taylor & Francis, 2002, ISBN 978-0-419-22890-5 p. 13
16. ^ D. Sangeeta and J. R. Lagraff "Inorganic materials chemistry desk reference", CRC Press, 2005, ISBN 978-0-8493-0910-6 p. 103
17. ^ a b N. P. Cheremisinoff "Handbook of Water and Wastewater Treatment Technologies", Butterworth-Heinemann, 2001, ISBN 978-0-7506-7498-0 p. 144
18. ^ P. J. Sinko and A. N. Martin "Martin's Physical Pharmacy and Pharmaceutical Sciences, 5th Edition, Lippincott Williams & Wilkins, 2005, ISBN 978-0-7817-5027-1 p. 544
19. ^ a b J. G. Speight "The Chemistry and Technology of Coal" CRC Press, 1994, ISBN 978-0-8247-9200-8 p. 202