Gas Pycnometer

	Micrometrics AccuPyc II 1345
Chamber Inserts	10 cm$^{3}$, 3.5 cm$^{3}$, 1 cm$^{3}$
Maximum Chamber Pressure	20.5 psig
Precision	$\pm$ 0.02% of nominal sample chamber volume
Accuracy	$\pm$ 0.03% of reading plus, $\pm$ 0.03% of sample capacity

The Micrometrics Gas Pycnometer uses high purity helium gas to determine the true volume of a sample. The sample is stored in in an air tight container, which is filled with helium gas, up to a certain pressure. This chamber is then opened up to a reference chamber with a precise known volume. The expansion of volume lowers the overall pressure, and there ratio between the initial and final pressure is used to calculate the true volume of the sample (the volume excluding contributions from pores). The primary application is measurement of porosity and true density.

Operating Principle

Gas pycnometery works by flooding a chamber of known volume with a non-reactive gas. All other gasses are purged out, so that only the gas to be used for the measurement remains. A sample of unknown volume is placed within the chamber. All gas must then be purged from the chamber to start the measurement process.

Because of this, the sample should be as dry as possible, and the sample chamber should be sealed unless a sample is being loaded or unloaded. Any moisture that enters the chamber will have an associated vapor pressure, which will screw measurements.

Once all gas has been evacuated from the chamber, helium gas is pumped to the sample chamber so that a certain pressure is obtained. Helium gas has several advantages over other non-reactive gasses, such as nitrogen. Helium is the smallest gas, which allows it to fill in pores, cracks, and other defects more effectively. It also exhibits very ideal behavior, which is necessary, as the calculation for sample volume relies on a derivation of the ideal gas law.

Diagram of a Gas Pycnometer

After the chamber has been flooded with the set amount of helium, a valve is opened, connecting the sample chamber to a reference chamber of known volume. The reference chamber is kept in a vacuum, so that the moles of gas remain constant. However, the pressure lowers as the helium redistributes itself between the sample and reference chambers.

The initial and final pressures of this process are used to calculate sample volume via this equation: ${\text{V}}_{s}={\text{V}}_{c}+{\frac {{\text{V}}_{R}}{1-(P_{1}/P_{2})}}$. V$_{c}$ is the volume of the sample chamber, and V$_{R}$ is the volume of the reference chamber, both of which are known. P$_{1}$ and P$_{2}$ and the measured pressures before and after the volume expansion.

The insertion of additional sample parameters such as mass and envelope density allow porosity, pore volume, and true density to be calculated with the use of the gas pycnometer. However, the only quantity directly measured by the instrument itself is true sample volume.

Density

Density is the ratio of the mass of an object to its volume. However, many objects are porous, or contain interstitial spaces, such as powders. This leads of our having several different classification of density.

True Density

True density is the ratio of the mass to the volume occupied by that mass. This means that the volume to pores, cracks, or other internal voids should not be considered in calculating true density. The gas pycnometer is particular useful for measuring this type of density.

Apparent Density

Apparent density is an approximation of true density, which is measured using a liquid rather than a gas. Depending on the surface energy of the sample being measured, as well as the properties of the liquid used, some pores and cavities will not be filled. Gas displacement is the difference between true and apparent density. To approximate true density with a liquid the contact angle between the liquid and the sample should be minimized. If the contact angle exceeds 90º, then the liquid will not fills pores in the sample, unless forced to do so by some external pressure.

Bulk Density

Bulk density is the density of a material, including the volume of pores, and interstitial spaces in a powder. In essence it is the volume that would be measured it you were to use a graduated cylinder or a measuring cup for the measurement.

Bulk density is useful as a measure of the autoadhesivenss of a sample. This is because the amount of interstitial space in powders depends on particle size, shape, moisture content, and inter particle forces.

Tap density is a similar measurement to bulk density obtained by lifting and dropping the contained ("tapping") to force the powder to settle more compactly. Tap density is almost always higher than bulk density.

Envelope or Geometric Density

Envelope or geometric density is measured like bulk density, but with a single particle. It takes into account the volume of the sample, and the volume of internal pores to calculate density. Envelope density is generally obtained by measuring the external dimensions of a sample, and computing the volume geometrically. Envelope density can also be measured using a non-wetting fluid, one whose contact angle is greater than 90º. Without external pressure, a non-wetting fluid will not fill any pores or cavities, which allows the envelope density to be calculated.

If the envelope density of the sample is entered in the gas pycnometer software, this can be used to calculated pore volume and porosity.

Effective Density

A sample may sometimes contain foreign contaminants, or totally encapsulated pores. In these cases, neither gas, nor liquid displacement techniques will provide the true density due to the alien particles and blind or sealed pores. When this is the case, the density measured via gas displacement is called the effective density.

Porosity

Porosity (ø) is ration of the volume taken up by pores within the material to the bulk volume. $\phi ={\frac {V_{B}-V_{S}}{V_{B}}}={\frac {V_{P}}{V_{B}}}$. The bulk volume (V$_{B}$) is the volume used to calculate bulk density, and the solid volume (V$_{S}$) is the volume used to calculate true density. The difference between two will be equal to the volume of the pores in the sample (V$_{P}$).

Porosity can be analyzed with the gas pycnometer if the correct parameters are provided. If you wish to study porosity, when creating your sample file you must select material parameters. So that porosity and pore volume may be calculated you may then supply either the envelope density, or the bulk density. Total Pore Volume is recorded in the "Pressure and Volume Table" report option. With the total pore volume, and the bulk volume of your sample, the porosity can be calculated manually.