Is it Possible to Calculate Density from Free Space Measurements?

A common question arises: can density be determined using the free space measured on a gas adsorption analyzer, rather than a device specifically designed for density measurement? This article explores the potential of this method and compares the results with those obtained using the Micromeritics AccuPyc II.

Gas adsorption instruments quantify the amount of gas adsorbed at different pressures, which is then used to derive surface area and porosity data. To measure the quantity of gas that adsorbs onto a sample, the instrument must first determine the volume within the sample tube that remains unoccupied by the sample, known as free space.

This free space is typically established through two measurements using helium, a gas that does not adsorb. The first measurement is taken at ambient temperature to determine ambient free space, while the second measurement, analysis free space, is conducted at the analysis temperature.

The volume of the sample can be calculated by subtracting the ambient free space of an empty tube from the ambient free space when the tube contains the sample. The sample's density is then determined by dividing its mass by the calculated volume.

A helium pycnometer functions in a comparable way. The instrument is calibrated using a reference object with a known volume, such as a sphere or a non-porous ceramic with a well-defined geometry, composition, and a well-known coefficient of thermal expansion. This calibration helps establish the volumes of the reference and sample chambers.

Once calibrated, the sample is placed in the sample chamber, and a process similar to free space determination is used to measure the volume occupied by the sample material. This measurement is typically repeated over 10 cycles to obtain an average volume for the material being tested.

Methods

In this case study, ambient free space was measured for empty 3/8 and 1/2-inch sample tubes. Analyses were then conducted on alumina, carbon black, stainless steel, tungsten, and tungsten carbide to determine their ambient free space. Samples were properly degassed to guarantee cleanliness and then weighed. Table 1 presents the ambient free space values, sample mass, and the corresponding calculated volumes and densities.

The AccuPyc II quantifies a sample’s volume via Boyle’s law. Since the reference and sample chambers are maintained at the same temperature within the same aluminum block, temperature measurements are unnecessary. The sample chamber is pressurized above ambient levels, driving the analysis gas into the pores to accurately measure the material's volume. This process is repeated across multiple cycles to obtain an average sample volume.

After removing the samples from the gas adsorption tubes, they were analyzed in the AccuPyc at 20 °C to determine their skeletal density. The cell and expansion volumes were recorded as 5.7898 cm³ and 8.3778 cm³, respectively. Table 2 compares the density values obtained by the AccuPyc with those calculated using the free space subtraction method.

Results

Figure 1. Calculated and measured density versus expected density. Image Credit: Micromeritics Instrument Corporation

Table 1. Different materials used with their respective density values calculated from free space determinations. Source: Micromeritics International Sales

Table 2. Summary of density values determined by Micromeritics AccuPyc II vs. free space subtraction method. Source: Micromeritics International Sales

Table 3. Ratio of sample to free space volume. Source: Micromeritics International Sales

Summary

Densities assessed on the AccuPyc were extremely close to expected values, while those obtained through the free space subtraction method were noticeably higher, as shown in Figure 1.

Using ambient free space to determine density is unconventional since this measurement is not typically intended for that purpose. On a gas adsorption analyzer, ambient free space is measured below atmospheric pressure and performed only once. In contrast, the AccuPyc pressurizes the sample chamber above atmospheric pressure, ensuring that gas enters pores open to the surface, and it repeats this process multiple times.

Ambient free space, both blank and sample, assessed by gas adsorption varies according to temperature. Therefore, the empty tube free space and the free space with the sample present must be achieved at the identical ambient temperature to reduce mistakes. AccuPyc assessments are recorded in an isothermal setting.

The AccuPyc, however, operates in an isothermal environment, utilizing high thermal conductivity construction materials to provide the stable temperature conditions necessary for accurate displacement volume measurements.

The AccuPyc performs best when the sample occupies the majority of the sample chamber's available volume. Achieving this on a gas adsorption instrument would require filling the sample tube to a similar extent, which is impractical and not recommended. The sample volume-to-free space ratios for the gas adsorption instrument, shown in Table 3, are significantly lower than the sample volume-to-cell volume ratio obtained with the AccuPyc, as displayed in Table 2.

The AccuPyc is specifically designed for accurate density measurements and is preferred over the subtraction method used with gas adsorption instruments, which are not optimized for determining density.

Reference Calculations

Ambient Free Space is Calculated Using the Following Equation:

Image Credit: Micromeritics Instrument Corporation

Boyle’s Law

P₁V₁=P₂V₂

References

1. Micromeritics Alumina Reference Material, Lot SA5214-19001A
2. Micromeritics Carbon Black Reference Material, Lot D-4

This information has been sourced, reviewed and adapted from materials provided by Micromeritics Instrument Corporation.

For more information on this source, please visit Micromeritics Instrument Corporation.