Reviewed by Olivia FrostOct 16 2024
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
Sample Sample Tube Diameter (in) Sample Mass (g) Free Space - Empty (cm3) Free Space - Sample (cm3) Volume Displaced (cm3) Calculated Density (g/cm3) Alumina 3/8 2.0333 10.1624 9.6885 0.4739 4.2906 Alumina 1/2 2.0025 15.0875 14.6123 0.4752 4.2140 Carbon Black 3/8 0.8231 9.0953 8.6962 0.3991 2.0624 Carbon Black 1/2 1.5965 15.8223 14.9907 0.8316 1.9198 Stainless Steel 3/8 7.3422 10.1624 9.2774 0.8850 8.2963 Stainless Steel 1/2 11.3741 15.0875 13.6854 1.4021 8.1122 Tungsten 3/8 15.6931 9.0953 8.3318 0.7635 20.5542 Tungsten 1/2 18.7127 15.8223 14.8641 0.9582 19.5290 Tungsten Carbide 3/8 9.6839 9.0953 8.5079 0.5874 16.4860 Tungsten Carbide 1/2 13.0748 15.1939 14.3654 0.8285 15.7813
Table 2. Summary of density values determined by Micromeritics AccuPyc II vs. free space subtraction method. Source: Micromeritics International Sales
Sample Calculated Density 3/8" (g/cm3) Calculated Density 1/2" (g/cm3) AccuPyc Density (g/cm3) Expected Density (g/cm3) Sample Volume to Cell Volume Alumina¹ 4.2906 4.2140 3.9590 3.95 0.1310 Carbon Black² 2.0624 1.9198 1.8907 1.90 0.1270 Stainless Steel 8.2963 8.1122 7.8592 7.93 0.2507 Tungsten 20.5542 19.5290 19.1721 19.28 0.1881 Tungsten Carbide 16.4860 15.7813 15.6422 15.63 0.1834
Table 3. Ratio of sample to free space volume. Source: Micromeritics International Sales
Sample Sample Tube Diameter (in) Sample Volume (cm3) Free Space Volume (cm3) Sample Volume to Free Space Volume Alumina 3/8 0.4739 10.1624 0.0466 Alumina 1/2 0.4752 15.0875 0.0315 Carbon Black 3/8 0.3991 9.0953 0.0439 Carbon Black 1/2 0.8316 15.8223 0.0526 Stainless Steel 3/8 0.8850 10.1624 0.0871 Stainless Steel 1/2 1.4021 15.0875 0.0929 Tungsten 3/8 0.7635 9.0953 0.0839 Tungsten 1/2 0.9582 15.8223 0.0606 Tungsten Carbide 3/8 0.5874 9.0953 0.0646 Tungsten Carbide 1/2 0.8285 15.1939 0.0545
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 Micromeritics Alumina Reference Material, Lot SA5214-19001A 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.