• Sep 22, 2022
• Particle Size
• By PTL

# Much Ado About Density: An Overview of Density for Solid Materials

Understanding the differences in density types is key to requesting the most appropriate analysis for your sample type and needs. This blog will explain some of the different density analyses for solids offered by PTL.

All density types are measures of mass divided by volume or D = m/v. Most commonly, mass is expressed in grams and volume is in cm3, though the SI unit for density is kg/m3. While weighing a body of solid sample on earth is relatively simple, what counts as sample volume might be more complicated than you think! This is especially true when the sample is porous and/or granular. It is the difference in how the sample volume is defined that gives rise to various types of density values.

### Bulk and Tapped Density

Likely, the type of density you will already be familiar with is bulk density. One of the ways to determine this density is by filling a graduated cylinder with granular material that has passed through a sieve and funnel to allow it to gently accumulate with minimal compaction. The difference between the mass of the graduated cylinder after and before filling is the sample mass. The volume you read on the graduated cylinder includes the volume of the solid granules, any void space within them (intraparticle void), and also any void space between them (interparticle void). The sample mass and volume are recorded; these values are divided to calculate density. If you need to fill the material into a container, knowing its bulk density could help.

Tapped density analysis begins with filling a graduated cylinder as described above for bulk density. This cylinder in then transferred to an instrument that “taps” the cylinder at a set drop height and taps per minute. The particles in the filled cylinder move and compact as much as possible, reducing the interparticle void space. This tapping procedure (following USP<616>) is repeated until a constant volume is achieved. Tapped density is calculated by the mass of sample divided by volume after tapping. Let’s say you are transporting your material by a rail car, the tapped density would be more representative of the sample properties at the end of the journey.

Bulk and Tapped density are both useful measurements that convey a powdered sample’s physical characteristics. Carr Index (CI) and Hausner ratio, both functions of bulk and tap density values, can give a general idea of a powder’s flow properties. The greater the difference between a sample’s bulk and tapped densities, the higher that material’s Hausner Ratio and CI will be. Higher Hausner Ratios and CI values equate to poorer flow characteristics, and vice versa. Read more about flowability in “Say Cheese … a Snapshot of Flowability in Cheese” by PTL’s Director of Analytical Services.

### True Density

We’ve pictured visually the differences between bulk and tapped density. But what about the rest of the spaces between those particles? How do we measure the volume and subsequent density of a powder if we want to account for all those spaces in between the particles, or any crevices in those particles? This is where true density comes into play. A gas pycnometer is used to flood a filled sample cup with helium or nitrogen gas. Given its size and inert nature, the gas is capable of filling the tiniest of space between particles as well as any irregularities, cracks, crevices, and pores of the sample in the cup. The volume of the empty cup is known; the volume of gas that can fit in the empty space is measured; the difference between these volumes is the volume of the solid sample filling the cup. Typically, a series of 10 volume determinations are made on a sample, then the density is calculated from the input mass and the average measured volume. A change in true density could indicate presence of an impurity in the material.

### Envelope and Particle Density

For some applications, you might want to know the volume of the solid sample along with its internal pores. Envision an irregular or porous block of material, then imagine encasing that block in shrink wrap. The volume encased within the shrink wrap would be the particle’s envelope density. For a material that is at least 2 mm in size, the envelope density can be determined using free-flowing powder in a container with a calibrated volume and some applied pressure.

For a granular material, the envelope density is also referred to as particle density. Determination of the particle density is usually not trivial, especially if the particle size distribution is broad.

### Density Determination Through Mercury Intrusion

Mercury intrusion porosimetry (MIP) analysis is one approach that can provide several density outputs. With this technique, an apparatus with a calibrated volume, called the penetrometer, is partially filled with the sample. Liquid mercury is introduced to the penetrometer at low pressures, where it simply envelopes the sample. The difference between the volume of mercury needed to fill the penetrometer with and without the sample indicates the bulk volume of the sample; the bulk density is reported using the input sample mass and bulk volume of the sample. The instrument then applies increasing pressure to the system, forcing mercury into any space that it can enter in the sample. Smaller void requires higher pressures to fill. For granular samples, the interparticle voids tends to be filled first, followed by internal pores. At the highest applied pressure, the skeletal or apparent density is reported. This density is similar in concept to the true density discussed earlier, though there may be some pores that helium can access that mercury simply could not. We should note that the density values can be calculated at any pressure point in the MIP analysis. For materials with very narrow particle size and pore size distributions, one MIP analysis could very well provide the bulk density, particle density, as well as apparent density. You can read more about the MIP technique in our blog post from March 2021.

The above-mentioned density types and methods of determination are certainly not an exhaustive list. Experts at Particle Technology Labs are always happy to help you determine the most suitable density analyses for your needs. Contact us today!

## Mercury Intrusion Porosimetry

Mercury intrusion porosimetry (MIP) is a powerful technique utilized for the evaluation of porosity, pore size distribution, and pore volume (among others) to characterize a wide variety of solid and powder materials. The instrument, known as a porosimeter, employs a pressurized chamber to force mercury to intrude into the voids in a porous substrate. As pressure is applied, mercury fills the larger pores first. As pressure increases, the filling proceeds...