Significance of Density of Powders: Bulk Density vs. True Particle Density

What is the density of material?

Density of powders - Size, Shape, Packing of Particles

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Before we start talking specifically about measuring the density of powders, let’s look at the concept of measuring density in general.

What does “density” mean?

According to Encyclopedia Britannica, density is defined as mass of a unit volume of a material substance. The formula for density of a substance is d=m/V, where d is density of material, m is mass, and V is volume it occupies.

Density measurement is commonly expressed in units of grams per cubic centimeter (g/cc) or (g/cm3) or grams per milliliter (g/ml). However, sometimes it is reported as kilograms per cubic meter (kg/m3) or kilograms per liter (kg/L).

Density varies with temperature and pressure which need to be specified if the density value must be known with high precision. Presence of impurities in the same volume, such as salinity of water, will also affect density.

How do we measure density?

Because density is a derived property which is defined based on the relationship of two other attributes of the material, weight and volume, it is usually not measured directly. It is calculated, or derived. It relies on us having a reliable accurate and precise measurement of the weight of material and the corresponding volume.

The task of doing these measurements and the calculation seems easy enough. We just need a precise scale and a good way to measure volume. What’s the catch?

The challenges in measuring density:

Measuring Density of Non-homogenouse Materials

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The catch comes from the fact that for many materials it is very difficult, if not currently impossible, to measure the weight and the volume precisely enough to enable us to divide the two measurements and calculate the density with sufficient accuracy and reliability required for the project.  

In addition, we are making several critical assumptions when measuring density.

Assumptions:

  1. We are assuming that the material is homogeneous throughout, all parts of it have the same density. For example, we are assuming that no air pockets or absorbed moisture is present on the surface or on the inside of the material. Very few materials in the world are that pure, consistent, and uniform throughout.
  2. We are assuming that the material that is made up of parts or components has perfect packing, with the components fitting perfectly together. This is definitely not true for powders and any situation where more than one part is measured simultaneously.
  3. We are assuming that there is no particle-to-particle variability. That might mean that every grain of salt or every peppercorn in our sample is identical in their density to every other.

These assumptions are justifiable in most cases, and may be acceptable when only a rough estimate of density is required. Being aware of these assumptions also helps us to understand the limitations to the accuracy and precision of the density measurement.

What is the difference between accuracy and precision?

Density Precision:

Precision refers to how reliable and consistent is the measurement. Is it repeatable and reproducible? If two different people measure it or use two different machines, how different would the measurement be? What if the same person measured the same sample using the same machine multiple times, how different would the resulting measurements be? How representative is the sample? Would the measurement change if a different sample was collected?

The closer the measurements are to each other, the higher the precision of the measurement.

Density Accuracy:

While precision compares how close the measurements are to each other or how much variation is there between measurements, accuracy refers to how close measurements are to the “true” value. For example, if we measure density to be 1.00g/cc and our measurement is reliable and reproducible, it is precise. But if the actual density of the material is 1.20g/cc, our measurement is not very accurate.

The closer the measurement is to the actual value, the higher the accuracy of the measurement.

How do we know what the actual value is? Often we don’t. Our volume and mass measurements are relying on the calibration levels of our equipment. Calibration of equipment depends on the calibration standards and procedures used. Calibration standards themselves carry a certain level of uncertainty. It is not possible to be conduct a measurement that is infinitely accurate and precise. There is always some degree of error.

What precision of density measurement is required?

Do we need to know the density of material roughly and approximately, just to get a relative idea of how heavy it is, or do we need to know the density precisely with the accuracy of many significant figures because it is a critical variable in the design of our medical device, drug delivery system, particle simulation experiment, isolation of biological cell, or fluid flow visualization experiment?

Density marker beads are an example of precision density microspheres that are used primarily in biotechnlogy industry to create density gradients, which are necessary for the separations and purification of biological cells, viruses and sub-cellular particles. Generally a set of several density marker beads covering a range of densities is used. The gradient is calibrated with beads that float at different heights within the column. When a test sample is added to the column it drops until the point of neutral buoyancy and the density is determined from the calibration chart.

These color-coded precision density particles are critical to separation of the biological cells based on their density, which makes both precision and accuracy of the density of each particle critically important.

Researchers and engineers are constantly pushing chemical manufacturers to develop the materials and measurement techniques that offer higher and higher precision of density of materials. They are also pushing us to manufacture materials with highly precise, accurate, and customizable density.

What is the density of powders?

This is where things start getting complicated. A lot of questions need to be answered. A lot of assumptions about the density of powder need to be made.

Density of powders - Measurements

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Powder is composed of at least thousands, and often millions, billions, trillions, etc. of small particles which might vary widely in their shape, size, and even density.

The challenges with accurately measuring density of powders begin with taking a statistically-significant and representative sample of the powder. Sampling of powders is both an art and a science in itself, for the following reasons:

    • Aggregation: Depending on the size and surface properties, powdered particles like to aggregate and stick together regardless of whether they are physically fused together or just held together by covalent forces.
    • Segregation: Smaller particles like to segregate from the larger particles, falling through the interstitial spaces between larger particles, and eventually collecting on the bottom of the container, creating a powdered mixture that is not homogeneous throughout.
    • Electrostatic charges: Small particles often exhibit strong electrostatic and electrophoretic forces which make them stick to surfaces that are used to transport them, further complicating dealing with the aggregation and segregation challenges described above.
    • Homogeneity: Knowing that it is statistically-improbably for the sample of small particles to be perfectly homogeneous, how do we ensure that all the various particles are accurately represented in our sample?

Because the answers to above questions and assumptions are not always clear, and the variables involved often cannot be perfectly controlled, there are many ways to define the density of powders, depending on what specific question we are trying to answer and what information we are looking for.

Bulk Density of Powders:

Bulk density is defined simply a measurement of mass of material per unit of volume. However, when we are talking about density of powders, bulk density is no longer a meaningful value, because even if the mass of the material is constant, the volume that the powder occupies can vary widely depending on how the powder is packed. Moreover, bulk density of powders can change over time as the powder settles in the container and the volume it occupies becomes smaller while the weight stays the same.

The shape of particles also will affect bulk density as shape affects individual particles’ ability to nest with other particles… Some materials are hygroscopic and will pull water from the atmosphere, which can dramatically change a material’s bulk density. A material’s surface friction or static charge also can affect — although minorly — its bulk density. 1

We can think of bulk density as the average density of a certain volume of the powder in a specific medium at specific conditions.

How is Bulk Density of Powders Measured:

Vibrated (or tapped) bulk density refers to the bulk density of the powder as the container that is filled with the powder is being continuously vibrated or tapped. As they vibrate, the individual particles with move-in closer together and achieve the highest packing efficiency, thus making the powder material denser, resulting in the highest bulk density for this specific powder and creating a reproducible measurement. Vibrated or tapped bulk density is a good approximation for the density of the powder after it got to sit and compress in the container for a significant period of time.

Poured bulk density refers to the bulk density of powder measured as the powdered material is poured into a container. The process of pouring helps to break up or reduce the challenges of aggregation, segregation, and electrostatic charges, and helps to make the powder more homogeneous. Because the pouring process creates a very loose structure of particles, it will produce a measurement of lower bulk density. Poured bulk density is a good approximation for the density of the powder as it is moving through a manufacturing process and getting transported or transferred between containers or processes.

Aerated bulk density is the bulk density of the powder measured as the powder is being aerated. The measurement of aerated bulk density can be important to know for various reasons, including the proper sizing or analysis of pneumatic conveying systems. 1

It is critical to know how the bulk density of the powder was measured in order to make an educated and informed use of the information.

True Particle Density of Powders:

True particle density (also known as skeletal density) represents an inherent physical property of the material and, unlike bulk density of powders, is not dependent on particle size, shape, or the degree of compaction and packing of the powder.  True particle density will not change over time.

Assuming the material has a high degree of homogeneity, the chemical composition of the material can be reliably determined if its true particle density is known. For example, if we are looking at glass microspheres but we don’t know what type of glass it is, we can make an accurate assessment of the composition by measuring the true particle density. Density of SodaLime glass is 2.5g/cc, Borosilicate glass is 2.2g/cc, Barium Titanate glass is above 4g/cc. If we know that the density of Poly(methyl methacrylate) or PMMA is approximately 1.2g/cc, but our acrylic particles measure slightly highly or lower, that is a good indication that we are probably dealing with a copolymer.

Knowing true particle density of particles allows scientists and engineers to accurately model and predict performance of these particles in specific applications.

How is True Particle Density of Powders Measured:

Traditional methods of measurement of volume by Archimedes’ principle of fluid displacement present a challenge in measuring true particle density of powders. The reason for this difficulty lies in the fact that we need an accurate measurement of the true volume that is occupied by the particles themselves, excluding any potential interior voids, cracks, or pores at the surface of particles. Liquids might penetrate into these irregularities in the continuity of the particle, and cause us to generate serious errors in the measurement of apparent volume when density is evaluated by liquid displacement.

For accurate and precise measurement of true particle density it is important that all air pockets, voids and/or pores in the packing of powder or in the surface of material itself are taken into account and subtracted when measuring the volume of the particles (true volume).

NIST-traceable density measurement of microspheres

All spheres from Cospheric LLC have NIST-traceable density measurements

Pycnometers are instruments designed to measure the true volume of solid materials by employing Archimedes’ principle of fluid (gas) displacement and the technique of gas expansion. Preferred gas for measuring true particle densities of powders is helium gas. Due to its small size, the helium gas will penetrate surface down to about one Angstrom, thereby enabling the measurement of powder volumes with great accuracy. The measurement of density by helium displacement often can reveal the presence of impurities and occluded pores which cannot be determined by any other method. 2

All Cospheric microspheres are characterized for true particle density by utilizing our proprietary density measurement technique which relies on NIST-calibrated gas pycnometry and high precision NIST-calibrated scale. To best support our customers’ research needs, every Cospheric product offered for sale is listed on Cospheric website with true particle density as part of product description.

What is Density of Microspheres?

Microspheres are typically defined as spherical particles between 1micron and 1000micron (mm) in diameter. Some microspheres are a naturally occuring byproduct of a chemical process. For example, the process of burning coal in thermal power plants produces fly ash containing ceramic microspheres made largely of alumina and silica. However, most of the microspheres on the global market are manufactured commercially as precision engineered materials with specific properties and functionality in mind. Density of microspheres is one of the critical properties of microspheres that are controlled during the manufacturing process.

Because microspheres are most often used a component of a system, and are mixed in with the other materials, true particle density (as opposed to bulk density) is critical to ensuring that the microspheres will be able to disperse and suspend in the containing media, float to the bottom, or sink to the surface.

Sources:

  1. Lewis, C., Measuring Bulk Density of Granular Materials Continuously In-Process, Powder and Bulk Engineering[][]
  2. Quantachrome Instruments website[]