Particle Basics

Basics of Particle Characterization

Particle characterization is the process of analyzing particles by particle shape, size, surface properties, charge properties, mechanical properties, microstructure and many more measurement parameters. There is a broad range of commercially available particle characterization techniques that can be used to measure particulate samples.

Size and shape are important attributes that affect the behavior of particulate substances. Spherical beads are easily and commonly characterized by a single size measure: “Diameter”. Irregular shapes are more difficult to characterize given their multi-dimensional structure. Powders used in manufacturing, for example, requires several measurement parameters to ensure flowability, packing and other performance functions.

Particle Size and Particle Shape Analysis are analytical techniques by which the distribution of sizes and shapes in a sample of particulate material is measured and reported. Particle size and particle shape analysis are an important tool in characterizing a wide range of final-product performance for quality control in many different industries, including paints, building materials, pharmaceutical, food industries and toners.

Key Insight: Particle size can be greatly impacted by shape. Spherical particles are adequately characterized by size-only techniques, while irregular particles require additional shape measurements. Learn more about shape impact on size results →

Highly irregular shaped particles are hard to characterize, but for raw material particles in manufacturing, just knowing particle size is not enough. To truly understand particle behavior, it is required to measure more shape parameters and have tools that use these shape parameters to predict performance.

Dynamic image analysis is becoming more popular as a complementary analysis method because end users are beginning to understand the importance of large amounts of data for a large sample population. The first and most basic report of any particle size and particle shape analysis comes in the form of a statistical histogram.

To illustrate the statistical results from sample analysis, results are divided into small classes or “bins,” and the number of particles in each size bin is reported. Size information can be displayed in volume, number, and surface-area weighted histograms, each offering valuable information about the analyzed sample.

Below are particle size histograms. Although they all may look different, these three histograms are of the same sample. Users should always view, at a very minimum, the number weighted distribution as well as the volume weighted distribution.

ECA Diameter — Volume Weighted

ECA Diameter — Number Weighted

Circularity, Smoothness & Aspect Ratio

In some cases, shape measurements are size-independent. These fraction measures range from a value of zero to one. A user could assume that the smoother a particle sample distribution is, the better the particles will flow.

Smoothness Distribution

ECA Diameter — Number Weighted

Number vs. Volume Weighting

Volume-weighted histograms emphasize the presence of larger particles, while number-weighted histograms reveal large quantities of fine particles that may cause clogging or filtration issues. Both views are essential for thorough characterization.

Volume vs. Number Weighted Distributions

Sieve Users: For information on using Dynamic Imaging to replace sieve analysis, see Sieve Correlation Using Dynamic Image Analysis →

A typical statistical result not only gives the graphical histogram, but also reports a large amount of data. Below is a sample of a size-based histogram and associated data.

Equivalent Circular Area Diameter — Histogram & Statistics

A typical size distribution is characterized by different values. One of the most common is the mean size. The number or arithmetic mean is purely the average value, frequently denoted as D1,0. Other means take into account volume weighting and area.

Weighted Dp,q Mean Diameter Formula

Dp,q Means Definitions

D[1,0] — Arithmetic Mean

The average of the diameters of all the particles in the sample.

D[2,0] — Surface Mean

The diameter of a particle whose surface area, if multiplied by the total number of droplets, will equal the total surface area of the sample.

D[3,0] — Volume Mean

The diameter of a particle whose volume, if multiplied by the total number of particles, will equate all of the sample’s volume.

D[3,2] — Sauter Mean

The diameter of a particle whose ratio of volume to surface area is the same as that of the complete sample.

D[4,3] — Volume Moment Mean

An indicator weighted on the volume of particles. Most commonly used by Laser Diffraction instrumentation.

The Mode is the most frequent size present.

The Harmonic Mean is N / Σ (ni / di)

Geometric means reflect the visual weighting of a log-size axis. The geometric mean diameter will appear as the center of a distribution on a log scale, while the usual arithmetic mean may sit a lot lower on the size scale (as smaller sizes are a lot more numerous than larger sizes).

Arithmetic Mean, Geometric Mean & Mode

Geometric Mean = Σ [ni · log(di)] / N

Measures of Spread

Standard deviation measures how wide the distribution is. The Coefficient of Variance is the ratio of the standard deviation to the mean: CV = σ / μ.

Standard Deviation Formula (μ = mean diameter D1,0)

Percentiles are a way of conducting size information as one or more numbers. The Median size splits the particles into two parts containing equal counts — also known as the 50th percentile.

D10

10% of particles are smaller than this size

D50

The median — splits sample into two equal count halves

D90

90% of particles are smaller than this size

The Volume Median, or 50th percentile by volume, splits the volume of the sample into two equal pieces. The two classes will hold equal volume but not an equal count of particles. Additional percentiles are available and customizable in the Insight software to meet the needs of any specific industry requirement.

Skewness & Kurtosis

Skewness

An indicator of how asymmetrical the distribution shape is, about the center. A positive value means further counts on the right side (tail), while a negative value means it tails to the left.

Σ ni(di – μ)³ / (σ³ · N)

Kurtosis

An indicator of how much the shape differs from the typical bell curve in a vertical sense.

[Σ ni(di – μ)⁴ / (σ⁴ · N)] – 3

This article is also available on AZoM.com →