Definition and Measurement Methods of Particle Size Distribution
Table of Contents
- What is Particle Size Distribution
- Methods for Measuring Particle Size Distribution
- Types of Particle Size Distribution
- How to Display Particle Size Distribution
- Distribution Statistics
- Definitions of Particle Shape and Particle Contour
- Laser Diffraction Particle Size Distribution Device Seminar Video
- Introduction to Particle Size Distribution Meters (LD・DLS)
What is Particle Size Distribution
Particle size distribution is a representation of the distribution of particle sizes, usually displayed as a histogram with particle diameter on the x-axis and frequency on the y-axis.
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Methods for Measuring Particle Size Distribution
The methods for measuring particle size distribution include the following types.
| Technology Name | Overview | Main Advantages | Principle | Measuring Device Components |
|---|---|---|---|---|
| Laser Diffraction Method | Technique for measuring particle size of materials from hundreds of nanometers to several millimeters in diameter | ・Wide dynamic range ・Quick measurement ・Reproducibility ・Instant feedback ・High sample throughput ・No calibration required ・Established technology (ISO13320) | Measures the angle change of scattered light intensity as laser light passes through particles and calculates the particle size distribution using Mie theory | 1. Optical Bench 2. Sample Dispersion Unit 3. Measuring Device Software |
| Dynamic Light Scattering (DLS) | Non-invasive method for measuring sub-nanometer particle sizes and polymer size | ・Ideal for nanomaterials and biomaterials ・Can measure with a small amount of sample ・Fast analysis ・Non-invasive | Particles in suspension undergo Brownian motion, analyzing the intensity fluctuations of scattered light due to laser light to determine particle size | 1. Laser Light Source 2. Scattered Light Detector 3. Digital Correlator |
| Automated Imaging Method | High-resolution method used for characterizing particles with diameters from about 1 micron to several millimeters | ・Measurement of shape differences ・Detection of agglomerates and contaminants ・Can be used with other measurement techniques | Captures individual particle images and analyzes size and shape, constructing statistically significant distributions | 1. Sample Presentation and Dispersion 2. Image Acquisition Optics 3. Data Analysis Software |
| Electrophoretic Light Scattering (ELS) | Methods for measuring electrophoretic mobility of particles or molecules to calculate zeta potential | ・Allows for comparison of materials ・Often combined with DLS and ELS | Charged particles move in an electric field, measuring speed to calculate zeta potential | 1. Electrode Cell 2. Laser Doppler Method 3. Phase Analysis Light Scattering (PALS) |
How to Display Particle Size Distribution
Particle size distribution is displayed as a graph showing the percentage for each particle size, yielding different results based on number basis (quantity) or volume basis (mass). Number basis shows the number of particles, and volume basis shows the particle volume.
When you look at things in detail, it’s rare to find objects of the exact same type that are exactly the same size.
For example, even with a single grain of sand, you may have larger or smaller ones. There are several ways to statistically express this variation in size.
Types of Particle Size Distribution
Expressed by “Distribution Curve”
A graphical representation of the size variation is called a “distribution curve.” The two commonly used types are:
- Frequency Distribution Curve: Indicates how much of a certain size of particles are present
- Accumulation Distribution Curve: Indicates how many particles larger than a certain size are present
Unless the sample being characterized is completely monodisperse (i.e., all particles are of exactly the same size), the statistical distribution of that sample consists of particles of various sizes.
Common methods for expressing this distribution include frequency distribution curves and accumulative (sieve under) distribution curves.
| Types of Weighted Distribution | Definition | Application |
|---|---|---|
| Number Weighted Distribution | A distribution where equal weight is given to each particle using counting methods like image analysis | Useful when knowing the absolute number of particles is important or high resolution is required |
| Volume/Mass Weighted Distribution | A distribution weighted by volume using static light scattering technologies like laser diffraction | Each particle’s contribution is proportional to its volume, relative contribution is proportional to the cube of particle size. It is also useful from a sales perspective |
| Intensity Weighted Distribution | A distribution weighted by light intensity using dynamic light scattering technology | Contribution of each particle depends on the intensity of scattered light, using Rayleigh approximation, very small particles’ relative contribution is proportional to the sixth power of diameter |
Differences in Basis and Data Conversion
The measurement method determines whether the basis is number or volume, and conversion is necessary when comparing data between different bases, especially converting volume basis data by laser diffraction to number basis is not recommended.
While it is possible to transform particle size data from one type of distribution to another, this requires making assumptions about the shape and physical characteristics of the particles.
For example, it should be expected that to measure particle size using image analysis, and volume-weighted size distribution may not exactly match the size distribution measured using laser diffraction.
It is important to note that when comparing particle size data of the same sample measured by different techniques, the size results may differ depending on the type of distribution being measured and reported.
This is clearly demonstrated in the example below using a sample made up of the same number of particles with diameters of 5nm and 50nm. In a number-weighted distribution, equal weight is given to both types of particles, emphasizing the presence of smaller 5nm particles.
On the other hand, in an intensity-weighted distribution, the larger 50nm particles have a signal a million times greater. In a volume-weighted distribution, intermediate data between the two is obtained.
While it is possible to transform particle size data from one type of distribution to another, this requires making assumptions about the shape and physical characteristics of the particles.
For example, it should be expected that to measure particle size using image analysis, and volume-weighted size distribution may not exactly match the size distribution measured using laser diffraction.
Distribution Statistics
“There are three kinds of lies: lies, damn lies, and statistics.” – Twain, Disraeli
Parameters Used in Particle Size Distribution Reports
Various statistical parameters can be calculated and reported to simplify the interpretation of particle size distribution data. Choosing the most appropriate statistical parameter for a sample depends on the purpose of that data and what it is being compared with.
For example, if you want to report the most numerous particle size in a sample being measured, you can choose from the following parameters.
| Index Name | Description | Example |
|---|---|---|
| Average Diameter | “Average” diameter of the population | – |
| Mode Diameter | Particle size with the highest frequency | For data {1, 2, 2, 3, 4}, the mode is 2. |
| Median Diameter | Diameter that divides the sample into two, where 50% of the larger and smaller particles are on either side. | For data {1, 2, 3, 4, 5}, the median is 3. For data {1, 2, 3, 4} it is (2 + 3) / 2 = 2.5. |
| Feret Diameter | A metric for measuring the shape of an object, referring to the longest diameter of an object. Useful for sizing particles or cells. | – |
| Martin Diameter | A metric for evaluating object shape, especially considering the irregularity of particle shape. | – |
If the shape of the particle size distribution is asymmetric, as often seen in many samples, the three values will not all be equal, as demonstrated in the picture below.
Average Diameter
There are many different definitions of averages depending on how the distribution data is collected and analyzed. The three most common definitions used in particle size measurement are as follows.
| Type of Average | Symbol | Description |
|---|---|---|
| Arithmetic Mean | D[1, 0] / Xnl | Definition: Most important when particle counting is the measurement target Application: Calculated when the total number of particles in a sample is known, limited to counting particles |
| Surface Area Moment Mean | D[3, 2] / Xsv | Definition: Relevant when specific surface area is important Application: Considers bioavailability, reactivity, solubility, clearly representing the presence of fine particles in a size distribution |
| Volume Moment Mean | D[4, 3] / Xvm | Definition: Reflects the diameter of particles forming the majority of sample volume Application: Clearly represents the presence of large particles in a size distribution, relevant to many samples |
Examples of the Surface Area Moment Mean and Volume Moment Mean are shown in the particle size distribution below. If the aim is to measure the diameter of coarse particles that make up the majority of the sample, D[4, 3] is most appropriate.
On the other hand, if measuring the percentage of existing fine particles is more significant in practice, using D[3, 2] is more appropriate.
Percentiles
In volume-weighted particle size distributions, often measured by laser diffraction, reporting parameters based on the maximum particle diameter accounting for a given percentage of the sample volume is frequently helpful.
Percentiles are defined as XaB and mean the following.
- X = Parameter, usually representing diameter
- Da = Distribution weighting (e.g., n for number, v for volume, i for intensity)
- B = The percentage of the sample smaller than this particle size (e.g., 50%, sometimes expressed as the decimal 0.5)
For example, Dv50 is the maximum particle diameter for which 50% of the sample volume is smaller, also referred to as the volume median diameter.
As shown in the figures below, Dv10, Dv50, and Dv90 are the most commonly reported percentile values.
By monitoring these three parameters, you can determine if significant changes are occurring in the main particle size or at the distribution’s extremes.
If these occur, it may indicate the presence of fine particles or large particles/agglomerates, as shown in the particle size distribution below.
Definitions of Particle Shape and Particle Contour
Since particles are complex three-dimensional objects, it’s necessary to simplify particle descriptions to perform measurements and data analysis similarly to particle size measurement.
Measurement of particle shape is most commonly carried out using image processing methods. In this case, the collected data is a two-dimensional projection of the particle profile. Particle shape parameters can be calculated from this two-dimensional projection using simple geometric calculations.
Particle Shape
The overall shape of a particle can be characterized using relatively simple parameters like the aspect ratio. Using the images of particles below as an example, the aspect ratio can be simply defined as follows:
Aspect Ratio = Width / Length
Particle Contour
Particle contours provide information on characteristics such as surface roughness, in addition to detecting agglomerated particles. To calculate particle contour parameters, a concept called convex perimeter is used.
Once the convex perimeter is obtained, parameters like envelope and solidity can be defined based on it. These parameters are calculated as follows:
- Envelope = Convex Perimeter / Actual Perimeter
- Solidity = Area Wrapped by Actual Perimeter / Area Wrapped by Convex Perimeter
Particles with very smooth contours have Convexity / Solidity values close to 1, while particles with rough contours or aggregated primary particles have Convexity / Solidity values lower than that.
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For Those Who Want More Details About Particle Size Distribution
This article is a summary of our popular white paper “Basic Guide to Particle Characterization”, ranking high in our blog’s downloadable materials ranking.
Contents of the Basic Guide
- Introduction 3
What is a Particle? 3
Why Measure Particle Characteristics? 3
Which Particle Characteristic Measurement is Important? 4
Particle Characteristics 5
Particle Size 5
Particle Size Distribution 6
Particle Shape 11
Particle Characterization Techniques 14
Which Particle Characterization Technique is Necessary? 14
Sampling 14
Sample Dispersion 15
Technique: Laser Diffraction Particle Size Measurement 17
Technique: Dynamic Light Scattering (DLS) 19
Principle 19
Technique: Automated Image Processing (Particle Image Imaging) 21
Technique: Electrophoretic Light Scattering (ELS) 23
Particle-Related In-characteristics: Rheology 24
References 25
Laser Diffraction Particle Size Distribution Device Seminar Video
An explanatory voice by our company specialist will be included.
It consists of 11 parts, each video lasting a few minutes to a maximum of 15 minutes.
Seminar Content on Particle Measurement
1. Definition of Particle Size Distribution
2. Measurement Accuracy and Device Usage
3. Principle of Laser Diffraction and Scattering Method
4. Configuration of Laser Diffraction and Scattering Devices (Mastersizer 3000)
5. Laser Diffraction and Scattering Devices for Spray Use
6. Process Equipment for Particle Size Distribution Measurement
7. Optimization of Measurement Conditions for Laser Diffraction and Scattering
8. Notice When Replacing Laser Diffraction and Scattering Equipment
9. Causes and Countermeasures for Common “Strange Data” in Laser Diffraction and Scattering
10. Summary of Laser Diffraction and Scattering Characteristics
Introduction to Particle Size Distribution Meters
1. Laser Diffraction Scattering Method Mastersizer
The Mastersizer is a particle size measuring device capable of high precision and high reproducibility with rapid data acquisition 10,000 times a second.
The Mastersizer Solves Common Measurement Problems!
Issue 1: Setting and optimizing the method (test method) is challenging
Issue 2: Differences between different models/makers’ devices are troublesome
Issue 3: Experience gap reflects on measurement results
Issue 4: Desire for confidence in measurement results
2. Zeta Potential Measurement Device Zetasizer
The Zetasizer series is a nano-user-friendly analytical device capable of particle size measurement, zeta potential measurement, and molecular weight measurement with a single unit.
The Zetasizer Solves Common Problems with Zeta Potential Measurement!
Problem 1: High salt concentration prevents accurate zeta potential measurement
Problem 2: The particles to be measured are near the performance limit of particle size
Problem 3: Uncertainty about the reliability of obtained results
Problem 4: Resolution limitations
Problem 5: Quick sample changes during measurement aren’t kept up with
Problem 6: Unknown particle concentration
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