Article 19 of 100 - Particle size analysis - working principle and real time applications

Authors: Muthu Pannirselvam, Mike Allan, Frank Antolasic and Robert Shanks

Particle size distribution

Particle size distribution is measuring Population of particles in a given sample, so to speak. This is expressed as frequency distribution curves or cumulative curves. Most of the laser diffraction based instrument measures volume distribution. Most of the particle size analyser (that use laser diffraction) uses the volume of the particle to measure its size.

Mie theory vs Fraunhofer theory

Mie theory assumes that the particles measured are perfect spheres. Most of the samples that we often analyse are not spherical (irregular in shape). Sphere is the only shape that can be described by one number (as there is no confusion of terms like edge or diagonal). Most of the analyser uses the volume of the particle to measure its size. This allows better results over a large size range. Recent instruments use Mie theory where as the traditional (in the past) instrument rely on Fraunhofer theory. Fraunhofer theory assumes that particle is opaque and transmits no light, all sizes of particle scatter with equal efficiencies and the particle is much larger than the wavelength of light used.

For references and other practical applications, particle size of a population of particles are denoted by a single number. The following terms are the basics to know (handy to analyse data)

• mode - most frequently occurring size in the sample (has no practical significance as a measure of central tendency, hardly used in real world applications)
• median - cumulative distribution as the 50 % size (this size divides the distribution into two equal parts). It is often used to describe in real world applications. 

• Dv50 = Mass median diameter or median of the volume distribution (size in microns at which 50 % of the sample is smaller and 50 % is larger)
• Dv10 = size of particle below which 10 % of the sample lies
• Dv 90 = size of particle below which 90 % of the sample lies 
• D[4,3] = Volume weighted mean or Mass moment mean diameter, also known as the De Broucker mean
• D[3,2] = Surface weighted mean or Sauter mean 
• Obscuration = measure of the amount of laser light lose due to the introduction of the sample into the analyser beam (ideal range is between 3 and 20 %, depending on the wet or dry dispersion unit and the sample analysed)
• Refractive index = value relates to the speed of laser (light) within the material, that allows the degree of refraction (bending of light) when light passes from one medium to another.Refractive indices of both dispersant and sample to be analysed are required. If you are analysing particle size of flyash by dispersing in water, then the following numbers are required for testing: Refractive index of water (1.33), Refractive index of flyash (1.73)
• Absorption index = an imaginary number that describes the amount of absorption that takes place as the light enter the particle.
• Cumulative distribution (F) is the integral of the frequency distribution (dF/dx)

Fs = cumulative distribution by surface

FM = cumulative distribution by mass (Note: mass distribution is the same as volume distribution)

Example to understand volume distribution: For example, if the volume distribution indicates that 20 % of the distribution is in the size category 10 to 20 microns (micro metre), this means that the volume of all particles with diameter in this range represents 20 % of the total volume of all particles. 

Particle size analysis - choosing the technique (wet or dry) - based on the end use of the sample

If the sample is to be used or stored in a dry form, a dry analysis may be preferred. 

Factors to consider (dry analysis)

1. Does the sample react with all wet dispersants (dissolve or swell or agglomerate in contact with liquid)?

2. Does the sample flows freely ? 

3. Does the sample sticky or clump together ?

4. Is the sample organic or inorganic ? If the user try to remove the moisture from the organic sample, then be conscious of the temperature the user choose on the oven ? Some organic contents breaks or degrades above a certain temperature ? Note the melting temperatures of those samples before drying the samples in an oven. 

5. Some samples are hygroscopic (that absorbs moisture). Choose a desiccator rather than an oven for those hygroscopic samples. 

Factors to consider (wet analysis)

• Most of the samples can be analysed by using water (as a dispersant)
• Water, Isopropyl alcohol, ethanol are some of the common solvents that have refractive index of 1.33, 1.36 and 1.39 respectively. Isopropyl alcohol and ethanol are commonly used solvents in a general dry or chemical labs (disinfectant to wipe off the lab benches). Choose grade of solvent based on the instrument specifications. Hexane, Acetone, Butanone are some other dispersants that could be used as dispersant (if the sample float on the surface of the dispersant)

Factors to consider in choosing a suitable dispersant

• safest, lowest cost and effective dispersant is water :) 
• Choose the selected dispersant in a glass beaker and visually observe (if the sample dissolve or disperse in the dispersant chosen. 

• Dispersant should not contain impurities or particles (check the instrument specifications for the smallest particle size allowable in water - 0.22 to 1 micron)
• Bubbles in water line or cells could be challenging as bubbles would affect the results

• if dispersant was volatile or strong solvent, then complete risk assessments (identify hazards) not only for handling but to dispose the dispersant(s) after analysis (ethanol, hexane, acetone, butanone cannot be disposed into the sink used for general purposes)

Admixtures 

• Sodium hexametaphosphate, sodium pyrophosphate, trisodium phosphate, ammonia are some of the common admixtures that can be used if the sample (powder) floats on the surface of the dispersant. 

• Admixtures aids the particle surface to become charged causing particles to repel each other.
• Admixtures are added in the range of 1 gram per litre

Surfactants

• Surfactants are other types of additives that can be used if the sample floats on the surface of the dispersant. 
• Surfactants will lower the surface tension and will promote wetting of the particles
• Surfactants are often added in minor quantities (1 mL per litre). 

Ultrasonics 

• Sonication can be applied to improve dispersion but it is not always required (check with the instrument supplier and also note the sample

Common problems that arise due to poor sample preparation or selection of poor dispersant or poor technique

1. sample dissolves, sample floats, sample agglomerates (clumps), sample sinks, sample swells

2. impurities in the dispersant 

3. bubbles (air)

4. condensation on the cell windows, bubbles on the cell windows

Beer-Lambert's law (can be used to calculate concentration of the sample

Other points to consider

• identify hazards and minimise risks around the samples and dispersants used during testing
• solvent capability for sample dispersion units including tubings and hoses connected to instrument
• do your own research via literature review and check with your instrument supplier for more details.
• few grams or milligrams of sample is used from a bulk volume of tonnes of materials (from a silo or hopper or container) - take all precautionary measures with sample preparation
• Zetasizer nanosizer and ALV fast Dynamic light scattering techniques used for samples in the range of 1 nm to 1000 nm. RMIT University have facilities that have potential to measure particle size ranging from 1 nm (approximately) to 3.5 mm (3500 micro m).

Feel free to contact me at [email protected] if you find any factual errors. Thanks.