What is Dispersion? Developing Methods for Wet Dispersion Optimization – Part 1

Method Development for Wet Dispersion in Laser Diffraction Particle Size Measurement

The ability to obtain reproducible results from a particle characterization technique is determined by three factors: 

• Representative sampling
• Stable state of dispersion
• Appropriate measurement conditions

The importance of each of these factors changes according to the size of particles being measured. For fine particles, dispersants and energy of dispersion are more crucial, while for coarse materials, sampling is more significant.

Figure 1 shows the risk factors associated with the measurement of fine or coarse particles in wet dispersion.

Dispersion 

The method of sample dispersion varies according to what is being measured. If quantifying the size and extent of agglomerates within a sample is vital, it may be necessary to measure under partially dispersed conditions. If the primary particle size is essential, the sample needs to be completely dispersed to break agglomerates. 

Dispersion starts with selecting a suitable dispersant. A dispersant for laser diffraction must meet the following criteria: 

• Maintains good wetting of the sample to enable dispersion 
• Does not dissolve the sample 
• Does not include bubbles 
• Has an appropriate viscosity 
• Passes laser light 
• Has a refractive index different from the sample 
• Is chemically compatible with the material used in the equipment 

Water is the most widely used dispersant. However, water may not be suitable for all samples because it may not wet or dissolve the sample well enough. 

According to a common rule, the solubility of the sample in the dispersant can be minimized by using a dispersant of opposite polarity. Still, the particles need to be wetted, which may be harder without the aid of a surfactant if the polarity difference is significant.

A list of dispersants ordered from high to low polarity is shown in Table 1. 

Dispersant	Polarity
Water/Deionized water	Very High Polarity
Organic acid
Alcohol (Methanol/Ethanol/Isopropyl Alcohol)	Medium
Simple Alkanes (Hexane/Heptane/Iso-Octane/Cyclohexane)
Long Chain Alkanes and Alkenes (Dodecane/Mineral Oil/Sunflower Oil/Palm Oil)	Very Low Polarity

Dispersing Powders in Liquids

There are three basic stages in dispersing powders within a liquid: 

• Wetting the sample
• Adding energy for full dispersion
• Stabilizing the dispersion

Wetting the Sample 

When testing a new material, it is advisable to perform beaker tests with different dispersants to check whether the sample is well-wetted. These visual tests are faster than performing particle size measurements across different dispersants. If the wetting between the particle and dispersant is good, one can confirm homogeneous suspension in the liquid, whereas poor wetting may show visible liquid droplets on the powder surface or cause noticeable agglomeration and sedimentation. 

The degree to which a powder is wetted by a dispersant is governed by the surface tension between particles and liquid. Thus, using a surfactant to reduce surface tension often improves wetting. Table 2 shows examples of steric and electrosteric surfactants that enhance dispersion.

Stabilization	Mechanism	Example
Steric	Adding long-chain molecules that can adsorb onto particle surfaces	Igepal CA-630, Tween 20/80, Span 20/80
Electrosteric	Adding long-chain molecules with charges	Anionic: SDS (Sodium Dodecyl Sulfate), AOT (Sodium bis-2-ethylhexyl sulfosuccinate)
		Cationic: CTAB (Cetrimonium bromide)

When using surfactants, adjusting the concentration is crucial. Generally, a drop or two of surfactant solution (at a few percent w/v, not highly concentrated) will improve wetting. Using too much surfactant may create bubbles or droplets, which can be misinterpreted as large particles.  

Using Energy to Disperse the Sample

After finding a suitable dispersant to wet the sample, assessing the dispersion state of the sample with the equipment is required. This procedure, termed a dispersion titration, typically encompasses three stages: 

1. A series of repeated measurements to assess the effect of sample titration
2. A series of measurements to evaluate the effect of ultrasound on the sample
3. A series of repeated measurements to evaluate the stability of measurements after ultrasound

Figure 2 shows an example of dispersion titration in water. Stage 1 shows gradual dispersion according to the stirrer speed, stage 2 illustrates accelerated dispersion when ultrasound is used, and stage 3 demonstrates stable particle size after ultrasound turns off. 

Dispersion titration displays the evolution in size distribution as agglomerates disperse, as illustrated in Figure 3. As the sample disperses, obscuration (related to the particle concentration in the system) increases because each agglomerate deconstructs into several primary particles as shown in Figure 4. 

For measurements in organic solvents, ultrasound must be applied incrementally, for instance applying it for a minute before measurements, then allowing some time for the dispersant’s temperature to stabilize.  

Otherwise, temperature gradients in the dispersant might cause erroneous peaks at large particle sizes. This process must be repeated until no further size increase due to ultrasound is observed. 

Dispersion titration allows measurement of the ultrasonic power and time required to disperse a sample to its primary particle size. If the overall dispersion titration is uniform and no further reduction in particle size is observed during ultrasonication, it may be that the sample is already fully dispersed without the use of ultrasound. 

Conversely, if a persistent decrease in particle size is observed, such that stable particle size without ultrasound is not reached, primary particles may be breaking down due to ultrasonication. 

If possible, verify the state of the dispersed sample by extracting it from the dispenser and examining it through a microscope or automated static image particle analysis equipment. Observations before and after ultrasonication can reveal if agglomerates are dispersed or if particles changed shape due to breakage. 

Stabilizing the Dispersion 

In the third stage, particle size must remain stable. Expectation for repeatability in laser diffraction measurements is addressed in the section on measurement precision. If particle size begins to increase due to re-agglomeration, additives may be necessary to stabilize the dispersion. 

Additives like sodium hexametaphosphate, ammonium citrate, and sodium pyrophosphate might help stabilize the suspension by adding charge to particle surfaces. Typically, additives are used at concentrations below 1w/v%. 

Emulsion Dispersion

Two key factors often aid in the dispersion of emulsions. 

First, the ideal dispersant includes the same surfactant and stabilizer used in sample dispersion. 

Second, pre-dispersion might be necessary to ensure stable dispersion, as adding samples directly to a tank could cause coagulation due to dissolution shock. 

Ultrasound should be avoided in emulsions as it could enhance emulsification and reduce the representativeness of sample results. 

 Additionally, controlling the stirrer speed in the dispersant device is crucial since excessive stirring speed could break droplets. The effect of stirrer speed is covered in the measurement condition section.  

Sampling

For all particle characterisation techniques, it is essential that the sample introduced into the instrument is representative of the bulk material. For coarse materials or samples with a broad particle size distribution, sampling can be the largest source of measurement error.

To obtain representative results, a sufficient number of particles must be measured. For example, more than 400 particles must be measured to determine the Dv90 with a standard error of less than 5%.

For a material with a Dv90 of 500 µm, approximately 0.5 g of sample is required to achieve this level of precision. As particle size increases, a larger sample mass is needed to ensure that a sufficient number of particles are included in the measurement. Consequently, the minimum sample mass required to obtain reproducible results also increases.

Figure 5 shows the minimum sample mass required to achieve a 5% standard error as a function of particle size. Measuring multiple subsamples and evaluating the variability of the results can help determine whether the sample mass and sampling procedure are adequate to provide representative measurements.

Read next: What is Dispersion? Developing Methods for Wet Dispersion Optimization – Part 2