Laser Diffraction

Exponential Business and Technologies Company

Bridging You and Nano

Laser Diffraction

Measuring the size of particles in suspended liquids or in dry powder format can be accomplished using particle size analysis based on the light scattering technique. Light refracted by a particle creates a scattering angle unique to its shape and size. The intensity of the scattering light is measured by an array of light detectors at different angles. The Mie Theory is the preferred method used to relate the measured scattering angle to the particle diameter. The Mie theory takes the complex refractive index of the particle into account when measuring the particle size. Nonetheless, in applications involving particles with high light absorption or with sizes significantly larger than the laser wavelength, the Fraunhofer Theory can be used to measure particle size. The Fraunhofer Theory is a simplified form of the Mie Theory; relating the scattering angle to the diameter of the particle and the light wavelength using the following equation:

where θ is the measured scattering angle, λ is the wavelength of the laser light and d is the diameter of the particle. The complex refractive index of the particle required for the Mie Theory is not needed for the Fraunhofer Theory. The light scattering technique has been readily applied to measure particle size and size distribution of particles with sizes ranging from 18nm to 2000µm.

particle size 1 particle size 2

Tornado Dry Particle System (left) and Universal Liquid Module (right) modules

Typical Experimental Results:

$laser diffraction$

Particle size of bottled water based on differential volume (top), surface area (middle) and
number (bottom).

Particle Size of Bottled Water Particles Based on Volume, Surface Area and Number Percentage

Test	Based on Volume %			Based on Surface Area %			Based on Number %
Test	Mean	Median	S.D.	Mean	Median	S.D.	Mean	Median	S.D.
1	2.87	2.82	0.53	2.77	2.71	0.52	2.59	2.52	0.47
2	3.32	3.09	1.06	3.01	2.74	0.96	2.55	2.36	0.72
3	4.27	4.14	1.83	3.49	2.82	1.66	2.49	2.19	0.99
Avg.	3.49	3.35	1.14	3.09	2.76	1.05	2.54	2.36	0.73
S.D.	0.72	0.69	0.65	0.37	0.05	0.57	0.05	0.16	0.26

$laser diffraction$

Particle size distributions based on differential volume (top left), surface area (top right) and number (bottom) for the tested coffee grounds made by Folgers, Starbucks and Dunn Brothers.

Particle Size of Coffee Grounds Based on Volume, Surface Area and Number Percentage

Brand	Based on Volume %			Based on Surface Area %			Based on Number %
Brand	Folgers	Starbucks	Dunn Bros.	Folgers	Starbucks	Dunn Bros.	Folgers	Starbucks	Dunn Bros.
Mean (µm)	748.7	558.3	608.1	365.2	247.3	142.8	21.32	17.04	0.68
Median (µm)	764.3	578.8	583.0	198.1	83.42	34.73	14.33	12.38	0.58
Standard Deviation (µm)	361.0	267.7	410.8	374.3	277.3	257.8	31.74	22.13	1.10

Applications:

Coffee Grounds	Complex Refractive Index	Dry Powder
Effect of Additives	Elastic Light Scattering	Extendable Size Detection Range
Fourier Lens	Fraunhofer Method	Liquid Suspension
Mie Theory	Mixture Purity	Motor Oils
Organic Mixtures	Particle Content	Particle Sizing
Particle Surfactants	Polarization Intensity Diffraction Scattering	Single Wavelength Detection
Soil	Tornado DPS	Universal Liquid Module

For more information please read our application notes.

Instruments: Beckman Coulter LS 13 320 Laser Diffraction Particle Size Analyzer with ULM and Sonication Control Unit connected

particle size 3 Key Specifications:

Particle Size Analysis Range	0.04-2000µm
Modules	Universal Liquid Module (ULM); Tornado Dry Powder System (Tornado DPS)
Analysis Theories	Fraunhofer; Mie
ULM Sample Requirements	Enough for 6-8% obscuration (40% with PIDS)
Tornado DPS Sample Requirements	10-30mL or enough for 10 seconds run time