# Principles of Operation for Disc Centrifuges

Both disc centrifuges separate particles according to size and density, making these methods ideal for high-resolution particle sizing. The Disc Centrifuge Photosedimentometer (DCP) uses visible light for detection, whereas the X-Ray Disc Centrifuge (XDC) uses a compact X-Ray source. Despite different sources of contrast, the two techniques both operate on similar principles. In both cases, planning a disc centrifuge experiment involves selecting an appropriate spin fluid and disc speed to achieve the desired level of separation in a specified runtime.

## Principles of Operation Part 1: The Disc Centrifuge Photosedimentometer (BI-DCP)

Particles scatter and for some, absorb light. A beam of LED light is used, and the following relationships describe the basic principles for the DCP. This analysis relies on a simplified form of light scattering, namely turbidity. Whereas static and dynamic light scattering rely on quantification of scattered light to calculate particle size, turbidity only requires that you be able to measure the light lost due to scattering and/or absorption, essentially via a reduction in transmittance.

• It =  I0 exp (-Qext * C * L)  where I0 = incident intensity and It  is transmitted intensity
• Qext = Extinction efficiency = f(dp, np/nf, λ)
• c = Mass concentration
• L = Path length (width of fluid segment in disc)
• Light is either absorbed or scattered, the sum of which is called extinction.
• Extinction is a strong function of particle size. Significant optical corrections are necessary for dp 5 μm
• Sensitive, but less quantitative for high density materials such as metal oxides where Qext is not easy to calculate accurately.

The key equation for diameter of the particle is:

Note that the relationship between time and particle size squared is inversely proportional.

Where:

t = time

ƞL = viscosity of the liquid

RD = radius of the detector

RI = radius to the meniscus

ρp = density of the particle

ρL = density of the liquid

The final particle size distribution obtained from the BI-DCP depends on hydrodynamics to the extent that this dictates the time required for a band of particles to pass the detector. The optical correction becomes more difficult when materials with complex refractive indices are considered, such as metal and metal oxide particles. These sorts of samples are better suited to X-Ray detection. Higher atomic mass nanomaterials tend to have higher densities, and thus sediment more rapidly. This is common with metal and metal oxide particles.

## Principles of Operation Part 2: The X-Ray disc centrifuge (BI-XDC)

Qext is a strong function of the particle size but it is not easy to calculate accurately for high density particles. The key difference is the use of µabs which is the x-ray absorption efficiency instead of Qext. It is not a function of particle size or refractive indices. There is no optical correction. Notice that the decay function includes µabs. At time 0, there is 100% absorption and therefore no signal. As time progresses and absorption declines the signal is generated and produces a cumulative size distribution.

• It = Io×exp(-µabs×c×L)             Io, It = Transmitted, Incident Intensity
• µabs = X-ray absorption efficiency ≠ f(dp, np/nf, λ)
• c = Mass concentration
• L = Path length (width of fluid segment in disc)

When X-rays are absorbed, they are absorbed in proportion to mass without any dependence on particle size or refractive indices. There is no optical correction. For high density materials with normally high refractive indexes, the mass weighted size distribution is quantitative.

References:

• Weiner, Bruce B., “Let There Be Light: Characterizing Physical Properties of Colloids, Nanoparticles & Proteins Using Light Scattering”, Chapter VII: Sedimentation & Centrifugation. Amazon, May 2019.
• Hodoroaba VD., Unger W., Shard A., “Characterization of Nanoparticles: Measurement Processes for Nanoparticles. Elsevier, Oct 2019
Posted on: Feb 16, 2021

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