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.

• I_t =  I₀ exp (-Q_ext * C * L)  where I₀ = incident intensity and I_t  is transmitted intensity
• Q_ext = Extinction efficiency = f(d_p, n_p/n_f, 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 d_p ≤ 5 μm
• Sensitive, but less quantitative for high density materials such as metal oxides where Q_ext 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

ƞ_L = viscosity of the liquid

R_D = radius of the detector

R_I = radius to the meniscus

ρ_p = density of the particle

ρ_L = 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)

Q_ext 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 µ_abs which is the x-ray absorption efficiency instead of Q_ext. It is not a function of particle size or refractive indices. There is no optical correction. Notice that the decay function includes µ_abs. 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.

• I_t = I_o×exp(-µ_abs×c×L)             I_o, I_t = Transmitted, Incident Intensity
• µ_abs = X-ray absorption efficiency ≠ f(d_p, n_p/n_f, 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