The X-ray Disc Centrifuge – A Unique Particle Sizing Technique

Summary

Disc centrifuges fractionate particles according to both size and density, making them ideal for high-resolution particle sizing. X-Ray based detection further simplifies the process of calculating a particle size distribution from a centrifugation-based instrument, eliminating optical corrections and approximations.  This has been shown to be especially relevant for metal particles and metal oxide, which have a wide array of industrial uses, and yet are poorly suited for characterization with traditional light scattering.

Introduction

Disc centrifuges exploit the tendency of particles to sediment according to both size and density, which is a form of fractionation, resulting in high-resolution particle sizing. The Disc Centrifuge Photosedimentometer (BI-DCP) and X-ray Disc Centrifuge (BI-XDC) are two unique technologies that offer high resolution particle sizing capability based on this principle.  In both cases the difference in hydrodynamics between particles of different sizes drives separation, while detection based on the Lambert Beer Law allows for quantification of amount (by volume, mass, number for example). For the BI-DCP, this quantification is based on optical turbidity, whereas for the BI-XDC, detection is based on attenuation of X-rays by the particles as they pass in front of the detector.  Particles in suspension pass the detector, where the rate of sedimentation is based on a known set of parameters including particle density, the density and viscosity of the fluid which the particles are moving through (the spin fluid), centrifugal forces exerted on the particles and the distance the particles must travel through the spin fluid to reach the detector.

Compared to other sizing technologies based on light scattering, centrifugation has no real bias such as angular dependence and can be performed at much higher concentrations. While a light source is used, these techniques are based on the measurement of the time it takes to spin the material through the spin fluid.  It is a rugged technique for which the theory is well developed.   A detailed explanation of theory and principles is contained in the appendices.

In this discussion we present three metal oxide sample data using X-ray disc centrifuge technique.

  • Zinc Oxide ZnO
  • Ferric Oxide Fe(III)2O3
  • Titanium Dioxide TiO2

In order to determine the most useful measurement technique for each material class we compare three industrially useful metal oxides.  These are:  Zinc Oxide, Ferric Oxide, and Titanium Dioxide.  Each are sold under a wide variety of different tradenames and can be prepared by numerous methods.  In each case submicron particles are formed. In addition to centrifuges date, results using DLS, a common method for submicron particle sizing, are also presented.

However, two characteristics of these materials make this (DLS) technique less suitable. One is high density which results in rapid gravitational sedimentation.  Two is high turbidity and for some materials  border on chalky or nearly opaque appearances except at very low concentrations, which makes this property less suitable for DLS.   Metal oxides are common components of paints and other pigment containing formulations and this turbidity is often unavoidable.  Titanium- and Zinc- oxides are commonly used as colorants or opacifiers in a number of common formulations types: personal care formulations such as sunscreens lotions; toothpastes; and creams; industrial formulations such as commercial paints and pigments. In this case their ability to scatter or otherwise attenuate visible light is a desired property used to modify the appearance of a product. Both metal oxides also attenuate ultraviolet light to a degree, which can be exploited to resist UV degradation of paints, or more directly to confer UV resistance to lotions and creams, as with sunscreens. Recent evidence suggests that TiO2 micro- and nanoparticles may have greater toxicity than ZnO, requiring substitution of zinc oxide for titanium oxide, in many products such as sunscreens.

In contrast ferric oxides are mainly of interest as base materials for production of other materials, although they can also be used directly for pigments.  While the source iron particles are crystalline in nature, they can adopt a wide variety of properties when incorporated into steel and iron. In most Industrial applications, characterization of the size of primary particles will be necessary to ensure desired material properties in the final alloy.

Results

The three metal oxides that will be compared are TiO2, ZnO, Fe2O3.  TiO2 and ZnO were prepared at concentrations of 2% (w/v) in 0.1% (w/v) tetrasodium pyrophosphate (TSPP), whereas Fe2O3 was dispersed in 0.1% Triton X-100 (TX100), a commercial nonionic surfactant.

image of disc centrifuge sedimentometry x-ray charts
The three metal oxides being compared are TiO2 , ZnO, Fe2O3. In each case XDC results (dashed red line) are compared with volume weighted distributions from DLS (solid black line)

Discussion

In each case DLS overestimates the mean particle size relative to XDC.  In order to make a more direct comparison, DLS results were transformed from Intensity Weighted- to Volume Weighted- distributions.  Light scattering is intrinsically intensity biased, and thus tends to overrepresent larger particles or aggregates.  The DLS particle size distribution for Fe2O3 is heavily influenced by the presence of what appear to be several very large, optically resolvable, particles.  As a result, the distribution is heavily skewed towards larger sizes, whereas it appears that the BI-XDC is capable of effectively resolving the two populations. This is seen to a much smaller extent with ZnO, in which a second population causes an otherwise broad distribution to appear bimodal.

Conclusions

Titanium and zinc oxides both appear oversized in DLS. Iron oxide appears dramatically oversized by DLS, suggesting that aggregated particles might comprise the majority of the signal obtained from light scattering.  This bias is overcome easily with the BI-XDC.  Unlike methods based on measuring scattered light, X-Ray detection has no bias towards larger sizes.  Because centrifugation exploits physical separation of differently sized particles, it is also capable of much greater resolution.

Appendix 1: BI-DCP, Disc Centrifuge Photosedimentometer

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:

image of particle diameter equation

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

Where:

disc centrifuge x-ray sedimentometry illustration

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.

Appendix 2: BI-XDC, X-Ray disc centrifuge

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
Applications: Sizing
Instruments: BI-XDCBI-DCP