How Do You Know The Real Size Of Your Nano Particles?

Analytik Ltd

Differential centrifugal sedimentation (DCS) is a novel and innovative, yet simple technique, which has become 'reborn' in recent years. Previous limitations and difficulties with the technique of sedimentation have been overcome using recent advances in technology, and some smart thinking regards instrumentation and disc design, and DCS is now a powerful tool in measuring nano particle size distributions down to around 3nm.

With the unique ability to resolve very close multi-modal particle distributions, and to distinguish extremely small shifts and changes in particle size, DCS is once more gaining in popularity.

The practical range of the technique is from around 3nm right up to 80 micron (exact range will be dependant on density) , however the real benefits over and above more traditional so-called nano particle sizing techniques are generally noticed below around 300nm.

These days, DCS has become fast, very simple to use, is highly accurate and reproducible, can measure up to 40 samples on the same 'run', does 'speed ramping' for measurement of broad distributions, and can even measure 'buoyant' or 'neutral density' particles, i.e. particles having a lower density to the medium in which they are dispersed.

Applications for DCS
There are a wide range of applications for which this technique can be applied, here are just a few of the more typical:

Pharmaceutical and Biological:

  • Virus and virus-like particles. A mixture of single adenovirus particles and multiple aggregations of the same adenovirus particles (fig 1.) can be easily resolved as can be seen below.

Virus and virus-like particles

The second set of data (fig 2.) shows samples taken at various stages during the adenovirus purification process.

Virus and virus-like particles

Fig 2.

  • Cells and cell fragments (culture)
  • Protein clusters
  • Liposomes
  • Micro encapsulated drugs


Polymer latexes and emulsions. A mixed dispersion of different sizes of polystyrene beads are resolved in Fig 3.

Polymer latexes and emulsions

  • Fillers (CaCO3, clay, barites, etc.)
  • SiO2 dispersions
  • Abrasives (of all types)
  • Impact modifier particles
  • Oil emulsions

Printing and painting:

  • Pigments - water and oil based.
  • Micro-fiber paint viscosity modifiers
  • Printer/copier toner powders
  • Inkjet inks
  • Carbon black
  • Magnetic iron oxide

Theory of Differential Sedimentation
Sedimentation of particles in a fluid has long been used to characterise particle size distribution. Stokes' law is used to determine an unknown distribution of spherical particle sizes by measuring the time required for the particles to settle a known distance in a fluid of known viscosity and density. Sedimentation can be either gravitational (1 g-force), or centrifugal (many g-force).

For a centrifuge running at constant speed and temperature, all of the parameters in the equation except time are constant during an analysis. The values for these are either well known or can be accurately measured.

Within a broad range of analysis conditions, a modified form of Stokes' law accurately measures the diameter of spherical particles based on their arrival time at the detector. Hence by introducing a known, traceable standard, the time scale can be calibrated to particle size.

V = D² (pP - pF) G / 18 n

D the particle diameter (cm)
pP particle density (g/ml)
pF the fluid density (g/ml)
G the gravitational acceleration (cm/sec2)
n the fluid viscosity (poise)

DCS Instrument Design
The most common design for DCS instruments is a hollow, optically clear disc that is driven by a variable speed motor. A typical disc cross section is shown in Fig 4. The disc can be of virtually any size, but manufacturers have settled on a diameter of approximately 125 to 150 mm.

The detector beam is usually monochromatic light of relatively short wavelength (400 nm - 500 nm); though some instruments use a longer wavelength (~650 nm), or X-rays. Shorter wavelength light gives better detector sensitivity when particles smaller than 100 nm are measured.

DCS Instrument Design

To prepare the instrument for analysis, the disc is set in motion at constant speed, and then the disc chamber is filled with a fluid which contains a slight density gradient. Samples are prepared for analysis by dilution in a fluid of slightly lower density than the least dense fluid in the disc.

The lower density fluid used for the sample reduces initial mixing of the fluid inside the disc with the sample. When a sample is injected (normally around 100 using a small syringe), it strikes the back inside face of the disc, and forms a thin film, which spreads as it accelerates radially toward the surface of the fluid.

When the sample dispersion reaches the fluid surface, it quickly spreads over the surface, because it is of lower density (it "floats" on the higher density fluid). Once a sample is on the fluid surface, sedimentation of individual particles begins. The injection of a sample is rapid (typically <50ms), so the starting time for an analysis is well defined, and the precision of sedimentation time is very good. When an analysis is complete, the instrument is ready for the next sample.

There is no need to empty and clean the centrifuge, so many samples can be run in sequence without stopping the centrifuge. Advances in modern instrument design have enabled compact, desktop, disc centrifuges capable of 24,000rpm and in the future up to 30,000rpm. This enables very short analysis times for even very small nano particles, for example, the earlier adenovirus data was measured in less than 10 minutes for each sample.

Special discs and techniques are now available to enable ramping of a disc centrifuges speed during an analysis. This is useful if, for example, a sample contains some relatively large particles as well as nano particles and both need to be measured. An initial slow centrifuge speed can be set to initially measure the larger particles. The speed is then ramped up to the maximum so that the nano particles can still be measured within a reasonable timeframe.

Discs have also been developed that now easily enable other, previously very difficult analysis. For example, where particles have a lower density than the medium in which they are dispersed, they have a tendency to float rather than sediment. Special low density discs, combined with reversal of the detector position, can now enable these type of samples to be measured with ease.

Figure 5 shows a centrifuge disc inside an instrument and the light source-detector towards the outside of the disc. Figure 6 shows the same disc in rotation during an analysis, the separated bands of differently sized particles can clearly be seen as they approach the detector towards the outside of the disc.

centrifuge disc inside an instrument and the light source-detector

Firstly an appropriate density gradient is built inside the already rotating centrifuge disc. The minimum density of the gradient should be slightly higher than the density of the liquid in which the sample is dispersed, and the maximum density should be no greater than the particles to be measured. Other than these conditions, the gradient can be constructed to provide optimum conditions depending on the degree of separation and resolution required, and speed of analysis. Gradient liquid used must be compatible with the liquid in which the sample is dispersed.

The most common and simple gradient to construct would be of sucrose solution, if the sample is in a buffer then a sucrose solution made up in the same buffer would be most appropriate. Organic solvents, mineral and vegetable oils can also be used in the case of non-aqueous sample systems. The gradient can be built using an automatic density gradient builder or can be done in steps manually, in the latter case a few minutes are required to allow the gradient to stabilize and become linear.

Next, a calibration standard of known size and density (eg. NIST traceable mono-dispersed polystyrene beads) is then injected to calibrate the time axis to particle size. The system is now ready for sample injections! Normally around 100 of each sample is injected, and to counteract any effects of increasing volume in the disc, it may be considered appropriate to inject a standard before each sample. Up to 40X 100 injections can normally be made before the disc becomes full and the whole process needs to be repeated with a new gradient. Autosamplers, similar to those used for liquid chromatography, can also be incorporated with a DCS system.

Density gradients can be stable for anything up to 72 hours, hence very often an instrument can be set up and calibrated at the beginning of a working day and left running the whole day, calibration standards and samples being injected as and when required. It is important to note how quiet a modern DCS instrument can be, despite operating at speeds of up to 24,000rpm!

In summary, typical routine operation of a DCS system is simply:
1. Set the centrifuge at the correct speed, based on particle size and particle density. (usually by retrieving an existing preset methodology from the software)
2. Fill the centrifuge chamber with appropriate density gradient fluid.
3. Calibrate the instrument by running a calibration standard.
4. Run samples.

Typical, modern, bench top DCS instrumentation can be very compact indeed, see figure 7

Typical, modern, bench top DCS instrumentation can be very compact indeed

The Future
Instruments will eventually be able to run at up to 30,000rpm, thus improving the speed of existing analysis even further, and also slightly extending the lower particle size limit.

Introduction to Differential Sedimentation - An Overall Conclusion
Differential Centrifugal Sedimentation is an extremely powerful tool for high resolution particle characterisation, especially in the size range 0.003 micron (3nm) to 10 micron. It enables very narrow distributions of particles differing in size by less than 2% to be resolved, and hence extremely small differences, changes or shifts in particle size to be accurately and reproducibly detected and measured.

The new method mentioned in this article for measurement of low density, neutral buoyancy particles, addresses the only previous technical limitation of DCS. Advances in recent instrumentation, have also overcome previous issues with the technique with respect to ease of use, speed of analysis, accuracy and multiple sample measurement.

The DCS instrumentation used for this article was a CPS Disc Centrifuge model DC24000. More information regarding this particular instrumentation can be found at and

Article by:
Ian Laidlaw, Managing Director of Analytik Ltd, Unit 4 The Acorn Centre, Chestnut Avenue, Biggleswade, Bedfordshire, SG18 0RA, Tel: 0870 991 4044, Fax: 0870 135 2488, Web: , Email: [email protected]

1. Stokes G.G. Mathematical and Physical Papers
2. Allen T. Particle Size Measurement, P120 (Chapman and Hall, London)
3. Fitzpatrick S.T. U.S. Patent 5,786,898, July 28, 1998
4. Fitzpatrick S.T. Various Particle Size Measurement Papers

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