PCS (Photon Correlation Spectroscopy) is a technique for measuring particle size distributions in the range 1 nanometre (nm) - 5 microns (approx.). Many important materials contain particles in this size range, including polymers, paints, inks and pharmaceuticals.

Why do we need another technique?

On another page we have described the use of Laser Light Scattering (LLS) to measure particle size distributions in the micron range (say 1 micron - 1 millimetre). PCS is also based on light scattering, so what's the difference? LLS makes use of the differences in the angular distribution of the light scattered from particles of different sizes. By measuring that distribution we can compute the sizes which gave rise to it. However, for particles smaller than about 1 micron the scattering becomes isotropic (ie. the same at all angles) so another technique is needed.

What is PCS?

When fine particles are suspended in a fluid they are constantly in random motion due to collisions with the molecules of the fluid. This is known as 'Brownian Motion' and was first observed in the 1820's. When the suspension is irradiated by a beam of laser light, some of the light is scattered by the particles (as in LLS). Very fine particles are smaller than the wavelength of light (typically 500 - 700 nm) and, as they move relative to the light beam, the phase of the light scattered from each particle will vary. The intensity of the scattered light, measured at some fixed point, is the sum of the light scattered from all of the individual particles, formed by constructive and destructive interference. This intensity will vary as the particles move and the rate of variation will depend on the speed of movement of the particles, which is in turn related to their size. This is why PCS is also known as 'Dynamic Light Scattering'.

How are the measurements done?

The sample, which is usually in the form of a suspension or emulsion, is diluted with water or some other compatible fluid to low density. Care must be taken in the sample preparation to exclude any large particles or 'dirt'; the intensity of scattering from individual particles varies as the sixth power of the diameter, so even a few large particles will seriously bias the result. The diluted sample, in a small vial, is placed in the laser beam. The temperature must be precisely controlled to prevent convection currents. The intensity of the light scattered at a particular angle (usually 90^o) is measured by a sensitive photomultiplier, with the result being sent to a multichannel correlator. Each channel of the correlator monitors the variation of the photon count over a particular timespan: hence 'Photon Correlation'. Different channels will be assigned to cover timespans from the very short (say 1ms or less) to longer times. At short time delays, the signal will be highly correlated as there will have been little movement of the particles; at longer times the correlation will be reduced, as the particles move, until eventually there is no correlation at all. The output from the correlator is an auto-correlation function indicating the rate of diffusion of the particles; knowing the temperature and viscosity of the fluid we can then use the Stokes-Einstein Law to calculate the particle size.

What do we get out of it?

Several types of mathematical analysis can be used to obtain size information from the auto-correlation function. The simplest uses a two parameter fit to estimate the mean size and polydispersity - a measure of the spread of the distribution (cumulant method). More complex analysis can be used to obtain volume or number vs. size distributions, separate bi- or multi-modal distributions, etc. Generally these methods will require some knowledge of the optical properties of the particles. Other techniques can be used to determine molecular weights of polymers, proteins, etc.