Technique description



General overview

The photon-correlation spectrometer PHOTOCOR Complex is based on the Photon Correlation Spectroscopy (PCS) technique and designed for measurements of sub-micron particle sizes, diffusion coefficients, viscosities, molecular weights of polymers in basic and applied studies.


Photon-Correlation Spectroscopy

The PCS method consists in determining the velocity distribution of particles movement by measuring dynamic fluctuations of intensity of scattered light. The disperse particles or macromolecules suspended in a liquid medium undergo Browning motion which causes the fluctuations of the local concentration of the particles, resulting in local inhomogeneities of the refractive index. This in turn results in fluctuations of intensity of the scattered light. The linewidth of the light scattered spectrum [gamma] (defined as the half-width at half-maximum) is proportional to the diffusion coefficient of the particles D:

(Eq.1) [Equation 1]

where

[Equation]

n is the refractive index of the medium, [lambda] the laser wavelength, and [theta] the scattering angle. With the assumption that the particles are spherical and non-interacting, the mean radius is obtained from the Stokes-Einstein equation:

(Eq.2) [Equation 2]

where [Boltzmann constant] is the Boltzmann constant, T the temperature, and [eta] the shear viscosity of the solvent.

Information about the light-scattering spectrum can be obtained from the autocorrelation function G(t) of the light-scattering intensity. For the simplest case of spherical monodisperse non-interacting particles in a dust-free fluid, the characteristic decay time of the correlation function is inversely proportional to the linewidth of the spectrum. Therefore, the diffusion coefficient and either particle size or viscosity can be found by fitting the measured correlation function to a single exponential function.

A characteristic autocorrelation function of the scattered light is shown below where the baseline b is proportional to the total intensity I, and it can be determined experimentally.

[Picture]

There exist two techniques of measuring the correlation function: heterodyning and homodyning. In heterodyne measurements, which are most suitable for small intensities, the scattered light is mixed coherently with a static light source at the incident wavelength, and the static field is added to the scattered fields at the photodetector. Eq.1 that connects the linewidth [gamma] and the diffusion coefficient D is given for a heterodyne spectrum. In homodyne measurements the photodetector receives scattered light only. Homodyning is most suitable for large intensities (e.g. near the critical point of the fluid, or for colloid systems). For a homodyne spectrum the connection between [gamma] and D reads:

(Eq.3) [Equation 3]

The PHOTOCOR Complex setup can operate in both homodyning and heterodyning regimes.


Original technique to study opaque liquids

An original technique to study non-transparent disperse systems, when the opacity makes particle size measurements by light scattering very difficult, has been developed. The problem involves two related aspects: strong light absorption in a sample resulting in the problem of detection of the scattered light and a complex refractive index creating difficulties for correct interpretation of the data. The modified optical scheme to perform particle size measurements in opaque liquids is presented below. A rectangular sample cell is placed at an angle of 450 with respect to the incident laser beam. The optical axis of the photodetecting system is normal to the front plane of the sample cell. The scattered light is collected from the region where the laser beam enters to the sample. A special asymmetric (non-coaxial) holder allows one to change the position of the scattering volume in accordance with the opacity of the sample and other experimental conditions. The laser beam is attenuated by an optical neutral glass to avoid the thermal lens effect. The conventional 900 geometry with the scattering volume placed at the corner of the sample cell can also be used for some very dilute but still opaque solutions.

[Picture]

A number of test measurements using some model opaque liquid systems have verified the adequacy of this experimental approach.


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