Brownian Motion and Autocorrelation Analysis of Scattered Light Intensity

1 BROWNIAN MOTION AND AUTOCORRELATION ANALYSIS OF SCATTERED LIGHT INTENSITY 

This section contains a general description of the principles by which the Coulter Model N4 Sub-Micron Particle Analyzer, used in this study to characterize artificial gas-in-water emulsions (see Section 10.4), determines sample particle size. The measuring principles are based on the theory of Brownian motion and photon correlation spectroscopy (ref. 464,465 see also Sections 10.2 and 10.4). 

The motion caused by thermal agitation and the random striking of particles in a liquid by the molecules of that liquid is called Brownian motion. This molecular striking results in a vibratory movement that causes suspended particles to diffuse throughout a liquid. If the colloidal particles can be assumed to be approximately spherical, then for a liquid of given viscosity (q), at a constant temperature (T), the rate of diffusion, or diffusion coefficient (D) is inversely related to the particle size according to the Stokes-Einstein relation (ref. 126)  

The constantly changing patterns of suspended particles while in Brownian motion can be analyzed by light-scattering spectroscopy. The Coulter Model N4 measures time-dependent 

A convenient and accurate analysis of these intensity fluctuations is performed by computing the auto-correlation function of the measured intensities, G(x), where 

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