Autocorrelation function, spatial arrangement

The Autocorrelation Function as a Quantitative Measure of Spatial Arrangements of Single Components and How These Components Change with Time... 

Also known as quasi-elastic light scattering, this technique monitors the tempord fluctuations in / (q) (Berne and Pecora, 1976 Chu, 1990). These fluctuations result from random thermal motions, which change the instantaneous spatial arrangement of molecules and thus the net scattered intensity. As these random motions result in microscopic concentration fluctuations, a mutual diffusion coefficient can be determined from the time constant of the decay of the time autocorrelation function of Liq, t). Rapid advances in laser and autocorrelator technology during the last two decades have made this experiment a routine characterization and research tool. 

Here B is an optical constant, or is the total polarizability of the particle, and n is the number of components in each particle. The indexes i and j refer to components of the same particle. If the assumption of independent particles was not made, then the indexes could refer to components of any two particles, and the autocorrelation expression could not be written as a simple sum of contributions from individual particles. The spatial vector r(r) refers to the center of mass of the particle. R(r). In the case of a nonspherical particle (arbitrary shape), Eq. (I0) would describe the coupled motion of the center of mass and the relative arrangement of the components of the particle. For spherical particles, translational and rotational motion arc uncoupled and we have a simplified expression for the electric field time correlation function ... 

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See also in sourсe #XX -- [ , ]

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