Light scattering. Mean statistical fluctuations

A new kind of fluctuations (concentration fluctuations) appear in solutions, so the full intensity of. scattered light has three terms  

It follows from the last two equations that away from the spinodal, Rk.so is small and increases as the configurative point approaches the spinodal. Lisnyanski (1961, 1966), Lisnyajiski and Vuks (1962, 1964, 1969), Vuks (1977) have proposed to characterize the level of concentration fluctuations by a concentration fluctuation function /  

Comparison of Eiquations 7, 8, 10 with experimental values of Rk,90 S lso causes great difficulties to express (St/dij) via experimentally measured values (cf. subsection 2.3.1) (Fabelinski, 1965 Kerker, 1969 Vuks, 1977). Vuks (1977) has proposed a formula firmly confirmed by light scattering data together with other independent methods  

If the last expression from Equation 6 is substituted to Equation 5, we obtain 

The last formula is valid for concentration expressed in any units, as the conversion factor reduces, so 

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The choice of P(/cross) as a statistical parameter for obtaining information is supported by the shape of its probability density function (PDF). This PDF has a maximum at /cross=0 and decreases very quickly as the intensity increases. It also may be observed that P(Icioss) remains finite even for values of /cross in excess of the mean of the cross-polarized scattered light () but the fluctuation of the values of / (/cross) increases. This means that some peaks of high cross-polarized intensity appear corresponding to cases in which the particles are close together. So, the values of /"(/cross) for /cross = 0 can be determined with the smallest relative error [5]. 

On a molecular scale liquid surfaces are not flat, but subject to Jluctuations. These irregularities have a stochastic nature, meaning that no external force is needed to create them, that they cannot be used to perform work and are devoid of order. Their properties can only be described by statistical means as explained in sec. 1.3.7. Surface fluctuations are also known as thermal ripples, or thermal waves, in distinction to mechanically created waves that will be discussed in detail in sec. 3.6. Except near the critical point, the amplitudes of these fluctuations are small, in the order of 1 nm, but they can, in principle, be measured by the scattering of optical light. X-ray and neutron beams. From the scattered intensity the root mean square amplitude can be derived and this quantity can, in turn, be related to the surface tension because this tension opposes the fluctuations ). 

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