Light scattering dielectric correlation function

Depolarized Dynamic Light Scattering and Dielectric Relaxation are related to the the multimolecular orientation correlation function... 

Since in the homodyne method only the scattered light impinges on the photocathode, E(t) in Eq. (4.3.1) is equal to the scattered field Es(t), so that is proportional to h(t)—which is consequently sometimes called the homodyne correlation function. The amplitude of Ea(t), the scattered field, is proportional to the instantaneous dielectric constant fluctuations in the scattering volume and, of course, fluctuates in the same manner. In certain circumstances the homodyne correlation function may be simply expressed in terms of h(t) or equivalently / (q, t) or / (q, t) of Eqs. (3.2.15) and (3.3.3b), respectively, as we now discuss. 

The isothermal time dependence of relaxation and fluctuation due to molecular motions in liquids at equilibrium usually cannot be described by the simple linear exponential function exp(-t/r), where t is the relaxation time. This fact is well known, especially for polymers, from measurements of the time or frequency dependence of the response of the equilibrium liquid to external stimuli such as in mechanical [6], dielectric [7, 33], and light-scattering [15, 34] measurements, and nuclear-magnetic-resonance spectroscopy [14]. The correlation or relaxation function measured usually decays slower than the exponential function and this feature is often referred to as non-exponential decay or non-exponentiality. Since the same molecular motions are responsible for structural recovery, certainly we can expect that the time dependence of the structural-relaxation function under non-equilibrium conditions is also non-exponential. An experiment by Kovacs on structural relaxation involving a more complicated thermal history showed that the structural-relaxation function even far from equilibrium is non-exponential. For example (Fig. 2.7), poly(vinyl acetate) is first subjected to a down-quench from Tq = 40 °C to 10 °C, and then, holding the temperature constant, the sample... 

Dielectric relaxation is sensitive to the time correlation function of the collective variable P(t) that is the total dipole moment, just as quasielastic light scattering is sensitive to the time correlation function of the collective variable YTj= exp(iq r (t)) that is the spatial Fourier component of the concentration. 

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