Relaxation function, dielectric experiments involving

Dielectric experiments that involve studies of the relaxation function (r) are denoted as time-domain experiments, while those related to the complex permittivity function e (co) are considered dynamic experiments. The latter have the advantage of introducing an experimental timescale ( l/(o), which, when compared to the different intrinsic timescales of the system (the relaxation time x), provides useful information on the molecular level. In terms of the single-relaxation-time model of Debye (1921,1929), the complex permittivity for a dipolar mechanism can be written as follows ... 

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... 

It is interesting to note that in dielectric relaxation experiments, the orientation autocorrelation function that is involved in the theory is... 

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