Fractional rotational diffusion behavior

In order to demonstrate how the anomalous relaxation behavior described by the hitherto empirical Eqs. (9)—(11) may be obtained from our fractional generalizations of the Fokker-Planck equation in configuration space (in effect, fractional Smoluchowski equations), Eq. (101), we first consider the fractional rotational motion of a fixed axis rotator [1], which for the normal diffusion is the first Debye model (see Section II.C). The orientation of the dipole is specified by the angular coordinate 4> (the azimuth) constituting a system of one rotational degree of freedom. Electrical interactions between the dipoles are ignored. 

As far as comparison with experimental data is concerned, the fractional Klein-Kramers model under discussion may be suitable for the explanation of dielectric relaxation of dilute solution of polar molecules (such as CHCI3, CH3CI, etc.) in nonpolar glassy solvents (such as decalin at low temperatures see, e.g., Ref. 93). Here, in contrast to the normal diffusion, the model can explain qualitatively the inertia-corrected anomalous (Cole-Cole-like) dielectric relaxation behavior of such solutions at low frequencies. However, one would expect that the model is not applicable at high frequencies (in the far-infrared region), where the librational character of the rotational motion must be taken... 

In this chapter, the binary mixture of GB particles of different aspect ratios has been studied by molecular dynamics simulation. The composition dependence of different static and dynamic properties has been studied. The radial distribution function has been found to show some interesting features. Simulated pressure and overall diffusion coefficient exhibit nonideal composition dependence. However, simulated viscosity does not show any clear nonideality. The mole fraction dependence of selfdiffusion coefficients qualitatively signals some kind of structural transition in the 50 50 mixture. The rotational correlation study shows the non-Debye behavior in its rank dependence. The product of translational diffusion coefficient and rotational correlation time (first rank) has been found to remain constant across the mixture composition and lie above the stick prediction. 

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