Anomalous diffusion, gigahertz, and terahertz spectroscopy of aliphatic ketones

The experimental results of the complex dielectric permittivity of aliphatic ketones in dilute solutions of inert solvent cyclohexane in the gigahertz (GHz) and terahertz (THz) frequencies of the electromagnetic spectrum are examined in terms of the theory of inertial anomalous diffusion of polar molecules, considered as an assembly of molecules with interacting dipolar groups, in polar liquids. The theory is based on the generalization of the Debye rotational diffusion model of dielectric relaxation of polar molecules. The model comprises two interacting dipolar groups-one lighter and the other heavier; each has a finite moment of inertia and each experiences a finite friction with an extensive range of damping or drag coefficient and the dipole moment ratio of the two groups. The lighter group refers to the reference molecule, whereas the heavier group simulates the neighboring molecules, and the two groups interact with each other via the dipole-dipole interaction potential. The resulting approximate expression contains terms in both the Rocard form and the Сole-Сole form. The experimental data on aliphatic ketones are shown to fit extremely well with the theory, and parameters of the fit offer physical significance. An agreement of the plot of the experimental data on dielectric loss versus frequency to the formulas derived from the model offers a mathematical basis of the semiempirical equations used in the literature to fit the experimental data. Experimental results of the dielectric loss of neat polar liquid acetone in GHz and THz, as an example, are shown to fit the theory; however, the interaction potential parameter compared to its dilute solution counterpart is significantly increased, reflecting the increase in the dipole-dipole interaction energy.