Dielectric Relaxation

A Practical Guide to Prabhakar Fractional Calculus

“…It is fairly well known in the literature [18,19,24,71,[151][152][153] that materials that display glass-liquid transitions or amorphous polymers tend to deviate substantially from the standard Debye relaxation model. Setting aside for the moment the Cole-Cole relaxation, that can be described in terms of standard fractional calculus [12,37,49], let us focus on the Havriliak-Negami model.…”

Effective Admittivity of Biological Tissues as a Coefficient of Elliptic PDE

“…The term dielectric relaxation [22] in a biological tissue connotes the delay or lag in its response to create the dielectric polarization following the application of electric field across the tissue sample. In other words, the dielectric relaxation of a tissue can be defined as the lag (momentary delay) in the dielectric constant which is usually caused by the delay in molecular polarization with respect to a change in applied electric field.…”

Study of hydrogen in coals, polymers, oxides, and muscle water by nuclear magnetic resonance; extension of solid-state high-resolution techniques. [Hydrogen molybdenum bronze]

“…Carbon-13 NMR, most notably, has in recent years assumed a major role in organic structure elucidation (13,14) and polymer studies (13)(14)(15)(16) , where it offers the possibility of direct investigation of molecular backbones. Also, the large chemical shift range of 13c results in highly resolved spectra, in which each cdrLo11 aLom in the molecular frameworlc typically corresponds to a separate peak in the spectrum Another developing area of NMR research which is of considerable current interest, is high resolution NEIR of solids (17)(18)(19). It is well known that NMR spectra of solids on the order of 0.1 to 1 Hz, and spectral line separ'ations of less than 0.1 Hz can be measured.…”

“…'features such as chemical shifts and spin-spin splittings, which identlfy'molecular environments and make NMR a broadly useful analytical and structural tool. In solids, on the other hand, the nuclear resonance behavior is usually dominated by magnetic dipole-dipole interactions among neighboring nuclei, resulting in severe line broadening and the obscuring of chemical shifts (17)(18)(19). In addition., anisotropic interactions such as the chemical shift anisotropy, and quadrupolar interactions for nuclei, with spin greater than 1/2, can lead to broad complex lineshapes in solids even when dipolar broadening .…”

“…motions of molecules in that state. Artificial, experimental manipulations of nuclear spins can similarly produce spectral linc narrowing in NMR (17)(18)(19)…”