Recognition of a new permittivity function for glycerol by the use of the eigen-coordinates method

Abstract

Measurements of real and imaginary parts of the relative complex permittivity of glycerol were carried out in the frequency range 1 mHz–1 MHz at different temperatures between 188 and 263 K. The permittivity data have been analyzed thoroughly by a new data curve-fitting approach that involves the so-called eigen-coordinates method in conjunction with a separation procedure and the inverse permittivity formulas. A new single permittivity function, based on the so-called recap element picture for a self-similar (fractal) structure, has been recognized to describe well such data over the entire frequency range studied. The recognized dielectric function enabled us to infer an electrical equivalent-circuit network for the glycerol sample studied that involves a series combination of two recap elements, reflecting the existence of two different dielectric relaxation processes in glycerol. The temperature dependence of the relaxation times τ 1( T) and τ 2( T) entering into the identified permittivity function was found to obey nearly an Arrhenius behaviour with activation energies E 1≈114 kJ/mol and E 2≈94 kJ/mol. The recognized permittivity function can be justified by presuming that the processes represented by the recap elements characterized by the parameters ( ν 1, τ 1, E 1) and ( ν 2, τ 2, E 2) are linked to `donor-like' and `acceptor-like' charges formed from the infinite hydroxyl hydrogen bonds.