Interconversion algorithm between mechanical and dielectric relaxation measurements for acetate of cis- and...

The dielectric and mechanical spectroscopies of acetate of cis- and trans-2-phenyl-5-hydroxymethyl-1,3-dioxane are reported in the frequency domain from 10(-2) to 10(6)Hz. This ester has been selected in this study for its predominant α relaxation with regard to the β relaxation, which can be neglected. This study consists of determining an interconversion algorithm between dielectric and mechanical measurements, given by using a relation between rotational and translational complex viscosities. These important viscosities were obtained from measures of the dielectric complex permittivity and by dynamic mechanical analysis, respectively. The definitions of rotational and translational viscosities were evaluated by means of fractional calculus, by using the fit parameters of the Havriliak-Negami empirical model obtained in the dielectric and mechanical characterization of the α relaxation. This interconversion algorithm is a generalization of the break of the Stokes-Einstein-Debye relationship. It uses a power law with an exponent defined as the shape factor, which modifies the translational viscosity. Two others factors are introduced for the interconversion, a shift factor, which displaces the translational viscosity in the frequency domain, and a scale factor, which makes equal values of the two viscosities. In this paper, the shape factor has been identified as the relation between the slopes of the moduli of the complex viscosities at higher frequency. This is interpreted as the degree of kinetic coupling between the molecular rotation and translational movements. Alternatively, another interconversion algorithm has been expressed by means of dielectric and mechanical moduli.