Fractional Fokker–Planck equation approach for the interconversion between dielectric and mechanical measurements

Abstract

This work describes a model of interconversion between mechanical and dielectric measurement. A previous version of this model has been proposed in the hereafter called “previous paper” [Díaz-Calleja, et al.Phys. Rev. E 72, 051505 (2005)], starting from a scaling relation between the translational and rotational viscosities present in a glass forming liquid near the glass transition temperature. Now, in order to improve the previous procedure, the following modifications have been made: (1) a definition of the rotational viscosity obtained from a fractional Fokker–Planck equation has been used, (2) the complex translational viscosity is taken as a non-Newtonian one, (3) a careful splitting of α and β relaxations is necessary, because the interconversión algorithm depends on the underlying molecular mechanism of each relaxation, and (4) the modulus and phase angle of complex viscosities were analyzed instead of real and imaginary parts of the complex viscosities. The proposed interconversion model, in the interval of frequencies 10−2–10+5 Hz, shows that the obtained results are more accurate than those one obtained in the previous paper.