Memory kernel formalism with fractional exponents and its application to dielectric relaxation

S.I. Hernández, L.F. del Castillo, Roxana M. del Castillo, Abel García-Bernabé and V. Compañ

Physica A: Statistical Mechanics and its Applications, 2023, vol. 612, issue C

Abstract: A fractal Fokker–Planck formalism applied to the dielectric relaxation in glass forming liquids is proposed. This formalism is a modality of the generalized equation of Langevin on the use of fractional-time derivatives simultaneously with the memory function to describe the dynamics of the dipolar-moment autocorrelation function. The goal is to get the description of the complex autocorrelation function numerically, and the real and imaginary parts of the second-order memory function, related to the kernel of the integral hierarchy representation of this autocorrelation function. The results exhibit the memory effect associates with α-dielectric relaxation mode. From the analysis, it is shown the existence of a maximum and the appropriated frequency limit in the imaginary and real parts, respectively, of the second-order memory function. That is required to describe experimental well the complex shear viscosity of the material.

Keywords: Second-order memory function (SOMF); Biphenyl-2-yl isobutyrate (OBPI); Dielectric relaxation; Autocorrelation function; Havriliak–Negami relaxation time (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:612:y:2023:i:c:s0378437123000419

DOI: 10.1016/j.physa.2023.128486

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