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

Author

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

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.

Suggested Citation

  • Hernández, S.I. & del Castillo, L.F. & del Castillo, Roxana M. & García-Bernabé, Abel & Compañ, V., 2023. "Memory kernel formalism with fractional exponents and its application to dielectric relaxation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 612(C).
    • Handle: RePEc:eee:phsmap:v:612:y:2023:i:c:s0378437123000419
    DOI: 10.1016/j.physa.2023.128486
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