Memory kernel formalism with fractional exponents and its application to dielectric relaxation
[EN] 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 dip...
| Autores: | , , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/202273 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/202273 |
| Access Level: | acceso abierto |
| Palavra-chave: | Second-order memory function (SOMF) Biphenyl-2-yl isobutyrate (OBPI) Dielectric relaxation Autocorrelation function Havriliak-Negami relaxation time MAQUINAS Y MOTORES TERMICOS |
| Resumo: | [EN] 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 alpha-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.The theoretical model was tested with experimental data from dielectric spec-troscopy of biphenyl-2-yl isobutyrate (OBPI), a glass forming liquid, in measurements in the frequency domain from 10-2 to 106 Hz. This ester has been selected in this study for its predominant alpha-relaxation when compared to the beta relaxation. The real and imaginary parts of the second-order memory function were evaluated by means of the proposed model and the aid of the parameters of the Havriliak-Negami relationship. |
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