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...
| Authors: | ; ; ; ; |
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| Format: | Article |
| Publication date: | 2023 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/202273 |
| Online Access: | https://riunet.upv.es/handle/10251/202273 |
| Access Level: | Open access |
| Keyword: | Second-order memory function (SOMF) Biphenyl-2-yl isobutyrate (OBPI) Dielectric relaxation Autocorrelation function Havriliak-Negami relaxation time MAQUINAS Y MOTORES TERMICOS |
| _version_ | 1878736333680148481 |
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| author | Hernández, S. I. |
| author2 | del Castillo, L.F. del Castillo, Roxana M. Garcia-Bernabe, Abel|||0000-0002-9740-0830 Compañ Moreno, Vicente|||0000-0001-8233-7472 |
| author2_role | author author author author |
| author_browse | Compañ Moreno, Vicente|||0000-0001-8233-7472 Garcia-Bernabe, Abel|||0000-0002-9740-0830 Hernández, S. I. del Castillo, L.F. del Castillo, Roxana M. |
| author_facet | Hernández, S. I. del Castillo, L.F. del Castillo, Roxana M. Garcia-Bernabe, Abel|||0000-0002-9740-0830 Compañ Moreno, Vicente|||0000-0001-8233-7472 |
| author_role | author |
| collection | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| description | [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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_8d2e8bee33c8c749eaf0b2fa18d8a08a |
| institution | Universitat Politècnica de València (UPV) |
| instname_str | Universitat Politècnica de València (UPV) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:riunet.upv.es:10251/202273 |
| publishDate | 2023 |
| publishDateSort | 2023 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| spelling | Memory kernel formalism with fractional exponents and its application to dielectric relaxation Hernández, S. I. del Castillo, L.F. del Castillo, Roxana M. Garcia-Bernabe, Abel|||0000-0002-9740-0830 Compañ Moreno, Vicente|||0000-0001-8233-7472 Second-order memory function (SOMF) Biphenyl-2-yl isobutyrate (OBPI) Dielectric relaxation Autocorrelation function Havriliak-Negami relaxation time MAQUINAS Y MOTORES TERMICOS [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. The authors wish to state, posthumously, the excellent research carried out by Prof. Luis F. Del Castillo in the field of the memory effect associated with polymeric materials. On the other hand, we thank Professor Niels Boye Olsen and Jeppe C. Dyre from Roskilde University (Denmark) for dielectric measurements. AG -B and VC gratefully acknowledge to Ministerio de Economia y Competitividad (MINECO) , Spain for financial support by the ENE/2015-69203-R project. AG -B thanks Vicerrectorado de Investigacion de la Universitat Politecnica de Valencia, Spain for the financing of the Project (PAID -11-21) . SIH is grateful to projects UNAM-DGAPA-PAPIIT IN114721, LANCAD-UNAM-DGTIC-276 and appreciate the technical support of Alejandro de Leon Cuevas, Alejandro Avalos and Luis Alberto Aguilar Bautista from Laboratorio Nacional de Visualizacion Cientifica Avanzada (LAVIS-UNAM) , and Beatriz Marcela Millan Malo from CFATA-UNAM. RMdC is grateful to projects LANCAD-UNAM-DGTIC-385 and UNAM-DGAPA-PAPIIT IN120120. LFdC is grateful to projects UNAM- DGAPA-PAPIIT IG-100618 and IN 114818, and also thanks to Raul Reyes Ortiz and Alberto Lopez Vivas for technical assistance. Elsevier https://riunet.upv.es/handle/10251/202273 |
| spellingShingle | Memory kernel formalism with fractional exponents and its application to dielectric relaxation Hernández, S. I. Second-order memory function (SOMF) Biphenyl-2-yl isobutyrate (OBPI) Dielectric relaxation Autocorrelation function Havriliak-Negami relaxation time MAQUINAS Y MOTORES TERMICOS |
| title | Memory kernel formalism with fractional exponents and its application to dielectric relaxation |
| title_full | Memory kernel formalism with fractional exponents and its application to dielectric relaxation |
| title_fullStr | Memory kernel formalism with fractional exponents and its application to dielectric relaxation |
| title_full_unstemmed | Memory kernel formalism with fractional exponents and its application to dielectric relaxation |
| title_short | Memory kernel formalism with fractional exponents and its application to dielectric relaxation |
| title_sort | Memory kernel formalism with fractional exponents and its application to dielectric relaxation |
| topic | Second-order memory function (SOMF) Biphenyl-2-yl isobutyrate (OBPI) Dielectric relaxation Autocorrelation function Havriliak-Negami relaxation time MAQUINAS Y MOTORES TERMICOS |
| topic_facet | Second-order memory function (SOMF) Biphenyl-2-yl isobutyrate (OBPI) Dielectric relaxation Autocorrelation function Havriliak-Negami relaxation time MAQUINAS Y MOTORES TERMICOS |
| url | https://riunet.upv.es/handle/10251/202273 |