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...

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Autores: 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
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución: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
Acceso en línea:https://riunet.upv.es/handle/10251/202273
Access Level:acceso abierto
Palabra clave:Second-order memory function (SOMF)
Biphenyl-2-yl isobutyrate (OBPI)
Dielectric relaxation
Autocorrelation function
Havriliak-Negami relaxation time
MAQUINAS Y MOTORES TERMICOS
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repository_id_str
dc.title.none.fl_str_mv Memory kernel formalism with fractional exponents and its application to dielectric relaxation
title Memory kernel formalism with fractional exponents and its application to dielectric relaxation
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_short 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_sort Memory kernel formalism with fractional exponents and its application to dielectric relaxation
dc.creator.none.fl_str_mv 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 Hernández, S. I.
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
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
dc.contributor.none.fl_str_mv Departamento de Termodinámica Aplicada
Escuela Técnica Superior de Ingeniería Industrial
UNIVERSIDAD POLITECNICA DE VALENCIA
Universidad Nacional Autónoma de México
Ministerio de Asuntos Económicos y Transformación Digital
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Second-order memory function (SOMF)
Biphenyl-2-yl isobutyrate (OBPI)
Dielectric relaxation
Autocorrelation function
Havriliak-Negami relaxation time
MAQUINAS Y MOTORES TERMICOS
topic Second-order memory function (SOMF)
Biphenyl-2-yl isobutyrate (OBPI)
Dielectric relaxation
Autocorrelation function
Havriliak-Negami relaxation time
MAQUINAS Y MOTORES TERMICOS
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.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-02-15
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/202273
url https://riunet.upv.es/handle/10251/202273
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 ENE2015-69203-R DESARROLLO Y EVALUACION DE NUEVAS MEMBRANAS POLIMERICAS REFORZADAS CON NANOFIBRAS PARA SU APLICACION EN PILAS DE COMBUSTIBLE CON ELEVADA ESTABILIDAD TERMICA
Universitat Politècnica de València https://doi.org/10.13039/501100004233 Programa PAID de Apoyo a la I+D+i PAID-11-21 Desarrollo, modelado y construcción de un Stack de pila de combustible polimérica a temperaturas moderadas para pequeño vehículo terrestre
Universidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica-PAPIIT LANCAD-UNAM-DGTIC-385
Universidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 IN120120
Universidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica- PAPIIT IN114818 Fenómenos de transporte y propiedades termodinámicas en materia blanda
Universidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 LANCAD-UNAM-DGTIC-276
Universidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica- PAPIIT IG100618 Separación adsortiva de olefinas y parafina
Universidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 IN114721
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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spelling Memory kernel formalism with fractional exponents and its application to dielectric relaxationHernández, S. I.del Castillo, L.F.del Castillo, Roxana M.Garcia-Bernabe, Abel|||0000-0002-9740-0830Compañ Moreno, Vicente|||0000-0001-8233-7472Second-order memory function (SOMF)Biphenyl-2-yl isobutyrate (OBPI)Dielectric relaxationAutocorrelation functionHavriliak-Negami relaxation timeMAQUINAS 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.ElsevierDepartamento de Termodinámica AplicadaEscuela Técnica Superior de Ingeniería IndustrialUNIVERSIDAD POLITECNICA DE VALENCIAUniversidad Nacional Autónoma de MéxicoMinisterio de Asuntos Económicos y Transformación DigitalRepositorio Institucional de la Universitat Politècnica de València Riunet20232023-02-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/202273reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 ENE2015-69203-R DESARROLLO Y EVALUACION DE NUEVAS MEMBRANAS POLIMERICAS REFORZADAS CON NANOFIBRAS PARA SU APLICACION EN PILAS DE COMBUSTIBLE CON ELEVADA ESTABILIDAD TERMICAUniversitat Politècnica de València https://doi.org/10.13039/501100004233 Programa PAID de Apoyo a la I+D+i PAID-11-21 Desarrollo, modelado y construcción de un Stack de pila de combustible polimérica a temperaturas moderadas para pequeño vehículo terrestreUniversidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica-PAPIIT LANCAD-UNAM-DGTIC-385Universidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 IN120120Universidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica- PAPIIT IN114818 Fenómenos de transporte y propiedades termodinámicas en materia blandaUniversidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 LANCAD-UNAM-DGTIC-276Universidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica- PAPIIT IG100618 Separación adsortiva de olefinas y parafinaUniversidad Nacional Autónoma de México https://doi.org/10.13039/501100005739 IN114721open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2022732026-06-13T07:49:27Z
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