{"id":"https://openalex.org/W1978556310","doi":"https://doi.org/10.1021/jp904741m","title":"Fractional Diffusion Equation and Impedance Spectroscopy of Electrolytic Cells","display_name":"Fractional Diffusion Equation and Impedance Spectroscopy of Electrolytic Cells","publication_year":2009,"publication_date":"2009-07-28","ids":{"openalex":"https://openalex.org/W1978556310","doi":"https://doi.org/10.1021/jp904741m","mag":"1978556310","pmid":"https://pubmed.ncbi.nlm.nih.gov/19637845"},"language":"en","primary_location":{"id":"doi:10.1021/jp904741m","doi":"https://doi.org/10.1021/jp904741m","is_oa":false,"landing_page_url":"https://doi.org/10.1021/jp904741m","pdf_url":null,"source":{"id":"https://openalex.org/S185621672","display_name":"The Journal of Physical Chemistry B","issn_l":"1520-5207","issn":["1520-5207","1520-6106"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320006","host_organization_name":"American Chemical Society","host_organization_lineage":["https://openalex.org/P4310320006"],"host_organization_lineage_names":["American Chemical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Physical Chemistry B","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060481487","display_name":"Ervin Kaminski Lenzi","orcid":"https://orcid.org/0000-0003-3853-1790","observed_orcids":["https://orcid.org/0000-0003-3853-1790"]},"institutions":[{"id":"https://openalex.org/I123443094","display_name":"Universidade Estadual de Maring\u00e1","ror":"https://ror.org/04bqqa360","country_code":"BR","type":"education","lineage":["https://openalex.org/I123443094"]},{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["BR","IT"],"is_corresponding":false,"raw_author_name":"E. K. Lenzi","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo, 5790 \u2212 87020-900 Maring\u00e1, Paran\u00e1, Brazil, and Dipartimento di Fisica del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo, 5790 \u2212 87020-900 Maring\u00e1, Paran\u00e1, Brazil, and Dipartimento di Fisica del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italia","institution_ids":["https://openalex.org/I123443094","https://openalex.org/I177477856"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006098704","display_name":"L. R. Evangelista","orcid":"https://orcid.org/0000-0001-7202-1386","observed_orcids":["https://orcid.org/0000-0001-7202-1386"]},"institutions":[{"id":"https://openalex.org/I123443094","display_name":"Universidade Estadual de Maring\u00e1","ror":"https://ror.org/04bqqa360","country_code":"BR","type":"education","lineage":["https://openalex.org/I123443094"]},{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["BR","IT"],"is_corresponding":true,"raw_author_name":"L. R. Evangelista","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo, 5790 \u2212 87020-900 Maring\u00e1, Paran\u00e1, Brazil, and Dipartimento di Fisica del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo, 5790 \u2212 87020-900 Maring\u00e1, Paran\u00e1, Brazil, and Dipartimento di Fisica del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italia","institution_ids":["https://openalex.org/I123443094","https://openalex.org/I177477856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024117597","display_name":"G. Barbero","orcid":"https://orcid.org/0000-0002-2282-9536","observed_orcids":["https://orcid.org/0000-0002-2282-9536"]},"institutions":[{"id":"https://openalex.org/I123443094","display_name":"Universidade Estadual de Maring\u00e1","ror":"https://ror.org/04bqqa360","country_code":"BR","type":"education","lineage":["https://openalex.org/I123443094"]},{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["BR","IT"],"is_corresponding":false,"raw_author_name":"G. Barbero","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo, 5790 \u2212 87020-900 Maring\u00e1, Paran\u00e1, Brazil, and Dipartimento di Fisica del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo, 5790 \u2212 87020-900 Maring\u00e1, Paran\u00e1, Brazil, and Dipartimento di Fisica del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italia","institution_ids":["https://openalex.org/I123443094","https://openalex.org/I177477856"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006098704"],"corresponding_institution_ids":["https://openalex.org/I123443094","https://openalex.org/I177477856"],"apc_list":null,"apc_paid":null,"fwci":3.6732,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.91274686,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":99},"biblio":{"volume":"113","issue":"33","first_page":"11371","last_page":"11374"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11434","display_name":"Electrochemical Analysis and Applications","score":0.0019000000320374966,"subfield":{"id":"https://openalex.org/subfields/1603","display_name":"Electrochemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12274","display_name":"Electrostatics and Colloid Interactions","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-diffusion-equation","display_name":"fractional diffusion equation","score":0.9890000224113464},{"id":"https://openalex.org/keywords/distributed-order-fractional-derivative","display_name":"distributed-order fractional derivative","score":0.6620000004768372},{"id":"https://openalex.org/keywords/electrochemical-impedance","display_name":"electrochemical impedance","score":0.8370000123977661},{"id":"https://openalex.org/keywords/electrolytic-cells","display_name":"electrolytic cells","score":0.9729999899864197},{"id":"https://openalex.org/keywords/poisson-equation","display_name":"Poisson equation","score":0.8510000109672546},{"id":"https://openalex.org/keywords/electric-field-distribution","display_name":"electric field distribution","score":0.949999988079071},{"id":"https://openalex.org/keywords/frequency-dependent-impedance","display_name":"frequency-dependent impedance","score":0.7400000095367432},{"id":"https://openalex.org/keywords/ion-transport","display_name":"ion transport","score":0.4269999861717224},{"id":"https://openalex.org/keywords/anomalous-diffusion","display_name":"anomalous diffusion","score":0.6119999885559082}],"concepts":[{"id":"https://openalex.org/C7040849","wikidata":"https://www.wikidata.org/wiki/Q899580","display_name":"Dielectric spectroscopy","level":4,"score":0.729667067527771},{"id":"https://openalex.org/C17829176","wikidata":"https://www.wikidata.org/wiki/Q179043","display_name":"Electrical impedance","level":2,"score":0.695975661277771},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.6579117774963379},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.6417332887649536},{"id":"https://openalex.org/C68801617","wikidata":"https://www.wikidata.org/wiki/Q162908","display_name":"Electrolyte","level":3,"score":0.6098194122314453},{"id":"https://openalex.org/C60799052","wikidata":"https://www.wikidata.org/wiki/Q46221","display_name":"Electric field","level":2,"score":0.4982445240020752},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4941284954547882},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.48956069350242615},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.46948227286338806},{"id":"https://openalex.org/C145148216","wikidata":"https://www.wikidata.org/wiki/Q36496","display_name":"Ion","level":2,"score":0.42129743099212646},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.41278210282325745},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.3908647298812866},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3632219731807709},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3593839406967163},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3387277126312256},{"id":"https://openalex.org/C113196181","wikidata":"https://www.wikidata.org/wiki/Q485223","display_name":"Analytical Chemistry (journal)","level":2,"score":0.3336840569972992},{"id":"https://openalex.org/C52859227","wikidata":"https://www.wikidata.org/wiki/Q7877","display_name":"Electrochemistry","level":3,"score":0.28961533308029175},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.2859587073326111},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2568601965904236},{"id":"https://openalex.org/C17525397","wikidata":"https://www.wikidata.org/wiki/Q176140","display_name":"Electrode","level":2,"score":0.24707958102226257},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.09849971532821655},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0929298996925354},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08705070614814758},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1021/jp904741m","doi":"https://doi.org/10.1021/jp904741m","is_oa":false,"landing_page_url":"https://doi.org/10.1021/jp904741m","pdf_url":null,"source":{"id":"https://openalex.org/S185621672","display_name":"The Journal of Physical Chemistry B","issn_l":"1520-5207","issn":["1520-5207","1520-6106"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320006","host_organization_name":"American Chemical Society","host_organization_lineage":["https://openalex.org/P4310320006"],"host_organization_lineage_names":["American Chemical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Physical Chemistry B","raw_type":"journal-article"},{"id":"pmid:19637845","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19637845","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The journal of physical chemistry. B","raw_type":"Letter"},{"id":"pmh:oai:iris.polito.it:11583/2281651","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11583/2281651","pdf_url":null,"source":{"id":"https://openalex.org/S7407055329","display_name":"PORTO@Iris","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:porto.polito.it:2281651","doi":null,"is_oa":false,"landing_page_url":"http://porto.polito.it/2281651/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1520-6106","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W433794350","https://openalex.org/W613592454","https://openalex.org/W1965339507","https://openalex.org/W1970403427","https://openalex.org/W1972376373","https://openalex.org/W1981246095","https://openalex.org/W1983397281","https://openalex.org/W1996846601","https://openalex.org/W1997050292","https://openalex.org/W2000952695","https://openalex.org/W2008878200","https://openalex.org/W2013652881","https://openalex.org/W2014430824","https://openalex.org/W2015526081","https://openalex.org/W2021852102","https://openalex.org/W2026946703","https://openalex.org/W2036654111","https://openalex.org/W2037940573","https://openalex.org/W2039457415","https://openalex.org/W2051221308","https://openalex.org/W2064361774","https://openalex.org/W2076987825","https://openalex.org/W2077388909","https://openalex.org/W2077631993","https://openalex.org/W2091607229","https://openalex.org/W2094906777","https://openalex.org/W2111271983","https://openalex.org/W2129509922","https://openalex.org/W2787959293","https://openalex.org/W3022182265","https://openalex.org/W3044006004","https://openalex.org/W4253968242","https://openalex.org/W4297606641"],"related_works":["https://openalex.org/W2775483934","https://openalex.org/W2144482552","https://openalex.org/W4280621833","https://openalex.org/W2320493753","https://openalex.org/W4221165695","https://openalex.org/W2163287999","https://openalex.org/W3192550126","https://openalex.org/W3164342535","https://openalex.org/W1974015033","https://openalex.org/W2050119786"],"abstract_inverted_index":{"The":[0,30,46,97],"influence":[1],"of":[2,9,17,33,64,89,100,106,124],"the":[3,6,15,23,34,38,51,61,68,76,86,90,101,107,116],"ions":[4],"on":[5,60,67],"electrochemical":[7],"impedance":[8,53,108],"a":[10,18,94,121],"cell":[11],"is":[12,27,40,58,75],"calculated":[13],"in":[14,21,93,120],"framework":[16],"complete":[19],"model":[20,48],"which":[22],"fractional":[24,62],"drift-diffusion":[25],"problem":[26],"analytically":[28],"solved.":[29],"resulting":[31],"distribution":[32],"electric":[35],"field":[36],"inside":[37],"sample":[39],"determined":[41],"by":[42],"solving":[43],"Poisson's":[44],"equation.":[45,70],"theoretical":[47],"to":[49,83,111,115],"determine":[50],"electrical":[52],"we":[54],"are":[55,109],"proposing":[56],"here":[57],"based":[59],"derivative":[63],"distributed":[65],"order":[66],"diffusion":[69],"We":[71],"argue":[72],"that":[73],"this":[74],"more":[77],"convenient":[78],"and":[79,103],"physically":[80],"significant":[81],"approach":[82],"account":[84],"for":[85],"enormous":[87],"variety":[88,123],"diffusive":[91],"regimes":[92],"real":[95,102],"cell.":[96],"frequency":[98],"dependence":[99],"imaginary":[104],"parts":[105],"shown":[110],"be":[112],"very":[113],"similar":[114],"ones":[117],"experimentally":[118],"obtained":[119],"large":[122],"electrolytic":[125],"samples.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":5}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
