On the existence of exact conditions in the theory of electrical double layers
It has long been thought that the total potential drop V across an isolated electrical double layer must be a monotonically increasing function of the surface charge density σ (i.e., ∂V/∂σ≥0). This result has been ‘‘established’’ by thermodynamic arguments of Landau and Lifshitz [Electrodynamics of ...
Gespeichert in:
Veröffentlicht in: | The Journal of chemical physics 1992-03, Vol.96 (5), p.3767-3771 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 3771 |
---|---|
container_issue | 5 |
container_start_page | 3767 |
container_title | The Journal of chemical physics |
container_volume | 96 |
creator | ATTARD, P WEI, D PATEY, G. N |
description | It has long been thought that the total potential drop V across an isolated electrical double layer must be a monotonically increasing function of the surface charge density σ (i.e., ∂V/∂σ≥0). This result has been ‘‘established’’ by thermodynamic arguments of Landau and Lifshitz [Electrodynamics of Continuous Media (Pergamon, Oxford, 1960)] and by a more recent statistical mechanical method of Blum et al. [J. Chem. Phys. 72, 1902 (1981)]. Here we describe statistical mechanical analyses for both constant and fluctuating charge models. It is shown that the derivation of Blum et al. is in error and that correct statistical mechanical treatments do not determine the sign of ∂V/∂σ. However, some rigorous bounds for related quantities are found. We also point out a mathematical problem in the method of Landau and Lifshitz which appears to invalidate their argument. We conclude that at present there is no rigorous proof that ∂V/∂σ must be positive and that the existence of negative values cannot be ruled out. |
doi_str_mv | 10.1063/1.461881 |
format | Article |
fullrecord | <record><control><sourceid>pascalfrancis_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1063_1_461881</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>5440950</sourcerecordid><originalsourceid>FETCH-LOGICAL-c254t-c188e85c486a5dd67095065f1b9e68403a860e52f756395cc1111b4c32112d5d3</originalsourceid><addsrcrecordid>eNo9kEFLxDAQhYMoWFfBn5CDBy9dZ9IkTY6y6Cos7kXPJZ2mGKntklSw_96uFQeGYeDjvcdj7BphjaCLO1xLjcbgCcsQjM1LbeGUZQACc6tBn7OLlD4AAEshM_ay7_n47rn_Dmn0PXk-tPPjaOQ09E0Yw9AnHhZo3iFOv0TnaYyBXMeb4avuPO_c5GO6ZGet65K_-rsr9vb48Lp5ynf77fPmfpeTUHLMaU7ojSJptFNNo0uwCrRqsbZeGwmFMxq8Em2pdGEVEc5TSyoEomhUU6zY7aJLcUgp-rY6xPDp4lQhVMceKqyWHmb0ZkEPLs152-h6CumfV1IezYsf-79a_w</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On the existence of exact conditions in the theory of electrical double layers</title><source>AIP Digital Archive</source><creator>ATTARD, P ; WEI, D ; PATEY, G. N</creator><creatorcontrib>ATTARD, P ; WEI, D ; PATEY, G. N</creatorcontrib><description>It has long been thought that the total potential drop V across an isolated electrical double layer must be a monotonically increasing function of the surface charge density σ (i.e., ∂V/∂σ≥0). This result has been ‘‘established’’ by thermodynamic arguments of Landau and Lifshitz [Electrodynamics of Continuous Media (Pergamon, Oxford, 1960)] and by a more recent statistical mechanical method of Blum et al. [J. Chem. Phys. 72, 1902 (1981)]. Here we describe statistical mechanical analyses for both constant and fluctuating charge models. It is shown that the derivation of Blum et al. is in error and that correct statistical mechanical treatments do not determine the sign of ∂V/∂σ. However, some rigorous bounds for related quantities are found. We also point out a mathematical problem in the method of Landau and Lifshitz which appears to invalidate their argument. We conclude that at present there is no rigorous proof that ∂V/∂σ must be positive and that the existence of negative values cannot be ruled out.</description><identifier>ISSN: 0021-9606</identifier><identifier>EISSN: 1089-7690</identifier><identifier>DOI: 10.1063/1.461881</identifier><identifier>CODEN: JCPSA6</identifier><language>eng</language><publisher>Woodbury, NY: American Institute of Physics</publisher><subject>Chemistry ; Electrochemistry ; Exact sciences and technology ; General and physical chemistry ; Properties of electrolytes: conductivity</subject><ispartof>The Journal of chemical physics, 1992-03, Vol.96 (5), p.3767-3771</ispartof><rights>1992 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c254t-c188e85c486a5dd67095065f1b9e68403a860e52f756395cc1111b4c32112d5d3</citedby><cites>FETCH-LOGICAL-c254t-c188e85c486a5dd67095065f1b9e68403a860e52f756395cc1111b4c32112d5d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27915,27916</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5440950$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>ATTARD, P</creatorcontrib><creatorcontrib>WEI, D</creatorcontrib><creatorcontrib>PATEY, G. N</creatorcontrib><title>On the existence of exact conditions in the theory of electrical double layers</title><title>The Journal of chemical physics</title><description>It has long been thought that the total potential drop V across an isolated electrical double layer must be a monotonically increasing function of the surface charge density σ (i.e., ∂V/∂σ≥0). This result has been ‘‘established’’ by thermodynamic arguments of Landau and Lifshitz [Electrodynamics of Continuous Media (Pergamon, Oxford, 1960)] and by a more recent statistical mechanical method of Blum et al. [J. Chem. Phys. 72, 1902 (1981)]. Here we describe statistical mechanical analyses for both constant and fluctuating charge models. It is shown that the derivation of Blum et al. is in error and that correct statistical mechanical treatments do not determine the sign of ∂V/∂σ. However, some rigorous bounds for related quantities are found. We also point out a mathematical problem in the method of Landau and Lifshitz which appears to invalidate their argument. We conclude that at present there is no rigorous proof that ∂V/∂σ must be positive and that the existence of negative values cannot be ruled out.</description><subject>Chemistry</subject><subject>Electrochemistry</subject><subject>Exact sciences and technology</subject><subject>General and physical chemistry</subject><subject>Properties of electrolytes: conductivity</subject><issn>0021-9606</issn><issn>1089-7690</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1992</creationdate><recordtype>article</recordtype><recordid>eNo9kEFLxDAQhYMoWFfBn5CDBy9dZ9IkTY6y6Cos7kXPJZ2mGKntklSw_96uFQeGYeDjvcdj7BphjaCLO1xLjcbgCcsQjM1LbeGUZQACc6tBn7OLlD4AAEshM_ay7_n47rn_Dmn0PXk-tPPjaOQ09E0Yw9AnHhZo3iFOv0TnaYyBXMeb4avuPO_c5GO6ZGet65K_-rsr9vb48Lp5ynf77fPmfpeTUHLMaU7ojSJptFNNo0uwCrRqsbZeGwmFMxq8Em2pdGEVEc5TSyoEomhUU6zY7aJLcUgp-rY6xPDp4lQhVMceKqyWHmb0ZkEPLs152-h6CumfV1IezYsf-79a_w</recordid><startdate>19920301</startdate><enddate>19920301</enddate><creator>ATTARD, P</creator><creator>WEI, D</creator><creator>PATEY, G. N</creator><general>American Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19920301</creationdate><title>On the existence of exact conditions in the theory of electrical double layers</title><author>ATTARD, P ; WEI, D ; PATEY, G. N</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c254t-c188e85c486a5dd67095065f1b9e68403a860e52f756395cc1111b4c32112d5d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1992</creationdate><topic>Chemistry</topic><topic>Electrochemistry</topic><topic>Exact sciences and technology</topic><topic>General and physical chemistry</topic><topic>Properties of electrolytes: conductivity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>ATTARD, P</creatorcontrib><creatorcontrib>WEI, D</creatorcontrib><creatorcontrib>PATEY, G. N</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>The Journal of chemical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>ATTARD, P</au><au>WEI, D</au><au>PATEY, G. N</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the existence of exact conditions in the theory of electrical double layers</atitle><jtitle>The Journal of chemical physics</jtitle><date>1992-03-01</date><risdate>1992</risdate><volume>96</volume><issue>5</issue><spage>3767</spage><epage>3771</epage><pages>3767-3771</pages><issn>0021-9606</issn><eissn>1089-7690</eissn><coden>JCPSA6</coden><abstract>It has long been thought that the total potential drop V across an isolated electrical double layer must be a monotonically increasing function of the surface charge density σ (i.e., ∂V/∂σ≥0). This result has been ‘‘established’’ by thermodynamic arguments of Landau and Lifshitz [Electrodynamics of Continuous Media (Pergamon, Oxford, 1960)] and by a more recent statistical mechanical method of Blum et al. [J. Chem. Phys. 72, 1902 (1981)]. Here we describe statistical mechanical analyses for both constant and fluctuating charge models. It is shown that the derivation of Blum et al. is in error and that correct statistical mechanical treatments do not determine the sign of ∂V/∂σ. However, some rigorous bounds for related quantities are found. We also point out a mathematical problem in the method of Landau and Lifshitz which appears to invalidate their argument. We conclude that at present there is no rigorous proof that ∂V/∂σ must be positive and that the existence of negative values cannot be ruled out.</abstract><cop>Woodbury, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.461881</doi><tpages>5</tpages></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0021-9606 |
ispartof | The Journal of chemical physics, 1992-03, Vol.96 (5), p.3767-3771 |
issn | 0021-9606 1089-7690 |
language | eng |
recordid | cdi_crossref_primary_10_1063_1_461881 |
source | AIP Digital Archive |
subjects | Chemistry Electrochemistry Exact sciences and technology General and physical chemistry Properties of electrolytes: conductivity |
title | On the existence of exact conditions in the theory of electrical double layers |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T22%3A56%3A58IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-pascalfrancis_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20existence%20of%20exact%20conditions%20in%20the%20theory%20of%20electrical%20double%20layers&rft.jtitle=The%20Journal%20of%20chemical%20physics&rft.au=ATTARD,%20P&rft.date=1992-03-01&rft.volume=96&rft.issue=5&rft.spage=3767&rft.epage=3771&rft.pages=3767-3771&rft.issn=0021-9606&rft.eissn=1089-7690&rft.coden=JCPSA6&rft_id=info:doi/10.1063/1.461881&rft_dat=%3Cpascalfrancis_cross%3E5440950%3C/pascalfrancis_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |