{"id":"https://openalex.org/W2002123449","doi":"https://doi.org/10.1103/physreve.77.020401","title":"Multipole expansion of the electrostatic interaction between charged colloids at interfaces","display_name":"Multipole expansion of the electrostatic interaction between charged colloids at interfaces","publication_year":2008,"publication_date":"2008-02-07","ids":{"openalex":"https://openalex.org/W2002123449","doi":"https://doi.org/10.1103/physreve.77.020401","mag":"2002123449","pmid":"https://pubmed.ncbi.nlm.nih.gov/18351972"},"language":"en","primary_location":{"id":"doi:10.1103/physreve.77.020401","doi":"https://doi.org/10.1103/physreve.77.020401","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.77.020401","pdf_url":null,"source":{"id":"https://openalex.org/S35412551","display_name":"Physical Review E","issn_l":"1539-3755","issn":["1539-3755","1550-2376"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0706.3977","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028004174","display_name":"\u00c1lvaro Dom\u00ednguez","orcid":"https://orcid.org/0000-0002-8529-9667","observed_orcids":["https://orcid.org/0000-0002-8529-9667"]},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. Dom\u00ednguez","raw_affiliation_strings":["F\u00edsica Te\u00f3rica, Universidad de Sevilla, Apartado 1065, Sevilla, Spain","F\u00edsica Te\u00f3rica, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"F\u00edsica Te\u00f3rica, Universidad de Sevilla, Apartado 1065, Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"F\u00edsica Te\u00f3rica, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023396798","display_name":"Derek Frydel","orcid":"https://orcid.org/0000-0002-9153-802X","observed_orcids":["https://orcid.org/0000-0002-9153-802X"]},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]},{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"D. Frydel","raw_affiliation_strings":["Institut f\u00fcr Theoretische und Angewandte Physik, Universit\u00e4t Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany","Max-Planck-Institut f\u00fcr Metallforschung, Heisenbergstrasse 3, D-70569 Stuttgart, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische und Angewandte Physik, Universit\u00e4t Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]},{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Metallforschung, Heisenbergstrasse 3, D-70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087062624","display_name":"Martin Oettel","orcid":"https://orcid.org/0000-0002-1128-2045","observed_orcids":["https://orcid.org/0000-0002-1128-2045"]},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Oettel","raw_affiliation_strings":["Institut f\u00fcr Physik, Johannes Gutenberg Universit\u00e4t Mainz, WA 331, D-55099 Mainz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Physik, Johannes Gutenberg Universit\u00e4t Mainz, WA 331, D-55099 Mainz, Germany","institution_ids":["https://openalex.org/I197323543"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6271,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.80053872,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"77","issue":"2","first_page":"020401","last_page":"020401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12274","display_name":"Electrostatics and Colloid Interactions","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T12274","display_name":"Electrostatics and Colloid Interactions","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T11915","display_name":"Pickering emulsions and particle stabilization","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10721","display_name":"Surfactants and Colloidal Systems","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic 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/multipole-expansion","display_name":"multipole expansion","score":0.8709999918937683},{"id":"https://openalex.org/keywords/electrostatic-interactions","display_name":"electrostatic interactions","score":0.8690000176429749},{"id":"https://openalex.org/keywords/charged-colloids","display_name":"charged colloids","score":0.9580000042915344},{"id":"https://openalex.org/keywords/dielectric-interfaces","display_name":"dielectric interfaces","score":0.6690000295639038},{"id":"https://openalex.org/keywords/dipole-dipole-repulsion","display_name":"dipole-dipole repulsion","score":0.7649999856948853},{"id":"https://openalex.org/keywords/effective-interaction-potential","display_name":"effective interaction potential","score":0.6209999918937683},{"id":"https://openalex.org/keywords/colloidal-aggregation","display_name":"colloidal aggregation","score":0.5519999861717224}],"concepts":[{"id":"https://openalex.org/C52765159","wikidata":"https://www.wikidata.org/wiki/Q1027847","display_name":"Multipole expansion","level":2,"score":0.9322025775909424},{"id":"https://openalex.org/C59789625","wikidata":"https://www.wikidata.org/wiki/Q181780","display_name":"Colloid","level":2,"score":0.8093219995498657},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.7121055126190186},{"id":"https://openalex.org/C173523689","wikidata":"https://www.wikidata.org/wiki/Q215589","display_name":"Dipole","level":2,"score":0.6896865963935852},{"id":"https://openalex.org/C117626034","wikidata":"https://www.wikidata.org/wiki/Q26336","display_name":"Electrostatics","level":2,"score":0.6221578121185303},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5888722538948059},{"id":"https://openalex.org/C133386390","wikidata":"https://www.wikidata.org/wiki/Q184996","display_name":"Dielectric","level":2,"score":0.5789106488227844},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.517989993095398},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4010865390300751},{"id":"https://openalex.org/C159467904","wikidata":"https://www.wikidata.org/wiki/Q2001702","display_name":"Chemical physics","level":1,"score":0.37137371301651},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.3596913814544678},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.31636762619018555},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.18184775114059448},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17521092295646667},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1356373429298401},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.12145408987998962},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1103/physreve.77.020401","doi":"https://doi.org/10.1103/physreve.77.020401","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.77.020401","pdf_url":null,"source":{"id":"https://openalex.org/S35412551","display_name":"Physical Review E","issn_l":"1539-3755","issn":["1539-3755","1550-2376"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},{"id":"pmid:18351972","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/18351972","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":"Physical review. E, Statistical, nonlinear, and soft matter physics","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:0706.3977","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0706.3977","pdf_url":"https://arxiv.org/pdf/0706.3977","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:edoc.mpg.de:362565","doi":null,"is_oa":false,"landing_page_url":"http://edoc.mpg.de/362565","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":"Physical Review E, v.77 (2008)","raw_type":"Article"},{"id":"doi:10.48550/arxiv.0706.3977","doi":"https://doi.org/10.48550/arxiv.0706.3977","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0706.3977","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0706.3977","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0706.3977","pdf_url":"https://arxiv.org/pdf/0706.3977","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.7599999904632568,"display_name":"Clean water and sanitation","id":"https://metadata.un.org/sdg/6"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1970492582","https://openalex.org/W1972799250","https://openalex.org/W1995118318","https://openalex.org/W2002659345","https://openalex.org/W2009228377","https://openalex.org/W2013389985","https://openalex.org/W2023099472","https://openalex.org/W2030011050","https://openalex.org/W2053457824","https://openalex.org/W2058539528","https://openalex.org/W2069694834","https://openalex.org/W2076065644","https://openalex.org/W2086698089","https://openalex.org/W2087259794","https://openalex.org/W2092230113","https://openalex.org/W2158722817"],"related_works":["https://openalex.org/W3099126059","https://openalex.org/W2998290009","https://openalex.org/W2169534113","https://openalex.org/W3155911810","https://openalex.org/W2728211344","https://openalex.org/W2026049526","https://openalex.org/W3098004172","https://openalex.org/W1527170430","https://openalex.org/W2072031328","https://openalex.org/W2798544026"],"abstract_inverted_index":{"The":[0,37,59,104],"general":[1],"form":[2],"of":[3,33,106],"the":[4,43,53,57,77],"electrostatic":[5],"potential":[6,62],"around":[7],"an":[8],"arbitrarily":[9,65],"charged":[10,66],"colloid":[11],"at":[12,85],"a":[13,17,20,34],"flat":[14],"interface":[15],"between":[16,63],"dielectric":[18],"and":[19,26,46,71],"screening":[21],"phase":[22],"(such":[23],"as":[24],"air":[25],"water,":[27],"respectively)":[28],"is":[29,40,52,68,112],"analyzed":[30],"in":[31,42],"terms":[32,91],"multipole":[35],"expansion.":[36],"leading":[38],"term":[39],"isotropic":[41,70],"interfacial":[44],"plane":[45],"varies":[47],"with":[48,99],"d(-3)":[49],"where":[50],"d":[51],"in-plane":[54],"distance":[55],"from":[56],"colloid.":[58],"effective":[60],"interaction":[61,90],"two":[64],"colloids":[67],"likewise":[69],"proportional":[72],"to":[73],"d(-3),":[74],"thus":[75],"generalizing":[76],"dipole-dipole":[78],"repulsion":[79],"first":[80],"found":[81],"for":[82,95,109],"point":[83],"charges":[84],"water":[86],"interfaces.":[87],"Anisotropic":[88],"attractive":[89],"can":[92],"arise":[93],"only":[94],"higher":[96],"powers":[97],"d(-n)":[98],"n":[100],">":[101],"or":[102],"=4.":[103],"relevance":[105],"these":[107],"findings":[108],"recent":[110],"experiments":[111],"discussed.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2}],"updated_date":"2026-10-01T08:54:57.152042","created_date":"2025-10-10T00:00:00"}