{"id":"https://openalex.org/W7204491304","doi":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","title":"Mathematical models and calculation methods for optimally distributed electrical conductivity and reaction surface area of 3D carbon cathodes in galvanic metallization of composite and nanocomposite materials","display_name":"Mathematical models and calculation methods for optimally distributed electrical conductivity and reaction surface area of 3D carbon cathodes in galvanic metallization of composite and nanocomposite materials","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204491304","doi":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482"},"language":"en","primary_location":{"id":"doi:10.15828/2075-8545-2026-18-4-469-482","doi":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","is_oa":true,"landing_page_url":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","pdf_url":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","source":{"id":"https://openalex.org/S2738232315","display_name":"Nanotechnologies in Construction A Scientific Internet-Journal","issn_l":"2075-8545","issn":["2075-8545"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","dongbi-c","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310312702","host_organization_name":"OOO \"CNT \u00abNanoStroitelstvo\u00bb","host_organization_lineage":["https://openalex.org/P4310312702"],"host_organization_lineage_names":["OOO \"CNT \u00abNanoStroitelstvo\u00bb"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nanotechnologies in Construction A Scientific Internet-Journal","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024071076","display_name":"Alexander Nikolaevich Koshev","orcid":"https://orcid.org/0000-0003-3057-4980","observed_orcids":["https://orcid.org/0000-0003-3057-4980"]},"institutions":[{"id":"https://openalex.org/I4210131065","display_name":"Penza State University of Architecture and Construction","ror":"https://ror.org/03kh0v816","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210131065"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A.N. Koshev","raw_affiliation_strings":["Penza State University of Architecture and Construction , 440028 , Penza , Germana Titova str. , 28 , Russian Federation"],"raw_orcid":"https://orcid.org/0000-0003-3057-4980","affiliations":[{"raw_affiliation_string":"Penza State University of Architecture and Construction , 440028 , Penza , Germana Titova str. , 28 , Russian Federation","institution_ids":["https://openalex.org/I4210131065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081427993","display_name":"Valentina Vladimirovna Kuzina","orcid":"https://orcid.org/0000-0003-4511-7176","observed_orcids":["https://orcid.org/0000-0003-4511-7176"]},"institutions":[{"id":"https://openalex.org/I4210131065","display_name":"Penza State University of Architecture and Construction","ror":"https://ror.org/03kh0v816","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210131065"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"V.V. Kuzina","raw_affiliation_strings":["Penza State University of Architecture and Construction , 440028 , Penza , Germana Titova str. , 28 , Russian Federation"],"raw_orcid":"https://orcid.org/0000-0003-4511-7176","affiliations":[{"raw_affiliation_string":"Penza State University of Architecture and Construction , 440028 , Penza , Germana Titova str. , 28 , Russian Federation","institution_ids":["https://openalex.org/I4210131065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210131065"],"apc_list":{"value":614,"currency":"USD","value_usd":614},"apc_paid":{"value":614,"currency":"USD","value_usd":614},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"4","first_page":"469","last_page":"482"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11200","display_name":"Electrodeposition and Electroless Coatings","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2508","display_name":"Surfaces, Coatings and Films"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11200","display_name":"Electrodeposition and Electroless Coatings","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2508","display_name":"Surfaces, Coatings and Films"},"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/T11947","display_name":"Molten salt chemistry and electrochemical processes","score":0.003700000001117587,"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/T10030","display_name":"Electrocatalysts for Energy Conversion","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/2105","display_name":"Renewable Energy, Sustainability and the Environment"},"field":{"id":"https://openalex.org/fields/21","display_name":"Energy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/three-dimensional-electrodes","display_name":"three-dimensional electrodes","score":0.6980000138282776},{"id":"https://openalex.org/keywords/metal-electrodeposition","display_name":"metal electrodeposition","score":0.8109999895095825},{"id":"https://openalex.org/keywords/electrical-conductivity-distribution","display_name":"electrical conductivity distribution","score":0.6520000100135803},{"id":"https://openalex.org/keywords/reactive-surface-area","display_name":"reactive surface area","score":0.9359999895095825},{"id":"https://openalex.org/keywords/optimal-control","display_name":"optimal control","score":0.8399999737739563},{"id":"https://openalex.org/keywords/pontryagin-s-maximum-principle","display_name":"Pontryagin maximum principle","score":0.9739999771118164},{"id":"https://openalex.org/keywords/boundary-value-problems","display_name":"boundary value problems","score":0.7699999809265137},{"id":"https://openalex.org/keywords/composite-materials","display_name":"composite materials","score":0.6340000033378601},{"id":"https://openalex.org/keywords/nanocomposites","display_name":"nanocomposites","score":0.9200000166893005},{"id":"https://openalex.org/keywords/coating-uniformity","display_name":"coating uniformity","score":0.6830000281333923}],"concepts":[{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.7964000105857849},{"id":"https://openalex.org/C29633239","wikidata":"https://www.wikidata.org/wiki/Q209440","display_name":"Galvanic cell","level":2,"score":0.6381000280380249},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.6335999965667725},{"id":"https://openalex.org/C92880739","wikidata":"https://www.wikidata.org/wiki/Q2639556","display_name":"Nanocomposite","level":2,"score":0.6304000020027161},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.5842000246047974},{"id":"https://openalex.org/C69990965","wikidata":"https://www.wikidata.org/wiki/Q65402698","display_name":"Electrical resistivity and conductivity","level":2,"score":0.5587000250816345},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.5396999716758728},{"id":"https://openalex.org/C49110097","wikidata":"https://www.wikidata.org/wiki/Q175233","display_name":"Cathode","level":2,"score":0.5153999924659729},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4767000079154968},{"id":"https://openalex.org/C140205800","wikidata":"https://www.wikidata.org/wiki/Q5860","display_name":"Carbon fibers","level":3,"score":0.4422000050544739},{"id":"https://openalex.org/C131540310","wikidata":"https://www.wikidata.org/wiki/Q907564","display_name":"Conductivity","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C513720949","wikidata":"https://www.wikidata.org/wiki/Q1778729","display_name":"Carbon nanotube","level":2,"score":0.3416999876499176},{"id":"https://openalex.org/C150077022","wikidata":"https://www.wikidata.org/wiki/Q3136137","display_name":"Response surface methodology","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C17525397","wikidata":"https://www.wikidata.org/wiki/Q176140","display_name":"Electrode","level":2,"score":0.3001999855041504},{"id":"https://openalex.org/C202374169","wikidata":"https://www.wikidata.org/wiki/Q124291","display_name":"Electrical conductor","level":2,"score":0.29899999499320984},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.2831000089645386},{"id":"https://openalex.org/C2781371449","wikidata":"https://www.wikidata.org/wiki/Q2367906","display_name":"Galvanic corrosion","level":3,"score":0.2816999852657318},{"id":"https://openalex.org/C155672457","wikidata":"https://www.wikidata.org/wiki/Q61231","display_name":"Nanoparticle","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C44038986","wikidata":"https://www.wikidata.org/wiki/Q764245","display_name":"Carbon black","level":3,"score":0.27079999446868896},{"id":"https://openalex.org/C52859227","wikidata":"https://www.wikidata.org/wiki/Q7877","display_name":"Electrochemistry","level":3,"score":0.25769999623298645},{"id":"https://openalex.org/C91145125","wikidata":"https://www.wikidata.org/wiki/Q7645963","display_name":"Surface conductivity","level":3,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.15828/2075-8545-2026-18-4-469-482","doi":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","is_oa":true,"landing_page_url":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","pdf_url":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","source":{"id":"https://openalex.org/S2738232315","display_name":"Nanotechnologies in Construction A Scientific Internet-Journal","issn_l":"2075-8545","issn":["2075-8545"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","dongbi-c","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310312702","host_organization_name":"OOO \"CNT \u00abNanoStroitelstvo\u00bb","host_organization_lineage":["https://openalex.org/P4310312702"],"host_organization_lineage_names":["OOO \"CNT \u00abNanoStroitelstvo\u00bb"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nanotechnologies in Construction A Scientific Internet-Journal","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9d3d0d57a47e44bca703f9433b29f42a","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/9d3d0d57a47e44bca703f9433b29f42a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"\u041d\u0430\u043d\u043e\u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u0441\u0442\u0440\u043e\u0438\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u0435, Vol 18, Iss 4, Pp 469-482 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.15828/2075-8545-2026-18-4-469-482","doi":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","is_oa":true,"landing_page_url":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","pdf_url":"https://doi.org/10.15828/2075-8545-2026-18-4-469-482","source":{"id":"https://openalex.org/S2738232315","display_name":"Nanotechnologies in Construction A Scientific Internet-Journal","issn_l":"2075-8545","issn":["2075-8545"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","dongbi-c","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310312702","host_organization_name":"OOO \"CNT \u00abNanoStroitelstvo\u00bb","host_organization_lineage":["https://openalex.org/P4310312702"],"host_organization_lineage_names":["OOO \"CNT \u00abNanoStroitelstvo\u00bb"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nanotechnologies in Construction A Scientific Internet-Journal","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.5690000057220459,"id":"https://metadata.un.org/sdg/7"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204491304.pdf","grobid_xml":"https://content.openalex.org/works/W7204491304.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4386609477","https://openalex.org/W4409906444"],"related_works":["https://openalex.org/W4409906444","https://openalex.org/W4200162222","https://openalex.org/W1989583970","https://openalex.org/W4244734219","https://openalex.org/W2058185759","https://openalex.org/W2050190651","https://openalex.org/W227533670","https://openalex.org/W2032134906","https://openalex.org/W2202295556","https://openalex.org/W3145523150"],"abstract_inverted_index":{"Introduction.The":[0],"task":[1],"of":[2,30,40,48,69,77,91,100,108,113,123,125,159,162,169,178,181,199,205,221,236,246,260,283,293,307,318,326],"uniformly":[3],"coating":[4],"carbon-graphite":[5,295,320,335],"fibers":[6,336],"with":[7,85,153,216,337],"metal":[8,61,138,182,222],"as":[9,55,57],"a":[10,16,49,67,116],"base":[11],"for":[12,98,128,226,263],"composite":[13],"materials":[14,81],"is":[15,20],"pressing":[17],"issue.Galvanic":[18],"metallization":[19,102,234,297],"preferred":[21],"due":[22],"to":[23,26,58,249,278,289,302,322,333],"the":[24,28,31,37,75,101,106,109,121,129,141,157,163,170,179,185,203,206,217,233,237,244,258,261,280,291,304,308,314,319,324,329],"ability":[25],"control":[27,149,154,200],"parameters":[29,96,201],"electrochemical":[32,219],"system.Materials":[33],"and":[34,44,66,71,83,95,104,136,165,172,196,212,232,256,271,288,313,332],"methods.To":[35],"determine":[36,303],"effective":[38,305],"values":[39,161,306],"specific":[41,166,310],"electrical":[42,311],"conductivity":[43,312],"reactive":[45,315],"surface":[46,167,316],"area":[47,168,317],"carbon":[50,79],"flow":[51],"three-dimensional":[52],"electrode":[53,142,171,186,230],"(FTE),":[54],"well":[56],"identify":[59],"rational":[60],"electrodeposition":[62,223,327],"modes,":[63],"mathematical":[64,207,210,247,268],"modeling":[65,269],"combination":[68],"calculated":[70],"experimental":[72],"data":[73],"regarding":[74],"feasibility":[76],"producing":[78],"fiber":[80],"(CFM)":[82],"FTEs":[84,255,287],"desired":[86,110,338],"properties":[87,231,292],"are":[88,214,275],"useful.Proper":[89],"selection":[90,198],"electrolyzer":[92],"operating":[93],"modes":[94],"allows":[97],"intensification":[99],"process":[103,235],"facilitates":[105],"production":[107],"composites.Results.Mathematical":[111],"models":[112,211,248,262],"electrolysis":[114,252,284],"using":[115,202],"CFM":[117],"were":[118,146],"developed":[119],"in":[120,156,224,229,254,286],"form":[122,158],"systems":[124],"differential":[126],"equations":[127,204],"potential":[130],"distribution":[131,183],"functions,":[132],"polarizing":[133],"current":[134],"density,":[135],"deposited":[137],"concentration":[139],"across":[140,184,328],"thickness.Boundary":[143],"value":[144],"problems":[145],"formulated.An":[147],"optimal":[148],"problem":[150],"was":[151,189],"posed":[152],"actions":[155],"distributed":[160,309],"resistivity":[164],"an":[173],"optimization":[174],"criterion":[175],"-an":[176],"indicator":[177],"uniformity":[180,325],"thickness.The":[187],"solution":[188],"based":[190],"on":[191],"S.L.":[192],"Pontryagin's":[193],"maximum":[194],"principle":[195],"direct":[197],"model.Discussion.The":[208],"proposed":[209],"methods":[213,270],"consistent":[215],"modern":[218],"theory":[220],"FTEs.Accounting":[225],"dynamic":[227],"changes":[228],"carbongraphite":[238],"filaments":[239],"that":[240],"comprise":[241],"it":[242],"expands":[243],"applicability":[245],"describe":[250],"real-world":[251,264],"processes":[253,285],"improves":[257],"adequacy":[259],"physicochemical":[265],"processes.Conclusion.The":[266],"presented":[267],"computational":[272],"algorithms":[273],"1)":[274],"used":[276],"both":[277],"study":[279],"theoretical":[281],"principles":[282],"analyze":[290],"actual":[294],"material":[296,321],"processes;":[298],"2)":[299],"allow":[300],"one":[301],"improve":[323],"TFE":[330],"thickness":[331],"produce":[334],"properties.":[339]},"counts_by_year":[],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2026-08-28T00:00:00"}