{"id":"https://openalex.org/W2091998376","doi":"https://doi.org/10.1063/1.1668651","title":"Even Moments of the End-to-End Distance of Polymeric Chains","display_name":"Even Moments of the End-to-End Distance of Polymeric Chains","publication_year":1968,"publication_date":"1968-06-15","ids":{"openalex":"https://openalex.org/W2091998376","doi":"https://doi.org/10.1063/1.1668651","mag":"2091998376"},"language":"en","primary_location":{"id":"doi:10.1063/1.1668651","doi":"https://doi.org/10.1063/1.1668651","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.1668651","pdf_url":null,"source":{"id":"https://openalex.org/S77047749","display_name":"The Journal of Chemical Physics","issn_l":"0021-9606","issn":["0021-9606","1089-7690","1520-9032"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","medline","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Chemical Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"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/A5113625633","display_name":"Kazuo Nagai","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kazuo Nagai","raw_affiliation_strings":["Government Industrial Research Institute, Osaka, Midorigaoka 1, Ikeda, Osaka, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Government Industrial Research Institute, Osaka, Midorigaoka 1, Ikeda, Osaka, Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5113625633"],"corresponding_institution_ids":[],"apc_list":{"value":3500,"currency":"USD","value_usd":3500},"apc_paid":null,"fwci":1.5153,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.74064362,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":95},"biblio":{"volume":"48","issue":"12","first_page":"5646","last_page":"5655"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12044","display_name":"Advanced Physical and Chemical Molecular Interactions","score":0.9804999828338623,"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/T12044","display_name":"Advanced Physical and Chemical Molecular Interactions","score":0.9804999828338623,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.006800000090152025,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.002300000051036477,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/end-to-end-distance","display_name":"end-to-end distance","score":0.8679999709129333},{"id":"https://openalex.org/keywords/polymer-chains","display_name":"polymer chains","score":0.8569999933242798},{"id":"https://openalex.org/keywords/even-moments","display_name":"even moments","score":0.9049999713897705},{"id":"https://openalex.org/keywords/rotational-isomeric-state-model","display_name":"rotational isomeric state model","score":0.7680000066757202},{"id":"https://openalex.org/keywords/bond-rotation","display_name":"bond rotation","score":0.6690000295639038},{"id":"https://openalex.org/keywords/polyethylene","display_name":"polyethylene","score":0.8769999742507935},{"id":"https://openalex.org/keywords/end-to-end-distance-distribution","display_name":"end-to-end distance distribution","score":0.6470000147819519}],"concepts":[{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.568484365940094},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.5420829057693481},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5294373035430908},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49315327405929565},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46496516466140747},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4247759282588959},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42428526282310486},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3927423059940338},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.35320836305618286},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.341462641954422},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.3069707751274109},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1723543107509613},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13558220863342285},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1150827407836914},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1063/1.1668651","doi":"https://doi.org/10.1063/1.1668651","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.1668651","pdf_url":null,"source":{"id":"https://openalex.org/S77047749","display_name":"The Journal of Chemical Physics","issn_l":"0021-9606","issn":["0021-9606","1089-7690","1520-9032"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","medline","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Chemical Physics","raw_type":"journal-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":13,"referenced_works":["https://openalex.org/W1966078937","https://openalex.org/W2005089987","https://openalex.org/W2016446475","https://openalex.org/W2025212096","https://openalex.org/W2028517822","https://openalex.org/W2054144814","https://openalex.org/W2059985598","https://openalex.org/W2063114990","https://openalex.org/W2072892016","https://openalex.org/W2080478255","https://openalex.org/W2328540233","https://openalex.org/W2621818417","https://openalex.org/W4237676835"],"related_works":["https://openalex.org/W2072829023","https://openalex.org/W2005089987","https://openalex.org/W2026868392","https://openalex.org/W1988593360","https://openalex.org/W1997449234","https://openalex.org/W2004673189","https://openalex.org/W1998272930","https://openalex.org/W2054144814","https://openalex.org/W1619041985","https://openalex.org/W2025212096"],"abstract_inverted_index":{"A":[0],"method":[1,158],"is":[2,36,70,78,91,128],"developed":[3],"for":[4,24,68,122],"calculating":[5],"even":[6,118,154],"moments":[7,119,155],"\u3008r2k\u3009":[8,69],"of":[9,14,20,54,64,81,111,131,136,141,164],"the":[10,18,21,79,94,99,129,137,142],"end-to-end":[11,143],"distance":[12],"r":[13],"polymeric":[15],"chains,":[16],"on":[17],"basis":[19],"rotational-isomeric-state":[22],"approximation":[23],"rotations":[25],"about":[26],"skeletal":[27],"bonds.":[28,133],"Expressions":[29],"are":[30,46,150,166],"obtained":[31,117],"in":[32,38,52,83],"a":[33,49,65,109,157],"form":[34],"which":[35,84],"applicable":[37],"principle":[39],"to":[40,56,93],"arbitrary":[41],"k,":[42],"but":[43],"practical":[44],"applications":[45],"limited":[47],"by":[48,97,156],"tremendous":[50],"increase":[51],"orders":[53],"matrices":[55],"be":[57],"treated,":[58],"with":[59],"increasing":[60],"k.":[61],"The":[62],"order":[63],"matrix":[66],"derived":[67],"Hk5s":[71],"=":[72],"(k":[73],"+":[74],"4)!(4!k!)\u22121s,":[75],"where":[76,126],"s":[77],"number":[80,130],"states":[82],"each":[85],"bond":[86],"can":[87],"exist.":[88],"An":[89],"application":[90],"made":[92],"polyethylene":[95],"chain":[96],"using":[98],"familiar,":[100],"three-state":[101],"(trans,":[102],"gauche,":[103],"and":[104,147,161],"gauche":[105],"prime)":[106],"model.":[107],"With":[108],"computer":[110],"relatively":[112],"low":[113],"ability,":[114],"we":[115],"have":[116],"through":[120,124],"\u3008r12\u3009":[121],"n":[123,127],"400,":[125],"C\u2013C":[132],"Approximate":[134],"values":[135],"distribution":[138],"function":[139],"Wn(r)":[140],"vector":[144],"r,":[145],"Wn(0),":[146],"\u3008r\u2212":[148],"1\u3009,":[149],"calculated":[151],"from":[152],"these":[153],"previously":[159],"developed,":[160],"mathematical":[162],"implications":[163],"them":[165],"discussed.":[167]},"counts_by_year":[{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}