{"paper":{"title":"Integral-equation analysis of transient diffusion-limited currents at disk electrodes: Asymptotic expansion and compact approximation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A Padé approximant yields a compact analytical expression for transient currents at disk electrodes over experimental time ranges.","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"Kazuhiko Seki, Masahiro Yamamoto, Yuko Yokoyama","submitted_at":"2026-04-10T12:40:59Z","abstract_excerpt":"The transient diffusion-limited current at a disk electrode following a change in interfacial ion concentration induced by a potential step is analyzed with direct relevance to chronoamperometric measurements. The mixed-boundary diffusion problem is formulated in the Laplace domain and reduced to a Fredholm integral equation that directly determines the Faradaic current. The steady-state limit recovers Saito's equation, while a systematic long-time asymptotic expansion quantifies the approach to steady state. A Pad\\'{e} approximant yields a compact analytical expression in the time domain that"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"A Padé approximant yields a compact analytical expression in the time domain that accurately describes the current over experimentally relevant time ranges.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The mixed-boundary diffusion problem can be reduced without loss of accuracy to a Fredholm integral equation in the Laplace domain whose solution directly determines the Faradaic current.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A Laplace-domain Fredholm integral equation plus Padé approximant yields a compact analytical expression for the transient diffusion-limited current at disk electrodes across relevant timescales.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A Padé approximant yields a compact analytical expression for transient currents at disk electrodes over experimental time ranges.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"441df9ecb145b6d8734279d7300999368996db9902d00c8209a80448e870eda7"},"source":{"id":"2604.09274","kind":"arxiv","version":1},"verdict":{"id":"bbd84ccb-d0a5-4ee4-b93d-28c968f18aa8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T16:45:11.395948Z","strongest_claim":"A Padé approximant yields a compact analytical expression in the time domain that accurately describes the current over experimentally relevant time ranges.","one_line_summary":"A Laplace-domain Fredholm integral equation plus Padé approximant yields a compact analytical expression for the transient diffusion-limited current at disk electrodes across relevant timescales.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The mixed-boundary diffusion problem can be reduced without loss of accuracy to a Fredholm integral equation in the Laplace domain whose solution directly determines the Faradaic current.","pith_extraction_headline":"A Padé approximant yields a compact analytical expression for transient currents at disk electrodes over experimental time ranges."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.09274/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":73,"sample":[{"doi":"10.1021/cr0680686","year":2008,"title":"Hapiot \\ and\\ author C","work_id":"5796d42d-685c-4abe-aa6b-737dbc85ccab","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/0022-0728(84)80051-0","year":1984,"title":"Winlove , author K","work_id":"c0f6336f-08ac-4f9e-9b9c-3cf9fb31ca75","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/0022-0728(91)85056-u","year":1991,"title":"Denuault , author M","work_id":"f1b5ebd9-bb5f-4e7f-8029-b3f5013ca31a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/0141-5425(91)90112-k","year":1991,"title":"O'Hare , author C","work_id":"080292ea-7164-4801-9830-25845139cb8a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1002/elan.1140050802","year":1993,"title":"Aoki ,\\ https://doi.org/10.1002/elan.1140050802 journal journal Electroanalysis \\ volume 5 ,\\ pages 627 ( year 1993 ) NoStop","work_id":"696e6aef-b2b9-4f2f-bfaf-411139893213","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":73,"snapshot_sha256":"7ac434485a50c0ecdc89c59269439a539817810b07a1a716e46c108f12959e6d","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}