{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"8ef34f1b0b02d3c9c10a73aef3ffbc3f64f6d5780cbc7b01fe09536cbc3b61b3","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","d2e1a0e2edfa903e19dc1ac511ff02be23c3d1ea69f8a5574e58047d30548a16"],"salt":"b1684669f66a710d6fa7517e5cb957f1094f977c3c7e4a07cfdbd45e797d34ae","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"bio.nucleation.tolman-length","kind":"well-posed","literature_status":"contested","n":"2","parents":[],"plain":"Classical nucleation theory uses the surface tension of a flat interface, but critical nuclei are only a few molecules across, where the curvature should change the tension. The size and even the sign of this correction is not agreed on.","posed_since":"1949","precise":"For a nucleus of radius $R$, $\\gamma(R) = \\gamma_{\\infty}(1 - 2$ $\\delta$ $/ R + ...)$ with Tolman length $\\delta$. Determine the sign and magnitude of delta for the Lennard-Jones liquid-vapor interface and for crystal-melt interfaces, and whether the expansion in $1/R$ is valid at critical-nucleus sizes of about 10 to 30 Angstrom.","problem_ref":"d2e1a0e2edfa903e19dc1ac511ff02be23c3d1ea69f8a5574e58047d30548a16","references":"","settled_by":"Consistent determinations of $\\delta$ from independent simulation methods (droplet and bubble free energies, virial route), and a test of the $1/R$ expansion against measured nucleation barriers.","status_note":"Simulations for the Lennard-Jones liquid-vapor case point to a small negative $\\delta$ of order $-0.1$ particle diameters (approximately), but crystal-melt values and the validity of the expansion are unsettled.","title":"Curvature correction to the surface tension of small nuclei","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"59bd3a0d2a5055cc5a5ff76d31a3f8833c7d30a46d0602fbf9804b371a783271","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"0d441ebcef163bd30b45fb8d565c4117a3abe61e50bcd3c79ab9ed54cd56b118","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"JZ9pS9SjVcyvR5rxeXGmg1iH--8NXV-gXB3-WsavqRLzu-1OFkRZvBHCOlhjVFaNJW7C57aoG1Kou2uG_HDtBg"},"schema":"pubphys.envelope/1"},"record_hash":"59bd3a0d2a5055cc5a5ff76d31a3f8833c7d30a46d0602fbf9804b371a783271","leaf_index":2602}