{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"a3b5fd6032a459ab27225d4299f76414a605f5464582c587447a7a1d747ec94b","created":"2026-10-03T07:17:57Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"d46c02244a1c39c0547b6d9496ef8e99273b48f9b8571282b10d094c4957c787","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"bio.nucleation.tolman-length","kind":"well-posed","literature_status":"contested","n":"1","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_inf (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":null,"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 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