nucleation

LIT-919: Nucleation

2 min read

Properties5
StatusActive — read in full 2026-10-11 (NOTE-708), from the NIHPA author manuscript at PMC2995260; worth reading as the line's one clear statement, in a single paper, of classical nucleation theory (n* = 64Ω²α³/Δμ³, ΔG* = 32Ω²α³/Δμ²), of where it fails, and of the two things the author puts beside it: a solution–crystal spinodal, past which the nucleus is one molecule and there is no barrier, and the two-step mechanism, in which crystals nucleate inside metastable dense-liquid clusters that form fast, so that ordering inside them is the slow step. Read the sections on the nucleus size and spinodal, the two-step rate law, and the rate-determining step. The quantitative case is one protein, lysozyme. For metastable clusters the mechanism is inferred from a fitted kinetic model, not observed, and the claim that substrates act on the prefactor rather than the barrier is argued, not measured. It complicates CLAIM-176: the physical threshold is a size that moves with supersaturation and vanishes near the spinodal, not a fixed count.
Version2
Tagsnatural-sciences, thermodynamics
SupportsCLAIM-185 — The nucleation threshold of an argument is whatever makes a structure persist: a persistent structure is available as an anchor, and more complex structure can evolve only on anchors
Cited as “paper” byNOTE-708 — Vekilov — Nucleation

Graph View

Peter G. Vekilov (2010), Crystal Growth & Design 10(12), 5007–5019 — DOI-10.1021/cg1011633

Key takeaways

Read in full (NOTE-708).

  • For lysozyme, measured homogeneous nucleation rates are about ten orders of magnitude below the classical estimate. The paper places the error in the prefactor, not the barrier: the barrier is taken from the data.
  • A solution–crystal spinodal, defined kinetically as where the nucleus shrinks to one molecule, explains why rates level off and then pass a maximum as supersaturation and cooling increase.
  • Crystals nucleate inside metastable dense-liquid clusters, which form fast and persist (milliseconds to seconds; populations steady for hours). Ordering inside a cluster is the slow step, and accounts for about 10⁹ of the 10¹⁰ shortfall. For metastable clusters this is inferred from a fitted model, not observed.
  • Near the spinodal, heterogeneous substrates must act by helping clusters order, not by lowering the barrier. Argued, not measured.

Standing in the record

Read on 2026-10-11 (NOTE-708), beside LIT-926, which is unread and which this paper does not cite. It likely carries the argument that LIT-926 was filed for. It complicates CLAIM-176 without undercutting it: the physical threshold is a size, n* ∝ Δμ⁻³, that moves with the driving force and reaches one molecule at the spinodal, where most practical crystallization is said to run. A fixed count has no counterpart. The two-step reading floated for the line (an idea recurs first as a loose cluster, and ordering is the bottleneck) keeps its shape, but nothing in the physics corresponds to an outside agent recognizing the cluster.

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