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Reply to Smallenburg: Near‐melting nucleation and the exponential growth of hard‐sphere nucleation times

Aug 2026 · AIChE Journal · 0 citations · 9 references
Physics

Abstract

Smallenburg reports near-melting point simulations and observes a well-predicted spontaneous nucleation with mixed, finite-time morphology, in a Comment on our recent Perspective. The Comment's incorrect broader takeaway --- that equilibrium coexistence is"readily achievable"--- rests on an untested generalization from a single state point near the phase envelope, and misses entirely the intriguing role played by Frenkel's underlying mechanism. We reiterate the salient point missed by the Comment: the nucleation time grows astronomically with just tenths of a percent of volume fraction away from 53%. This phenomenology emerges from the entropy exchange mechanism Frenkel described, which predicts that spontaneous phase separation is dynamically accessible only down to about 53% volume fraction from the melting point, and astronomically long waiting times through most of the remaining phase envelope. We provide here calculations to address the potential misconception created by the Comment.

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