Robustness of classical nucleation theory to chemical heterogeneity of crystal nucleating substrates

TL;DR

The paper investigates whether classical nucleation theory (CNT) remains predictive for heterogeneous crystal nucleation on chemically heterogeneous substrates. Using molecular dynamics and jumpy forward-flux sampling on a Lennard-Jones liquid, it compares a uniform liquiphilic wall to a checkerboard pattern of liquiphilic and liquiphobic patches, focusing on the CNT assumptions of a fixed contact angle and barrier scaling. It demonstrates that the CNT-based temperature dependence, ln R = ln A + C/(T(T−T_m)^2), describes both homogeneous and heterogeneous rates, with contact angles remaining nearly constant due to pinning and vertical growth on patterned surfaces; free-energy calculations reconcile apparent shifts in $T_m$ and corroborate the melting temperatures. The results illuminate why CNT often succeeds in experimental contexts with heterogeneous nucleation surfaces and offer design insights for substrates that control crystallization by patch geometry and chemistry.

Abstract

Heterogeneous nucleation is a process wherein extrinsic impurities facilitate freezing by lowering nucleation barriers and constitutes the dominant mechanism for crystallization in most systems. Classical nucleation theory (\textsc{Cnt}) has been remarkably successful in predicting the kinetics of heterogeneous nucleation, even on chemically and topographically non-uniform surfaces, despite its reliance on several restrictive assumptions, such as the idealized spherical-cap geometry of the crystalline nuclei. Here, we employ molecular dynamics simulations and jumpy forward flux sampling to investigate the kinetics and mechanism of heterogeneous crystal nucleation in a model atomic liquid. We examine both a chemically uniform, weakly attractive liquiphilic surface and a checkerboard surface comprised of alternating liquiphilic and liquiphobic patches. We find the nucleation rate to retain its canonical temperature dependence predicted by \textsc{Cnt} in both systems. Moreover, the contact angles of crystalline nuclei exhibit negligible dependence on nucleus size and temperature. On the checkerboard surface, nuclei maintain a fixed contact angle through pinning at patch boundaries and vertical growth into the bulk. These findings offer insights into the robustness of \textsc{Cnt} in experimental scenarios, where nucleating surfaces often feature active hotspots surrounded by inert or liquiphobic domains.

Figures (13)

• Figure 1: Schematic representations of (a) a chemically uniform and (b) a checkerboard-patterned surface. Black and light gray particles correspond to liquiphilic and liquiphobic patches, respectively. (c) Temperature dependence of homogeneous and heterogeneous nucleation rates in the Lj system. The symbols correspond to actual rates computed from jFFS with error bars smaller than symbol sizes. The curves correspond to Cnt fits according to Eqs. \ref{['eq:CNT-T-hom']} and \ref{['eq:CNT-T-het']} with $T_{m}$ as a fixed parameter (solid line) and as a fitting parameter (dashed line). Homogeneous nucleation rates are obtained from Refs. Haji-Akbari2018Forward-fluxParameters and HussainJCP2022.
• Figure 2: $p(z)$ of crystalline nuclei recorded at the last jFfs milestone (corresponding to $\sim262$ particles) of the rate calculation conducted in the checkerboard system at $k_BT/\varepsilon_{AA}=0.507$.
• Figure 3: Radial number density profiles alongside their respective hyperbolic tangent fits for the 2nd-6th layers of crystalline nuclei comprised of $\sim91$ particles obtained at $k_BT/\varepsilon_{AA}=0.510$ in the checkerboard system. (First layer excluded due to peculiarities of pruning.)
• Figure 4: Drop profile of a crystalline nucleus on the checkerboard surface at $k_BT/\varepsilon_{AA}=0.536$ with a cluster size of $\sim$841 particles. Filled circles correspond to individual $r_{\text{drop}}$'s computed for different layers, while the black curve corresponds to the quadratic fit. The estimated contact angle is illustrated in red.
• Figure 5: Two distinct paths within the $p-T$ diagram utilized for the liquid thermodynamic integration in the Lj system. Both paths go around the critical point as reported in Ref. Smit1992 and yield identical chemical potentials for the liquid.