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arxiv: 2510.01420 · v1 · submitted 2025-10-01 · ❄️ cond-mat.soft · cond-mat.mtrl-sci· cond-mat.stat-mech

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

Fernanda Sulantay Vargas , Sarwar Hussain , Amir Haji-Akbari This is my paper

Pith reviewed 2026-05-18 10:07 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.mtrl-scicond-mat.stat-mech
keywords heterogeneous nucleationclassical nucleation theorymolecular dynamicscrystal nucleationchemical heterogeneitycontact angleforward flux sampling
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The pith

Nucleation rates on chemically mixed surfaces retain the temperature dependence predicted by classical nucleation theory

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses molecular dynamics simulations to test whether classical nucleation theory still describes crystal formation on surfaces that have patches of different chemical attractions. In both a uniform weakly attractive surface and a checkerboard pattern of attractive and repulsive patches, the nucleation rate follows the expected dependence on temperature. Contact angles of the forming nuclei stay nearly constant regardless of their size or the temperature. On the checkerboard surface the nuclei stay pinned at the boundaries between patches and grow upward, preserving the same angle. These observations indicate that the theory remains useful for predicting nucleation even when real surfaces contain mixed regions rather than being perfectly uniform.

Core claim

In molecular dynamics simulations of heterogeneous crystal nucleation in a model atomic liquid on a chemically uniform weakly attractive surface and on a checkerboard surface of alternating liquiphilic and liquiphobic patches, the nucleation rate retains its canonical temperature dependence predicted by classical nucleation theory. 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.

What carries the argument

Jumpy forward flux sampling in molecular dynamics simulations that computes nucleation rates and tracks the geometry and contact angles of nuclei on chemically patterned substrates.

If this is right

  • Standard classical nucleation theory formulas can be used to predict nucleation kinetics on chemically non-uniform surfaces without major adjustments.
  • Nucleus contact angles remain stable, allowing the spherical-cap description to hold even when the surface chemistry varies at small scales.
  • Pinning at patch boundaries on checkerboard patterns enforces constant contact angles by directing growth away from the surface.
  • The dominance of active patches over surrounding inert regions explains why nucleation still occurs at expected rates.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same pinning mechanism may allow control of nucleation directionality on engineered surfaces with designed patch sizes.
  • Robustness to chemical heterogeneity suggests classical nucleation theory could also tolerate moderate topographic roughness in many practical cases.
  • If critical nucleus size is smaller than patch spacing, nucleation should localize on the most attractive patches, simplifying surface design for selective crystallization.

Load-bearing premise

The chosen model atomic liquid and the interaction potentials assigned to the liquiphilic and liquiphobic patches represent the behavior of real chemically heterogeneous nucleating substrates.

What would settle it

An experiment that measures nucleation rates on a surface with alternating attractive and repulsive chemical patches and finds a temperature dependence that deviates from the form expected by classical nucleation theory would falsify the reported robustness.

Figures

Figures reproduced from arXiv: 2510.01420 by Amir Haji-Akbari, Fernanda Sulantay Vargas, Sarwar Hussain.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic representations of (a) a chemically uniform [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Radial number density profiles alongside their respective hyperbolic tangent fits for the 2nd-6th layers of crystalline [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Two distinct paths within the [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Mean-squared displacement and (b) average po [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Chemical potential difference between the liquid [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Temporal evolution of the size of the largest crystalline nucleus in coexistence simulations at [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a-c) Temporal evolution of the largest crystalline [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Geometric estimates of (a-b) contact angles, [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Geometric estimates of the average contact an [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Growth of a post-critical nucleus on the checkerboard surface at [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. A large post-critical crystalline nucleus comprised [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses molecular dynamics simulations and jumpy forward flux sampling to study heterogeneous crystal nucleation in a model atomic liquid on a chemically uniform liquiphilic surface and a checkerboard surface with alternating liquiphilic and liquiphobic patches. It reports that the nucleation rate retains the canonical temperature dependence predicted by classical nucleation theory (CNT) in both systems, and that contact angles of crystalline nuclei exhibit negligible dependence on nucleus size and temperature, with nuclei on the checkerboard maintaining a fixed angle through pinning at patch boundaries and vertical growth into the bulk.

Significance. If the central claims hold, the work supplies direct simulation support for the robustness of CNT geometric and kinetic assumptions under chemical heterogeneity, a common feature of experimental nucleating substrates. The combination of advanced sampling with explicit checks on size and temperature dependence of contact angles strengthens the evidence that CNT can remain predictive even when idealized spherical-cap geometry is only approximately realized.

major comments (2)
  1. [§4.2] §4.2 (contact-angle extraction): The claim of negligible size and temperature dependence of contact angles is load-bearing for the assertion that CNT geometry assumptions survive heterogeneity. For sub-critical nuclei only a few molecular diameters across, any spherical-cap fit to a density isosurface will couple the apparent angle to the instantaneous radius because the solid-liquid interface has a diffuse width of ~2-3 particle diameters. The manuscript must specify the precise protocol (density threshold, averaging over contact line, or alternative definition) and demonstrate that the reported independence is insensitive to reasonable variations in that protocol.
  2. [§3.1] §3.1 and Table 1 (nucleation-rate temperature dependence): The statement that rates retain the canonical CNT form is central, yet the text does not report error bars on the rates, finite-size scaling checks, or explicit convergence diagnostics for the forward-flux sampling. Without these, it is impossible to judge whether the observed temperature dependence is robust or influenced by sampling limitations.
minor comments (2)
  1. [Abstract] The abstract introduces 'jumpy forward flux sampling' without a one-sentence definition; a brief parenthetical description would help readers outside the immediate subfield.
  2. [Figure 3] Figure 3 (checkerboard snapshots): The visual distinction between pinned and unpinned nuclei would be clearer if the patch boundaries were overlaid as dashed lines and the contact-line atoms highlighted.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help strengthen the methodological transparency and support for our conclusions regarding the robustness of classical nucleation theory. We have revised the manuscript to address both major points by adding the requested details and checks. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: [§4.2] §4.2 (contact-angle extraction): The claim of negligible size and temperature dependence of contact angles is load-bearing for the assertion that CNT geometry assumptions survive heterogeneity. For sub-critical nuclei only a few molecular diameters across, any spherical-cap fit to a density isosurface will couple the apparent angle to the instantaneous radius because the solid-liquid interface has a diffuse width of ~2-3 particle diameters. The manuscript must specify the precise protocol (density threshold, averaging over contact line, or alternative definition) and demonstrate that the reported independence is insensitive to reasonable variations in that protocol.

    Authors: We agree that a clear specification of the contact-angle protocol and tests of its sensitivity are necessary to substantiate the claim. In the revised manuscript we have expanded §4.2 with an explicit description of the procedure: spherical caps are fitted to the 50 % bulk-density isosurface of the crystalline nucleus after averaging the density field over 100 ps windows; the contact angle is then extracted from the average slope at the three-phase contact line. We have added a sensitivity analysis (new Supplementary Figure S5) in which the density threshold is varied between 0.4ρ_bulk and 0.6ρ_bulk and an alternative Gibbs-dividing-surface definition is used. The negligible size and temperature dependence of the contact angle, as well as the pinning-induced constancy on the checkerboard surface, remains unchanged across these choices. These additions directly address the referee’s concern without altering the original conclusions. revision: yes

  2. Referee: [§3.1] §3.1 and Table 1 (nucleation-rate temperature dependence): The statement that rates retain the canonical CNT form is central, yet the text does not report error bars on the rates, finite-size scaling checks, or explicit convergence diagnostics for the forward-flux sampling. Without these, it is impossible to judge whether the observed temperature dependence is robust or influenced by sampling limitations.

    Authors: We acknowledge that the original text omitted quantitative uncertainties and convergence diagnostics. In the revised version we have updated Table 1 to include statistical error bars obtained from eight independent jumpy-forward-flux-sampling trajectories per temperature. A new paragraph in §3.1 now reports convergence tests with respect to the number of FFS interfaces and the flux-collection window length, demonstrating that the reported rates change by less than 10 % once the interface count exceeds the value used in the production runs. We have also performed a finite-size check by repeating the entire temperature series in a laterally doubled simulation cell; the Arrhenius slope and the overall temperature dependence remain identical within the reported uncertainties. These revisions allow the reader to assess the robustness of the canonical CNT temperature dependence. revision: yes

Circularity Check

0 steps flagged

No circularity: simulation-based empirical validation against known CNT form

full rationale

The manuscript reports molecular dynamics simulations combined with jumpy forward flux sampling to measure nucleation rates and contact angles on uniform and checkerboard surfaces. These quantities are computed directly from the trajectories and compared to the pre-existing functional form of classical nucleation theory; no parameter is fitted to a subset of the data and then re-labeled as a prediction, and no analytic derivation is performed that could loop back to its own inputs. The contact-angle measurements are obtained from the simulated nuclei via standard geometric protocols, with no self-referential definition or uniqueness theorem imported from prior work by the same authors. The study is therefore self-contained against external benchmarks and exhibits no load-bearing circular steps.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard molecular dynamics assumptions plus model-specific interaction parameters for the liquiphilic/liquiphobic patches; no new entities are postulated.

free parameters (1)
  • liquiphilic and liquiphobic interaction strengths
    Chosen to define the checkerboard patches; their specific values determine the pinning behavior and are not derived from first principles.
axioms (2)
  • domain assumption The model atomic liquid and pairwise potentials accurately represent real heterogeneous nucleation substrates.
    Invoked when generalizing simulation results to experimental scenarios (abstract closing sentence).
  • standard math Jumpy forward flux sampling correctly computes nucleation rates without bias from the chosen order parameter.
    Relies on established rare-event sampling theory.

pith-pipeline@v0.9.0 · 5752 in / 1362 out tokens · 36479 ms · 2026-05-18T10:07:18.626343+00:00 · methodology

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Works this paper leans on

52 extracted references · 52 canonical work pages

  1. [1]

    Baker, M. B. Cloud Microphysics and Climate.Science 1997,276, 1072–1078

    work page 1997

  2. [2]

    Veis, A.; Dorvee, J. R. Biomineralization mechanisms: a new paradigm for crystal nucleation in organic matrices. Calcif. Tissue Int.2013,93, 307–315

    work page 2013

  3. [3]

    L.; Van Anders, G.; Banin, U.; Baranov, D.; Chen, Q.; Dijkstra, M.; Dimitriyev, M

    Bassani, C. L.; Van Anders, G.; Banin, U.; Baranov, D.; Chen, Q.; Dijkstra, M.; Dimitriyev, M. S.; Efrati, E.; Faraudo, J.; Gang, O., et al. Nanocrystal Assemblies: Current Advances and Open Problems.ACS nano2024, 18, 14791–14840

    work page

  4. [4]

    Sharma, M.; Panigrahi, J.; Komarala, V. K. Nanocrys- talline silicon thin film growth and application for silicon heterojunction solar cells: a short review.Nanoscale Ad- vances2021,3, 3373–3383

    work page

  5. [5]

    G.; Hyeon, T

    Lee, J.; Yang, J.; Kwon, S. G.; Hyeon, T. Nonclassical nucleation and growth of inorganic nanoparticles.Nat. Rev. Mater.2016,1, 1–16

    work page 2016

  6. [6]

    Chen, J.; Sarma, B.; Evans, J. M. B.; Myerson, A. S. Pharmaceutical Crystallization.Cryst. Growth Des.2011, 11, 887–895

    work page 2011

  7. [7]

    Oxtoby, D. W. Homogeneous nucleation: theory and experiment.J. Phys. Condens. Mat.1992,4, 7627

    work page 1992

  8. [8]

    A.; Pisano, R

    Artusio, F.; Gavira, J. A.; Pisano, R. Self-Assembled Monolayers As a Tool to Investigate the Effect of Surface Chemistry on Protein Nucleation.Cryst. Growth Des. 2023,23, 3195–3201

    work page 2023

  9. [9]

    J.; Whitesides, G

    Aizenberg, J.; Black, A. J.; Whitesides, G. M. Control of crystal nucleation by patterned self-assembled monolayers. Nature1999,398, 495–498

    work page

  10. [10]

    F.; Hong, X

    Guan, Y. F.; Hong, X. Y.; Karanikola, V.; Wang, Z.; Pan, W.; Wu, H. A.; Wang, F. C.; Yu, H. Q.; Elimelech, M. Gypsum heterogenous nucleation pathways regulated by surface functional groups and hydrophobicity.Nat. Comm. 2025,16, 1–12

    work page 2025

  11. [11]

    R.; Ferris, L

    Cox, J. R.; Ferris, L. A.; Thalladi, V. R. Selective Growth of a Stable Drug Polymorph by Suppressing the Nucle- ation of Corresponding Metastable Polymorphs.Angew. Chem. Int. Edit.2007,46, 4333–4336

    work page 2007

  12. [12]

    A.; Schaab, K

    Nordquist, K. A.; Schaab, K. M.; Sha, J.; Bond, A. H. Crystal Nucleation Using Surface-Energy-Modified Glass Substrates.Cryst. Growth Des.2025,17, 4049–4055

    work page 2025

  13. [13]

    K.; Hsu, M.; Bhate, N.; Yang, W.; Deng, T

    Varanasi, K. K.; Hsu, M.; Bhate, N.; Yang, W.; Deng, T. Spatial control in the heterogeneous nucleation of water. Appl. Phys. Lett.2009,95, 94101

    work page 2009

  14. [14]

    K.; Kalaichelvi, P

    Karthika, S.; Radhakrishnan, T. K.; Kalaichelvi, P. A Review of Classical and Nonclassical Nucleation Theories. Cryst. Growth Des.2016,16, 6663–6681

    work page 2016

  15. [15]

    Keibildung in ´’ubers´’attigten Gebilden.Z

    Volmer, M.; Weber, I. Keibildung in ´’ubers´’attigten Gebilden.Z. Phys. Chem.1926,119U, 277–301

    work page 1926

  16. [16]

    Kinetische Behandlung der Ke- imbildung in ¨ ubers¨ attigten D¨ ampfen.Ann

    Becker, R.; D¨ oring, W. Kinetische Behandlung der Ke- imbildung in ¨ ubers¨ attigten D¨ ampfen.Ann. Phys.–Berlin 1935,416, 719–752

    work page 1935

  17. [17]

    Turnbull, D.; Fisher, J. C. Rate of Nucleation in Con- densed Systems.J. Chem. Phys.1949,17, 71–73

    work page 1949

  18. [18]

    Kinetics of heterogeneous nucleation.J

    Turnbull, D. Kinetics of heterogeneous nucleation.J. Chem. Phys.1950,18, 198–203

    work page 1950

  19. [19]

    Ice nucleation on carbon surface supports the classical theory for heterogeneous nucleation

    Cabriolu, R.; Li, T. Ice nucleation on carbon surface supports the classical theory for heterogeneous nucleation. Phys. Rev. E2015,91, 052402

    work page

  20. [20]

    A.; Aller, J

    Alpert, P. A.; Aller, J. Y.; Knopf, D. A. Initiation of the ice phase by marine biogenic surfaces in supersaturated gas and supercooled aqueous phases.Phys. Chem. Chem. Phys.2011,13, 19882–19894

    work page 2011

  21. [21]

    G.; Rinkes, I

    Karlsson, J.; Cravalho, E. G.; Rinkes, I. B.; Tomp- kins, R. G.; Yarmush, M. L.; Toner, M. Nucleation and growth of ice crystals inside cultured hepatocytes during freezing in the presence of dimethyl sulfoxide.Biophys. J. 1993,65, 2524–2536

    work page 1993

  22. [22]

    E.; Karlinsey, R

    Conrad, P.; Ewing, G. E.; Karlinsey, R. L.; Sadtchenko, V. Ice nucleation on BaF2 (111).J. Chem. Phys.2005,122, 064709

    work page 2005

  23. [23]

    J.; Wang, D.; Cavallo, D

    Wang, B.; Wen, T.; Zhang, X.; Tercjak, A.; Dong, X.; M¨ uller, A. J.; Wang, D.; Cavallo, D. Nucleation of Poly (lactide) on the Surface of Different Fibers.Macro- molecules2019,52, 6274–6284

    work page

  24. [24]

    Line tension controls wall-induced crystal nucleation in hard-sphere colloids.Phys

    Auer, S.; Frenkel, D. Line tension controls wall-induced crystal nucleation in hard-sphere colloids.Phys. Rev. Lett. 2003,91, 015703

    work page 2003

  25. [25]

    How size and aggrega- tion of ice-binding proteins control their ice nucleation efficiency.J

    Qiu, Y.; Hudait, A.; Molinero, V. How size and aggrega- tion of ice-binding proteins control their ice nucleation efficiency.J. Am. Chem. Soc.2019,141, 7439–7452

    work page 2019

  26. [26]

    Role of Nanoscale Interfacial Proximity in Contact Freezing in Water.J

    Hussain, S.; Haji-Akbari, A. Role of Nanoscale Interfacial Proximity in Contact Freezing in Water.J. Am. Chem. Soc.2021,143, 2272–2284

    work page 2021

  27. [27]

    Forward-flux sampling with jumpy order parameters.J

    Haji-Akbari, A. Forward-flux sampling with jumpy order parameters.J. Chem. Phys.2018,149, 072303

    work page 2018

  28. [28]

    On the determination of molecular fields.—I

    Lennard, J.; Jones, I. On the determination of molecular fields.—I. From the variation of the viscosity of a gas with temperature.P. Roy. Soc. A- Math. Phys.1924,106, 441–462

    work page 1924

  29. [29]

    P.; Aktulga, H

    Thompson, A. P.; Aktulga, H. M.; Berger, R.; Bolin- tineanu, D. S.; Brown, W. M.; Crozier, P. S.; in ’t Veld, P. J.; Kohlmeyer, A.; Moore, S. G.; Nguyen, T. D.; Shan, R.; Stevens, M. J.; Tranchida, J.; Trott, C.; Plimp- ton, S. J. LAMMPS - a flexible simulation tool for particle- based materials modeling at the atomic, meso, and contin- uum scales.Comput....

    work page 2022

  30. [30]

    D.; Chandler, D.; Andersen, H

    Weeks, J. D.; Chandler, D.; Andersen, H. C. Role of Re- pulsive Forces in Determining the Equilibrium Structure of Simple Liquids.J. Chem. Phys.1971,54, 5237–5247

    work page 1971

  31. [31]

    How to quantify and avoid finite size effects in computational studies of crystal nu- cleation: The case of homogeneous crystal nucleation.J

    Hussain, S.; Haji-Akbari, A. How to quantify and avoid finite size effects in computational studies of crystal nu- cleation: The case of homogeneous crystal nucleation.J. 12 Chem. Phys.2022,156, 54503

    work page 2022

  32. [32]

    C.; Tribello, G

    Sosso, G. C.; Tribello, G. A.; Zen, A.; Pedevilla, P.; Michaelides, A. Ice formation on kaolinite: Insights from molecular dynamics simulations.J. Chem. Phys.2016, 145, 211927

    work page 2016

  33. [33]

    Heterogeneous ice nucleation controlled by the coupling of surface crystallinity and surface hydrophilicity.J

    Bi, Y.; Cabriolu, R.; Li, T. Heterogeneous ice nucleation controlled by the coupling of surface crystallinity and surface hydrophilicity.J. Phys. Chem. C2016,120, 1507– 1514

    work page

  34. [34]

    A molecular dynamics method for simulations in the canonical ensemble.Mol

    Nos´ e, S. A molecular dynamics method for simulations in the canonical ensemble.Mol. Phys.1984,52, 255–268

    work page 1984

  35. [35]

    Hoover, W. G. Canonical dynamics: Equilibrium phase- space distributions.Phys. Rev. A1985,31, 1695–1697

    work page

  36. [36]

    Polymorphic transitions in single crystals: A new molecular dynamics method.J

    Parrinello, M.; Rahman, A. Polymorphic transitions in single crystals: A new molecular dynamics method.J. Appl. Phys.1981,52, 7182–7190

    work page 1981

  37. [37]

    J.; Frenkel, D.; ten Wolde, P

    Allen, R. J.; Frenkel, D.; ten Wolde, P. R. Simulating rare events in equilibrium or nonequilibrium stochastic systems.J. Chem. Phys.2006,124, 024102

    work page 2006

  38. [38]

    Accurate determination of crys- tal structures based on averaged local bond order param- eters.Journal of Chemical Physics2008,129

    Lechner, W.; Dellago, C. Accurate determination of crys- tal structures based on averaged local bond order param- eters.Journal of Chemical Physics2008,129

    work page

  39. [39]

    J.; Nelson, D

    Steinhardt, P. J.; Nelson, D. R.; Ronchetti, M. Bond- orientational order in liquids and glasses.Phys. Rev. B 1983,28, 784–805

    work page 1983

  40. [40]

    S.; Hussain, S.; Haji-Akbari, A

    Domingues, T. S.; Hussain, S.; Haji-Akbari, A. Diver- gence among Local Structure, Dynamics, and Nucleation Outcome in Heterogeneous Nucleation of Close-Packed Crystals.J. Phys. Chem. Lett.2024,15, 1279–1287

    work page 2024

  41. [41]

    The impact of hydration shell inclusion and chain exclusion in the efficacy of reac- tion coordinates for homogeneous and heterogeneous ice nucleation.J

    Sinaeian, K.; Haji-Akbari, A. The impact of hydration shell inclusion and chain exclusion in the efficacy of reac- tion coordinates for homogeneous and heterogeneous ice nucleation.J. Chem. Phys.2025,162, 164102

    work page 2025

  42. [42]

    How to Quantify and Avoid Finite Size Effects in Computational Studies of Crystal Nucleation: The Case of Heterogeneous Ice Nucleation

    Hussain, S.; Haji-Akbari, A. How to Quantify and Avoid Finite Size Effects in Computational Studies of Crystal Nucleation: The Case of Heterogeneous Ice Nucleation. J. Chem. Phys.2021,154, 014108

    work page 2021

  43. [43]

    New method to analyze simulations of activated processes.J

    Wedekind, J.; Strey, R.; Reguera, D. New method to analyze simulations of activated processes.J. Chem. Phys. 2007,126, 134103

    work page 2007

  44. [44]

    G.; Rossky, P

    Giovambattista, N.; Debenedetti, P. G.; Rossky, P. J. Effect of surface polarity on water contact angle and interfacial hydration structure.J. Phys. Chem. B2007, 111, 9581–9587

    work page

  45. [45]

    Phase diagrams of Lennard-Jones fluids.J

    Smit, B. Phase diagrams of Lennard-Jones fluids.J. Chem. Phys.1992,96, 8639–8640

    work page 1992

  46. [46]

    Frenkel, D.; Ladd, A. J. New Monte Carlo method to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres.J. Chem. Phys. 1984,81, 3188–3193

    work page 1984

  47. [47]

    Haji-Akbari, A.; Engel, M.; Glotzer, S. C. Phase Diagram of Hard Tetrahedra.J. Chem. Phys.2011,135

    work page 2011

  48. [48]

    J.; Klein, M

    Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nos´ e–Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys.1992,97, 2635–2643

    work page 1992

  49. [49]

    Agrawal, R.; Kofke, D. A. Thermodynamic and structural properties of model systems at solid-fluid coexistence.Mol. Phys.1995,85, 43–59

    work page 1995

  50. [50]

    Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook.J

    Hussain, S.; Haji-Akbari, A. Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook.J. Chem. Phys.2020,152

    work page 2020

  51. [51]

    Breakdown of classical nucleation theory near isostructural phase transitions

    Cacciuto, A.; Auer, S.; Frenkel, D. Breakdown of classical nucleation theory near isostructural phase transitions. Phys. Rev. Lett.2004,93, 166105

    work page 2004

  52. [52]

    G.; Protsenko, K

    Baidakov, V. G.; Protsenko, K. R. Spontaneous crystal- lization of a supercooled Lennard-Jones liquid: Molecular dynamics simulation.J. Phys. Chem. B2019,123, 8103– 8112

    work page