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The seeding method: A test case for classical nucleation theory in small systems

Thomas Philippe, Yijian Wu, Aymane Graini

TL;DR

This paper tests classical nucleation theory (CNT) in small, confined systems by applying the NVT seeding MD approach to Lennard-Jones condensation. By inserting a pre-formed liquid seed into a vapor in a finite box, the authors identify two CNT states and extract stable cluster radii $R^*$ and vapor densities $\rho_v^*$, then compare these with CNT predictions using several thermodynamic models. CNT predictions based on the Johnson–Zollweg–Gubbins (JZG) equation of state show very good agreement with seeded MD across a range of temperatures; the KN equation of state also performs well at low temperature, while density functional theory (DFT) and ideal-gas approximations become unreliable at higher temperatures, though the latter remains practically useful for initializing seeds. Overall, the seeding method provides an efficient, robust framework to benchmark CNT in finite systems and offers guidance on which thermodynamic models are most reliable for predicting nucleation in confined environments.

Abstract

Molecular dynamics simulations are widely used to investigate nucleation in first-order phase transitions. Brute-force simulations, though popular, are limited to conditions of high metastability, where the critical cluster and the nucleation barrier are small. The seeding method has recently emerged as a powerful alternative for exploring lower supersaturation regimes by initiating simulations with a pre-formed nucleus. In confined systems (NVT ensemble), the seeded simulations are particularly effective for determining stable cluster properties and provide a stringent test case for classical nucleation theory (CNT). In this work, we perform NVT seeded simulations of Lennard-Jones condensation in small systems and compare them with CNT predictions based on several thermodynamic models, including equations of state, perturbation theory, and ideal gas approximation. We find that CNT accurately predicts stable cluster radii across a wide range of conditions. Notably, even the very simple ideal gas approximation proves useful for initializing seeded simulations. Furthermore, seeded simulation results correspond to the critical cluster radii of infinite systems: CNT predictions with good equations of state show very good agreement with simulations, while the perturbation theory and the ideal gas approximation perform well at low temperatures but deviate significantly at high temperatures.

The seeding method: A test case for classical nucleation theory in small systems

TL;DR

This paper tests classical nucleation theory (CNT) in small, confined systems by applying the NVT seeding MD approach to Lennard-Jones condensation. By inserting a pre-formed liquid seed into a vapor in a finite box, the authors identify two CNT states and extract stable cluster radii and vapor densities , then compare these with CNT predictions using several thermodynamic models. CNT predictions based on the Johnson–Zollweg–Gubbins (JZG) equation of state show very good agreement with seeded MD across a range of temperatures; the KN equation of state also performs well at low temperature, while density functional theory (DFT) and ideal-gas approximations become unreliable at higher temperatures, though the latter remains practically useful for initializing seeds. Overall, the seeding method provides an efficient, robust framework to benchmark CNT in finite systems and offers guidance on which thermodynamic models are most reliable for predicting nucleation in confined environments.

Abstract

Molecular dynamics simulations are widely used to investigate nucleation in first-order phase transitions. Brute-force simulations, though popular, are limited to conditions of high metastability, where the critical cluster and the nucleation barrier are small. The seeding method has recently emerged as a powerful alternative for exploring lower supersaturation regimes by initiating simulations with a pre-formed nucleus. In confined systems (NVT ensemble), the seeded simulations are particularly effective for determining stable cluster properties and provide a stringent test case for classical nucleation theory (CNT). In this work, we perform NVT seeded simulations of Lennard-Jones condensation in small systems and compare them with CNT predictions based on several thermodynamic models, including equations of state, perturbation theory, and ideal gas approximation. We find that CNT accurately predicts stable cluster radii across a wide range of conditions. Notably, even the very simple ideal gas approximation proves useful for initializing seeded simulations. Furthermore, seeded simulation results correspond to the critical cluster radii of infinite systems: CNT predictions with good equations of state show very good agreement with simulations, while the perturbation theory and the ideal gas approximation perform well at low temperatures but deviate significantly at high temperatures.

Paper Structure

This paper contains 6 sections, 7 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Simulation details
  3. Classical nucleation theory
  4. Results
  5. Summary
  6. Simulation data

Figures (2)

  • Figure 1: Evolution of critical radius against box density of confined system with different box sizes and at different temperatures: (a) $T=0.7$, (b) $T=0.8$, (c) $T=0.9$, (d) $T=1$, and (e) $T=1.1$. Legends are in the bottom right. Color lines represent predictions and markers represent MD results. Vertical dotted black lines indicate the binodal limit for each temperature.
  • Figure 2: Evolution of critical radius against vapor density at different temperatures: (a) $T=0.7$, (b) $T=0.8$, (c) $T=0.9$, (d) $T=1$, and (e) $T=1.1$. Markers represent measurements from seeded MD simulations of confined system, and their error bars represent standard deviations in $\rho_v^*$ and $R^*$. Black lines represent CNT predictions with different thermodynamic models.