Deviation from equilibrium conditions in molecular dynamic simulations of homogeneous nucleation

Assessment of Anharmonicities in Clusters: Developing and Validating a Minimum-Information Partition Function

Precise thermodynamic calculations are essential for understanding the dynamics of cluster systems and new particle formation. However, the widely employed harmonic statistical mechanical approach often falls short in terms of accuracy. In this study, we present an improved statistical model that incorporates vibrational anharmonicity via a novel partition function that requires only one additional system-specific input parameter. In addition to considering vibrational aspects, we also account for anharmonicity related to the configurational space. The role of anharmonicities is thoroughly examined in the case of general clusters, where the complete sets of conformers, mechanically stable spatial arrangements, are known up to clusters composed of 14 monomers. By performing consistent Monte Carlo simulations on these systems, we benchmark the statistical model's efficacy in reproducing key thermodynamic properties (formation free energy and potential energy) in the classical limit. The model exhibits exceptional alignment with simulations, accurately reproducing free energies within a precision of 2kBT and reliably capturing cluster melting temperatures. Furthermore, we demonstrate the significance and applicability of the model by reproducing thermodynamic barriers in homogeneous gas-phase nucleation of larger clusters. The transferability of our developed approach extends to more complex molecular systems and bears relevance for atmospheric multicomponent clusters, in particular.

Multiscale approach to the theory of nonisothermal homogeneous nucleation

Molecular dynamics (MD) of the Lennard-Jones cluster in the environment of supersaturated vapor at fixed temperature and density is used for the investigation of nonisothermal nucleation. The results allow one to single out different processes occurring at different time scales, the Ornstein-Uhlenbeck fluctuations at the short time scale and a combination of slow diffusion and drift of the fluctuation packet that represents a cluster, at the long time scale. The multiscale approach is developed, in which a separate treatment of different time scales makes it possible to consider strongly correlated cluster size and temperature. This reduces the nonisothermal cluster evolution to a one-dimensional problem. The fluctuation packet drift velocity and diffusivity are calculated based on the cluster microscopic thermophysical parameters determined in this work from MD data for isothermal clusters. The proposed approach is consistent with the results of our MD simulation.

Further cautionary tales on thermostatting in molecular dynamics: Energy equipartitioning and non-equilibrium processes in gas-phase simulations

Molecular dynamics (MD) simulations of gas-phase chemical reactions are typically carried out on a small number of molecules near thermal equilibrium by means of various thermostatting algorithms. Correct equipartitioning of kinetic energy among translations, rotations, and vibrations of the simulated reactants is critical for many processes occurring in the gas phase. As thermalizing collisions are infrequent in gas-phase simulations, the thermostat has to efficiently reach equipartitioning in the system during equilibration and maintain it throughout the actual simulation. Furthermore, in non-equilibrium simulations where heat is released locally, the action of the thermostat should not lead to unphysical changes in the overall dynamics of the system. Here, we explore issues related to both obtaining and maintaining thermal equilibrium in MD simulations of an exemplary ion-molecule dimerization reaction. We first compare the efficiency of global (Nosé-Hoover and Canonical Sampling through Velocity Rescaling) and local (Langevin) thermostats for equilibrating a system of flexible compounds and find that of these three only the Langevin thermostat achieves equipartition in a reasonable simulation time. We then study the effect of the unphysical removal of latent heat released during simulations involving multiple dimerization events. As the Langevin thermostat does not produce the correct dynamics in the free molecular regime, we only consider the commonly used Nosé-Hoover thermostat, which is shown to effectively cool down the reactants, leading to an overestimation of the dimerization rate. Our findings underscore the importance of thermostatting for the proper thermal initialization of gas-phase systems and the consequences of global thermostatting in non-equilibrium simulations.

Nonisothermal nucleation in the gas phase is driven by cool subcritical clusters

Nucleation of clusters from the gas phase is a widely encountered phenomenon, yet rather little is understood about the underlying out-of-equilibrium dynamics of this process. The classical view of nucleation assumes isothermal conditions where the nucleating clusters are in thermal equilibrium with their surroundings. However, in all first-order phase transitions, latent heat is released, potentially heating the clusters and suppressing the nucleation. The question of how the released energy affects cluster temperatures during nucleation as well as the growth rate remains controversial. To investigate the nonisothermal dynamics and energetics of homogeneous nucleation, we have performed molecular dynamics simulations of a supersaturated vapor in the presence of thermalizing carrier gas. The results obtained from these simulations are compared against kinetic modeling of isothermal nucleation and classical nonisothermal theory. For the studied systems, we find that nucleation rates are suppressed by two orders of magnitude at most, despite substantial release of latent heat. Our analyses further reveal that while the temperatures of the entire cluster size populations are elevated, the temperatures of the specific clusters driving the nucleation flux evolve from cold to hot when growing from subcritical to supercritical sizes and resolve the apparent contradictions regarding cluster temperatures. Our findings provide unprecedented insight into realistic nucleation events and allow us to directly assess earlier theoretical considerations of nonisothermal nucleation.

Molecular Dynamics of Heterogeneous Systems on GPUs and Their Application to Nucleation in Gas Expanding to a Vacuum

Expansion of water vapor through a small orifice to a vacuum produces liquid or frozen clusters which in the experiment serve as model particles for atmospheric aerosols. Yet, there are controversies about the shape of these clusters, suggesting that the nucleation process is not fully understood. Such questions can be answered by molecular dynamics simulations; however, they require microsecond-scale runs with thousands of molecules and accurate energy conservation. The available highly parallel codes typically utilize domain decomposition and are inefficient for heterogeneous systems as clusters in a dilute gas. In this work, we present an implementation of molecular dynamics on graphics processing units based on the Verlet list and apply it to several systems for which experimental data are available. We reproduce sufficiently sized clusters but not the experimentally observed clusters of irregular shape.

Homogeneous nucleation of carbon dioxide in supersonic nozzles II: molecular dynamics simulations and properties of nucleating clusters

Large scale molecular dynamics simulations of the homogeneous nucleation of carbon dioxide in an argon atmosphere were carried out at temperatures between 75 and 105 K. Extensive analyses of the nucleating clusters' structural and energetic properties were performed to quantify these details for the supersonic nozzle experiments described in the first part of this series [Dingilian et al., Phys. Chem. Chem. Phys., 2020, 22, 19282-19298]. We studied ten different combinations of temperature and vapour pressure, leading to nucleation rates of 10²³-10²⁵ cm^-3 s^-1. Nucleating clusters possess significant excess energy from monomer capture, and the observed cluster temperatures during nucleation - on both sides of the critical cluster size - are higher than that of the carrier gas. Despite strong undercooling with respect to the triple point, most clusters are clearly liquid-like during the nucleation stage. Only at the lowest simulation temperatures and vapour densities, clusters containing over 100 molecules are able to undergo a second phase transition to a crystalline solid. The formation free energies retrieved from the molecular dynamics simulations were used to improve the classical nucleation theory by introducing a Tolman-like term into the classical liquid-drop model expression for the formation free energy. This simulation-based theory predicts the simulated nucleation rates perfectly, and improves the prediction of the experimental rates compared to self-consistent classical nucleation theory.

Homogeneous nucleation of carbon dioxide in supersonic nozzles I: experiments and classical theories

We studied the homogeneous nucleation of carbon dioxide in the carrier gas argon for concentrations of CO2 ranging from 2 to 39 mole percent using three experimental methods. Position-resolved pressure trace measurements (PTM) determined that the onset of nucleation occurred at temperatures between 75 and 92 K with corresponding CO2 partial pressures of 39 to 793 Pa. Small angle X-ray scattering (SAXS) measurements provided particle size distributions and aerosol number densities. Number densities of approximately 1012 cm-3, and characteristic times ranging from 6 to 13 μs, resulted in measured nucleation rates on the order of 5 × 1017 cm-3 s-1, values that are consistent with other nucleation rate measurements in supersonic nozzles. Finally, we used Fourier transform infrared (FTIR) spectroscopy to identify that the condensed CO2 particles were crystalline cubic solids with either sharp or rounded corners. Molecular dynamics simulations, however, suggest that CO2 forms liquid-like critical clusters before transitioning to the solid phase. Furthermore, the critical clusters are not in thermal equilibrium with the carrier gas. Comparisons with nucleation theories were therefore made assuming liquid-like critical clusters and incorporating non-isothermal correction factors.

Ice Nucleation of Confined Monolayer Water Conforms to Classical Nucleation Theory

We confirmed that monolayer water confined by parallel graphene sheets spontaneously crystallizes from a structurally and dynamically heterogeneous liquid phase under moderate supercooling via direct molecular dynamics simulation. Square-lattice-like geometric order is observed at the early stage of nucleation and is preserved during the entire nucleus growth process. The diffusion coefficient and free energy profile in the cluster space extracted from a Bayesian trajectory analysis agree well with the classical nucleation theory (CNT) prediction and yield thermodynamic quantities exhibiting linear temperature dependence. The effectiveness of maximum cluster size as the descriptor of ice nucleation dynamics in the CNT framework can be attributed to the dynamical time scale decoupling and strong structural pattern dependence of density fluctuation in the liquid phase.