Atomic structure and water arrangement on K-feldspar microcline (001).

The properties of clouds, such as their reflectivity or their likelihood to precipitate, depend on whether the cloud droplets are liquid or frozen. Thus, understanding the ice nucleation mechanisms is essential for the development of reliable climate models. Most ice nucleation in the atmosphere is heterogeneous, i.e., caused by ice nucleating particles such as mineral dusts or organic aerosols. In this regard, K-feldspar minerals have attracted great interest recently as they have been identified as one of the most important ice nucleating particles under mixed-phase cloud conditions. The mechanism by which feldspar minerals facilitate ice nucleation remains, however, elusive. Here, we present atomic force microscopy (AFM) experiments on microcline (001) performed in an ultrahigh vacuum and at the solid-water interface together with density functional theory (DFT) and molecular dynamics (MD) calculations. Our ultrahigh vacuum data reveal features consistent with a hydroxyl-terminated surface. This finding suggests that water in the residual gas readily reacts with the surface. Indeed, the corresponding DFT calculations confirm a dissociative water adsorption. Three-dimensional AFM measurements performed at the mineral-water interface unravel a layered hydration structure with two features per surface unit cell. A comparison with MD calculations suggests that the structure observed in AFM corresponds to the second hydration layer rather than the first water layer. In agreement with previous computation results, no ice-like structure is seen, questioning an explanation of the ice nucleation ability by lattice match. Our results provide an atomic-scale benchmark for the clean and water-covered microcline (001) plane, which is mandatory for understanding the ice nucleation mechanism on feldspar minerals.

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.

Ion-Molecule Rate Constants for Reactions of Sulfuric Acid with Acetate and Nitrate Ions.

Atmospheric nucleation from precursor gases is a significant source of cloud condensation nuclei in the troposphere and thus can affect the Earth's radiative balance. Sulfuric acid, ammonia, and amines have been identified as key nucleation precursors in the atmosphere. Studies have also shown that atmospheric ions can react with sulfuric acid to form stable clusters in a process referred to as ion-induced nucleation (IIN). IIN follows similar reaction pathways as chemical ionization, which is used to detect and measure nucleation precursors via atmospheric pressure chemical ionization mass spectrometers. The rate at which ions form clusters depends on the ion-molecule rate constant. However, the rate constant varies based on the ion composition, which is often not known in the atmosphere. Previous studies have examined ion-molecule rate constants for sulfuric acid and nitrate ions but not for other atmospherically relevant ions like acetate. We report the relative rate constants of ion-molecule reactions between nitrate and acetate ions reacting with sulfuric acid. The ion-molecule rate constant for acetate and sulfuric acid is estimated to be a factor of 1.9-2.4 times higher than that of the known rate constant for nitrate and sulfuric acid. Using quantum chemistry, we find that acetate has a higher dipole moment and polarizability than nitrate. This may contribute to an increase in the collision cross-sectional area between acetate and sulfuric acid and lead to a greater reaction rate constant than nitrate. The ion-molecule rate constant for acetate with sulfuric acid will help quantify the contribution of acetate ions to atmospheric ion-induced new particle formation.

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.

New Particle Formation from the Vapor Phase: From Barrier-Controlled Nucleation to the Collisional Limit.

Studies of vapor phase nucleation have largely been restricted to one of two limiting cases-nucleation controlled by a substantial free energy barrier or the collisional limit where the barrier is negligible. For weakly bound systems, exploring the transition between these regimes has been an experimental challenge, and how nucleation evolves in this transition remains an open question. We overcome these limitations by combining complementary Laval expansion experiments, providing new particle formation data for carbon dioxide over a uniquely broad range of conditions. Our experimental data together with a kinetic model using rate constants from high-level quantum chemical calculations provide a comprehensive picture of new particle formation as nucleation transitions from a barrier-dominated process to the collisional limit.

Liquid Water and Interfacial, Cubic, and Hexagonal Ice Classification through Eclipsed and Staggered Conformation Template Matching.

We propose a novel method based on template matching for the recognition of liquid water, cubic ice (ice Ic), hexagonal ice (ice Ih), clathrate hydrates, and different interfacial structures in atomistic and coarse-grained simulations of water and ice. The two template matrices represent staggered and eclipsed conformations, which are the building blocks of hexagonal and cubic ice and clathrate crystals. The algorithm is rotationally invariant and highly robust against imperfections in the ice structure, and its sensitivity for recognizing ice-like structures can be tuned for different applications. Unlike most other algorithms, it can discriminate between cubic, hexagonal, clathrate, mixed, and other interfacial ice types and is therefore well suited to study complex systems and heterogeneous ice nucleation.

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.

Tip dependence of three-dimensional scanning force microscopy images of calcite-water interfaces investigated by simulation and experiments.

In this study, we have investigated the influence of the tip on the three-dimensional scanning force microscopy (3D-SFM) images of calcite-water interfaces by experiments and simulations. We calculated 3D force images by simulations with the solvent tip approximation (STA), Ca, CO3 and OH tip models. For all the 3D images, the z profiles at the surface Ca and CO3 sites alternately show oscillatory peaks corresponding to the hydration layers. However, the peak heights and spacings become larger when the mechanical stability of the tip becomes higher. For analyzing the xy slices of the 3D force images, we developed the extended STA (E-STA) model which allowed us to reveal the strong correlation between the hydration structure just under the tip and the atomic-scale force contrasts. Based on these understandings on the image features showing the strong tip dependence, we developed a method for objectively estimating the similarity between 3D force images. With this method, we compared the simulated images with the three experimentally obtained ones. Among them, two images showed a relatively high similarity with the image obtained by the simulation with the Ca or the CO3 tip model. Based on these agreements, we characterized the hydration structure and mechanical stability of the experimentally used tips. The understanding and methodology presented here should help us to derive accurate information on the tip and the interfacial structure from experimentally obtained 3D-SFM images.

Resolving Point Defects in the Hydration Structure of Calcite (10.4) with Three-Dimensional Atomic Force Microscopy.

It seems natural to assume that defects at mineral surfaces critically influence interfacial processes such as the dissolution and growth of minerals in water. The experimental verification of this claim, however, is challenging and requires real-space methods with utmost spatial resolution, such as atomic force microscopy (AFM). While defects at mineral-water interfaces have been resolved in 2D AFM images before, the perturbation of the surrounding hydration structure has not yet been analyzed experimentally. In this Letter, we demonstrate that point defects on the most stable and naturally abundant calcite (10.4) surface can be resolved using high-resolution 3D AFM-even within the fifth hydration layer. Our analysis of the hydration structure surrounding the point defect shows a perturbation of the hydration with a lateral extent of approximately one unit cell. These experimental results are corroborated by molecular dynamics simulations.

Atomistic simulation of the measurement of mechanical properties of gold nanorods by AFM.

Mechanical properties of nanoscale objects can be measured with an atomic force microscope (AFM) tip. However, the continuum models typically used to relate the force measured at a certain indentation depth to quantities such as the elastic modulus, may not be valid at such small scales, where the details of atomistic processes need to be taken into account. On the other hand, molecular dynamics (MD) simulations of nanoindentation, which can offer understanding at an atomistic level, are often performed on systems much smaller than the ones studied experimentally. Here, we present large scale MD simulations of the nanoindentation of single crystal and penta-twinned gold nanorod samples on a silicon substrate, with a spherical diamond AFM tip apex. Both the sample and tip sizes and geometries match commercially available products, potentially linking simulation and experiment. Different deformation mechanisms, involving the creation, migration and annihilation of dislocations are observed depending on the nanorod crystallographic structure and orientation. Using the Oliver-Pharr method, the Young's moduli of the (100) terminated and (110) terminated single crystal nanorods, and the penta-twinned nanorod, have been determined to be 103 ± 2, 140 ± 4 and 108 ± 2 GPa, respectively, which is in good agreement with bending experiments performed on nanowires.

Can Point Defects in Surfaces in Solution be Atomically Resolved by Atomic Force Microscopy?

While the atomic force microscope (AFM) is able to image mineral surfaces in solution with atomic resolution, so far, it has been a matter of debate whether imaging point defects is also possible under these conditions. The difficulties stem from the limited knowledge of what types of defects may be stable in the presence of an AFM tip, as well as from the complicated imaging mechanism involving interactions between hydration layers over the surface and around the tip apex. Here, we present atomistic molecular dynamics and free energy calculations of the AFM imaging of vacancies and ionic substitutions in the calcite (101[over ¯]4) surface in water, using a new silica AFM tip model. Our results indicate that both calcium and carbonate vacancies, as well as a magnesium substitution, could be resolved in an AFM experiment, albeit with different imaging mechanisms.

Understanding 2D atomic resolution imaging of the calcite surface in water by frequency modulation atomic force microscopy.

Frequency modulation atomic force microscopy (FM-AFM) experiments were performed on the calcite (10[Formula: see text]4) surface in pure water, and a detailed analysis was made of the 2D images at a variety of frequency setpoints. We observed eight different contrast patterns that reproducibly appeared in different experiments and with different measurement parameters. We then performed systematic free energy calculations of the same system using atomistic molecular dynamics to obtain an effective force field for the tip-surface interaction. By using this force field in a virtual AFM simulation we found that each experimental contrast could be reproduced in our simulations by changing the setpoint, regardless of the experimental parameters. This approach offers a generic method for understanding the wide variety of contrast patterns seen on the calcite surface in water, and is generally applicable to AFM imaging in liquids.

Ab initio Kinetic Monte Carlo simulations of dissolution at the NaCl-water interface.

We have used ab initio molecular dynamics (AIMD) simulations to study the interaction of water with the NaCl surface. As expected, we find that water forms several ordered hydration layers, with the first hydration layer having water molecules aligned so that oxygen atoms are on average situated above Na sites. In an attempt to understand the dissolution of NaCl in water, we have then combined AIMD with constrained barrier searches, to calculate the dissolution energetics of Na(+) and Cl(-) ions from terraces, steps, corners and kinks of the (100) surface. We find that the barrier heights show a systematic reduction from the most stable flat terrace sites, through steps to the smallest barriers for corner and kink sites. Generally, the barriers for removal of Na(+) ions are slightly lower than for Cl(-) ions. Finally, we use our calculated barriers in a Kinetic Monte Carlo as a first order model of the dissolution process.

A simple approximation for forces exerted on an AFM tip in liquid.

The critical quantity in understanding imaging using an atomic force microscope is the force the sample exerts on the tip. We put forward a simple one-to-one force to water density relationship, explain exactly how it occurs, and in which circumstances it holds. We argue that two wide classes of atomic force microscope (AFM) tip should lead to at least qualitative agreement with our model and represent a significant fraction of AFM tips as currently prepared. This connection between the short-range force and the unperturbed equilibrium water density removes the need to perform simulations for each tip location, conservatively speeding up simulations by around three orders of magnitude compared to current methods that explicitly calculate the force on a tip model at each point in space.

Free Energy Approaches for Modeling Atomic Force Microscopy in Liquids.

High resolution atomic force microscopy (AFM) in liquids offers atomic scale insight into the structure at water/solid interfaces and is perhaps the only tool capable of resolving the nature of formed hydration layers. However, convolution between the imaging signal and the tip/surface interactions and hydration layers means that interpretation is far from straightforward. Modeling the complex imaging mechanism of atomic force microscopy in liquids requires calculation of the free energy profile as a function of the distance between AFM tip and surface. Its derivative is the best approximation for the force acting on the AFM tip, including entropic contributions from interactions with water molecules in hydration layers over the surface and around the tip apex. In order to establish a reliable approach for these simulations, we compare two methods of calculating free energy profiles from atomistic molecular dynamics simulations, umbrella sampling and free energy perturbation, on two model surfaces, calcium fluoride and calcium carbonate. Our results demonstrate that both methods effectively provide equivalent free energy profiles but offer different possibilities in terms of efficiency, constraints, and analysis of the free energy components.