Seeding approach to nucleation in the NVT ensemble: The case of bubble cavitation in overstretched Lennard Jones fluids

Methane hydrate phase equilibrium considering dissolved methane concentrations and interfacial geometries from molecular simulations

Natural gas hydrates, mainly existing in permafrost and on the seabed, are expected to be a new energy source with great potential. The exploitation technology of natural gas hydrates is one of the main focuses of hydrate-related studies. In this study, a large-size liquid aqueous solution wrapping a methane hydrate system was established and molecular dynamics simulations were used to investigate the phase equilibrium conditions of methane hydrate at different methane concentrations and interfacial geometries. It is found that the methane concentration of a solution significantly affects the phase equilibrium of methane hydrates. Different methane concentrations at the same temperature and pressure can lead to hydrate formation or decomposition. At the same temperature and pressure, in a system reaching equilibrium, the size of spherical hydrate clusters is coupled to the solution concentration, which is proportional to the Laplace pressure at the solid-liquid interface. Lower solution concentrations reduce the phase equilibrium temperature of methane hydrates at the same pressure; as the concentration increases, the phase equilibrium temperature gradually approaches the actual phase equilibrium temperature. In addition, the interfacial geometry of hydrates affects the thermodynamic stability of hydrates. The spherical hydrate particles have the highest stability for the same volume. Through this study, we provide a stronger foundation to understand the principles driving hydrate formation/dissociation relevant to the exploitation of methane hydrates.

Molecular insights into complexation between protein and silica: Spectroscopic and simulation investigations

The synergistic effect of protein-silica complexation leads to exacerbated membrane fouling in the membrane desalination process, exceeding the individual impacts of silica scaling or protein fouling. However, the molecular-level dynamics of silica binding to proteins and the resulting structural changes in both proteins and silica remain poorly understood. This study investigates the complexation process between silica and proteins-negatively charged bovine serum albumin (BSA) and positively charged lysozyme (LYZ) at neutral pH-using infrared spectroscopy (IR), in situ attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), and multiple computational simulations. The findings reveal that both protein and silica structures undergo changes during the complexation process, with calcium ions in the solution significantly exacerbating these alterations. In particular, in situ ATR-FTIR combined with two-dimensional correlation spectroscopy analysis shows that BSA experiences more pronounced unfolding, providing additional binding sites for silica adsorption compared to LYZ. The adsorbed proteins promote silica polymerization from lower-polymerized to higher-polymerized species. Furthermore, molecular dynamics simulations demonstrate greater conformational variation in BSA through root-mean-square-deviation analysis and the bridging role of calcium ions via mean square displacement analysis. Molecular docking and density functional theory calculations identify the binding sites and energy of silica on proteins. In summary, this research offers a comprehensive understanding of the protein-silica complexation process, contributing to the knowledge of synergistic behaviors of inorganic scaling and organic fouling on membrane surfaces. The integrated approach used here may also be applicable for exploring other complex complexation processes in various environments.

Hierarchical approximations to the nucleation work in the entire range of metastability

The work W to form a nucleus (also known as the critical nucleus) is a key quantity in the description of nucleation phenomena because of its exponentially strong effect on the nucleation rate. The present study provides a general approximate expression for W, which comprises a hierarchy of approximations to the dependence of W on the experimentally controlled overpressure Δp of a nucleating multicomponent phase. This general expression is used to derive explicit formulas for the lowest-order members of the W(Δp) hierarchy as well as for the respective lowest-order approximations to the Δp dependences of the nucleus surface tension, the nucleus radius, the Gibbs-Tolman length, and the stationary nucleation rate. The second-order and the third-order approximations to the W(Δp) dependence are confronted with available W(Δp) data, and the latter is found to agree very well with the data. The results obtained are applicable to homogeneous single-component or multicomponent nucleation from the binodal to the spinodal of the old phase, i.e., in the entire range of the old-phase metastability.

A Deep Potential model for liquid-vapor equilibrium and cavitation rates of water

Computational studies of liquid water and its phase transition into vapor have traditionally been performed using classical water models. Here, we utilize the Deep Potential methodology-a machine learning approach-to study this ubiquitous phase transition, starting from the phase diagram in the liquid-vapor coexistence regime. The machine learning model is trained on ab initio energies and forces based on the SCAN density functional, which has been previously shown to reproduce solid phases and other properties of water. Here, we compute the surface tension, saturation pressure, and enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K and evaluate the Deep Potential model performance against experimental results and the semiempirical TIP4P/2005 classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier and nucleation rate at negative pressures for the isotherm of 296.4 K. We find that the nucleation rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005 water model due to an underestimation in the surface tension from the Deep Potential model. From analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water model, which is (0.091 ± 0.008) nm at 296.4 K. Finally, we identify that water molecules display a preferential orientation in the liquid-vapor interface, in which H atoms tend to point toward the vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behavior is more pronounced for planar interfaces than for the curved interfaces in bubbles. This work represents the first application of Deep Potential models to the study of liquid-vapor coexistence and water cavitation.

The water cavitation line as predicted by the TIP4P/2005 model

The formation of vapor bubbles in a metastable liquid, cavitation, is an activated process due to the free energy cost of having both phases at contact. Such an energetic penalty enables the existence of the liquid beyond its thermodynamic borders. Establishing the stability limits of a liquid as ubiquitous as water has important practical implications and has thereby attracted a lot of attention. Different experimental strategies and theoretical analyses have been employed to measure and predict the cavitation line, or the pressure-temperature kinetic stability border of liquid water. Understanding the location of the cavitation line requires knowing the cavitation rate dependence on pressure and temperature. Such dependency is difficult to obtain in experiments, and we use molecular simulations with the TIP4P/2005 model to fill this gap. By deeply overstretching liquid water below the saturation pressure, we are able to observe and quantify spontaneous cavitation. To deal with a lower overstretching regime, we resort to the Seeding technique, which consists of analyzing simulations of a liquid containing a vapor bubble under the theoretical framework of Classical Nucleation Theory. Combining spontaneous cavitation with Seeding, we get a wide overview of the cavitation rate. We study two different temperatures (450 and 550 K) and complement our perspective with the results previously obtained at 296.4 K [Menzl et al., Proc. Natl. Acad. Sci. 113, 13582 (2016)] to establish a broad simulation-experiment comparison. We find a good agreement between simulations and both isobaric heating and isochoric cooling experiments using quartz inclusions. We are, however, unable to reconcile simulations with other experimental techniques. Our results predict a decrease in the solid-liquid interfacial free energy as the liquid becomes increasingly overstretched with a temperature independent Tolman length of 0.1 nm. Therefore, the capillarity approximation underestimates the nucleation rate. Nonetheless, it provides a fair indication of the location of the cavitation line given the steep rate vs pressure dependence. Overall, our work provides a comprehensive view of the water cavitation phenomenon and sets an efficient strategy to investigate it with molecular simulations.

Free energy of critical droplets-from the binodal to the spinodal

Arguably, the main challenge of nucleation theory is to accurately evaluate the work of formation of a critical embryo in the new phase, which governs the nucleation rate. In Classical Nucleation Theory (CNT), this work of formation is estimated using the capillarity approximation, which relies on the value of the planar surface tension. This approximation has been blamed for the large discrepancies between predictions from CNT and experiments. In this work, we present a study of the free energy of formation of critical clusters of the Lennard-Jones fluid truncated and shifted at 2.5σ using Monte Carlo simulations, density gradient theory, and density functional theory. We find that density gradient theory and density functional theory accurately reproduce molecular simulation results for critical droplet sizes and their free energies. The capillarity approximation grossly overestimates the free energy of small droplets. The incorporation of curvature corrections up to the second order with the Helfrich expansion greatly remedies this and performs very well for most of the experimentally accessible regions. However, it is imprecise for the smallest droplets and largest metastabilities since it does not account for a vanishing nucleation barrier at the spinodal. To remedy this, we propose a scaling function that uses all relevant ingredients without adding fitting parameters. The scaling function reproduces accurately the free energy of the formation of critical droplets for the entire metastability range and all temperatures examined and deviates from density gradient theory by less than one k_BT.

Solubility of Methane in Water: Some Useful Results for Hydrate Nucleation

In this paper, the solubility of methane in water along the 400 bar isobar is determined by computer simulations using the TIP4P/Ice force field for water and a simple LJ model for methane. In particular, the solubility of methane in water when in contact with the gas phase and the solubility of methane in water when in contact with the hydrate has been determined. The solubility of methane in a gas-liquid system decreases as temperature increases. The solubility of methane in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the triple point T₃ at a certain pressure. We also determined T₃ by the three-phase direct coexistence method. The results of both methods agree, and we suggest 295(2) K as the value of T₃ for this system. We also analyzed the impact of curvature on the solubility of methane in water. We found that the presence of curvature increases the solubility in both the gas-liquid and hydrate-liquid systems. The change in chemical potential for the formation of hydrate is evaluated along the isobar using two different thermodynamic routes, obtaining good agreement between them. It is shown that the driving force for hydrate nucleation under experimental conditions is higher than that for the formation of pure ice when compared at the same supercooling. We also show that supersaturation (i.e., concentrations above those of the planar interface) increases the driving force for nucleation dramatically. The effect of bubbles can be equivalent to that of an additional supercooling of about 20 K. Having highly supersaturated homogeneous solutions makes possible the spontaneous formation of the hydrate at temperatures as high as 285 K (i.e., 10K below T₃). The crucial role of the concentration of methane for hydrate formation is clearly revealed. Nucleation of the hydrate can be either impossible or easy and fast depending on the concentration of methane which seems to play the leading role in the understanding of the kinetics of hydrate formation.

Homogeneous ice nucleation rates for mW and TIP4P/ICE models through Lattice Mold calculations

Water freezing is the most common liquid-to-crystal phase transition on Earth, however, despite its critical implications on climate change and cryopreservation among other disciplines, its characterization through experimental and computational techniques remains elusive. In this work, we make use of computer simulations to measure the nucleation rate (J) of water at normal pressure under different supercooling conditions, ranging from 215 to 240K. We employ two different water models, mW, a coarse-grained potential for water, and TIP4P/ICE, an atomistic non-polarizable water model that provides one of the most accurate representations of the different ice phases. To evaluate J, we apply the Lattice Mold technique, a computational method based on the use of molds to induce the nucleus formation from the metastable liquid under conditions at which observing spontaneous nucleation would be unfeasible. With this method, we obtain estimates of the nucleation rate for ice Ih, Ic and a stacking mixture of ice Ih/Ic; reaching consensus with most of the previously reported rates, although differing with some others. Furthermore, we confirm that the predicted nucleation rates by the TIP4P/ICE model are in better agreement with experimental data than those obtained through the mW potential. Taken together, our study provides a reliable methodology to measure nucleation rates in a simple and computationally efficient manner which contributes to benchmarking the freezing behaviour of two popular water models.

On the thermodynamics of curved interfaces and the nucleation of hard spheres in a finite system

We determine, for hard spheres, the Helmholtz free energy of a liquid that contains a solid cluster as a function of the size of the solid cluster by means of the formalism of the thermodynamics of curved interfaces. This is done at the constant total number of particles, volume, and temperature. We show that under certain conditions, one may have several local minima in the free energy profile, one for the homogeneous liquid and others for the spherical, cylindrical, and planar solid clusters surrounded by liquid. The variation of the interfacial free energy with the radius of the solid cluster and the distance between equimolar and tension surfaces are inputs from simulation results of nucleation studies. This is possible because stable solid clusters in the canonical ensemble become critical in the isothermal-isobaric ensemble. At each local minimum, we find no difference in chemical potential between the phases. At local maxima, we also find equal chemical potential, albeit in this case the nucleus is unstable. Moreover, the theory allows us to describe the stable solid clusters found in simulations. Therefore, we can use it for any combination of the total number of particles, volume, and global density as long as a minimum in the Helmholtz free energy occurs. We also study under which conditions the absolute minimum in the free energy corresponds to a homogeneous liquid or to a heterogeneous system having either spherical, cylindrical, or planar geometry. This work shows that the thermodynamics of curved interfaces at equilibrium can be used to describe nucleation.

Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics

Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process and correctly calculating the relative free energies of different polymorphs. Here, we demonstrate, for the prototypical case of urea nucleation from the melt, how one can learn such a one-dimensional reaction coordinate as a function of prespecified order parameters and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of the generic thermodynamic and structural order parameters using the "spectral gap optimization of order parameters (SGOOP)" approach [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. U.S.A. (2016)] and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insights into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes an accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. We believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.

Crystallisation and polymorph selection in active Brownian particles

We explore crystallisation and polymorph selection in active Brownian particles with numerical simulation. In agreement with previous work (Wysocki et al. in Europhys Lett 105:48004, 2014), we find that crystallisation is suppressed by activity and occurs at higher densities with increasing Péclet number ([Formula: see text]). While the nucleation rate decreases with increasing activity, the crystal growth rate increases due to the accelerated dynamics in the melt. As a result of this competition, we observe the transition from a nucleation and growth regime at high [Formula: see text] to "spinodal nucleation" at low [Formula: see text]. Unlike the case of passive hard spheres, where preference for FCC over HCP polymorphs is weak, activity causes the annealing of HCP stacking faults, thus strongly favouring the FCC symmetry at high [Formula: see text]. When freezing occurs more slowly, in the nucleation and growth regime, this tendency is much reduced and we see a trend towards the passive case of little preference for either polymorph.

Droplet condensation in the lattice gas with density functional theory

A density functional for the lattice gas with next-neighbor attractions (Ising model) from fundamental measure theory is applied to the problem of droplet states in three-dimensional, finite systems. The density functional is constructed via an auxiliary model with hard lattice gas particles and lattice polymers to incorporate the attractions. Similar to previous simulation studies, the sequence of droplets changing to cylinders and to planar slabs is found upon increasing the average density ρ[over ¯] in the system. Owing to the discreteness of the lattice, additional effects in the state curve for the chemical potential μ(ρ[over ¯]) are seen upon lowering the temperature away from the critical temperature [oscillations in μ(ρ[over ¯]) in the slab portion and spiky undulations in μ(ρ[over ¯]) in the cylinder portion as well as an undulatory behavior of the radius of the surface of tension R_{s} in the droplet region]. This behavior in the cylinder and droplet region is related to washed-out layering transitions at the surface of liquid cylinders and droplets. The analysis of the large-radius behavior of the surface tension γ(R_{s}) gave a dominant contribution ∝1/R_{s}^{2}, although the consistency of γ(R_{s}) with the asymptotic behavior of the radius-dependent Tolman length seems to suggest a weak logarithmic contribution ∝lnR_{s}/R_{s}^{2} in γ(R_{s}). The coefficient of this logarithmic term is smaller than a universal value derived with field-theoretic methods.

Equivalence between condensation and boiling in a Lennard-Jones fluid

Condensation and boiling are phase transitions highly relevant to industry, geology, and atmospheric science. These phase transitions are initiated by the nucleation of a drop in a supersaturated vapor and of a bubble in an overstretched liquid, respectively. The surface tension between both phases, liquid and vapor, is a key parameter in the development of such nucleation stage. Whereas the surface tension can be readily measured for a flat interface, there are technical and conceptual limitations to obtain it for the curved interface of the nucleus. On the technical side, it is quite difficult to observe a critical nucleus in experiments. From a conceptual point of view, the interfacial free energy depends on the choice of the dividing surface, being the surface of tension the one relevant for nucleation. We bypass the technical limitation by performing simulations of a Lennard-Jones fluid where we equilibrate critical nuclei (both drops and bubbles). Regarding the conceptual hurdle, we find the relevant cluster size by searching the radius that correctly predicts nucleation rates and nucleation free energy barriers when combined with Classical Nucleation Theory. With such definition of the cluster size we find the same value of the surface tension for drops and bubbles of a given radius. Thus, condensation and boiling can be viewed as two sides of the same coin. Finally, we combine the data coming from drops and bubbles to obtain, via two different routes, estimates of the Tolman length, a parameter that allows describing the curvature dependence of the surface tension in a theoretical framework.

Nucleation work, surface tension, and Gibbs-Tolman length for nucleus of any size

In the framework of the Gibbs approach to nucleation thermodynamics, expressions are derived for the nucleation work, nucleus size, surface tension, and Gibbs-Tolman length in homogeneous single-component nucleation at a fixed temperature. These expressions are in terms of the experimentally controlled overpressure of the nucleating phase and are valid for the entire overpressure range, i.e., for nucleus of any size. Analysis of available data for bubble and droplet nucleation in Lennard-Jones fluid shows that the theory describes well the data by means of a single free parameter, the Gibbs-Tolman length of the planar liquid/vapor interface. It is found that this length is about one-tenth of the Lennard-Jones molecular-diameter parameter and that it is positive for the bubble nucleus and negative for the droplet nucleus. In a sufficiently narrow temperature range, the nucleation work, nucleus radius, scaled surface tension, and Gibbs-Tolman length are apparently universal functions of scaled overpressure.