Solid-liquid Interfacial Free Energy Research Articles

Hydrogen-bond linking is crucial for growing ice VII embryos.

We use molecular dynamics simulations to examine the homogeneous nucleation of ice VII from metastable liquid water. An unsupervised machine learning classification identifies two distinct local structures composing Ice VII nuclei. The seeding method, combined with the classical nucleation theory (CNT), predicts the solid-liquid interfacial free energy, consistent with the value from the mold integration method. Meanwhile, the nucleation rates estimated from the CNT framework and brute force spontaneous nucleations are inconsistent, and we discuss the reasons for this discrepancy. Structural and dynamical heterogeneities suggest that the potential birthplace for an ice VII embryo is relatively ordered, although not necessarily relatively immobile. Moreover, we demonstrate that without the formation of hydrogen-bond links, ice VII embryos do not grow.

Capillary Condensation of Water in Graphene Nanocapillaries.

Recent experiments have revealed that the macroscopic Kelvin equation remains surprisingly accurate even for nanoscale capillaries. This phenomenon was so far explained by the oscillatory behavior of the solid-liquid interfacial free energy. We here demonstrate thermodynamic and capillarity inconsistencies with this explanation. After revising the Kelvin equation, we ascribe its validity at nanoscale confinement to the effect of disjoining pressure. To substantiate our hypothesis, we employed molecular dynamics simulations to evaluate interfacial heat transfer and wetting properties. Our assessments unveil a breakdown in a previously established proportionality between the work of adhesion and the Kapitza conductance at capillary heights below 1.3 nm, where the dominance of the work of adhesion shifts primarily from energy to entropy. Alternatively, the peak density of the initial water layer can effectively probe the work of adhesion. Unlike under bulk conditions, high confinement renders the work of adhesion entropically unfavorable.

Morphological diversity in directionally-solidified microstructures with varying anisotropy of solid-liquid interfacial free energy

Morphological diversity in directionally-solidified microstructures of fcc-based binary alloys was investigated using quantitative phase-field simulation. The growth morphology for each set of anisotropy parameters was identified from the degree of undercooling of the dendrite tip and a morphology map was constructed. We investigated the effects of solidification conditions and alloy systems on growth morphology and found that the pulling speed has a significant effect, while temperature gradient and partition coefficient have only small effects on the morphology selection. Furthermore, we examined the emergence of doublon and triplet dendrites under conditions of weak interfacial anisotropy.

Nanoscale insights on the freezing front propagation and ion behaviors during seawater freezing

Seawater freezing holds significant importance in scientific and industrial applications. However, there is a lack of in-depth understanding of the nanoscale mechanism of seawater freezing. In this study, the nanoscale characteristics and mechanisms of seawater freezing are investigated by the molecular dynamics method. Since the solid-liquid interfacial free energy decreases with increasing subcooling or decreasing NaCl solution concentration, the speed of freezing front propagation increases. The formation of nano brine pockets is observed, which is analyzed based on the solid-liquid interfacial free energy. The energy barriers of Na+ and Cl− diffusing from the freezing front into the NaCl solution are smaller than these of diffusing into the hexagonal ice. As a result, most Na+ and Cl− are rejected into the solution, whereas only a few dope into the hexagonal ice. Furthermore, the energy barrier of Cl− diffusion into hexagonal ice is smaller than that of Na+, which makes the amount of Cl− doping into hexagonal ice greater than that of Na+. This study contributes to a deeper understanding of nanoscale characteristics and mechanisms of seawater freezing, which shall promote related technologies such as seawater freeze desalination.

Machine learning-assisted MD simulation of melting in superheated AlCu validates the Classical Nucleation Theory

The validity of the Classical Nucleation Theory (CNT), the standard tool for describing and predicting nucleation kinetics in metastable systems, has been under scrutiny for almost a century. While the CNT is commonly employed to describe liquid → crystal and liquid ↔ vapor phase transitions, its application to the crystal → liquid case has been limited because of the experimental challenges in achieving superheating states and detecting homogeneous liquid nucleation. In this study, we performed comprehensive molecular dynamics (MD) simulations of spontaneous melting of a superheated AlCu crystal under atmospheric pressure at five temperatures, covering a superheating range of T/TL = 1.1–1.3, where TL is the liquidus temperature. Two realistic AlCu models were investigated: one described by the modified embedded atom method (MEAM) and the other by an interatomic potential generated by an artificial neural network machine learning (ML) approach, extensively trained on an ab initio dataset of liquid and crystal configurations. Fifty independent melting events were simulated at each temperature. By analyzing the distribution of melting times using the Poisson law, the homogeneous nucleation rate was determined through the mean lifetime method. Additionally, the Zeldovich factor, critical nucleus size, and work of formation were obtained using the mean first-passage time method, utilizing the disorder parameter based on atomic displacements (liquid-like atoms in the superheated crystal) as the reaction coordinate. Also, the effective atomic transport coefficient across the metastable crystal/critical liquid nucleus interface was determined by MD simulations as the interfacial attachment coefficient for nuclei growth rates. Using these simulation-generated data, the theoretical nucleation rates were calculated by the CNT with no fitting parameters. We found excellent agreement between the theoretically and MD-computed liquid nucleation rates for both MEAM and ML crystals. Notably, the effective solid-liquid interfacial free energy value obtained from the MD data aligns with its recent experimental measure. Moreover, the CNT qualitatively and quantitatively described the underlying details of liquid drop nucleation in our ML solid, unprecedentedly and accurately reproducing the kinetic prefactor and the size, formation energy, and growth rate of the critical nuclei. Thus, the melting of the AlCu model created through machine learning-processed quantum calculations, that is, not relying on hand-crafted interatomic potential functions, was successfully described by the CNT phenomenological formalism, without any adjustable parameters. This finding confirms the CNT as a very reliable descriptor of homogeneous nucleation in the superheated AlCu alloy and generalizes this theory as a powerful tool for analyzing and predicting the kinetics of crystal-liquid transitions.

Temperature-dependent growth kinetic and crystallization behavior of the supercooled erythritol as a phase change material in long-term heat storage

Along with the development of long-term heat storage, the utilization of sugar alcohol with large supercooling has been valued in recent years. However, the heat release rate is not easy to control, and the supercooling would be easily influenced by accident factors. Different from the research of directly developing the composites to control the heat release rate and keep stable supercooling, this paper investigated the temperature-dependence crystal growth of erythritol coupled with diffusion-limited kinetics to find the mechanism for better understanding the utilization of supercooling upon different heat needs. The mean crystal growth rate (vm) on supercooled erythritol and the thermodynamic parameters were characterized experimentally. A nucleation factor J* was proposed to improve the modern Wilson-Frenkel equation, which enables a more accurate reflection of the nucleation effect on the practical vm. The sensitivity analysis indicates that the diffusion coefficient (D) and liquid–solid interfacial free energy (IFE1) have a great impact on vm, with 62% and 37% correlations. To verify this result, 0.1 wt% PVA was added to erythritol, which resulted in a significant reduction in the vm maximum by 33.3%. An oil seal was added to reduce the liquid–air interfacial free energy (IFE2) of erythritol, which significantly extended the supercooling duration to 5 days with a 12% cumulative crystallization fraction. Moreover, the crystal morphology analysis revealed that the maximum growth rate had preferred orientations of (211), the largest grain boundary size of 9.2 mm, and exhibited three-dimensional growth. This work can aid in the creation of a dependable heat release model for sugar alcohols in long-term heat storage systems.

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 550K) and complement our perspective with the results previously obtained at 296.4K [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 0.1nm. 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.

Direct Measurement of Solid-Liquid Interfacial Energy Using a Meniscus

Solid-liquid interactions are central to diverse processes. The interaction strength can be described by the solid-liquid interfacial free energy (γ_{SL}), a quantity that is difficult to measure. Here, we present the direct experimental measurement of γ_{SL} for a variety of solid materials, from nonpolar polymers to highly wetting metals. By attaching a thin solid film on top of a liquid meniscus, we create a solid-liquid interface. The interface determines the curvature of the meniscus, analysis of which yields γ_{SL} with an uncertainty of less than 10%. Measurement of classically challenging metal-water interfaces reveals γ_{SL}∼30-60 mJ/m^{2}, demonstrating quantitatively that water-metal adhesion is 80% stronger than the cohesion energy of bulk water, and experimentally verifying previous quantum chemical calculations.

Melting temperature, critical nucleus size, and interfacial free energy in single FCC metals — A Molecular Dynamics study of liquid–solid phase equilibria

Molecular dynamics simulations in the isobaric–isenthalpic ensemble are used to derive various important parameters related to nucleation from the melt. In particular, by using results from liquid–solid phase equilibria, we present a simple, yet reliable, approach to extract melting temperature, critical nucleus size, and liquid–solid interfacial free energy for six different embedded atom FCC systems. Our approach is based on the fundamental thermodynamic relation given by the Gibbs–Thomson equation that uses the heat released during solidification to drive growth of the solid phase until thermodynamic equilibrium is achieved. Equilibrium between the liquid and solid phases is identified by a steady-state evolution in the temperature of the two-phase system.

Computing the solid-liquid interfacial free energy and anisotropy of the Al-Mg system using a MEAM potential with atomistic simulations

The solid–liquid interfacial free energy, γ, and its associated anisotropy were computed for the Al-Mg binary alloy system using Molecular Dynamics (MD) simulations in conjunction with the capillary fluctuation method (CFM). Interactions between atoms were modeled based on a second nearest neighbor modified embedded atom method (MEAM) potential, a successor to the established embedded atom method (EAM) potential. The MEAM potential predicts a melting temperature of 938 K ± 17 K for pure Al and the solid–liquid phase equilibria as a function of temperature and composition was found using Monte Carlo technique implemented in Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The average interfacial free energy, γ0, for pure Al was found to be 135.94 ± 3.62 mJ/m2 which agrees well with experimental values and an interfacial free energy relationship of γ100>γ110>γ111 was found across the majority of the temperatures which is consistent with FCC metals. The anisotropy values were found to fall within the 100 growth direction along the orientation selection map suggesting the addition of Mg stabilizes this growth direction. The results from the MEAM potential compares qualitatively well with other EAM potentials, however, experiences larger errors at lower temperatures.

Computing contact angles for oil-water-rock systems via thermodynamic integration.

Wettability of rock surfaces with respect to oil and water, which is characterized by the contact angle, is an important factor that determines the efficacy of enhanced oil recovery operations. Experimental determination of contact angles for oil-water-rock systems is expensive and time-consuming due to the extremely long times needed for the establishment of adsorption equilibrium at the liquid-solid interface. Hence, molecular simulations form an attractive tool for computing contact angles. In this work, we use the cleaving wall technique that was developed previously in our group [R. K. R. Addula and S. N. Punnathanam, J. Chem. Phys. 153, 154504 (2020)] to compute solid-liquid interfacial free energy, which is then combined with Young's equation to compute the oil-water contact angle on silica surfaces. The silica surface is modeled with the INTERFACE force field that has been developed to accurately reproduce experimental data. We have considered three different surface chemistries of silica, namely, Q2, Q3, and Q4, in this study. Our calculations reveal that while the Q2 and Q3 surfaces are completely wetted by water, the Q4 surface is partially non-wetted by water. All the simulations needed for this calculation can be performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) molecular package. This should facilitate wider adoption of the Young's equation route to compute contact angles for systems comprised of complex molecules.

Model for the Solid-Liquid Interfacial Free Energy at High Pressures.

The free energy involved in the formation of an interface between two phases (e.g., a solid-liquid interface) is referred to as the interfacial free energy. For the case of solidification, the interfacial free energy dictates the height of the energy barrier required to nucleate stable clusters of the newly forming solid phase and is essential for producing an accurate solidification kinetics model using classical nucleation theory (CNT)-based methods. While various methods have been proposed for modeling the interfacial free energy for solid-liquid interfaces in prior literature, many of these formulations involve making restrictive assumptions or approximations, such as the system being at or near equilibrium (i.e., the system temperature is approximately equal to the melt temperature) or that the system is at pressures close to atmospheric. However, these approximations and assumptions may break down in highly non-equilibrium situations, such as in dynamic-compression experiments where metastable liquids that are undercooled by hundreds of kelvin or overpressurized by several gigapascals or more are formed before eventually solidifying. We derive a solid-liquid interfacial free-energy model for such high-pressure conditions by considering the enthalpies of interactions between pairs of atoms or molecules. We also consider the contribution of interface roughness (disordering) by incorporating a multilayer interface model known as the Temkin n-layer model. Our formulation is applicable to a diverse variety of materials, and we demonstrate it by developing models specifically for two different materials: water and gallium. We apply our interfacial free-energy formulation to CNT-based kinetics simulations of several suites of dynamic-compression experiments that cause liquid water to solidify to the high-pressure solid polymorph ice VII and have found good agreement to the observed kinetics with only minor empirical fitting.

Mechanism insights into liquid polarity regulation for enhanced dewatering of waste-activated sludge: Specifically focusing on the solid-liquid affinity reduction depending on phase-transfer and conformational features of amphiphilic protein

This study proposed that decreasing liquid polarity could weaken the intermolecular polar force at solid-liquid interface of waste-activated sludge (WAS). Accordingly, a process for enhanced sludge dewatering through liquid polarity regulation was established. The liquid polarity was quantified by dielectric constant and the decrease of liquid dielectric constant below 50 was found to significantly improve the solid-liquid separation performance of WAS in terms of filterability by >70%. The differential scanning calorimeter (DSC) coupled with mass spectrum (MS) identified that 60 °C was the appropriate temperature for liquid amendment (i.e., acetonitrile) recovery from filtered sludge cake, and the corresponding energy consumption was calculated to be at most 799.0 J/g, which was substantially lower than that of water evaporation by sludge drying. The NaCl addition with 75% of saturated concentration could non-thermally recover 91.7 ± 4.9% of acetonitrile amendment from filtrate by salting-out. The great potentials in energy saving and recycle of chemicals make the newly proposed approach act as alternatives for the conventional process (i.e., mechanically dewatering + drying). Regarding the mechanism of liquid polarity regulation for enhanced WAS dewatering, the solid-liquid interfacial free energy was found to be reduced by 39.4% with the liquid dielectric constant decreasing from 78.50 to 41.00. Also, Tandem Mass Tags (TMT) proteomics tracked the phase-transfer of amphiphilic proteins with decreasing liquid polarity, which found that the solubilization of proteins involved in the Gene Ontology (GO) classifications of “membrane protein complex” and “membrane protein complex/outer membrane” could facilitate the enhanced solid-liquid separation of WAS. The conformational analysis on those differential proteins was further conducted to reveal the structure attributes of amphiphilic proteins for the phase-transfer feature. The proteins with more exposed amino acid residues (i.e., average solvent accessibility index over 1.8) tended to dissolve in the liquid phase with lower polarity, which was accompanied with the reduced interfacial free energy of WAS. On the contrary, the proteins with buried amino acid residues (e.g., the central hydrophobic β-sheet is surrounded by the hydrophilic α-helix) precipitated in the solid phase with the decreasing liquid polarity. All these findings are expected to create a novel option for dewatering WAS with recyclable liquid conditioning agents, and provide the improved mechanistic insights into the migration of interfacial compositions controlling the dewaterability of WAS.

An atomistic simulation study of rapid solidification kinetics and crystal defects in dilute Al–Cu alloys

Rapid solidification kinetics of dilute Al–Cu alloys is simulated using a quantum mechanics based bond-order potential (BOP), in free solidification conditions, to determine kinetic and thermodynamic properties of solidification, as well as point defects and chemical ordering of the solidified structures. We measure the anisotropic kinetic coefficient, anisotropic solid–liquid interface energy, as well as solute trapping kinetics in terms of partition coefficient versus velocity and solute drag coefficient. Furthermore, solid–liquid interface free energy and its anisotropy are measured in equilibrium simulations, showing reasonably good agreement with previous studies. We also verified the self-consistency of the MD simulations, by comparing the interfacial temperature vs. velocity to that predicted by the continuous growth model. These solid–liquid interface properties are important for quantitative parametrization of larger scale solidification modeling techniques such as phase field models. We also investigated the point defect content, local chemical ordering, and local crystalline structures in the rapidly solidified samples. We found clustering of solute with vacancies, whereas copper atoms repelled each other in these dilute alloy simulations. In addition to vacancies, a large number of interstitials were found. In solidification velocities approaching the complete solute trapping regime, we found that the vacancies and interstitials formed in conjunction, i.e. as Frenkel pairs. Finally, in addition to FCC, we detected BCC and HCP phases, where the latter two were accompanied by an increase in local copper content. Understanding the formation of point defects and their relationship to chemical ordering is an important step towards controlling the formation of pre-precipitates and precipitates, which are an important strengthening mechanism for aluminum–copper alloys.

Inverse analysis of anisotropy of solid-liquid interfacial free energy based on machine learning

A machine leaning-based approach is proposed for the inverse analysis of the anisotropy parameters of solid–liquid interfacial free energy. The interface shape distribution (ISD) map, which characterizes the details of the dendrite morphology, was selected as the input of a convolutional neural network (CNN). The ISD maps for a free-growing dendrite during the isothermal solidification of a model alloy system were obtained by quantitative phase-field simulations and used as the training and test data for the CNN. Two anisotropy parameters were estimated with errors of less than 5%, which can be further improved by increasing the size of the training dataset.

The influence of Pb content on the interfacial free energy of solid Sn in eutectic Pb–Sn liquid mixtures using molecular dynamics simulations

ABSTRACT The solid–liquid interfacial free energy (γ) for binary Pb–Sn systems at different concentrations and crystal orientations is calculated using molecular dynamics (MD) simulation that employs a modified-embedded atom method interatomic potential. First, the solid–liquid interface is constructed in MD simulations according to its calculated phase diagram. Then, the capillary fluctuation method (CFM) is employed for the calculation of the solid–liquid interfacial stiffness. A novel systematic approach is proposed that eliminates the error in the linear approximation of the CFM. The results show that orientation of the solid Sn crystal does not have a significant influence on the value of the stiffness, which explains the experimentally observed spherical shape of Sn particles in eutectic liquid Pb–Sn mixtures. The calculated γ for pure Sn is in good agreement with experimental counterparts. In addition, this study finds that γ slightly increases with increasing the concentration of Pb in the eutectic liquid Pb–Sn mixture, which agrees with available experimental data.

Pressure Dependence of the Crystallization Rate for the S-Enantiomer and a Racemic Mixture of Ibuprofen.

This paper examines the pressure effect on the crystallization rate of the pharmaceutically active enantiomerically pure S-enantiomer and the racemic mixture of the well-known drug ibuprofen. Performed experimental studies revealed that at ambient pressure S-ibuprofen crystallizes faster than the racemic mixture. When the pressure increases, the crystallization rate slows down for both systems, but interestingly it is more apparent in the case of the S-enantiomer. It is found that this experimentally observed trend can be understood based on the predictions of the classical nucleation theory. We suggest that the solid–liquid interfacial free energy is the main reason for the observed variations in S- and RS-ibuprofen’s stability behaviors. Employing a special method of computational studies, i.e., the capillary fluctuation method, we show that the increase in pressure affects the solid–liquid interfacial free energy for S- and RS-ibuprofen in an entirely different way. Importantly, the detected differences correspond to the experimentally observed variations in the overall crystallization rates.

Layering misalignment and negative temperature dependence of interfacial free energy of B2-liquid interfaces in a glass forming system

From molecular dynamics simulations and the capillary fluctuation method, the solid-liquid interfacial free energy (γ0) has been computed for the B2-liquid interface in the Cu-Zr system. Consistent with previous results for the FCC-liquid interface in Cu-Zr and Al-Sm but atypical of most alloys, γ0 was found to increase as the temperature is lowered. In addition, the temperature dependence was obtained for model Lennard-Jones B2-liquid alloys. In all cases the unusual temperature dependence of γ0 is correlated with an atomic structure of the interfacial region characterized by a misalignment of the number density peaks between solvents and solutes. In cases where the number density peaks are aligned, the typical temperature dependence is observed. The results are discussed in terms of the Gibbs theory of the thermodynamics of interfaces. It is proposed that the unique interfacial structure and the atypical temperature dependence of γ0 are hallmarks of an easy glass forming alloy.

Interfacial properties between ionic‐liquid‐based electrolytes and lithium‐ion‐battery separator

AbstractFor lithium salts, ionic liquids (ILs) are promising alternatives to conventional solvents in lithium‐ion batteries (LIBs) due to a more favorable high‐voltage operating window, and due to improved safety through reduction of flammability. Toward better understanding of wetting properties of IL‐based electrolytes on a LIB separator, wetting properties affect electrochemical performance, experimental studies were made to determine the influence of solvent, lithium‐salt type and salt concentration. Surface tensions and advancing contact angles were measured for two pure ILs ([C4C1im][BF4] and [C4C1im][OTf]) and for four IL/alkylcarbonate solvent blends (1:1 mass ratio, [C4C1im][BF4]/PC, [C4C1im][BF4]/DMC, [C4C1im][OTf]/PC, and [C4C1im][OTf]/ DMC) with several concentrations of a lithium salt (LiClO4, LiPF6, and LiTFSI). A significant improvement of wettability of pure ILs was observed by adding DMC, while adding PC with surface tension higher than that of pure ILs is detrimental to wetting behavior. Contact angles decrease by adding LiTFSI but show almost no change upon addition of LiPF6 or LiClO4. Surface tensions follow the same trend as that for contact angles. Incorporation of TFSI− anion gives favorable separator wettability. Estimates were made for interfacial properties of the separator (dispersive and polar components of the surface free energy for solid‐vapor, for liquid–vapor, and for solid–liquid interfacial free energy).

Computation of the solid-liquid interfacial free energy in hard spheres by means of thermodynamic integration.

We used a thermodynamic integration scheme, which is specifically designed for disordered systems, to compute the interfacial free energy of the solid-liquid interface in the hard-sphere model. We separated the bulk contribution to the total free energy from the interface contribution, performed a finite-size scaling analysis, and obtained for the (100)-interface γ=0.591(11)k_{B}Tσ^{-2}.