Liquid Free Energy Research Articles

Ion solvation free energy calculations based on first-principles molecular dynamics thermodynamic integration.

Numerous electrochemistry reactions require the precise calculation of the ion solvation energy. Despite the significant progress in the first-principles calculations for crystals and defect formation energies for solids, the liquid system free energy calculations still face many challenges. Ion solvation free energies can be calculated via different semiempirical ways, e.g., using implicit solvent models or cluster of explicit molecule models; however, systematically improving these models is difficult due to their lack of a solid theoretical base. A theoretically sound approach for calculating the free energy is to use thermodynamic integration. Nevertheless, owing to the difficulties of self-consistent convergence in first-principles calculations for unphysical atomic configurations, the computational alchemy approach has not been widely used for first-principles calculations. This study proposes a general approach to use first-principles computational alchemy for calculating the ion solvation energy. This approach is also applicable for other small molecules. The calculated ion solvation free energies for Li+, Na+, K+, Be2+, Mg2+, and Ca2+ are close to the experimental results, and the standard deviation due to molecular dynamics fluctuations is within 0.06eV.

An Enhanced Sampling Approach for Computing the Free Energy of Solid Surface and Solid–Liquid Interface

AbstractFree energies of a solid surface and a solid–liquid interface play significant roles in thermodynamics. Due to the limited availability of experimental data, computational methods offer effective alternatives for calculating these properties. This study adopts advanced frameworks of the logarithmic mean force dynamics method to present an enhanced sampling approach for the calculation of the free energy at different temperatures. To achieve this, the free energy profile is constructed along with a pre‐established collective variable within the melting transition and cleavage processes. The values of the solid surface and solid–liquid interface free energies are then extrapolated from the excess free energy related to the formation and persistence of the solid surface or the solid–liquid interface. Furthermore, this methodology is employed to calculate the temperature dependence of the free energy measurements for the (100) and (110) surfaces and interfaces of Cu. It is shown that this methodology is robust and readily applicable in contemporary models of atomic interactions and various systems.

Phase diagram of the TIP4P/Ice water model by enhanced sampling simulations.

We studied the phase diagram for the TIP4P/Ice water model using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice-liquid free energy differences from biased coexistence simulations that reversibly sample the melting and growth of layers of ice. We computed a total of 19 melting points for five different ice polymorphs, which are in excellent agreement with the melting lines obtained from the integration of the Clausius-Clapeyron equation. For proton-ordered and fully proton-disordered ice phases, the results are in very good agreement with previous calculations based on thermodynamic integration. For the partially proton-disordered ice III, we find a large increase in stability that is in line with previous observations using direct coexistence simulations for the TIP4P/2005 model. This issue highlights the robustness of the approach employed here for ice polymorphs with diverse degrees of proton disorder. Our approach is general and can be applied to the calculation of other complex phase diagrams.

Predicting Melt Curves of Energetic Materials Using Molecular Models

AbstractIn this work, the solid–liquid coexistence curves of classical fully flexible atomistic models of α‐RDX and β‐HMX were calculated using thermodynamically rigorous methodologies that identify where the free energy difference between the phases is zero. The free energy difference between each phase at a given state point was computed using the pseudosupercritical path (PSCP) method, and Gibbs–Helmholtz integration was used to evaluate the solid–liquid free energy difference as a function of temperature. This procedure was repeated for several pressures to determine points along the coexistence curve, which were then fit to the Simon–Glatzel functional form. While effective, this method is computationally expensive. An alternative approach is to compute the melting point at a single pressure via the PSCP method, and then use the Gibbs–Duhem integration technique to trace out the coexistence curve in a more computationally economical manner. Both approaches were used to determine the coexistence curve of α‐RDX. The Gibbs–Duhem integration method was shown to generate a melt curve that is in good agreement with the PSCP‐derived melt curve, while only costing ∼10 % of the computational resources used for the PSCP method. For α‐RDX, the predicted melting temperature increases significantly more for a given increase in pressure when compared to available experimental data.

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.

A Simple Equation for the Free Energy of Liquids.

A simple, three-parameter equation is proposed for the free energy of classical fluids composed of molecules which are not hydrogen bonded. Agreement with experiment is much the same as has been obtained from more complicated three-parameter equations. For spherical and nearly spherical molecules, semiquantitative relations between intermolecular pair potential parameters and the parameters of the proposed equation were found. For alkanes, relations between the parameters and carbon number were noted. These relationships contribute to the understanding of fluid state properties in terms of the properties of the molecules of which they are composed.

The solid–liquid interface free energy of Al: A comparison between molecular dynamics calculations and experimental measurements

In this study, molecular dynamics (MD) simulations were performed to calculate the solid–liquid interface (SLI) free energy and its anisotropy of Al using the capillary fluctuation method (CFM) and a third generation of charge-optimized many body (COMB3) potential. The two thresholds (ϕmin, ϕmax) used to define interfacial atoms and the thickness of the bin (Δ) used to define the SLI profile significantly affect the obtained stiffness. The influence of the three parameters is discussed and optimal values for these parameters are also given. The magnitude of the SLI free energy of pure Al at the melting point is found to be 172.67 ± 22.90 mJ/m2 through a detailed discussion of available experimental results. This result is compared with the SLI free energies of Al calculated from the COMB3 potential, two embedded-atom method (EAM) potentials and a modified embedded-atom method (MEAM) potential. It is found that both the COMB3 potential and the MEAM potential give predictions of the SLI free energy very close to the true value, while the EAM potentials underestimate this value quite a lot.

Performance of the standard exchange-correlation functionals in predicting melting properties fully from first principles: Application to Al and magnetic Ni

We apply the efficient two-optimized references thermodynamic integration using Langevin dynamics method [Phys. Rev. B 96, 224202 (2017)] to calculate highly accurate melting properties of Al and magnetic Ni from first principles. For Ni we carefully investigate the impact of magnetism on the liquid and solid free energies including longitudinal spin fluctuations and the reverse influence of atomic vibrations on magnetic properties. We show that magnetic fluctuations are effectively canceling out for both phases and are thus not altering the predicted melting temperature. For both elements, the generalized gradient approximation (GGA) and the local-density approximation (LDA) are used for the exchange-correlation functional revealing a reliable ab initio confidence interval capturing the respective experimental melting point, enthalpy of fusion, and entropy of fusion.

Phase transformation from rutile to anatase with oxygen ion dose in the TiO2 layer formed on a Ti substrate

The oxygen plasma immersion ion implantation (O-PIII) method was used to form a TiO2 layer on a Ti substrate. The content of the anatase polycrystalline phase increased from 5.1% to 22.3% of the total TiO2 amount with a higher O+ ion dose. The oxygen ion doses were 3.6 × 1016 ions, 8.1 × 1016 ions, 1.26 × 1017 ions, for 1, 2, and 3 h, respectively, with ion energies of E ≈ 0.8 keV. The polycrystalline phases and morphology of the obtained films were characterized by XRD, FESEM, AFM, and Raman spectroscopy. The chemical bond analysis and layer-by-layer measurements for TiO2 layer thickness evaluation were performed by XPS. The photocatalytic decomposition reaction constants of a methylene blue solution increased from 3.2 × 10−3 min−1 to 4.2 × 10−3 min−1 under UV-A irradiation and the liquid free surface energy increased from 39.0 mJ/m2 to 49.5 mJ/m2 with a higher O-PIII treatment doses. These results were explained by the partial phase transition of the TiO2 layer from rutile to anatase. Thus, the increase in the O+ ions implantation dose into the Ti substrate invoked the reduction of material density from Ti (ρ = 4.506 g/cm3) through TiO2 rutile (4.23 g/cm3) to TiO2 anatase (3.78 g/cm3) phase.

Spontaneous translation of nanodroplet over a heterogeneous surface due to thermal cycles: role of solid–liquid interfacial fluctuations

ABSTRACTWe study the molecular-scale features of the solid surface that result in the spontaneous motion of a nanodroplet due to the periodic variation of temperature. We first employ a thermodynamic model to predict the variation of solid–fluid interfacial properties that can result in the above motion. The model identifies a composite (surface couple) made of two surfaces that are characterised by a large difference between the entropic parts of the solid–liquid interfacial free energies. In order to understand the molecular-scale features of the two surfaces that may form a surface couple, we performed grand canonical Monte Carlo simulations of Lennard Jones fluid and crystalline surfaces made of Lennard Jones-like atoms. We then used the cumulant expansions of the perturbation formulas to divide the interfacial entropy into two parts: The one that is directly affected by the solid–fluid attraction (direct part), and the other (indirect part) that is indirectly affected by the solid–fluid attraction via the alteration of interfacial fluctuations. Our results indicate that two surfaces form a surface couple if the differences between their chemical natures lead to large differences in the indirect part of the interfacial entropy, while the direct part remains relatively unaffected.

From a Liquid to a Crystal without Going through a First-Order Phase Transition: Determining the Free Energy of Melting with Glassy Intermediates.

The excess free energy of a liquid relative to an Einstein crystal reference state is calculated without going through a first-order phase transition. This is accomplished by going through an arrested glassy state to avoid a direct liquid to gas or liquid to crystal transition. The method is demonstrated by calculating the free energy difference between liquid water and ice Ih using the TIP4P and WAIL water models. TIP4P ice Ih melts at 232 ± 1 K, in close agreement with other estimates in the literature. WAIL ice melts at 272 ± 1 K, in good agreement with that of real water, which serves as a good validation of the quality of the WAIL model. The glassy intermediate method is easy to implement and amicable to parallel executions. We expect this method to have broad applications for calculating the liquid excess free energies for other materials.

Influence of operating conditions on wetting and wettability in membrane distillation using Detection of Dissolved Tracer Intrusion (DDTI)

This study aimed to evaluate the effects of operating parameters (temperature (Tf), Reynolds number (Re), and salinity (Cf) on wettability (contact angle, liquid entry pressure and surface free energy) and wetting indicators evaluated with the recently developed Detection of Dissolved Tracer Intrusion (DDTI) method in Vacuum Membrane Distillation (VMD) for desalination. A 0.22 μm PVDF membrane was subjected to VMD considering a large NaCl feed salinity (22 to 310 g/L). In a first step, the effects and interactions of the operating parameters on the totally wetted surface ratio (ωs) was studied using Box Behnken design of experiments. It was shown that for salt concentrations below 166 g/L the ωs is low and is poorly affected by Re and Tf, whereas for a salt concentration of 310 g/L the influence of Tf and Re becomes sensitive, and high Tf and high Re are required to avoid wetting. In a second step, the effect of salinity was evaluated as a proportion of the liquid intrusion. Here it appears that the range of salinity influences the wetting mechanisms, with an evidence of total wetting only for hypersaline concentrations (higher than 200 g/L).

Efficient approach to compute melting properties fully from ab initio with application to Cu

Applying thermodynamic integration within an ab initio-based free-energy approach is a state-of-the-art method to calculate melting points of materials. However, the high computational cost and the reliance on a good reference system for calculating the liquid free energy have so far hindered a general application. To overcome these challenges, we propose the two-optimized references thermodynamic integration using Langevin dynamics (TOR-TILD) method in this work by extending the two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD) method, which has been originally developed to obtain anharmonic free energies of solids, to the calculation of liquid free energies. The core idea of TOR-TILD is to fit two empirical potentials to the energies from density functional theory based molecular dynamics runs for the solid and the liquid phase and to use these potentials as reference systems for thermodynamic integration. Because the empirical potentials closely reproduce the ab initio system in the relevant part of the phase space the convergence of the thermodynamic integration is very rapid. Therefore, the proposed approach improves significantly the computational efficiency while preserving the required accuracy. As a test case, we apply TOR-TILD to fcc Cu computing not only the melting point but various other melting properties, such as the entropy and enthalpy of fusion and the volume change upon melting. The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and the local-density approximation (LDA) are used. Using both functionals gives a reliable ab initio confidence interval for the melting point, the enthalpy of fusion, and entropy of fusion.

Parametrization of halogen bonds in the CHARMM general force field: Improved treatment of ligand–protein interactions

A halogen bond is a highly directional, non-covalent interaction between a halogen atom and another electronegative atom. It arises due to the formation of a small region of positive electrostatic potential opposite the covalent bond to the halogen, called the ‘sigma hole.’ Empirical force fields in which the electrostatic interactions are represented by atom-centered point charges cannot capture this effect because halogen atoms usually carry a negative charge and therefore interact unfavorably with other electronegative atoms. A strategy to overcome this problem is to attach a positively charged virtual particle to the halogen. In this work, we extend the additive CHARMM General Force Field (CGenFF) to include such interactions in model systems of phenyl-X, with X being Cl, Br or I including di- and trihalogenated species. The charges, Lennard-Jones parameters, and halogen-virtual particle distances were optimized to reproduce the orientation dependence of quantum mechanical interaction energies with water, acetone, and N-methylacetamide as well as experimental pure liquid properties and relative hydration free energies with respect to benzene. The resulting parameters were validated in molecular dynamics simulations on small-molecule crystals and on solvated protein–ligand complexes containing halogenated compounds. The inclusion of positive virtual sites leads to better agreement across experimental observables, including preservation of ligand binding poses as a direct result of the improved representation of halogen bonding.

The anisotropy of hexagonal close-packed and liquid interface free energy using molecular dynamics simulations based on modified embedded-atom method

This work aims to comprehensively study the anisotropy of the hexagonal close-packed (HCP)-liquid interface free energy using molecular dynamics (MD) simulations based on the modified-embedded atom method (MEAM). As a case study, all the simulations are performed for Magnesium (Mg). The solid–liquid coexisting approach is used to accurately calculate the melting point and melting properties. Then, the capillary fluctuation method (CFM) is used to determine the HCP-liquid interface free energy (γ) and anisotropy parameters. In CFM, a continuous order parameter is employed to accurately locate the HCP-liquid interface location, and the HCP symmetry-adapted spherical harmonics are used to expand γ in terms of its anisotropy parameters (ε20, ε40, ε60 and ε66). Eight slip and twinning planes (basal, two prismatic, two pyramidal, and three twinning planes) are considered as the HCP-liquid interface planes. An average HCP-liquid interface free energy of 122.2 (mJ/m2), non-zero ε20, ε40, and ε66 parameters, and approximately zero ε60 parameter for Mg are predicted. Using these findings, the first preferred dendrite growth direction in solidification of Mg is predicted as [112¯0], which is in agreement with experiments. Also, a second preferred dendrite growth direction for Mg is predicted as [336¯2].

Liquid crystal free energy relaxation by a theoretically informed Monte Carlo method using a finite element quadrature approach.

A theoretically informed Monte Carlo method is proposed for Monte Carlo simulation of liquid crystals on the basis of theoretical representations in terms of coarse-grained free energy functionals. The free energy functional is described in the framework of the Landau-de Gennes formalism. A piecewise finite element discretization is used to approximate the alignment field, thereby providing an excellent geometrical representation of curved interfaces and accurate integration of the free energy. The method is suitable for situations where the free energy functional includes highly non-linear terms, including chirality or high-order deformation modes. The validity of the method is established by comparing the results of Monte Carlo simulations to traditional Ginzburg-Landau minimizations of the free energy using a finite difference scheme, and its usefulness is demonstrated in the context of simulations of chiral liquid crystal droplets with and without nanoparticle inclusions.

Investigation on the morphology and surface free energy of the AlGaN thin film

The purpose of this paper is to analyze surface properties of AlGaN thin film produced using thermionic vacuum arc technique. Thermionic vacuum arc is an alternative deposition technique for GaN thin films that produces in a very short production time for GaN-based solid-state applications. XRD results showed that AlGaN thin film with cubic crystal structure on a amorphous glass was grown. Conductivity type of AlGaN thin film is determined as p-type by hot-probe method which is a very simple method. The surface morphology was analyzed and discussed using field emission scanning electron microscopy (FESEM) and atomic force microscopy. The contact angles in four different testing liquid and surface free energy of the AlGaN thin film were investigated by optical tensiometer.

Evaluation of CM5 Charges for Nonaqueous Condensed-Phase Modeling.

Partial atomic charges for neutral molecules from quantum mechanical calculations are typically scaled for use in molecular modeling of liquid-phase systems. Optimal scale factors of 1.14 for CM1A and 1.27 for CM5 charges were previously determined for minimizing errors in free energies of hydration. The adequacy of the 1.14*CM1A and 1.27*CM5 models are evaluated here in pure liquid simulations in combination with the OPLS-AA force field. For 22 organic liquids, the 1.14*CM1A and 1.27*CM5 models yield mean unsigned errors (MUEs) of ca. 1.40 kcal/mol for heats of vaporization. Not surprisingly, this reflects overpolarization with the scale factors derived for aqueous media. Prediction of pure liquid properties using CM5 charges is optimized using a scale factor of 1.14, which reduces the MUE for heats of vaporization to 0.89 kcal/mol. However, due to the impracticality of using different scale factors in different explicit-solvent condensed-phase simulations, a universal scale factor of 1.20 emerged for CM5 charges. This provides a balance between errors in computed pure liquid properties and free energies of hydration. Computation of free energies of hydration by the GB/SA method further found that 1.20 is equally suited for use in explicit or implicit treatments of aqueous solvation. With 1.20*CM5 charges, a variety of condensed-phase simulations can be pursued while maintaining average errors of 1.0 kcal/mol in key thermodynamic properties.

Surface and spectroscopic properties of CdSe/ZnS/PVC nanocomposites

It is valuable to understand the way the wettability is affected by the solid and the liquid surface free energies. For this study, transparent films of CdSe/ZnS/PVC nanocomposites have been prepared and characterized by FTIR and contact angle measurements. Moreover, the presence of polar interactions at the liquid/polymer interfaces, which show a proportionality to the polar components of the liquid surface energy for pure polyvinyl chloride (PVC) and all CdSe/ZnS/PVC nanocomposites, is also studied. By using the surface polarizability hypothesis, there is possibility to obtain the dispersion component of surface‐free energies of pure PVC and also its nanocomposites from the contact angles measurement of only polar liquids. This approximately is coincident with that published data for pure PVC obtained from both polar and nonpolar liquids' contact angles. In addition to this, the absorption spectra and the photoluminescence illustrate clearly the effect of CdSe/ZnS quantum dots on their host matrix. The calculated values of the optical parameters, such as energy gap and Urbach energy, illustrate an inverse proportionality between them. POLYM. COMPOS., 38:749–758, 2017. © 2015 Society of Plastics Engineers

Quantifying a two-mode phase-field crystal model for BCC metals at melting point

A recently developed two-mode phase-field crystal (PFC) model (Wu et al., 2010; Asadi and Asle Zaeem, 2015) is applied for quantitative modeling of body centered cubic (BCC) crystals at their melting points. This model incorporates the first two density wave vectors of BCC crystals in its formulation and consists of three model parameters (two independent and one dependent) in its dimensionless form. A systematic study is presented to show that the two independent parameters of the model control the material properties such as solid and liquid densities and the structure factor. An iterative procedure is presented to determine the PFC model parameters for specific BCC materials using their liquid structure factor and the fluctuation amplitude of atoms in their crystalline state. As a case study, the two-mode PFC model parameters are determined for Fe at its melting point. The calculated model parameters and results of the PFC model are validated by comparing the calculated expansion in melting, solid and liquid densities, elastic constants, and bulk modulus of Fe with the available experimental and computational data in the literature. In addition, to show the potential application of this PFC model, the solid–liquid interface free energy and surface anisotropy of Fe are determined and compared with their available counterparts in the literature.