Dependence Of Free Energy Research Articles

Chemical short range order in MgPb alloys

Magnesium and its alloys are the ideal materials for the automotive and aerospace applications due to their light weight, excellent physical and mechanical properties. In recent years, great effort is being made to synthesise Mg-alloys which are superior in corrosion performance and endowed with required thermal and mechanical properties. Despite of the growing interest in such alloys, very little studies exist which analyse the microscopic level bonding and the atomic order which are ultimately responsible for their thermal stability and synthesisation. In the present work, we have used the compound formation model (2Mg + Pb↔Mg2Pb) to establish the interconnection between the microscopic interactions to the observed thermodynamic properties. It has been used to compute the concentration and the temperature dependence of the excess free energy, concentration fluctuations and chemical short range order which suggests that a reasonable degree of chemical order exist in the alloys.

Deformation–activation model of viscous flow of glass-forming liquids

We suggest a model, according to which the local low activation stretching of a valence bond network is a necessary condition for the realization of an elementary act of viscous flow of inorganic glasses and their melt-activated transition of the kinetic unit (bridge atom) into a deformed microregion. Exactly this kind of local configurational change of structure of a kinetic unit responsible for yield plays an important role in the temperature dependence of the viscosity of these systems, especially in the vicinity of vitrification of liquids. In the framework of this model the temperature dependence of free activation energy of viscous flow of glass melts in the wide temperature range is described and explained.

Thermal properties of the nuclear surface

The thermal evolution of a few thermodynamic properties of the nuclear surface like its thermodynamic potential energy, entropy and the symmetry free energy are examined for both semi-infinite nuclear matter and finite nuclei. The Thomas-Fermi model is employed. Three Skyrme interactions, namely, SkM$^*$, SLy4 and SK255 are used for the calculations to gauge the dependence of the nuclear surface properties on the energy density functionals. For finite nuclei, the surface observables are computed from a global liquid-drop inspired fit of the energies and free energies of a host of nuclei covering the entire periodic table. The hot nuclear system is modelled in a subtracted Thomas-Fermi framework. Compared to semi-infinite nuclear matter, substantial changes in the surface symmetry energy of finite nuclei are indicated; surface thermodynamic potential energies for the two systems are, however, not too different. Analytic expressions to fit the temperature and asymmetry dependence of the surface thermodynamic potential of semi-infinite nuclear matter and the temperature dependence of the surface free energy of finite nuclei are given.

Pressure Tuning of Electron Attachment to Benzoquinones in Nonpolar Fluids: Continuous Adjustment of Free Energy Changes

Changing pressure from 1 to 2500 bar continuously tunes free energy changes for electron attachment to molecules in nonpolar liquids by nearly 0.3 eV. Rate constants for electron attachment to substituted benzoquinones were determined over an extended free energy range of nearly 1 eV by a combination of solute, pressure, temperature, and use of solvents with differing energies of the quasifree electron, V0: tetramethylsilane (TMS) and 2,2,4-trimethylpentane (TMP). The rates of attachment to both benzoquinone (BQ) and 2,5-dichlorobenzoquinone in TMS increase as the pressure increases to 2500 bar, while in TMP the rates are higher but change little with pressure; the rate of attachment to fluoranil in TMS is similarly high at 1 bar but decreases with increasing pressure. Together the observed rate constants can be qualitatively interpreted to yield a rate vs free energy relation having both normal and Marcus inverted region behavior. Because the electron attachment reactions yield excited states, quantitative interpretation of the free energy dependence requires knowledge of the excited state energies. The electron enters the second lowest π* orbital to form a π*-π* excited state, which quickly relaxes to the lower n-π* excited state. The rate of attachment to this excited state is low when the free energy of reaction, ΔG°, is positive and increases as ΔG° decreases until near -0.2 eV, after which the rate decreases. While excited state energies are uncertain, reasonable estimates are obtained from absorption, excitation, and fluorescence spectra of the product radical anions measured here. The results are modeled using Marcus theory with inclusion of a high frequency molecular vibration.

Adsorption of iodide ions on liquid (Ga + In) electrode from mixed solutions with constant ionic strength in dimethylsulfoxide

The adsorption of iodide ions on a liquid (Ga + In) electrode of an eutectic composition (14.2 at % In) from mixed electrolyte (xc M NaJ + (1 − x)c M NaClO4) solutions in dimethylsulfoxide containing surface inactive ions ClO4− with the constant ionic strength of 0.1 M is studied by measuring differential capacitance curves at 305 K. The analysis of experimental data for the studied interval of iodide ion concentration shows that the charge of specifically adsorbed ions on the liquid electrode surface is much lower as compared with the charge found for their adsorption from aqueous solutions of the same electrolyte. The applicability of various adsorption isotherms for the description of experimental data is analyzed. The virial isotherm with the linear dependence of the adsorption free energy on the electrode charge provides the best description. The obtained data on adsorbability of iodide ions are compared with available literature data in aqueous and dimethylsulfoxide solutions on various electrodes.

Thermodynamic modelling of liquids: CALPHAD approaches and contributions from statistical physics

We describe current approaches to thermodynamic modelling of liquids for the CALPHAD method, the use of available experimental methods and results in this type of modelling, and considerations in the use of atomic‐scale simulation methods to inform a CALPHAD approach. We begin with an overview of the formalism currently used in CALPHAD to describe the temperature dependence of the liquid Gibbs free energy and outline opportunities for improvement by reviewing the current physical understanding of the liquid. Brief descriptions of experimental methods for extracting high‐temperature data on liquids and the preparation of undercooled liquid samples are presented. Properties of a well‐determined substance, B2 O3, including the glass transition, are then discussed in detail to emphasize specific modelling requirements for the liquid. We then examine the two‐state model proposed for CALPHAD in detail and compare results with experiment and theory, where available. We further examine the contributions of atomic‐scale methods to the understanding of liquids and their potential for supplementing available data. We discuss molecular dynamics (MD) and Monte Carlo methods that employ atomic interactions from classical interatomic potentials, as well as contributions from ab initio MD. We conclude with a summary of our findings.

Temperature dependence of the crystal-liquid interfacial free energy and the endpoint of the melting line

The crystal-liquid interfacial free energy γ has been calculated as a function of the crystal orientation in a molecular dynamics experiment in a system of Lennard-Jones (LJ) particles with a cutoff radius of the potential rc(*)=rc/σ=6.78 at a triple-point temperature Tt(*)=kBTt/ε=0.692 and temperatures above (in the region of the stable coexistence of liquid and solid phases) and below (metastable continuation of the coexistence curve of liquid and solid phases) the temperature Tt(*). At T(*)=Tt(*), for determining γ use was made of the method of cleaving potential. The temperature dependence of γ on the crystal-liquid coexistence curve has been determined by the Gibbs-Cahn thermodynamic integration method. In the region of stable phase coexistence (T(*)>Tt(*)) good agreement with the data of Davidchack and Laird [J. Chem. Phys. 118, 7651 (2003)] has been obtained with respect to the character of the temperature dependence of γ and the orientation anisotropy. In the region of metastable phase coexistence (T(*)<Tt(*)) at the approach to the endpoint of the melting line (TK(*)=0.529) (the existence of which was established first by Baidakov and Protsenko [Phys. Rev. Lett. 95, 015701 (2005)]) the interfacial free energy decreases, approaching at T(*)=TK(*) the orientation-averaged value γ0K(*)=γ0Kσ(2/ε)=0.365. The paper discusses the behavior of the excess interfacial energy, excess interfacial entropy and excess interfacial stress on the metastable extension of the melting line and close to T(*)=TK(*).

Size-Dependent Surface Free Energy and Tolman-Corrected Droplet Nucleation of TIP4P/2005 Water.

Classical nucleation theory is notoriously inaccurate when using the macroscopic surface free energy for a planar interface. We examine the size dependence of the surface free energy for TIP4P/2005 water nanodroplets (radii ranging from 0.7 to 1.6 nm) at 300 K with the mitosis method, that is, by reversibly splitting the droplets into two subclusters. We calculate the Tolman length to be -0.56 ± 0.09 Å, which indicates that the surface free energy of water droplets that we investigated is 5-11 mJ/m(2) greater than the planar surface free energy. We incorporate the computed Tolman length into a modified classical nucleation theory (δ-CNT) and obtain modified expressions for the critical nucleus size and barrier height. δ-CNT leads to excellent agreement with independently measured nucleation kinetics.

Color screening potential at finite density in two-flavor lattice QCD with Wilson fermions

We investigate the chemical-potential ($\ensuremath{\mu}$) dependence of static-quark free energies in both the real and imaginary $\ensuremath{\mu}$ regions, performing lattice QCD simulations at imaginary $\ensuremath{\mu}$ and extrapolating the results to the real-$\ensuremath{\mu}$ region with analytic continuation. Lattice QCD calculations are done on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}4$ lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group-improved Iwasaki gauge action. Static-quark potentials are evaluated from the Polyakov-loop correlation functions in the deconfinement phase. To perform the analytic continuation, the potential calculated at imaginary $\ensuremath{\mu}=i{\ensuremath{\mu}}_{\mathrm{I}}$ is expanded into a Taylor expansion series of $i{\ensuremath{\mu}}_{\mathrm{I}}/T$ up to fourth order and the pure imaginary variable $i{\ensuremath{\mu}}_{\mathrm{I}}/T$ is replaced by the real one ${\ensuremath{\mu}}_{\mathrm{R}}/T$. At real $\ensuremath{\mu}$, the fourth-order term sizably weakens the $\ensuremath{\mu}$ dependence of the potential. At long distance, all of the color-singlet and -nonsinglet potentials tend to twice the single-quark free energy, indicating that the interactions between static quarks are fully color screened for finite $\ensuremath{\mu}$. For both real and imaginary $\ensuremath{\mu}$, the color-singlet $q\overline{q}$ and the color-antitriplet $qq$ interactions are attractive, whereas the color-octet $q\overline{q}$ and the color-sextet $qq$ interactions are repulsive. The attractive interactions have a stronger $\ensuremath{\mu}/T$ dependence than the repulsive interactions. The color-Debye screening mass is extracted from the color-singlet potential at imaginary $\ensuremath{\mu}$, and the mass is extrapolated to real $\ensuremath{\mu}$ by analytic continuation. The screening mass thus obtained has a stronger $\ensuremath{\mu}$ dependence than the prediction of hard-thermal-loop perturbation theory at both real and imaginary $\ensuremath{\mu}$.

Density-temperature scaling of the fragility in a model glass-former

Dynamical quantities e.g. diffusivity and relaxation time for some glass-formers may depend on density and temperature through a specific combination, rather than independently, allowing the representation of data over ranges of density and temperature as a function of a single scaling variable. Such a scaling, referred to as density-temperature (DT) scaling, is exact for liquids with inverse power law (IPL) interactions but has also been found to be approximately valid in many non-IPL liquids. We have analyzed the consequences of DT scaling on the density dependence of the fragility in a model glass-former. We find the density dependence of kinetic fragility to be weak, and show that it can be understood in terms of DT scaling and deviations of DT scaling at low densities. We also show that the Adam-Gibbs relation exhibits DT scaling and the scaling exponent computed from the density dependence of the activation free energy in the Adam-Gibbs relation, is consistent with the exponent values obtained by other means.

Temperature effect on the small-to-large crossover lengthscale of hydrophobic hydration

The thermodynamics of hydration is expected to change gradually from entropic for small solutes to enthalpic for large ones. The small-to-large crossover lengthscale of hydrophobic hydration depends on the thermodynamic conditions of the solvent such as temperature, pressure, presence of additives, etc. We attempt to shed some light on the temperature dependence of the crossover lengthscale by using a probabilistic approach to water hydrogen bonding that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of both its distance to a solute and solute radius. Incorporating that approach into the density functional theory, one can examine the solute size effects on its hydration over the entire small-to-large lengthscale range at a series of different temperatures. Knowing the dependence of the hydration free energy on the temperature and solute size, one can also obtain its enthalpic and entropic contributions as functions of both temperature and solute size. These functions can provide some interesting insight into the temperature dependence of the crossover lengthscale of hydrophobic hydration. The model was applied to the hydration of spherical particles of various radii in water in the temperature range from T = 293.15 K to T = 333.15 K. The model predictions for the temperature dependence of the hydration free energy of small hydrophobes are consistent with the experimental and simulational data on the hydration of simple molecular solutes. Three alternative definitions for the small-to-large crossover length-scale of hydrophobic hydration are proposed, and their temperature dependence is obtained. Depending on the definition and temperature, the small-to-large crossover in the hydration mechanism is predicted to occur for hydrophobes of radii from one to several nanometers. Independent of its definition, the crossover length-scale is predicted to decrease with increasing temperature.

Structural, electronic, phonon and thermodynamic properties of hypothetical type-VIII clathrates Ba8Si46 and Ba8Al16Si30 investigated by first principles

We present the results of first principles calculations of the structural, electronic, elastic, vibrational, and thermodynamic properties of the hypothetical silicon-based, guest containing type-VIII clathrates Ba8Si46 and Ba8Al16Si30. We obtained the lattice constant, formation energy, band structure, density of states, elastic constants, sound velocity, and Debye temperature using the density functional theory with generalized gradient approximation (GGA). We calculated phonon dispersion and vibrational density of states spectra using the density functional perturbation energy within GGA. We computed the temperature dependent specific heat, vibrational entropy, and vibrational Helmholtz free energy by utilizing quasi-harmonic approximation. We found that replacing some silicon atoms in the framework with aluminum atoms leads to the decrease of the fundamental band gap from 1.0 in Ba8Si46 to 0.18 eV in Ba8Al16Si30. Moreover, the guest Ba atoms produced localized phonon modes lying below 1.2, 1.8 THz for Ba8Si46, and Ba8Al16Si30, respectively, which lead to the reduction of the acoustic bandwidth of the host material. The effect of replacing Si atoms with Al on the properties of the interest is also discussed.

Sequence dependent free energy profiles of localized B- to A-form transition of DNA in water

DNA carries an inherent polymorphism, which surfaces under various external conditions. While B-form remains predominant under normal physiological conditions for most of the DNA sequences, low humidity and increased ion concentration cause B- to A-form transition. Certain proteins and molecules also sometimes cause local deformation of the DNA to the specific A-form. Previous experimental and computational studies focused on the overall B- to A-form transition. Here for the first time we investigated thermodynamics and mechanism of B- to A-form transition in water for various DNA sequences at a local dinucleotide base pair level. We introduced a new reaction coordinate Zp', based on the unique order parameter Zp, to drive B- to A-form transition locally and thereby calculate free energy profiles for the same for all the ten different dinucleotide steps embedded in a twelve base pair DNA. Results show that the trend of "A" and "B" philicity observed in experiment is preserved even at this local dinucleotide level, indicating its localized origin. Higher free energy cost obtained here is attributed to the cost of creating B∕A junctions along with formation of B->A transition at dimer level. We find that while water energetically stabilizes A-form for all the ten different dinucleotide steps to various extents, entropy acts against it. Therefore, we find that the stability of B-form DNA in water is entropic in origin. Mechanism of the conversion appears to be triggered by Slide; however, backbone parameters change concertedly.

Note: Homogeneous TIP4P/2005 ice nucleation at low supercooling

We present a partial free energy profile for the homogeneous nucleation of ice using an all-atom model of water at low supercooling, at which ice growth dynamics are reasonably accessible to simulation. We demonstrate that the free energy profile is well described by classical nucleation theory, and that the nucleation barrier is entropic in origin. We also estimate to first order the temperature dependence of the interfacial free energy.

Density Functional Theory for Protein Transfer Free Energy

We cast the problem of protein transfer free energy within the formalism of density functional theory (DFT), treating the protein as a source of external potential that acts upon the solvent. Solvent excluded volume, solvent-accessible surface area, and temperature dependence of the transfer free energy all emerge naturally within this formalism, and may be compared with simplified "back of the envelope" models, which are also developed here. Depletion contributions to osmolyte induced stability range from 5 to 10 kBT for typical protein lengths. The general DFT transfer theory developed here may be simplified to reproduce a Langmuir isotherm condensation mechanism on the protein surface in the limits of short-ranged interactions, and dilute solute. Extending the equation of state to higher solute densities results in non-monotonic behavior of the free energy driving protein or polymer collapse. Effective interaction potentials between protein backbone or side chains and TMAO are obtained, assuming a simple backbone/side chain two-bead model for the protein with an effective 6-12 potential with the osmolyte. The transfer free energy δg shows significant entropy: d(δg)/dT ≈ 20 kB for a 100-residue protein. The application of DFT to effective solvent forces for use in implicit-solvent molecular dynamics is also developed. The simplest DFT expressions for implicit-solvent forces contain both depletion interactions and an "impeded-solvation" repulsive force at larger distances.

Solvent cavitation under solvophobic confinement

The stability of liquids under solvophobic confinement can tip in favor of the vapor phase, nucleating a liquid-to-vapor phase transition that induces attractive forces between confining surfaces. In the case of water adjacent to hydrophobic surfaces, experimental and theoretical evidence support confinement-mediated evaporation stabilization of biomolecular and colloidal assemblies. The macroscopic thermodynamic theory of cavitation under confinement establishes the connection between the size of the confining surfaces, interfacial free energies, and bulk solvent pressure with the critical evaporation separation and interfacial forces. While molecular simulations have confirmed the broad theoretical trends, a quantitative comparison based on independent measurements of the interfacial free energies and liquid-vapor coexistence properties has, to the best of our knowledge, not yet been performed. To overcome the challenges of simulating a large number of systems to validate scaling predictions for a three-dimensional fluid, we simulate both the forces and liquid-vapor coexistence properties of a two-dimensional Lennard-Jones fluid confined between solvophobic plates over a range of plate sizes and reservoir pressures. Our simulations quantitatively agree with theoretical predictions for solvent-mediated forces and critical evaporation separations once the length dependence of the solvation free energy of an individual confining plate is taken into account. The effective solid-liquid line tension length dependence results from molecular scale correlations for solvating microscopic plates and asymptotically decays to the macroscopic value for plates longer than 150 solvent diameters. The success of the macroscopic thermodynamic theory at describing two-dimensional liquids suggests application to surfactant monolayers to experimentally confirm confinement-mediated cavitation.

Thermodynamic and structural signatures of water-driven methane-methane attraction in coarse-grained mW water

Hydrophobic interactions are responsible for water-driven processes such as protein folding and self-assembly of biomolecules. Microscopic theories and molecular simulations have been used to study association of a pair of methanes in water, the paradigmatic example of hydrophobic attraction, and determined that entropy is the driving force for the association of the methane pair, while the enthalpy disfavors it. An open question is to which extent coarse-grained water models can still produce correct thermodynamic and structural signatures of hydrophobic interaction. In this work, we investigate the hydrophobic interaction between a methane pair in water at temperatures from 260 to 340 K through molecular dynamics simulations with the coarse-grained monatomic water model mW. We find that the coarse-grained model correctly represents the free energy of association of the methane pair, the temperature dependence of free energy, and the positive change in entropy and enthalpy upon association. We investigate the relationship between thermodynamic signatures and structural order of water through the analysis of the spatial distribution of the density, energy, and tetrahedral order parameter Qt of water. The simulations reveal an enhancement of tetrahedral order in the region between the first and second hydration shells of the methane molecules. The increase in tetrahedral order, however, is far from what would be expected for a clathrate-like or ice-like shell around the solutes. This work shows that the mW water model reproduces the key signatures of hydrophobic interaction without long ranged electrostatics or the need to be re-parameterized for different thermodynamic states. These characteristics, and its hundred-fold increase in efficiency with respect to atomistic models, make mW a promising water model for studying water-driven hydrophobic processes in more complex systems.

Dependence of Interaction Free Energy between Solutes on an External Electrostatic Field

To explore the athermal effect of an external electrostatic field on the stabilities of protein conformations and the binding affinities of protein-protein/ligand interactions, the dependences of the polar and hydrophobic interactions on the external electrostatic field, −Eext, were studied using molecular dynamics (MD) simulations. By decomposing Eext into, along, and perpendicular to the direction formed by the two solutes, the effect of Eext on the interactions between these two solutes can be estimated based on the effects from these two components. Eext was applied along the direction of the electric dipole formed by two solutes with opposite charges. The attractive interaction free energy between these two solutes decreased for solutes treated as point charges. In contrast, the attractive interaction free energy between these two solutes increased, as observed by MD simulations, for Eext = 40 or 60 MV/cm. Eext was applied perpendicular to the direction of the electric dipole formed by these two solutes. The attractive interaction free energy was increased for Eext = 100 MV/cm as a result of dielectric saturation. The force on the solutes along the direction of Eext computed from MD simulations was greater than that estimated from a continuum solvent in which the solutes were treated as point charges. To explore the hydrophobic interactions, Eext was applied to a water cluster containing two neutral solutes. The repulsive force between these solutes was decreased/increased for Eext along/perpendicular to the direction of the electric dipole formed by these two solutes.

Importance of configurational contributions to the free energy of nanoclusters

An effective simulation method based on the Wang-Landau Monte Carlo algorithm is used in order to demonstrate the significance of the configurational contributions to the free energy of embedded nanoclusters. Starting from the most stable cluster configuration the simulation provides all geometrically different, but simply connected and sufficiently compact configurations of a nanocluster of a given size and the respective formation energies. The knowledge of these data allows the calculation of the free formation and free binding energy of the cluster at T ≠ 0. The method is applied to coherent Cu clusters in bcc-Fe. It is shown that even at moderate temperatures the configurational contributions to the free formation and binding energy must not be neglected. The dependence of the monomer free binding energy on clusters size is found to change significantly with increasing temperature which has a considerable effect on the pathway of cluster evolution. Therefore, present investigations provide an essential contribution to the improvement of the input parameters for object kinetic Monte Carlo simulations and rate theory used in multi-scale simulations of the nanostructure evolution. The calculation scheme developed in this work is rather general and applicable to many types of embedded nanoclusters. Compared to the method of overlapping distributions hitherto used in some cases to determine the configurational part of the free energy the new method has major advantages. Various tests are performed in order verify the presented approach and to compare with the results of the other calculation procedure. A roadmap is proposed to include the vibrational contributions to the free energy of the clusters within the framework of the method employed in this work.

Temperature and length scale dependence of solvophobic solvation in a single-site water-like liquid

The temperature and length scale dependence of solvation properties of spherical hard solvophobic solutes is investigated in the Jagla liquid, a simple liquid that consists of particles interacting via a spherically symmetric potential combining a hard core repulsion and a longer ranged soft core interaction, yet exhibits water-like anomalies. The results are compared with equivalent calculations for a model of a typical atomic liquid, the Lennard-Jones potential, and with predictions for hydrophobic solvation in water using the cavity equation of state and the extended simple point charge model. We find that the Jagla liquid captures the qualitative thermodynamic behavior of hydrophobic hydration as a function of temperature for both small and large length scale solutes. In particular, for both the Jagla liquid and water, we observe temperature-dependent enthalpy and entropy of solvation for all solute sizes as well as a negative solvation entropy for sufficiently small solutes at low temperature. This feature of water-like solvation is distinct from the strictly positive and temperature independent enthalpy and entropy of cavity solvation observed in the Lennard-Jones fluid. The results suggest that, compared to a simple liquid, it is the presence of a second thermally accessible repulsive energy scale, acting to increasingly favor larger separations for decreasing temperature, that is the essential characteristic of a liquid that favors low-density, open structures, and models hydrophobic hydration, and that it is the presence of this second energy scale that leads to the similarity in the behavior of water and the Jagla liquid. In addition, the Jagla liquid dewets surfaces of large radii of curvature less readily than the Lennard-Jones liquid, reflecting a greater flexibility or elasticity in the Jagla liquid structure than that of a typical liquid, a behavior also similar to that of water's hydrogen bonding network. The implications of the temperature and length scale dependence of solvation free energies in water-like liquids are explored with a simple model for the aggregation of solvophobic solutes. We show how aggregate stability depends upon the size of the aggregate and the size of its constituent solutes, and we relate this dependence to cold-induced destabilization phenomena such as the cold-induced denaturation of proteins.