Liquid-vapor Coexistence Line Research Articles

Structure of liquid-vapor interfaces: Perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence x-ray diffraction.

Grazing-incidence x-ray diffraction (GIXRD) is a scattering technique that allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of surface tension and interface roughness. However, the corresponding standard data analysis at nonzero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here, we overcome this ambiguity by proposing a physically consistent model of the bulk contribution based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we extend the model to account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the x-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid-vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision computer simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid-vapor coexistence line. A sensitivity analysis shows that our findings are robust with respect to the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.

Liquid-vapour coexistence line and percolation line of rose water model

Monte Carlo simulations and Wertheim’s thermodynamic perturbation theory (TPT) are used to predict the phase diagram and percolation curve for the simple two-dimensional rose model of water. In the rose model of water, the water molecules are modelled as two-dimensional Lennard-Jones disks, with additional rose potentials for orientation dependent pairwise interactions that mimic formation of hydrogen bonds. Modifying both the shape and range of a 3-petal rose function, it was constructed an efficient and dynamical mimic of the 2D Mercedes Benz (MB) water model and experimental water. The liquid part of the phase space is explored using grand canonical Monte Carlo simulations and two versions of Wertheim’s TPT for associative fluids. We find that the theory reproduces well the physical properties of hot water but is less successful at capturing the more structured hydrogen bonding that occurs in cold water. In addition to reporting the phase diagram and percolation curve of the model, it is shown that the improved TPT predicts the phase diagram rather well, while the standard one predicts a phase transition at lower temperatures. For the percolation line, both versions have problems predicting the correct position of the line at high temperatures.

AbInitio Nuclear Thermodynamics.

We propose a new MonteCarlo method called the pinhole trace algorithm for abinitio calculations of the thermodynamics of nuclear systems. For typical simulations of interest, the computational speedup relative to conventional grand-canonical ensemble calculations can be as large as a factor of one thousand. Using a leading-order effective interaction that reproduces the properties of many atomic nuclei and neutron matter to a few percent accuracy, we determine the location of the critical point and the liquid-vapor coexistence line for symmetric nuclear matter with equal numbers of protons and neutrons. We also present the first abinitio study of the density and temperature dependence of nuclear clustering.

Widom line and noise-power spectral analysis of a supercritical fluid

We have performed extensive molecular dynamics simulations to study noise-power spectra of density and potential energy fluctuations of a Lennard-Jones model of a fluid in the supercritical region. Emanating from the liquid-vapor critical point, there is a locus of isobaric specific heat maxima, called the Widom line, which is often regarded as an extension of the liquid-vapor coexistence line. Our simulation results show that the noise-power spectrum of the density fluctuations on the Widom line of the liquid-vapor transition exhibits three distinct 1/f^{γ} behaviors with exponents γ=0, 1.2, and 2, depending on the frequency f. We find that the intermediate frequency region with an exponent γ∼ 1 appears as the temperature approaches the Widom temperature from above or below. On the other hand, we do not find three distinct regions of 1/f^{γ} in the power spectrum of the potential energy fluctuations on the Widom line. Furthermore, we find that the power spectra of both the density and potential energy fluctuations at low frequency have a maximum on the Widom line, suggesting that the noise power can provide an alternative signature of the Widom line.

J053023 酸素分子間のスピン-スピン相互作用が熱物性に及ぼす影響

In this paper, we have discussed the spin-spin interaction effect of oxygen based on the evaluation of the liquid-vapor coexistence line of oxygen, using the Monte Carlo (MC) calculations with an ab-initio potential for the quintet oxygen as a dimer (Bartolomei et al., J. Chem. Phys., 2008) and that with a semi empirical model by Aquilanti et al. (J. Am. Chem. Soc., 1999) for the triplet and the singlet oxygen. As a result, an important spin-spin interaction effect on the dense oxygen was qualitatively extracted.

Correlation among several physicochemical properties of alkali metals in the light of the corresponding states principle

The objective of this work is to analyse several physicochemical properties (practically all equilibrium properties) for alkali metals (Li, Na, K, Rb and Cs) from the corresponding states principle along the liquid–vapour coexistence line. Selecting the best experimental data, we plot the reduced quantities versus reduced temperature. In all cases, the behaviour of these substances is well correlated. For K, Rb and Cs, a common line adequately represents such behaviour. From the results, we conclude the validity of this principle in the context.

The dipole moment distribution on water is improved by using large flexibility and large bending angle

A highly flexible model of water with fixed charges is used to study properties of water. The bending angle of an isolated molecule is 125○ that was chosen to match the experimental dipole moment. The geometry of water in the liquid phase is made closer to that of the rigid SPC/E model by decreasing the bending angle spring constant, k Θ. The new model, called SPCE-FHΘ, is a modified version of the recently proposed SPCE-FH [J. Alejandre, G.A. Chapela, F. Bresme and J.-P. Hansen, J. Chem. Phys. 130, 174505 (2009)] to simulate ionic solutions which includes short ranged interactions on the hydrogen atoms. By increasing angle flexibility it is possible to obtain, in the liquid phase at ambient conditions, bending angles ⟨Θ(HOH)⟩ ∼ 109○, dipole moment ⟨μ⟩ ∼ 2.5 D and dielectric constant ⟨ε⟩ ∼ 80. The dipole moment distribution at room temperature goes from 1.5 to 3.5 D due to large fluctuations in bending angle and has the same trend found in ab initio simulations of liquid water. The dipole moment profile at the interface of water varies from 1.9 D in the vapour phase to 2.5 D in the liquid region at 400 K. The SPCE-FHΘ gives dipole moment, dielectric constant, coexisting densities and surface tension along the liquid–vapour coexistence line closer to the experimental values than those obtained for the SPC/E force field.

The fundamental vibrational shift of HCl diluted in dense Ar and Kr

The fundamental infrared band vibrational shifts of HCl diluted in dense Ar and Kr have been calculated by means of molecular dynamics simulation techniques and compared with the experimental data reported by Pérez et al. (J. Chem. Phys. 122, 194507 (2005)). The results have been analysed along the liquid–vapour coexistence line as in several supercritical states, with good agreement between the theoretical and experimental values.

Thermodynamic properties and electrical conductivity of a tight-binding hard-sphere model for liquid metals

We have carried out self-consistent Monte–Carlo simulations for a model fluid of monovalent atoms which interact via hard-sphere repulsions and an attraction arising from the free energy of its valence electrons. This attractive energy is derived from a tight-binding model with an electronic hopping which decays exponentially with distance. The liquid–vapor phase diagram and the structural properties are obtained in the present work. Also, we present the results from various theoretical approaches to the electronic conductivity along the liquid–vapor coexistence line. The results are compared with experimental data for cesium.

On some thermophysical properties of alkanes along the liquid–vapour coexistence line and the corresponding states principle

The Grüneisen thermodynamic parameter, the internal pressure and the long wavelength limit of the static structure factor have been evaluated from basic thermal quantities (pressure, density or volume, heat capacities at constant pressure and volume and sound velocity) using only exact thermodynamic relations for the complete sequence of n-alkanes (n = 1–24) along the liquid–vapour coexistence line. A common behaviour has been observed in accordance with the corresponding states principle. Expressions depending on reduced temperature and the chain length have been obtained for these quantities fitting very well the values assigned to the quantities aforementioned.

Bridge functions near the liquid-vapor coexistence curve in binary Lennard-Jones mixtures

We have carried out extensive molecular-dynamics simulation studies of binary Lennard-Jones mixtures to calculate directly the bridge function at state points lying in a very narrow single fluid phase region between the vapor-liquid and solid-liquid coexistence lines [Lamm and Hall, Fluid Phase Equilib. 182, 37 (2001); 194-197, 197 (2002)]. By varying the density close to the liquid-vapor coexistence line, significant deviations are observed at intermediate distances between the simulated bridge function and two widely used approximate closures in the integral equation theory of liquids, viz. the hybrid mean spherical approximation and the Duh-Henderson closures. The overall qualitative agreement remains the same with small variation in temperature that brings the system closer to either the liquid-vapor or liquid-solid coexistence curve. We also report a comparison of the direct and indirect correlation functions obtained from our simulation studies as well as from the integral equation theory of liquids. Our results emphasize the need for developing new closures applicable to binary fluid mixtures over a wide range of thermodynamic parameters.

Wetting transitions of ionic solutions.

Cahn's phenomenological theory of wetting of a solid substrate by a saturated vapor is generalized to the case where the substrate is charged and the wetting film contains counterions, with or without added salt. The electrostatic contribution to the grand potential associated with these ions is calculated within a nonlinear Poisson-Boltzmann theory. In the salt-free case, when the wetting film includes only counterions released by the substrate, the wetting transition is always first order, regardless of its nature in a neutral system. When salt is present, other wetting scenarios may arise, depending on the salt concentration and substrate surface charge. Over a restricted range of salt concentrations, a wetting scenario similar to that of prewetting, is predicted to occur along the liquid-vapor coexistence line. This scenario includes a discontinuous wetting transition between microscopic and mesoscopic film thicknesses, followed by a continuous divergence of the film thickness at higher temperatures.

Surface tension of a square well fluid

We performed Monte Carlo simulations in the canonical ensemble on the liquid–vapor interface of a square well fluid with interaction range of λ=1.5σ. The system contains a liquid slab surrounded by vapor. The surface tension is calculated during simulations by using an original procedure that allows the calculation of the pressure tensor components. The surface tension decreases monotonically with temperature. Coexisting densities and pressure along the liquid–vapor coexistence line have also been obtained and good agreement is found with results calculated from bulk simulations.

Phase transitions and critical behaviour of simple fluids and their mixtures

It has become clear that the self-consistent Ornstein–Zernike approximation(SCOZA) is a microscopic liquid-state theory that is able to predict thelocation of the critical point and of the liquid–vapour coexistence line of asimple fluid with high accuracy. However, applications of the SCOZAto continuum systems have been restricted up to now to liquids wherethe interatomic potentials consist of a hard-core part with an attractivetwo-Yukawa-tail part. We present here a reformulation of the SCOZA that isbased on the Wertheim–Baxter formalism for solving the mean-sphericalapproximation for a hard-core–multi-Yukawa-tail fluid. This SCOZA version offersmore flexibility and opens access to systems where the interactions can berepresented by a suitable linear combination of Yukawa tails. We demonstratethe power of this generalized SCOZA for a model system of fullerenes;furthermore, we study the critical behaviour of a system with an explicitlydensity-dependent interaction where the phenomenon of double criticality isobserved. Finally, we extend our SCOZA version to the case of a binarysymmetric mixture and present and discuss results for phase diagrams.

The generic van der Waals equation of state and self-diffusion coefficients of liquids

In this paper we use the generic van der Waals equation of state to define the free volume of liquids along the liquid–vapor coexistence line (liquids curve) in the case of liquid argon and along three isotherms in the high-pressure regime in the case of liquid methane. With the free volume computed from the cavity function obtained by means of a Monte Carlo simulation method, we have calculated the self-diffusion coefficients of liquid argon and liquid methane. The Cohen–Turnbull free volume theory is used to calculate them. With the empirical parameter appearing in the Cohen–Turnbull theory suitably adjusted, the theoretical and experimental values of the self-diffusion coefficients agree very well with regard to the density and temperature dependence for the cases of available data compared. A pair of analytic formulas for density dependence of the self-diffusion coefficient is obtained by using the approximate cavity functions for hard spheres and tested against the experimental data on methane. A comparison of the analytic formulas with experiment is also very good.

Structure and Properties of Diatomic Liquid HF. II

We give the results of a computer simulation of fluid hydrogen chloride for general states along the liquid-vapor coexistence line. We used the intermolecular potential functions only of the separation of chlorides of molecules and an electric dipole interaction which has an orientational dependence.

Orbital free ab initio molecular dynamics study of expanded liquid Cs

Orbital free ab initio molecular dynamics is applied to study the static structure and some dynamic properties of liquid Cs at several states along the liquid–vapour coexistence line. Two different kinetic energy functionals are used, namely, the Thomas–Fermi–von Weizsäcker functional and a simplified average density one, and the comparison with experimental data favours the latter, especially at high temperatures. We also show that the approximation of the electron density by a superposition of pseudatomic densities is poor at high temperatures, while acceptable near the triple point. However, the pseudoatom density predicted by linear response theory appears to be too diffuse even close to the triple point.

X-ray diffraction measurements on expanded fluid Rb

An investigation of the density dependence of the structure in liquid rubidium was performed along the liquid vapour coexistence line up to temperatures of 1573 K and 50 bar, and corresponding densities between 1.45 and 0.87 g/cm 3 . All experiments were carried out at the beamline ID30 of the European Synchrotron Radiation Facility (ESRF) in Grenoble. The diffraction pattern could be measured using the combination of a newly developed high-temperature high-pressure scattering setup and monochromatized X-rays of about 50 keV with an imaging plate detector. Although the duration of a single experiment took only approximately 20 s, an extreme improvement in scattering statistics and an extended Q-range could be achieved compared with a previous neutron scattering result on the same system.

Monatomic-Molecular Transition in Expanded Rubidium

S(Q,{omega}) for liquid rubidium measured along the liquid vapor coexistence line exhibits monatomic behavior from normal density down to twice the critical density. At this density we observe excitations characteristic of a harmonic oscillator. We interpret this as evidence for the passage of the fluid from a monatomic to a molecular state. First principle total energy calculations for lattices of ribidium at 0K predict that expansion favors spin pairing and leads to a lattice of dimers with an increase in vibron energy with decreasing density. The excellent agreement of the calculated vibron energy with the experimental result provides theoretical support for the appearance of molecules. {copyright} {ital 1997} {ital The American Physical Society}

Structure and Properties of Diatomic Liquid HCl

We give the results of a computer simulation of fluid hydrogen chloride for general states along the liquid-vapor coexistence line. We used the intermolecular potential functions only of the separation of chlorides of molecules and an electric dipole interaction which has an orientational dependence.