Liquid-vapor Coexistence Line Research Articles

A Gibbs ensemble Monte Carlo study of phase coexistence in model C60

Extensive Gibbs ensemble Monte Carlo (GEMC) simulations of a rigid molecule model of C60, characterized by a deeply attractive short-ranged interaction potential, are performed with the aim to establish the effect of the system size on the existence and location of the liquid–vapor binodal line and of its critical point. The results obtained with N=300, 600, and 1500 particles indicate that the position and the overall shape of the binodal is only minorly influenced by finite size effects. The estimated critical temperature and density at the different N fall in the ranges 1920–1940 K, and 0.4–0.45 nm−3, respectively. The results are discussed by making reference to previous studies of finite size effects in GEMC simulations. The GEMC predictions are also compared with previous computer simulation and theoretical calculations for the same model fluid. The agreement is on the whole satisfactory for both the liquid–vapor coexistence line and the critical point parameters. On the basis of previously determined freezing lines of C60, and of the actual binodal line, different estimates of the location of the triple point are also made. Triple point temperatures are found, in any case, definitely lower (by at least 150 K) than the critical temperatures, thus confirming the existence of a relatively narrow liquid phase region in the phase diagram, as predicted in previous molecular dynamics and theoretical works. The existence of such a liquid phase for the adopted model potential is discussed and assessed in the more general framework of liquid–vapor coexistence conditions in fluids interacting through short-ranged forces. The possibility to get the liquid phase of “real life” C60, hitherto not observed experimentally, is also discussed in connection with recent high temperature experimental results on fullerite samples.

Brownian Dynamics Simulations of Domain Growth in Lennard-Jones Fluids

Abstract The evolution of the structural, thermodynamic and rheological properties of a three dimensional Lennard-Jones fluid is followed as it is quenched from a supercritical state into the two phase gas-liquid coexistence region of the phase diagram. Domain growth is revealed in the appearance of a peak in the structure factor at kmax ∼ [sgrave] LJ −1 which moves to lower k with time, and whose peak height S(k max) increases with time. k max −1 and S(k max) show a power law dependence with time with exponents in the range 0.2–0.3 and 0.7–1.0, respectively, depending somewhat on the destination state point and broadly consistent with previous theory and simulation. The kinetics of domain growth depends on the value of temperature and density quenched to in the two-phase region. For quenches close to the liquid-vapour coexistence line, an initial period marked by a lack of growth in the low k peak (‘latency’) is followed by power law behaviour, which is indicative of growth by nucleation. Quenches to wel...

Polarizable point-charge model for water: Results under normal and extreme conditions

Molecular dynamics simulations of liquid water under normal and extreme conditions are performed using the polarizable point-charge (PPC) model. This efficient three-site model explicitly incorporates results from ab initio studies of the water molecule in applied electric fields. The structural, thermodynamic, and dielectric properties, and the self-diffusion coefficient are examined at a number of temperatures ranging from 263 to 573 K. These simulation results are compared with available experimental data along the liquid–vapor coexistence line; the agreement is very good for all properties studied. The temperature of maximum density for the PPC model is found to coincide with the experimentally observed value of 277 K. The spatial coordination of water molecules in the liquid and the anisotropy of the self-diffusion tensor are analyzed at various state points. Increased directional anisotropy in the local translational diffusion, suggestive of prenucleation phenomena, can be observed at T=263 K. Above T=473 K the local translational anisotropy becomes rather insensitive to temperature variation indicating a weakening of the correlations between water molecules. Rototranslational dynamics and nonlinear polarization effects arising in polarizable models for water are discussed along with their phenomenological implications. The dimer properties for the PPC potential are also reported.

Theoretical analysis of the far-infrared spectra of HCl in liquid Ar along the Ar liquid-vapour coexistence line

We present the theoretical evolution of the far-infrared spectra of HCl in liquid Ar along the Ar liquid-vapour coexistence line obtained from a quantum spectral theory incorporating memory and line mixing effects. The involved time autocorrelation functions associated to the first order anisotropic interaction are calculated by means of classical molecular dynamics techniques. The radial form of the HCl-Ar anisotropic potential is considered as effective in nature with a density-dependent well depth. Numerical results for six Ar thermodynamic states show that the calculated spectra change from those showing a weak, residual rotational structure at high densities and low temperatures to those showing clear, resolved rotational lines as temperature increases and density decreases.

Hall mobility of electrons in liquid xenon

Reports the Hall mobility of electrons injected into liquid xenon whose thermodynamic state is varied along the liquid-vapour coexistence line from the triple point to 272 K. Contrary to what would be expected from transport theory, when omega c tau <1, the Hall angle is not a linear function of the magnetic field. This is particularly important near the mobility maximum, and is interpreted as arising from interference effects. Their importance is a consequence of the fact that, to first order, at the mobility maximum, the electron-phonon interaction is zero while elastic scattering by large density fluctuations persists. Hot electron effects support this interpretation. Beyond 272 K no Hall signal could be detected. Although this is an indication that hopping conductivity is dominant, it is shown that the eventual localized states cannot be associated with electrons trapped into density fluctuations associated with the pure fluid.

Motion of electrons in liquid xenon: Evidence for non-Boltzmann transport.

This letter reports the Hall mobility of electrons injected into liquid xenon whose thermodynamic state is varied along the liquid-vapor coexistence line from the triple point to 275 K. Contrary to what would be expected from transport theory, when ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$\ensuremath{\tau}1, the Hall angle is not a linear function of the magnetic field. This is particularly important near the mobility maximum and is interpreted as arising from interference effects. Their importance is a consequence of the fact that at the mobility maximum, the electron-phonon interaction is zero while elastic scattering by large density fluctuations persists.

Certain aspects of the behaviour of saturated-fluid phases

The existence of maxima of certain products of thermodynamic properties along the liquid-vapour co-existence line is brought out. These maxima occur at specific reduced temperatures independent of the nature of the liquid. The behaviour of saturatedvapour enthalpy is analyzed in detail. A relation between the temperature at which this property depicts a maximum and the molecular length parameter is derived considering over 40 crygenic liquids, hydrocarbon and refrigerants.

The influence of the fluid–wall interaction potential on the structure of a simple fluid in a narrow slit

The structure of a Lennard-Jones fluid in a narrow planar slit is studied for different kinds of wall–fluid interaction potentials by applying anisotropic integral equation theories. Density profiles and in some cases the force between the walls as a function of the slit width are calculated. It is found that when the state of the fluid in the slit is close to the liquid–vapor coexistence line, there must exist a distinct attractive minimum in the wall potential in order to induce an oscillatory density profile in the slit. Then, the force as a function of the slit width is also oscillatory. The repulsive part of the wall potential has little influence on the oscillatory behavior. When the wall potential consists of a very soft repulsive part close to the wall followed by a diffuse attractive minimum further out, the layer structure disappears completely. However, when the pressure of the fluid is raised above the vapor pressure, the oscillatory structure slowly reappears. These results are utilized to discuss certain experimental surface force measurements where solid, molecularly smooth walls have been modified by adsorption of amphiphiles. It is suggested that the main reason why the oscillatory forces do not appear in such systems is that the attractive part of the wall potential becomes diffuse and not that the repulsive wall becomes soft.

Hall mobility of electrons in liquid and solid argon.

The Hall mobility of electrons injected in liquid argon has been measured along the liquid-vapor coexistence line, along a portion of the 50-atm isobar, and in the solid at the triple point. From a comparison of these results with the published time-of-flight (TOF) mobility data, it is concluded that the low-field TOF data in the liquid coincide with the low-field drift mobility. From a comparison of the ratio of the Hall and TOF mobilities with its counterpart calculated on the basis of different models, it is concluded that only the model in which the scattering is due to both phonons and nearly static density fluctuations can explain the experimental data. There is excellent agreement between the mobility observed in the solid (2820 ${\mathrm{cm}}^{2}$/V s) and what one would expect if the calculated phonon scattering in the liquid would be extrapolated to the density of the solid. This provides support for the density-dependent effective mass that was used as a parameter in the model calculation. What remains unexplained, in the framework of a single spherical parabolic band, is the magnetic field dependence of the Hall angle near the mobility maximum.

A simple property of a simple liquid

It has been observed that for a computer-simulated Lennard-Jones 12-6 liquid on the liquid-vapour coexistence line, the distribution function, p(f), for a cartesian component of the force on an atom, f, is remarkably close to exponential in form over a wide range of f. There appears to be no simple theoretical reason for this simple result. An approximate theoretical analysis is given which confirms this behaviour and suggests that it may be quite general for liquids with approximately spherically symmetric, short-ranged, interparticle potentials.

RISM study of sulphur dioxide at the liquid-vapour coexistence line

Sulphur dioxide is studied by the reference interaction site model. The site-site potential was modelled by the Lennard-Jones potential functions and direct correlation functions were calculated for thermodynamic points close to the liquid-vapour coexistence line. By means of the correlation functions the pressure and mean potential energy have been calculated. The results were compared with molecular dynamics results and also with experimental data. It turned out that the RISM procedure is competitive with the molecular dynamics method only in a relatively narrow temperature range close to the midpoint between the triple point and the critical point. There the agreement between RISM and molecular dynamics method is quite encouraging and also the experimental values of pressure and mean potential energy and compressibility are satisfactorily reproduced. On either side of this region RISM does not reproduce properly the structure and energetics of the liquid SO 2 system.

The chemical potential of a liquid on the liquid-vapour coexistence line and the lattice-gas model

The lattice-gas model predicts that a certain chemical potential is constant along the liquid-vapour coexistence line. It is shown that this is true to a few percent for two simulated atomic liquids and for several real liquids (argon, nitrogen and hydrogen chloride). More complex liquids (water) show substantial deviations.

Investigation of the chemical potential by molecular dynamics simulation

The Widom test particle method is implemented in molecular dynamics simulations to investigate the chemical potential of various fluids. This method is found to be reliable and accurate at liquid density if a sufficient number of simulated particles are taken into account. In order to save computing time an importance sampling technique is used during the simulation. Moreover, it is shown that the size of the simulated system can generate spurious results. Finally, the role of the chemical potential as a test for the effective pair potentials is illustrated for one example: the liquid-vapour coexistence line of chlorine.

The two-dimensional liquid-vapor coexistence line of methane adsorbed on graphite

We measured the specific heat of two-dimensional films of CH 4 adsorbed on graphite for several coverages and we observed broad peaks at the liquid-vapor transition. The critical temperature is estimated to be 70 ± 1 K, somewhat lower than reported in previous measurements. At intermediate coverages the liquid-vapor boundary is very flat indicating that it could be described by a 2D Ising model. We measured also for some coverages the triple temperature at 56.2 K and the commensurate-incommensurate transition at about 50 K, both in reasonable agreement with previous measurements.

The two-dimensional liquid-vapor coexistence line of methane adsorbed on graphite

The two-dimensional liquid-vapor coexistence line of methane adsorbed on graphite

Motion of electrons in a classical liquid: injected electron Hall mobility in liquid neopentane along the liquid-vapor coexistence line between the triple and the critical point

Motion of electrons in a classical liquid: injected electron Hall mobility in liquid neopentane along the liquid-vapor coexistence line between the triple and the critical point

Hall Mobility of Electrons Injected into Fluid Neopentane (Dimethyl Propane) along the Liquid-Vapor Coexistence Line between the Triple and the Critical Points

Measurements of the Hall and the time-of-flight mobilities of electrons injected into neopentane along the liquid-vapor coexistence curve between the triple and the critical points are reported. The ratio of the Hall mobility to time-of-flight mobility always exceeds unity; it decreases linearly from 1.8 at low temperatures to 1.4 near 410 K and increases thereafter to nearly 5.8 in the vicinity of the critical point. This is suggestive of localized states associated with density fluctuations. These density fluctuations are probably the dominant scattering mechanism that determines the Hall mobility.

The liquid-vapour coexistence line by computer simulation à la Widom

It is shown that the Widom method of evaluating the chemical potential of a fluid [6] which has been exploited recently to obtain liquid entropies and vapour pressures by computer simulation [5] can be used very simply and economically to predict the liquid-vapour coexistence line and the vapour pressure given the form of the potential. The method is illustrated explicitly for liquid chlorine and liquid bromine. It is quite general, is simpler to use than might have been anticipated and provides a powerful test of an assumed form of intermolecular potential.

Pure vibrational Raman spectra of simple liquids: O2, N2, CO, CH4, CF4

Interferometric techniques have been applied in a high resolution study of the polarized Raman components (Q branches) corresponding to the totally symmetric vibrational modes of CO, CH4, and CF4 in the liquid phase. Additional unpublished data for N2 and O2, as well as limited results of dilution studies in liquid argon, are reported. Emphasis is placed upon the measurement of variations in frequency shift and spectral width along the liquid–vapor coexistence line from the triple point to within 0.2 K of the critical point for each pure liquid. The character of the observed linewidth variations exhibits distinct differences from liquid to liquid, especially in the neighborhood of the triple and critical points. A consistent interpretation of the results suggests that a substantial contribution to the N2 and O2 linewidths is associated with the effect of intramolecular vibration–rotation coupling. The CH4 data support the predictions of Hills and Madden (i) that the long wavelength, hydrodynamic, density fluctuations can play an important role in determining the linewidth in the critical region, and (ii) that a transition from fast to slow modulation conditions should be observable as the critical point is approached. CF4 may represent a case where slow modulation conditions hold throughout a large part of the liquid range.

Brillouin scattering studies of simple liquids: O2, N2, CO, CH4

The technique of Brillouin scattering has been used to obtain new velocity and attenuation data for thermal sound waves in liquids O2, N2, CO, and CH4. Measurements of Brillouin shift and linewidth were made along the liquid–vapor coexistence line in each case and, when combined with previously published results, comprise a reasonably complete set of data covering the saturated liquid ranges of all four cryogenic materials. Where possible, comparisons are made with corresponding ultrasonic data.