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We report equilibrium molecular simulation data for the classical Lennard-Jones (LJ) model, covering all thermodynamic states where the crystal is stable, as well as fluid states near coexistence with the crystal; both fcc and hcp polymorphs are considered. These data are used to compute coexistence lines and triple points for equilibrium among the fcc, hcp, and fluid phases. All results are obtained with very high accuracy and precision such that coexistence conditions are obtained with one to two significant figures more than previously reported. All properties are computed in the limit of an infinite cutoff radius of the LJ potential and in the limit of an infinite number of atoms; furthermore, the effect of vacancy defects on the free energy of the crystals is included. Data are fit to a semi-empirical equation of state to within their estimated precision, and convenient formulas for the thermodynamic and coexistence properties are provided. Of particular interest is the liquid-vapor-fcc triple point temperature, which we compute to be 0.694 55 ± 0.000 02 (in LJ units).

The phase diagram (pressure versus temperature) of the pure fluid is typically envisioned as being featureless apart from the presence of the liquid-vapor coexistence curve terminating at the critical point. However, a number of recent authors have proposed that this simple picture misses important features, such as the Widom line, the Fisher-Widom line, and the Frenkel line. In our paper we discuss another way of augmenting the pure fluid phase diagram, lines of zero thermodynamic curvature $R=0$ separating regimes of fluid solid-like behavior ($R>0$) from gas-like or liquid-like behavior ($R, Comment: 38 pages, 22 figures, 58 references

Fully a priori predictions are reported for the vapor-liquid equilibria (VLE) properties of Ar, Kr, and Xe using molecular simulation techniques and recently developed ab initio two-body interatomic potentials. Simulation data are reported at temperatures from near the triple point to close to the critical point. The two-body ab initio potentials exaggerate the size of the experimental VLE temperature-density envelope, overestimating the critical temperature and underestimating the vapor pressure. These deficiencies can be partially rectified by the addition of a density-dependent three-body term. At many temperatures, the ab initio + three-body simulations for Kr and Xe predict the vapor pressure to an accuracy that is close to experimental uncertainty. The predicted VLE coexisting densities for Xe almost match experimental data. The improvement with experiment is also reflected in more accurate enthalpies of vaporization. The fully a priori predictions for all of the VLE properties of either Kr or Xe are noticeably superior to simulations using the Lennard-Jones potential.

This paper determines the thermodynamic phase diagram of the EXP system of particles interacting by the purely repulsive exponential pair potential. The solid phase is face-centered cubic (fcc) at low densities and pressures. At higher densities and pressures, the solid phase is body-centered cubic (bcc) with a re-entrant liquid phase at the highest pressures simulated. The investigation first identifies the phase diagram at zero temperature at which the following four crystal structures are considered: fcc, bcc, hexagonal close packed, and cubic diamond. There is a T = 0 phase transition at pressure 2.651 × 10−3 with the thermodynamically stable structure being fcc below and bcc above this pressure. The densities of the two crystal structures at the phase transition are 1.7469 × 10−2 (fcc) and 1.7471 × 10−2 (bcc). At finite temperatures, the fcc–bcc, fcc-liquid, and bcc-liquid coexistence lines are determined by numerical integration of the Clausius–Clapeyron equation and validated by interface-pinning simulations at selected state points. The bcc-fcc phase transition is a weak first-order transition. The liquid-fcc–bcc triple point, which is determined by the interface-pinning method, has temperature 5.9 × 10−5 and pressure 2.5 × 10−6; the triple-point densities are 1.556 × 10−3 (liquid), 1.583 × 10−3 (bcc), and 1.587 × 10−3 (fcc).

The results are reported of an equilibrium molecular dynamics simulation study of the shear viscosity, η, and self-diffusion coefficient, D, of the Lennard-Jones liquid using the Green-Kubo (GK) method. Semiempirical analytic expressions for both GK time correlation functions were fitted to the simulation data and used to derive analytic expressions for the time dependent diffusion coefficient and shear viscosity, and also the correlation function frequency transforms. In the case of the shear viscosity for a state point near the triple point, a sech function was found to fit the correlation function significantly better than a gaussian in the ballistic short time regime. A reformulation of the shear GK formula in terms of a time series of time integrals (“viscuits”) and contributions to the viscosity from components based on the initial stress (“visclets”) enable the GK expressions to be recast in terms of probability distributions which could be used in coarse grained stochastic models of nanoscale flow. The visclet treatment shows that stress relaxation is statistically independent of the initial stress for equilibrium and metastable liquids, suggesting that shear stress relaxation in liquids is diffusion controlled. By contrast, the velocity autocorrelation function is sensitive to the initial velocity. Weak oscillations and a plateau at intermediate times originate to a greater extent from the high velocity tail of the Maxwell-Boltzmann velocity distribution. Simple approximate analytic expressions for the mean square displacement and the self Van Hove correlation function are also derived.

The dielectric-constant gas thermometer of Physikalisch-Technische Bundesanstalt (PTB) developed for measuring the Boltzmann constant with a relative uncertainty of 1.9 parts per million was used for determining the virial coefficients of the three noble gases, helium, neon, and argon, at the triple point of water (0.01 ○C). For this purpose, isotherms were measured up to a maximum pressure of 7 MPa. The evaluation of the highly accurate data by fitting is required to derive an extended working equation for the dependence of the gas pressure on the dielectric constant. The following values have been obtained for the second B and third C virial coefficients, with the standard uncertainties given in parentheses as a multiple of the last digit, considering literature data for the dielectric virial coefficients: helium: BDCGTHe0.01 ○C=11.925715 cm3/mol, CDCGTHe0.01 ○C=113.4958 cm6/mol2; neon: BDCGTNe0.01 ○C=10.994528 cm3/mol, CDCGTNe0.01 ○C=215.815 cm6/mol2; argon: BDCGTAr0.01 ○C=−21.233144 cm3/mol, CDCGTAr0.01 ○C=1143.339 cm6/mol2. These values are compared with the results of the latest ab initio calculations of the second and third virial coefficients.

The thermodynamic, structural, and vapor-liquid equilibrium properties of neon are comprehensively studied using ab initio, empirical, and semi-classical intermolecular potentials and classical Monte Carlo simulations. Path integral Monte Carlo simulations for isochoric heat capacity and structural properties are also reported for two empirical potentials and one ab initio potential. The isobaric and isochoric heat capacities, thermal expansion coefficient, thermal pressure coefficient, isothermal and adiabatic compressibilities, Joule-Thomson coefficient, and the speed of sound are reported and compared with experimental data for the entire range of liquid densities from the triple point to the critical point. Lustig's thermodynamic approach is formally extended for temperature-dependent intermolecular potentials. Quantum effects are incorporated using the Feynman-Hibbs quantum correction, which results in significant improvement in the accuracy of predicted thermodynamic properties. The new Feynman-Hibbs version of the Hellmann-Bich-Vogel potential predicts the isochoric heat capacity to an accuracy of 1.4% over the entire range of liquid densities. It also predicts other thermodynamic properties more accurately than alternative intermolecular potentials.

In 1897 Ostwald formulated his step rule for formation of the most stable crystal state for a system with crystal polymorphism. The rule describes the irreversible way a system converts to the crystal with lowest free energy. But in fact the irreversible way a supercooled gas below the triple point temperature $T_{tr.p.}$ crystallizes via a liquid droplet is an example of Ostwald's step rule. The homogeneous nucleation in the supersaturated gas is not to a crystal, but to a liquid-like critical nucleus. We have for the first time performed constant energy (NVE) Molecular Dynamics (MD) of homogeneous nucleation without the use of a thermostat. The simulations of homogeneous nucleation in a Lennard-Jones system from supersaturated vapor at temperatures below $T_{tr.p.}$ reveals that the nucleation to a liquid-like critical nucleus is initiated by a small cold cluster [S. Toxvaerd, J. Chem. Phys. \textbf{143} 154705 (2015)]. The release of latent heat at the subsequent droplet growth increases the temperature in the liquid-like droplet, which for not deep supercooling and/or low supersaturation, can exceed $T_{tr.p.}$. The temperature of the liquid-like droplet increases less for a low supersaturation and remains below $T_{tr.p.}$, but without a crystallization of the droplet for long times. The dissipation of the latent heat into the surrounding gas is affected by a traditional MD thermostat, with the consequence that droplet growth is different for (NVE) MD and constant temperature (NVT) MD., Comment: 13 pages, 4 figures

The location of the melting line (ML) of the Lennard-Jones (LJ) system and its associated physical properties are investigated using molecular dynamics computer simulation. The radial distribution function and the behavior of the repulsive and attractive parts of the potential energy indicate that the ML is not a single isomorph, but the isomorphic state evolves gradually with temperature, i.e., it is only "locally isomorphic." The state point dependence of the unitless isomorphic number, X̃, for a range of static and dynamical properties of the LJ system in the solid and fluid states, and for fluid argon, are also reported. The quantity X̃ typically varies most with state point in the vicinity of the triple point and approaches a plateau in the high density (temperature) limit along the ML.

The second virial coefficient (B), Boyle temperature (TB), and temperature maximum (Tmax) are determined for the n-m Lennard-Jones/Mie (LJ/M) potential. The full range of n, m behavior is investigated between the 5-4 LJ/M, hard sphere (n = ∞) + attractive (m ≥ 4) term (HSAm), and hard sphere potential limits. The (n = m + 1)-m LJ/M potential has an important role in characterising the overall behavior of second virial coefficient properties. Different TB, Tmax behavior is observed for n(constant)-m LJ/M and n-m(constant) LJ/M potentials. In the former case, there are two distinct linear (5 ≤ n ≤ 30) and non-linear regions (n > 30). In the latter case, there is a minimum in Tmax in two distinct non-linear regions (4 ≤ m ≤ 34 and 35 ≤ m ≤ 150) followed by a maximum TB region (m ≥ 151). Analytical relationships for some of the behavior are determined and numerical values of TB for a range of n and m values are reported. Molecular simulation data are used to determine simple relationships between TB and both the critical temperature and triple point temperature for the special case of the n-6 LJ/M potential.

Molecular Dynamics simulations are reported for the structural and thermodynamic properties of submonolayer xenon adsorbed on the $(111)$ surface of platinum for temperatures up to the (apparently incipient) triple point and beyond. While the motion of the atoms in the surface plane is treated with a standard two-dimensional molecular dynamics simulation, the model takes into consideration the thermal excitation of quantum states associated with surface-normal dynamics in an attempt to describe the apparent smoothing of the corrugation with increasing temperature. We examine the importance of this thermal smoothing to the relative stability of several observed and proposed low-temperature structures. Structure factor calculations are compared to experimental results in an attempt to determine the low temperature structure of this system. These calculations provide strong evidence that, at very low temperatures, the domain wall structure of a xenon monolayer adsorbed on a Pt$(111)$ substrate possesses a chaotic-like nature, exhibiting long-lived meta-stable states with pinned domain walls, these walls having narrow widths and irregular shapes. This result is contrary to the standard wisdom regarding this system, namely that the very low temperature phase of this system is a striped incommensurate phase. We present the case for further experimental investigation of this and similar systems as possible examples of chaotic low temperature phases in two dimensions., 13+9 pages, 6+6 figures. Change in the title, closer to published version

This paper argues that the viscosity of simple fluids at densities above that of the triple point is a specific function of temperature relative to the freezing temperature at the density in question. The proposed viscosity expression, which is arrived at in part by reference to the isomorph theory of systems with hidden scale invariance, describes computer simulations of the Lennard-Jones system as well as argon and methane experimental data and simulation results for an effective-pair-potential model of liquid sodium.

The structure and thermodynamic properties of the liquid–vapor interface are of fundamental interest for numerous technological implications. For simple molecules, e.g., argon and water, the molecular condensation/evaporation behavior depends strongly on their translational motion and the system temperature. Existing molecular dynamics (MD) results are consistent with the theoretical predictions based on the assumption that the liquid and vapor states in the vicinity of the liquid–vapor interface are isotropic. Additionally, similar molecular condensation/evaporation characteristics have been found for long-chain molecules, e.g., dodecane. It is unclear, however, whether the isotropic assumption is valid and whether the molecular orientation or the chain length of the molecules affects the condensation/evaporation behavior at the liquid–vapor interface. In this study, MD simulations were performed to study the molecular condensation/evaporation behavior of the straight-chain alkanes, i.e., butane, octane, and dodecane, at the liquid–vapor interface, and the effects of the molecular orientation and chain length were investigated in equilibrium systems. The results showed that the condensation/evaporation behavior of chain molecules primarily depends on the molecular translational energy and the surface temperature and is independent of the molecular chain length. Furthermore, the orientation at the liquid–vapor interface was disordered when the surface temperature was sufficiently higher than the triple point and had no significant effect on the molecular condensation/evaporation behavior. The validity of the isotropic assumption was confirmed, and we conclude that the condensation/evaporation coefficients can be predicted by the liquid-to-vapor translational length ratio, even for chain molecules.

Molecular dynamics simulations have been performed to study equilibrium and dynamical aspects of solvation of excess electrons in supercritical ammonia along the T=450 K isotherm. The interval of supercritical densities investigated spans from typically dense liquid down to dilute vapor ambients. Equilibrium aspects of solvation were analyzed using combined path integral-molecular dynamics techniques. The transition from localized to quasifree states, described in terms of the isomorphic electron-polymer spatial extent, was observed at approximately one fourth of the triple point density, a value somewhat higher than that recently reported for supercritical water [D. Laria and M. Skaf, J. Phys. Chem. A 106, 8066 (2002)]. The density of electronic eigenstates shows typically one s- and three p-like bound states that gradually lose their symmetry characteristics as the density lowers. The computed ground state absorption spectrum exhibits redshifts in the absorption bands as the density decreases; these shifts are much larger than those reported by pulse radiolysis experiments. By performing adiabatic dynamics, we also investigate mechanisms for solvent relaxation at high and intermediate supercritical densities following a vertical excitation of the electron.

Molecular dynamics computer simulations of crystallization of a Lennard-Jones system under confinement conditions in the vicinity of the triple point are reported. We calculate the force exerted on a crystal by a melt when it crystallizes. The force due to crystallization is reflected in the disjoining pressure isotherms as a characteristic peak. We find that at conditions of high confinement, i.e., pore thicknesses of ≈1 nm, the disjoining pressure can rise up to ≈108 Pa. We also analyze the dependence of the crystallization under confinement as a function of temperature. Confinement can stabilize the crystal phase at temperatures significantly higher than the melting temperature. For the systems studied in this work, a pore of 1 nm thickness stabilizes the crystal phase at temperatures up to 45% higher than the normal melting temperature. In addition we consider the disjoining pressure profile along confining pore slits of finite lengths. The finite size effects due to the pore length modifies the value...

Three distinct liquid–liquid coexistence regions were observed for ST2 model water by restricted ensemble Monte Carlo simulations of the isotherms of homogenized systems and by phase equilibria simulations in the Gibbs ensemble. The lowest density liquid–liquid transition meets the liquid–vapor phase transition at a triple point and ends in a metastable critical point. A percolation analysis evidences, that the phase separations at the lowest and highest densities can be attributed to the separation of differently coordinated water molecules. The densities of the obtained four phases of supercooled water correlate with experimentally observed densities of amorphous ice.

The density dependence of time correlation functions for the solvation energy in a simple Lennard-Jones liquid has been investigated by molecular dynamics computer simulations. Considering argon dissolved in liquid argon, mechanical solvation dynamics has been studied treating interactions between excited solute states and the solvent by changes in the Lennard-Jones well-depth parameter, the Lennard-Jones size parameter, and a combination of the two. Densities have been varied from supercritical to triple point densities at a constant temperature of 151 K. In addition, a thermodynamic state close to the argon triple point has been considered. All the solvation energy time correlation functions have been broken down into their partial two- and three-body contributions giving an insight into the cancellation effect of solvation dynamics. It is found that the well-depth solvation process produces slowly decaying time correlation functions for the solvation dynamics at lower densities. In this case, the solva...

We performed measurements of a series of adsorption–desorption isotherms of nitrogen into MCM-41 and SBA-15 mesoporous molecular sieves with different pore sizes in a wide temperature range between a bulk triple point (Tt) and a bulk critical point (Tc). The hysteresis loop shrinks with increasing temperature and eventually disappears at the hysteresis critical temperature (Tch), in accord with the appearance of metastable states in a single pore. We estimated the exact pore sizes of our samples from comparing the experimental equilibrium pressure at 77 K with the NLDFT isotherms, where the condensation pressures at 77 K were determined by extrapolating a plot of the equilibrium pressure versus temperature measured above Tch. The pore critical temperature (Tcp) was also determined from the inflection point in a plot of the inverse slope of the adsorption step against temperature. Tch is always lower than Tcp. Both plots of (Tc−Tch)/Tc versus d/rp and (Tc−Tcp)/Tc versus d/rp form straight lines passing thr...

The phase diagram of the Gay–Berne model with anisotropy parameters k53, k 855 has been evaluated by means of computer simulations. For a number of temperatures, NPT simulations were performed for the solid phase leading to the determination of the free energy of the solid at a reference density. Using the equation of state and free energies of the isotropic and nematic phases available in the existing literature the fluid–solid equilibrium was calculated for the temperatures selected. Taking these fluid–solid equilibrium results as the starting points, the fluid–solid equilibrium curve was determined for a wide range of temperatures using Gibbs–Duhem integration. At high temperatures the sequence of phases encountered on compression is isotropic to nematic, and then nematic to solid. For reduced temperatures below T50.85 the sequence is from the isotropic phase directly to the solid state. In view of this we locate the isotropic–nematic–solid triple point at TINS50.85. The present results suggest that the high-density phase designated smectic B in previous simulations of the model is in fact a molecular solid and not a smectic liquid crystal. It seems that no thermodynamically stable smectic phase appears for the Gay–Berne model with the choice of parameters used in this work. We locate the vapor–isotropic liquid–solid triple point at a temperature TVIS50.445. Considering that the critical temperatures is Tc50.473, the Gay–Berne model used in this work presents vapor–liquid separation over a rather narrow range of temperatures. It is suggested that the strong lateral attractive interactions present in the Gay–Berne model stabilizes the layers found in the solid phase. The large stability of the solid phase, particularly at low temperatures, would explain the unexpectedly small liquid range observed in the vapor–liquid region.

Using self-consistent field theory we investigate the properties of interfaces and of bubbles that nucleate in response to a pressure change. We use a simple phenomenological equation of state for a compressible mixture of two polymers. The parameters are chosen as to mimic the behavior of a polymer in a supercritical solvent and the phase behavior in the bulk corresponds to class III in the classification of Konynenburg and Scott. At low pressure, the density of the volatile solvent is small and the interface and nucleation properties are similar to a one-component fluid. At higher pressure, however, there is a triple point at which the polymer coexists with a vapor of the solvent and a mixed solvent-rich liquid. The vicinity of the triple point alters the interface and nucleation behavior: There is a thick wetting layer of the (metastable) solvent-rich liquid at the interface between polymer and vapor, and the solvent condenses into a solvent-rich liquid inside small bubbles. We explore the dependence of the nucleation barrier on temperature, pressure and molecular weight dispersity of the polymer and relate our findings to the binodal and spinodal of the bulk.

We provide a physical insight into the mechanism of the bulk viscosity ζ and construct a new formula for ζ directly from microscopic information such as the interatomic potential and the pair distribution function. This is an outstanding advantage when compared to the previously proposed formulas in all of which ζ is expressed only in terms of a macroscopic quantity, i.e., pressure. In other words, our new formula makes it possible for the first time to discuss the relation between the macroscopic quantity ζ and the microscopic properties such as the interatomic potential and the pair distribution function. This new formula is derived by solving the time development equation of the pair distribution function. Among some of the previously proposed formulas, we prove that the Green–Kubo formula and the Heyes formula are both equivalent to our new formula when the macroscopic quantity—pressure—in their expressions is described by means of interatomic potentials and pair distribution functions under appropriate conditions. This fact confirms the validity of our formula, which reinforces the aforementioned advantage. We calculate ζ near the triple point of the Lennard-Jones fluid using our formula, the Green–Kubo formula, and the Heyes formula. The obtained values of ζ are in good agreement with each other.

We propose a density-functional theory for the study of the phase behavior of discotic molecules interacting via a Gay–Berne potential. The attractions are treated perturbatively in a van der Waals-type manner while the virial series of the repulsions is resummed approximately with the inclusion of the exact second-order Onsager result. On this basis we have studied the isotropic (I)–nematic (N)–columnar (Co) phase behavior for various aspect ratios of the discotic molecules. For small aspect ratios (i.e., large nonsphericities) the phase diagram is found to involve a I–N–Co triple point where the two I–N and N–Co first-order transitions are transformed into a direct I–Co first-order transition. For larger aspect ratios the domain where the N-phase is stable shrinks and disappears above a critical value of the aspect ratio. When compared to the available simulation data it is found that the theory underestimates this critical aspect ratio.

Interfacial melting of ice has been examined by infrared spectroscopy for the first time. Thin ice films, from 10 to 20 nm thick, were prepared on a face of a germanium prism and studied over a range of temperatures just below the triple point. Interrogation was by attenuated total reflection (ATR) spectroscopy. Interfacial melting regions were distinguished from the underlying ice by comparisons of their spectra with the well established infrared signatures of bulk water and ice. Near the triple point, e.g., −0.15 °C, the spectroscopic profile of the surface melting region is indistinguishable from that of liquid water. This is compelling evidence that the commonly labeled quasi-liquid layer is indeed like liquid water. The extent of infrared extinction from ice films was used to determine the thickness of the quasi-liquid layers. At −0.03 °C the thickness is 15 nm corresponding to 40 monolayers of liquid but at −10 °C less than a monolayer remains. We compare our measurements of surface melting with those of others, sometimes finding discrepancies in thickness by two orders of magnitude. The promise of infrared spectroscopy to the further study of interfacial melting of ice is discussed.

The ability of ab initio interatomic potentials to accurately predict vapor-liquid phase equilibria is investigated. Monte Carlo simulations are reported for the vapor-liquid equilibria of argon and krypton using recently developed accurate ab initio interatomic potentials. Seventeen interatomic potentials are studied, formulated from different combinations of two-body plus three-body terms. The simulation results are compared to either experimental or reference data for conditions ranging from the triple point to the critical point. It is demonstrated that the use of ab initio potentials enables systematic improvements to the accuracy of predictions via the addition of theoretically based terms. The contribution of three-body interactions is accounted for using the Axilrod-Teller-Muto plus other multipole contributions and the effective Marcelli-Wang-Sadus potentials. The results indicate that the predictive ability of recent interatomic potentials, obtained from quantum chemical calculations, is comparable to that of accurate empirical models. It is demonstrated that the Marcelli-Wang-Sadus potential can be used in combination with accurate two-body ab initio models for the computationally inexpensive and accurate estimation of vapor-liquid phase equilibria.

We present a density functional approach to describe the solid−liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO2. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO2 at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.

We consider a simple fluid confined between two parallel walls (substrates), separated by a distance L. The walls exert competing surface fields so that one wall is attractive and may be completely wet by liquid (it is solvophilic) while the other is solvophobic. Such asymmetric confinement is sometimes termed a `Janus Interface'. The second wall is: (i) purely repulsive and therefore completely dry (contact angle 180 degrees) or (ii) weakly attractive and partially dry (the contact angle is typically in the range 160-170 degrees). At low temperatures, but above the bulk triple point, we find using classical density functional theory (DFT) that the fluid is highly structured in the liquid part of the density profile. In case (i) a sequence of layering transitions occurs: as L is increased at fixed chemical potential (mu) close to bulk gas--liquid coexistence, new layers of liquid-like density develop discontinuously. In contrast to confinement between identical walls, the solvation force is repulsive for all wall separations and jumps discontinuously at each layering transition and the excess grand potential exhibits many metastable minima as a function of the adsorption. For a fixed temperature T=0.56Tc, where Tc is the bulk critical temperature, we determine the transition lines in the L, mu plane. In case (ii) we do not find layering transitions and the solvation force oscillates about zero. We discuss how our mean-field DFT results might be altered by including effects of fluctuations and comment on how the phenomenology we have revealed might be relevant for experimental and simulation studies of water confined between hydrophilic and hydrophobic substrates, emphasizing it is important to distinguish between cases (i) and (ii)., 16 pages, 13 figures

Freezing of gases adsorbed on open surfaces (e.g., graphite) and in narrow pores is a widespread phenomenon which is a subject of a large number of publications. Modeling of the gas/liquid–solid transition is usually accomplished with a molecular simulation technique. However, quantitative analysis of the gas/liquid–solid coexistence and thermodynamic properties of the solid layer still encounters serious difficulties. This is mainly due to the effect of simulation box size on the lattice constant. Since the lattice constant is a function of loading and temperature, once the ordering transition has occurred, the simulation box size must be corrected in the course of simulation according to the Gibbs–Duhem equation. A significant problem is also associated with accurate prediction of the two-dimensional liquid–solid coexistence because of a small difference in densities of coexisting phases. The aim of this study is thermodynamic analysis of the two-dimensional phase coexistence in systems involving crystal-like free of defects layers in narrow slit pores. A special attention was paid to the determination of triple point temperatures. It is shown that intrinsic properties of argon monolayer adsorbed on the graphite surface are similar to those of isolated monolayer accommodated in the slit pore having width of two argon collision diameters. Analysis of the latter system is shown to be clearer and less time-consuming than the former one, which has allowed for explanation of the experimentally observed two-stage melting transition of argon monolayer on graphite without invoking the periodic surface potential modulation and orientational transition.

The orbital free ab initio molecular dynamics method is applied to study the static and dynamic structure of liquid Al near the triple point. The method uses a new kinetic energy functional, along with a local pseudopotential constructed within the same kinetic energy functional. The results obtained for the dynamic structure factor are compared with recent experimental data.

Molecular dynamics simulations have been used to study the effects of the corrugation in the holding potential of nitrogen molecules on the structure of fluid monolayer and submonolayer films of the molecules on a solid substrate. Structures of monolayer and submonolayer fluid films of nitrogen molecules adsorbed on graphite and on a model uncorrugated “smooth” graphite surface are compared. For films on the “smooth” graphite surface the melting temperature is lowered by 7 K. Contrary to what is found for films on the corrugated surface, the simulations show that there is a region of liquid–gas coexistence, demonstrating that this is a normal triple point system. A discrepancy between calculated and experimental melting temperatures of submonolayer films was traced to the intermolecular potentials. These have been tested by comparing molecular dynamics simulations of isosteric heats of adsorption in fluid films with experimental measurements. The establishment of the effects of the corrugation in the hold...

We have studied the wetting behavior of Ne adsorbed on solid CO2 by means of a quartz crystal microbalance technique. In contrast to recent density functional calculations that predict a prewetting transition near the bulk critical point of Ne, we have observed the more common triple-point wetting behavior.

A modification of an existing model for formamide interactions in the liquid phase makes it possible to study the bulk liquid and its free surface at conditions near the triple point, i.e., 300 K and essentially zero pressure, by (MD) molecular-dynamics simulation. Density profiles and orientation profiles in the surface region show the depth and gradual loss of the molecular ordering in the transition from bulk vapor to the bulk liquid. Near edge x-ray absorption fine structure (NEXAFS) resonance intensity spectra are computed from the orientation profiles, so that comparison should be possible with experimental depth resolved NEXAFS spectra.

We study adsorption of hydrogen-bonded fluids in slit-like pores with strongly attractive walls, in the framework of the four-site associating Lennard-Jones model. The density profiles, as well as the phase behavior, are obtained by using a density functional method. We have found that, at temperatures lower than the critical temperature of the bulk fluid, the confined fluid undergoes one or more layering transitions dependent on the pore width, followed by capillary condensation. Each of the transitions is localized by analyzing the grand thermodynamic potential. The density profiles of nonbonded and differently bonded particles demonstrating changes of the structure of the fluid in the pore along the coexistence are discussed briefly. The critical temperature for capillary condensation is lower for confined fluid, compared with that for the bulk liquid–vapor transition, as expected. However, an increase of the energy of association between fluid species increases the critical temperatures for layering transitions and for capillary condensation. The envelope of the capillary condensation is narrower than the bulk liquid–vapor phase diagram. The ratio between the critical temperatures for layering transitions and capillary condensation depends on the pore width. The critical temperature for the second layering is always lower than for the first one. The triple point temperature between either the second layering transition and the capillary condensation (in wider pores) or the first layering transition and the capillary condensation (in narrower pores) increases with decreasing pore width. The triple point temperature between the layering transitions is much lower than the relevant temperature between the second layering transition and the capillary condensation. The triple point temperatures also depend on the association energy. We have shown that highly bonded fluid species prevail at triple point temperatures.

Fluids of hard bent-core molecules have been studied using theory and computer simulation. The molecules are composed of two hard spherocylinders, with length-to-breadth ratio L/D, joined by their ends at an angle 180°−γ. For L/D=2 and γ=0,10,20°, the simulations show isotropic, nematic, smectic, and solid phases. For L/D=2 and γ=30°, only isotropic, nematic, and solid phases are in evidence, which suggests that there is a nematic-smectic-solid triple point at an angle in the range 20°

It is shown that the classical expression for the change in grand potential of a system on formation of a cluster of radius R is modified by a factor [1−(2w+6δT)/R], to first order in 1/R, where w is a correction due to the nonzero compressibilities of liquid and vapor (near the triple point, w is approximately equal to the product of liquid compressibility and surface tension), and δT is the coefficient in the expression relating the surface tension of the droplet, γ(R), to the planar surface tension, γ∞, i.e., γ(R)=γ∞(1−2δT/R). An expression for δT is derived involving the pair and triplet correlation functions and the density profile of the planar surface. This complements the expression for δT involving the pair distribution function derived by Blokhuis and Bedeaux; the equivalence of the two expressions in the low density limit is demonstrated. Calculations of δT and w are performed using mean-field density functional theory for the Yukawa potential and an r−6 potential, as well as using the square-g...

The Green-Kubo formalism for evaluating transport coefficients by molecular dynamics has been applied to flexible, multicenter models of linear and branched alkanes in the gas phase and in the liquid phase from ambient conditions to close to the triple point. The effects of integration time step, potential cutoff and system size have been studied and shown to be small compared to the computational precision except for diffusion in gaseous n-butane. The RATTLE algorithm is shown to give accurate transport coefficients for time steps up to a limit of 8 fs. The different relaxation mechanisms in the fluids have been studied and it is shown that the longest relaxation time of the system governs the statistical precision of the results. By measuring the longest relaxation time of a system one can obtain a reliable error estimate from a single trajectory. The accuracy of the Green-Kubo method is shown to be as good as the precision for all states and models used in this study even when the system relaxation time becomes very long. The efficiency of the method is shown to be comparable to nonequilibrium methods. The transport coefficients for two recently proposed potential models are presented, showing deviations from experiment of 0%–66%.

We extend the Quantum Cluster Equilibrium (QCE/3-21G-level) theory of liquid water to include larger icelike clusters, including tetrahedral and fullerenelike clusters up to 26-mers. A low-energy tetrakaidecahedral 24-mer (labeled w24_0, with two hexagonal apical faces bridged by 12 pentagons in a cooperatively charge-balanced H-bond pattern) is found to lead to a new low-T phase that bounds both liquid and vapor regions in first-order transition lines, giving rise to a true QCE triple point. We characterize the microstructural composition and macroscopic properties of this “Bucky-ice” phase and examine its dependence on calculated energetics and vibrational properties of constituent clusters. Although the Bucky-ice phase differs in significant respects from physical ice-I (e.g., melting point ∼20 K too high, molar volume ∼5% too low), it manifests qualitatively correct thermodynamic features of true ice polymorphs, suggesting an important role of clathratelike clusters in the liquid/solid transition region.

We present a study of the solid-fluid phase equilibrium for flexible hard sphere site united atom models of n-alkanes using Monte Carlo computer simulation. We have considered models with different torsional potentials to examine the effect this has on the phase diagram. Extensive calculations of the fluid and solid phase equations of state have been made and solid phase free energies have also been determined. The initial solid phase structure used for each system was that which allows the chains to reach the highest density at close packing. The data for hard core chain models have been used as a reference system in a generalized van der Waals or mean field calculation of the n-alkane phase diagrams. This theory reproduces trends in the triple point temperature seen in experimental data. These trends are interpreted in terms of the changes in the close packed densities of the solids with chain length and the effect of the torsional energy on the relative stability of the fluid and solid phases.

The phase diagram of a system of hard spheres with short-range tetrahedral association has been determined by computer simulation and theory. The fluid phase and two solid phases were considered. One of these solid phases is a low-density solid closely related in structure to ice Ic and the other is a high-density solid closely related in structure to ice VII. At high temperatures freezing occurs into the high-density solid whereas at low temperatures freezing occurs into the low-density solid. At an intermediate temperature a triple point is found where the fluid coexists with the two solids simultaneously. Although the low-density solid melts to a high-density fluid, this transition is found to be metastable with respect to the transformation into a high-density solid. This is evidence that short-range tetrahedral attractive forces are not in and of themselves sufficient to explain the anomalous melting of water. Our results indicate that vapor–liquid equilibrium for the model is preempted by solidification. Monte Carlo simulation results for the fluid phase are described successfully by Wertheim’s theory whereas those of the solid phases are described qualitatively by the cell theory.The phase diagram of a system of hard spheres with short-range tetrahedral association has been determined by computer simulation and theory. The fluid phase and two solid phases were considered. One of these solid phases is a low-density solid closely related in structure to ice Ic and the other is a high-density solid closely related in structure to ice VII. At high temperatures freezing occurs into the high-density solid whereas at low temperatures freezing occurs into the low-density solid. At an intermediate temperature a triple point is found where the fluid coexists with the two solids simultaneously. Although the low-density solid melts to a high-density fluid, this transition is found to be metastable with respect to the transformation into a high-density solid. This is evidence that short-range tetrahedral attractive forces are not in and of themselves sufficient to explain the anomalous melting of water. Our results indicate that vapor–liquid equilibrium for the model is preempted by solidifica...

Molecular dynamics computer simulation was carried out to investigate the dynamics of vapor phase homogeneous nucleation at the triple point temperature under supersaturation ratio 6.8 for a Lennard-Jones fluid. To control the system temperature, the 5000 target particles were mixed with 5000 soft-core carrier gas particles. The observed nucleation rate is seven orders of magnitude larger than prediction of a classical nucleation theory. The kinetically defined critical nucleus size, at which the growth and decay rates are balanced, is 30–40, as large as the thermodynamically defined value of 25.4 estimated with the classical theory. From the cluster size distribution in the steady state region, the free energy of cluster formation is estimated, which diminishes the difference between the theoretical prediction and the simulational result concerning the nucleation rate.

The solid-liquid equilibrium of hard dumbbells with embedded point dipoles is calculated using a generalized van der Waals theory to account for long range attractive forces. Molecular parameters are chosen to model a methyl chloride molecule. The solid free energy is calculated using the cell theory of Lennard-Jones and Devonshire with the dipolar contribution estimated by static lattice sums. Thermodynamic perturbation theory is used to add dipolar effects to a hard dumbbell fluid equation of state. The resulting phase equilibria show that the dipole does have a significant effect in determining the stable solid structure on freezing. In particular, the dipole moment stabilizes a non-close-packed orthorhombic structure, similar to the known solid structure of methyl chloride. An increase in the ratio of triple point temperature to critical point temperature is also observed as the dipole moment is increased, as is a decrease in the density change on freezing. At high pressure and temperature a solid-solid-liquid triple point is found, above which the system freezes into the close-packed structure.

Camphene has been studied over ranges of pressure up to 9.5 GPa and temperature up to 1300 °C by in situ resist-volumetric, x-ray diffraction, and Raman scattering measurements as well as by postcompression analyses on retrieved samples. In the solid state, polymerized and amorphous phases appeared. The melting temperature was found to increase with increasing pressure and the melting line showed a small deflection at about 4 GPa, which was attributed to a triple point among the two solid phases and the liquid. Another amorphous phase was retrieved from a region right above the melting line. Heat treatment at temperatures beyond the melting line by about 200 °C and higher yielded turbostratic and graphitic carbons.

For clusters produced by condensation from a gas phase, a basis for identifying the dimensionless thermodynamic and kinetic parameters which characterize cluster formation is provided by arranging an expression for the mass rate of production of critical-size clusters into dimensionless form. The experimentally observed dependence of the cluster size on source pressure dictates the choice between two alternative classical expressions for the nucleation rate. An earlier analysis of dimer formation in free jets guides the combining of the thermodynamic and kinetic parameters into a single scaling parameter which facilitates correlating the size of clusters in free jets for all rare gases, including 4He, using a single curve. Important facets of the correlation are (a) the explicit dependence of the scaling parameter on the surface tension and, for the rare gases other than 4He, the evaluation of the surface tension at the triple point, and (b) the use of real-fluid properties for the density and sound speed...

A new modified hypernetted-chain integral equation for simple fluids is proposed in order to extract the bridge function by means of an iterative and self-consistent process based on the renormalization of the indirect correlation function. We have tested the method for pure Lennard-Jones potential, and our results are compared to those obtained with classical parametrized bridge functions as well as Monte Carlo simulation. It is a matter of fact that the role of the renormalization of the indirect correlation function is to improve the behavior of the bridge function all over the range of distances. Many states near the triple point and under supercritical conditions have been investigated: at high densities, very good agreement is found for structural quantities and thermodynamic properties as compared to other accurate constructions, whereas at low densities our results reduce to those of the standard integral equations.

With Brewster angle autocorrelation spectroscopy involving a combination of Brewster angle microscopy and autocorrelation technique we present quantitative measurements of the tilt angle in octadecanol carried out at the triple point of the next nearest neighbor tilted L2′, the nontilted destorted hexagonal LS(Rot I), and the hexagonal LS(Rot II) phases. We show that the transition from the tilted phase to the nontilted phases, which changes from first order (L2′/LS(Rot I)) to second order (L2′/LS(Rot II)), is associated with strong hysteresis effects in the L2′ phase, leading to an ambiguity of the tilt angle in the vicinty of the triple point. The behavior gives indications for a hindered first-order phase transition within the L2′ phase.

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.

The OH stretching vibrational spectrum of water was measured in a wide range of temperatures across the triple point, 269 K

We present a modification of the molecular dynamics simulation method with a unit pore cell with imaginary gas phase [M. Miyahara, T. Yoshioka, and M. Okazaki, J. Chem. Phys. 106, 8124 (1997)] designed for determination of phase equilibria in nanopores. This new method is based on a Monte Carlo technique and it combines the pore cell, opened to the imaginary gas phase (open pore cell), with a gas cell to measure the equilibrium chemical potential of the confined system. The most striking feature of our new method is that the confined system is steadily led to a thermodynamically stable state by forming concave menisci in the open pore cell. This feature of the open pore cell makes it possible to obtain the equilibrium chemical potential with only a single simulation run, unlike existing simulation methods, which need a number of additional runs. We apply the method to evaluate the equilibrium chemical potentials of confined nitrogen in carbon slit pores and silica cylindrical pores at 77 K, and show that the results are in good agreement with those obtained by two conventional thermodynamic integration methods. Moreover, we also show that the proposed method can be particularly useful for determining vapor-liquid and vapor-solid coexistence curves and the triple point of the confined system.

Grazing incidence x‐ray scattering (GIXS) and Brewster angle microscopy (BAM) are used to determine the π–T phase diagram of Behenic acid monolayers supported on the surface of water (pH=2.0) over the temperature range of 3 °C to 20.6 °C. The phase diagram is constructed from measurements taken during isothermal compressions in which the surface pressure relaxed to a stable value at each surface density, and during temperature scans at fixed average surface density. The phase diagram is different than those previously reported for Behenic acid primarily because of the surface pressure relaxation. For temperatures less than 12 °C the phase diagram exhibits similar phases and topology as the published diagrams, although the location of the phases in the π–T plane is different. Temperature scans combined with the isotherms, and the Clausius–Clapeyron relation are used to determine three coexistence lines that meet in a triple point. Changes in entropy across the phase boundaries are determined. Near room tem...

We present in this paper a computer simulation study of the phase behavior of the Gay–Berne liquid crystal model. The effect of the anisotropic attractive interactions on stabilizing orientationally ordered phases is analyzed by varying the anisotropy parameter κ′ at fixed values of the molecular elongation parameter κ. Molecular dynamics simulations have been performed at constant density and temperature along several isotherms and approximate transition densities are reported. It is found that, for a given value of the molecular elongation κ=3, smectic order is favored at lower densities as κ′ increases. When κ′ is lowered, the smectic phase is preempted by the nematic phase. As a result, the nematic phase becomes increasingly stable at lower temperatures as κ′ is decreased. Additionally, we have studied the liquid–vapor coexistence region for different values of κ′ by using Gibbs ensemble and Gibbs–Duhem Monte Carlo techniques. We have found evidence of a vapor–isotropic–nematic triple point for κ′=1 and κ′=1.25. For temperatures below this triple point, we have observed nematic–vapor coexistence as is found for many liquid crystals in experiments.

We investigate the problem of wetting transitions in polymer blends near a hard surface or wall by using a Monte Carlo technique to study the wetting transition along a path of increasing surface chemical potential. We introduce a parameter es which describes the monomer–monomer interactions in the layer adjacent to the wall. This parameter is shown to behave similarly to the parameter g, used in mean field theory to describe the change in monomer–monomer interactions due to the wall. We identify a wetting tricritical point which may be defined either with respect to es or the bulk density. For bulk densities less than the tricritical bulk density we obtain first‐order transitions while for bulk densities greater than the tricritical bulk density we obtain critical wetting transitions, in accordance with mean‐field theory. We also show how the molecular weight of the polymer can be varied to obtain first‐order or critical wetting, as desired.