Crystal growth of bcc titanium from the melt and interfacial properties: A molecular dynamics simulation study.

The crystal growth kinetics and interfacial properties of titanium (Ti) are studied using molecular dynamics computer simulation. The interactions between the Ti atoms are modeled via an embedded atom method potential. First, the free solidification method (FSM) is used to determine the melting temperature Tm at zero pressure where the transition from liquid to body-centered cubic crystal occurs. From the simulations with the FSM, the kinetic growth coefficients are also determined for different orientations of the crystal, analyzing how the coupling to the thermostat affects the estimates of the growth coefficients. At Tm, anisotropic interfacial stiffnesses and free energies as well as kinetic growth coefficients are determined from capillary wave fluctuations. The so-obtained growth coefficients from equilibrium fluctuations and without the coupling of the system to a thermostat agree well with those extracted from the FSM calculations.

Premelting of ice adsorbed on a rock surface.

Considering ice-premelting on a quartz rock surface (i.e. silica) we calculate the Lifshitz excess pressures in a four layer system with rock-ice-water-air. Our calculations give excess pressures across (1) ice layer, (2) water layer, and (3) ice-water interface for different ice and water layer thicknesses. We analyse equilibrium conditions where the different excess pressures take zero value, stabilized in part by repulsive Lifshitz interactions. In contrast to previous investigations which considered varying thickness of only one layer (ice or water), here we present theory allowing for simultaneous variation of both layer thicknesses. For a given total thickness of ice and water, this allows multiple alternative equilibrium solutions. Consequently the final state of a system will depend on initial conditions and may explain variation in experimental measurements of the thicknesses of water and ice layers.

Effect of molecular flexibility of Lennard-Jones chains on vapor-liquid interfacial properties.

We have determined the interfacial properties of short fully flexible chains formed from tangentially bonded Lennard-Jones monomeric units from direct simulation of the vapor-liquid interface. The results obtained are compared with those corresponding to rigid-linear chains formed from the same chain length, previously determined in the literature [F. J. Blas, A. I. M.-V. Bravo, J. M. Míguez, M. M. Piñeiro, and L. G. MacDowell, J. Chem. Phys. 137, 084706 (2012)]. The full long-range tails of the potential are accounted for by means of an improved version of the inhomogeneous long-range corrections of Janecek [J. Phys. Chem. B 129, 6264 (2006)] proposed recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2008)] valid for spherical as well as for rigid and flexible molecular systems. Three different model systems comprising of 3, 5, and 6 monomers per molecule are considered. The simulations are performed in the canonical ensemble, and the vapor-liquid interfacial tension is evaluated using the test-area method. In addition to the surface tension, we also obtained density profiles, coexistence densities, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the chain length and rigidity on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapor-liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. Comparison between predictions for fully flexible and rigid-linear chains, formed by the same number of monomeric units, indicates that the main effects of increasing the flexibility, i.e., passing from a rigid-linear to a fully flexible chain, are: (a) to decrease the difference between the liquid and vapor densities; (b) to decrease the critical temperature and to increase the critical density; (c) to smooth the density profiles along the interfacial region; (d) to increase the interfacial thickness; and (e) to decrease the vapor-liquid surface tension.

Vapor-liquid interfacial properties of rigid-linear Lennard-Jones chains.

We have obtained the interfacial properties of short rigid-linear chains formed from tangentially bonded Lennard-Jones monomeric units from direct simulation of the vapour-liquid interface. The full long-range tails of the potential are accounted for by means of an improved version of the inhomogeneous long-range corrections of Janecek [J. Phys. Chem. B 110, 6264-6269 (2006)] proposed recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] valid for spherical as well as for rigid and flexible molecular systems. Three different model systems comprising of 3, 4, and 5 monomers per molecule are considered. The simulations are performed in the canonical ensemble, and the vapor-liquid interfacial tension is evaluated using the test-area method. In addition to the surface tension, we also obtain density profiles, coexistence densities, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the chain length and rigidity on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapor-liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. The surface tension has been scaled by critical properties and represented as a function of the difference between coexistence densities relative to the critical density.

Universal scaling behaviour of surface tension of molecular chains.

We use and extend the universal relationship recently proposed by Galliero [G. Galliero, J. Chem. Phys. 133, 074705 (2010)], based on a combination of the corresponding-states principle of Guggenheim [E. A. Guggenheim, J. Chem. Phys. 13, 253 (1945)] and the parachor approach of Macleod [J. Macleod, Trans. Faraday Soc. 19, 38 (1923)], to predict the vapour-liquid surface tension of fully flexible chainlike Lennard-Jones molecules. In the original study of Galliero, the reduced surface tension of short-chain molecules formed by up to five monomers is expressed as a unique function of the difference between the liquid and vapour coexistence densities. In this work, we extend the applicability of the recipe and demonstrate that it is also valid for predicting the surface tension of two different chainlike molecular models, namely, linear tangent chains that interact through the Lennard-Jones intermolecular potential and fully flexible chains formed by spherical segments interacting through the square-well potential. Computer simulation data for vapour-liquid surface tension of fully flexible and rigid linear Lennard-Jones, and fluid flexible square-well chains is taken from our previous works. Our results indicate that the universal scaling relationship is able to correlate short- and long-chain molecules with different degrees of flexibility and interacting through different intermolecular potentials.

Phase diagram of water under an applied electric field.

Simulations are used to investigate for the first time the anisotropy of the dielectric response and the effects of an applied electric field E(ex) on the phase diagram of water. In the presence of electric fields ice II disappears from the phase diagram. When E(ex) is applied in the direction perpendicular to the ac crystallographic plane the melting temperatures of ices III and V increase whereas that of ice Ih is hardly affected. Ice III also disappears as a stable phase when E(ex) is applied in the direction perpendicular to the ab plane. E(ex) increases by a small amount the critical temperature and reduces slightly the temperature of the maximum density of liquid water. The presence E(ex) modifies all phase transitions of water but its effect on solid-solid and solid-fluid transitions seems to be more important and different depending on the direction of E(ex).

Dielectric constant of ices and water: a lesson about water interactions.

In this paper, the dielectric constant has been evaluated for ices Ih, III, V, VI, and VII for several water models using two different methodologies. Using Monte Carlo simulations, with special moves to sample proton-disordered configurations, the dielectric constant has been rigorously evaluated. We also used an approximate route in which proton-disordered configurations satisfying the Bernal-Fowler rules were generated following the algorithm proposed by Buch et al. (Buch, V.; Sandler, P.; Sadlej, J. J. Phys. Chem. B 1998, 102, 8641), and the dielectric constant was estimated assuming that all configurations have the same statistical weight (as Pauling did when estimating the residual entropy of ice). The predictions of the Pauling model for the dielectric constant differ in general from those obtained rigorously by computer simulations because proton-disordered configurations satisfying the Bernal-Fowler rules can differ in their energies by as much as 0.10-0.30 NkT (at 243 K). These differences in energy significantly affect properties that vary from one configuration to another such as polarization, leading to different values of the dielectric constant. The Pauling predictions differ from the simulation results, especially for SPC/E and TIP5P, but yield reasonable results for TIP4P-like models. We suggest that for three charge models the polarization factor (G) in condensed phases depends on the ratio of the dipole to the quadrupole moment. The SPC/E, TIP5P, TIP4P, TIP4P/2005, TIP4P/ice models of water are unable to describe simultaneously both the experimental dielectric constants of water and ice Ih. Nonpolarizable models cannot describe the dielectric constants of the different condensed phases of water because their dipole moments (about 2.3 D) are much smaller that those estimated from first principles (of the order of 3 D). However, the predictions of TIP4P models provide an overall qualititatively correct description of the dielectric constant of the condensed phases of water, when the dipole moment of the model is scaled to the estimated value obtained from first principle calculations. Such scaling fails completely for SPC/E, TIP3P, and TIP5P as these models predict a completely different dielectric constant for ice Ih and water at the melting point, in complete disagreement with experiment. The dielectric constant of ices, as the phase diagram predictions, seems to contain interesting information about the orientational dependence of water interactions.

Coarse-graining dipolar interactions in simple fluids and polymer solutions: Monte Carlo studies of the phase behavior.

In this paper we investigate the phase diagram of pure dipolar substances and their mixtures with short alkanes, using grand canonical Monte Carlo simulations of simplified coarse-grained models. Recently, an efficient coarse-grained model for simple quadrupolar molecules, based on a Lennard-Jones (LJ) interaction plus a spherically averaged quadrupolar potential, has been shown to be successful in predicting single-component and mixture phase diagrams. Motivated by these results, we investigate the phase diagrams of simple dipolar molecules (and their mixtures with alkanes) using a spherically averaged potential. First, we test the model on pure components. A generalized (state-dependent) mapping procedure allows us to recycle Monte Carlo results of the simple Lennard-Jones (LJ) potential. Considering ammonia, nitrous oxide, and hydrogen sulfide, we generally observe improvements in the single-component phase diagram compared to a pure LJ description, but also some discrepancies in the coexistence pressure near the critical point and in the liquid branch of the coexistence densities well below criticality. In addition, we present results for mixtures. We consider mixtures of ammonia (NH3) with methane (CH4), nonane (C9H20) and hexadecane (C16H34)--for which experimental results are available--and compare the predictions from this modeling ansatz with predictions from simple LJ models. We also present results for the hydrogen sulfide-pentane mixture (H2S and C5H12) for which big discrepancies between simulations and experiments are present. Possible explanations for these discrepancies and limitations of the modeling are discussed.

Coarse-grained models for fluids and their mixtures: Comparison of Monte Carlo studies of their phase behavior with perturbation theory and experiment.

The prediction of the equation of state and the phase behavior of simple fluids (noble gases, carbon dioxide, benzene, methane, and short alkane chains) and their mixtures by Monte Carlo computer simulation and analytic approximations based on thermodynamic perturbation theory is discussed. Molecules are described by coarse grained models, where either the whole molecule (carbon dioxide, benzene, and methane) or a group of a few successive CH(2) groups (in the case of alkanes) are lumped into an effective point particle. Interactions among these point particles are fitted by Lennard-Jones (LJ) potentials such that the vapor-liquid critical point of the fluid is reproduced in agreement with experiment; in the case of quadrupolar molecules a quadrupole-quadrupole interaction is included. These models are shown to provide a satisfactory description of the liquid-vapor phase diagram of these pure fluids. Investigations of mixtures, using the Lorentz-Berthelot (LB) combining rule, also produce satisfactory results if compared with experiment, while in some previous attempts (in which polar solvents were modeled without explicitly taking into account quadrupolar interaction), strong violations of the LB rules were required. For this reason, the present investigation is a step towards predictive modeling of polar mixtures at low computational cost. In many cases Monte Carlo simulations of such models (employing the grand-canonical ensemble together with reweighting techniques, successive umbrella sampling, and finite size scaling) yield accurate results in very good agreement with experimental data. Simulation results are quantitatively compared to an analytical approximation for the equation of state of the same model, which is computationally much more efficient, and some systematic discrepancies are discussed. These very simple coarse-grained models of small molecules developed here should be useful, e.g., for simulations of polymer solutions with such molecules as solvent.

Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: the case of carbon dioxide.

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter q=Q(*4)T*, where Q* is the reduced quadrupole moment of the molecule and T* the reduced temperature. The model can be applied to a variety of small quadrupolar molecules. We focus on carbon dioxide as a test case, but consider nitrogen and benzene, too. Experimental critical temperature, density, and quadrupolar moment are sufficient to fix the parameters of the model. The resulting agreement with experiments is excellent and marks a significant improvement over approaches which neglect quadrupolar effects. The same coarse-grained model was also applied in the framework of perturbation theory in the mean spherical approximation. As expected, the latter deviates from the Monte Carlo results in the critical region, but is reasonably accurate at lower temperatures.

Computer simulation study of the global phase behavior of linear rigid Lennard-Jones chain molecules: comparison with flexible models.

The global phase behavior (i.e., vapor-liquid and fluid-solid equilibria) of rigid linear Lennard-Jones (LJ) chain molecules is studied. The phase diagrams for three-center and five-center rigid model molecules are obtained by computer simulation. The segment-segment bond lengths are L = sigma, so that models of tangent monomers are considered in this study. The vapor-liquid equilibrium conditions are obtained using the Gibbs ensemble Monte Carlo method and by performing isobaric-isothermal NPT calculations at zero pressure. The phase envelopes and critical conditions are compared with those of flexible LJ molecules of tangent segments. An increase in the critical temperature of linear rigid chains with respect to their flexible counterparts is observed. In the limit of infinitely long chains the critical temperature of linear rigid LJ chains of tangent segments seems to be higher than that of flexible LJ chains. The solid-fluid equilibrium is obtained by Gibbs-Duhem integration, and by performing NPT simulations at zero pressure. A stabilization of the solid phase, an increase in the triple-point temperature, and a widening of the transition region are observed for linear rigid chains when compared to flexible chains with the same number of segments. The triple-point temperature of linear rigid LJ chains increases dramatically with chain length. The results of this work suggest that the fluid-vapor transition could be metastable with respect to the fluid-solid transition for chains with more than six LJ monomer units.

Phase diagram of water from computer simulation.

The phase diagram of water as obtained from computer simulations is presented for the first time for two of the most popular models of water, TIP4P and SPC/E. This Letter shows that the prediction of the phase diagram is an extremely stringent test for any water potential function, and that it may be useful in developing improved potentials. The TIP4P model provides a qualitatively correct description of the phase diagram, unlike the SPC/E model which fails in this purpose. New behavior not yet observed experimentally is predicted by the simulations: the existence of metastable reentrant behavior in the melting curves of the low density ices (I,III,V) such that it could be possible to transform them into amorphous phases by adequate changes in pressure.

Tracing the phase diagram of the four-site water potential (TIP4P).

We present here the phase diagram for one of the most popular water models, the four-point transferable intermolecular potential (TIP4P) model. We show that TIP4P model, does indeed provide a qualitatively correct description of the phase diagram of water. The melting line of the five-point transferable intermolecular potential (TIP5P) at low pressures is also presented.

Phase behavior of n-alkanes in supercritical solution: a Monte Carlo study.

We present a coarse-grained model for n-alkanes in a supercritical solution, which is exemplified by a mixture of hexadecane and CO2. For pure hexadecane, the Monte Carlo simulations of the coarse-grained model reproduce the experimental phase diagram and the interfacial tension with good accuracy. For the mixture, the phase behavior sensitively depends on the compatibility of the polymer with the solvent. We present a global phase diagram with critical lines, which is in semiquantitative agreement with experiments. In this context we developed two computational schemes: The first adopts Wang-Landau sampling to the off-lattice grand canonical ensemble, the second combines umbrella sampling with an extrapolation scheme to determine the weight function. Additionally, we use Wertheim's theory (TPT1) to obtain the equation of state for our coarse-grained model of supercritical mixtures and discuss the behavior for longer alkanes.

Isotropic-nematic phase transition: Influence of intramolecular flexibility using a fused hard sphere model.

The role of flexibility on the liquid crystal isotropic-nematic phase transition has been studied by means of Monte Carlo simulation. We present equations of state for the isotropic-nematic branches and, in the isotropic phase, numerically calculated values for the virial coefficients B2, B3, and B4. We have studied two models: 11 hard sphere monomers fused in a linear configuration with a reduced bond length of 0.6 and a 15-monomer version of this model in which monomers at one end of the chain become flexible. We have observed spontaneous nematic liquid crystal formation for both of the fully rigid models, and also for models with up to six flexible monomers in the tail. We conclude that molecular flexibility has a strongly destabilizing effect on the nematic phase. This is probably due to the decrease in shape anisotropy that flexible tails allow.