Effect of shape on liquid-vapor coexistence and surface properties of parallelepiped molecules.

Liquid-vapor coexistence is calculated via molecular dynamics for a variety of parallelepiped shaped molecules. Models are constructed as an array of tangential hard spheres interacting with an attractive square-well potential. Each shape is formed by varying the number of spheres in their three sides. The initial density of the system is chosen close to the critical density of a SW fluid to obtain an equilibrated liquid-vapor coexistence curve by the process of spinodal decomposition. A pattern that relates the geometry of the molecular models and the existence or non-existence of a liquid-vapor orthobaric curve is shown.

Study of the hard-disk system at high densities: the fluid-hexatic phase transition.

Integral equations of uniform fluids have been considered unable to predict any characteristic feature of the fluid-solid phase transition, including the shoulder that arises in the second peak of the fluid-phase radial distribution function, RDF, of hard-core systems obtained by computer simulations, at fluid densities very close to the structural two-step phase transition. This reasoning is based on the results of traditional integral approximations, like Percus-Yevick, PY, which does not show such a shoulder in hard-core systems, neither in two nor three dimensions. In this work, we present results of three Ansätze, based on the PY theory, that were proposed to remedy the lack of PY analytical solutions in two dimensions. This comparative study shows that one of those Ansätze does develop a shoulder in the second peak of the RDF at densities very close to the phase transition, qualitatively describing this feature. Since the shoulder grows into a peak at still higher densities, this integral equation approach predicts the appearance of an orientational order characteristic of the hexatic phase in a continuous fluid-hexatic phase transition.

Room temperature ionic liquids: A simple model. Effect of chain length and size of intermolecular potential on critical temperature.

A model of a room temperature ionic liquid can be represented as an ion attached to an aliphatic chain mixed with a counter ion. The simple model used in this work is based on a short rigid tangent square well chain with an ion, represented by a hard sphere interacting with a Yukawa potential at the head of the chain, mixed with a counter ion represented as well by a hard sphere interacting with a Yukawa potential of the opposite sign. The length of the chain and the depth of the intermolecular forces are investigated in order to understand which of these factors are responsible for the lowering of the critical temperature. It is the large difference between the ionic and the dispersion potentials which explains this lowering of the critical temperature. Calculation of liquid-vapor equilibrium orthobaric curves is used to estimate the critical points of the model. Vapor pressures are used to obtain an estimate of the triple point of the different models in order to calculate the span of temperatures where they remain a liquid. Surface tensions and interfacial thicknesses are also reported.

Fluid-solid coexistence from two-phase simulations: binary colloidal mixtures and square well systems.

Molecular dynamics simulations are performed to clarify the reasons for the disagreement found in a previous publication [G. A. Chapela, F. del Río, and J. Alejandre, J. Chem. Phys. 138(5), 054507 (2013)] regarding the metastability of liquid-vapor coexistence on equimolar charged binary mixtures of fluids interacting with a soft Yukawa potential with κσ = 6. The fluid-solid separation obtained with the two-phase simulation method is found to be in agreement with previous works based on free energy calculations [A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006)] only when the CsCl structure of the solid is used. It is shown that when pressure is increased at constant temperature, the solids are amorphous having different structures, densities, and the diagonal components of the pressure tensor are not equal. A stable low density fluid-solid phase separation is not observed for temperatures above the liquid-vapor critical point. In addition, Monte Carlo and discontinuous molecular dynamics simulations are performed on the square well model of range 1.15σ. A stable fluid-solid transition is observed above the vapor-liquid critical temperature only when the solid has a face centered cubic crystalline structure.

Self-assembly of kagome lattices, entangled webs and linear fibers with vibrating patchy particles in two dimensions.

A vibrating version of patchy particles in two dimensions is introduced to study self-assembly of kagome lattices, disordered networks of looping structures, and linear arrays. Discontinuous molecular dynamics simulations in the canonical ensemble are used to characterize the molecular architectures and thermodynamic conditions that result in each of those morphologies, as well as the time evolution of lattice formation. Several versions of the new model are tested and analysed in terms of their ability to produce kagome lattices. Due to molecular flexibility, particles with just attractive sites adopt a polarized-like configuration and assemble into linear arrays. Particles with additional repulsive sites are able to form kagome lattices, but at low temperature connect as entangled webs. Abundance of hexagonal motifs, required for the kagome lattice, is promoted even for very small repulsive sites but hindered when the attractive range is large. Differences in behavior between the new flexible model and previous ones based on rigid bodies offer opportunities to test and develop theories about the relative stability, kinetics of formation and mechanical response of the observed morphologies.

Phase diagram of a square-well model in two dimensions.

The phase behavior of a two-dimensional square-well model of width 1.5σ, with emphasis on the low-temperature and/or high-density region, is studied using Monte Carlo simulation in the canonical and isothermal-isobaric ensembles, and discontinuous molecular-dynamics simulation in the canonical ensemble. Several properties, such as equations of state, Binder cumulant, order parameters, and correlation functions, were computed. Numerical evidence for vapor, liquid, hexatic, and triangular solid is given, and, in addition, a non-compact solid with square-lattice symmetry is obtained. The global phase diagram is traced out in detail (or sketched approximately whenever only inaccurate information could be obtained). The solid region of the phase diagram is explained using a simple mean-field model.

Liquid-vapor equilibrium and surface properties of short rigid chains with one long range attractive potential.

Liquid-vapor coexistence and interfacial properties of short lineal rigid vibrating chains with three tangent monomers in two and three dimensions are calculated. The effect of the range and position of a long ranged square well attractive potential is studied. Orthobaric densities, vapor pressures, surface tensions, and interfacial widths are reported. Two types of molecules are studied. Chains of three tangent hard sphere monomers and chains of three and five tangent hard sphere monomers interacting with a square well attractive potential with λ(∗) = λ∕σ = 1.5 in units of the hard core diameter σ. The results are reported in two and three dimensions. For both types of chains, a long ranged square well attractive potential is located at various positions in the chain to investigate its effect in the properties of the corresponding systems. Results for hard sphere chains are presented for a series of different sizes of λ(∗) between 2.5 and 5. For square well chains the position in the chain of the long ranged potential has no influence in the coexistence and interfacial properties. Critical temperatures increase monotonically with respect to λ(∗) and critical densities decrease systematically for both types of chains. When the long ranged potential is located in the middle monomer of the hard sphere chains no critical point is found for λ(∗) < 2.4. No critical point is found when the long ranged potential is located in one of the extremes of the hard sphere chains.

Effect of flexibility on liquid-vapor coexistence and surface properties of tangent linear vibrating square well chains in two and three dimensions.

The effect of flexibility on liquid-vapor and interfacial properties of tangent linear vibrating square well chains is studied. Surface tension, orthobaric densities, vapor pressures, and interfacial thicknesses are reported and analyzed using corresponding states principles. Discontinuous molecular dynamics simulations in two and three dimensions are performed on rigid tangent linear vibrating square well chains of different lengths. In the case of two dimensions, simulation results of completely flexible tangent linear vibrating square well chains are also reported. Properties are calculated for chains of 2-12 monomers. Rigidity is controlled by trapping the first and last monomer in the chain in a vibrating well at half of the distance of the whole chain. Critical property values are reported as obtained from orthobaric densities, surface tensions, and vapor pressures. For the fully flexible chains, the critical temperatures increase with chain length but the effect saturates. In contrast, the critical temperatures increase for the rigid chains until no more critical point is found.

Liquid-vapor equilibrium and interfacial properties of square wells in two dimensions.

Liquid-vapor coexistence and interfacial properties of square wells in two dimensions are calculated. Orthobaric densities, vapor pressures, surface tensions, and interfacial thicknesses are reported. Results are presented for a series of potential widths λ* = 1.4, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 5, where λ* is given in units of the hard core diameter σ. Critical and triple points are explored. No critical point was found for λ* < 1.4. Corresponding states principle analysis is performed for the whole series. For λ* = 1.4 and 1.5 evidence is presented that at an intermediate temperature between the critical and the triple point temperatures the liquid branch becomes an amorphous solid. This point is recognized in Armas-Pérez et al. [unpublished] as a hexatic phase transition. It is located at reduced temperatures T* = 0.47 and 0.35 for λ* = 1.4 and 1.5, respectively. Properties such as the surface tension, vapor pressure, and interfacial thickness do not present any discontinuity at these points. This amorphous solid branch does not follow the corresponding state principle, which is only applied to liquids and gases.

Liquid-vapor phase diagram and surface properties in oppositely charged colloids represented by a mixture of attractive and repulsive Yukawa potentials.

The liquid-vapor phase diagrams of equal size diameter σ binary mixtures of screened potentials have been reported for several ranges of interaction using Monte Carlo simulation methods [J. B. Caballero, A. M. Puertas, A. Fernandez-Barbero, F. J. de las Nieves, J. M. Romero-Enrique, and L. F. Rull, J. Chem. Phys. 124, 054909 (2006); A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006)]. Both works report controversial results about the stability of the phase diagram with the inverse Debye screening length κ. Caballero found stability for values of κσ up to 20 while Fortini reported stability for κσ up to 20 while Fortini reported stability for κσ ≤ 4. In this work a spinodal decomposition process where the liquid and vapor phases coexist through an interface in a slab geometry is used to obtain the phase equilibrium and surface properties using a discontinuous molecular dynamics simulations for mixtures of equal size particles carrying opposite charge and interacting with a mixture of attractive and repulsive Yukawa potentials at different values of κσ. An crude estimation of the triple point temperatures is also reported. The isothermal-isobaric method was also used to determine the phase stability using one phase simulations. We found that liquid-vapor coexistence is stable for values of κσ > 20 and that the critical temperatures have a maximum value at around κσ = 10, in agreement with Caballero et al. calculations. There also exists a controversy about the liquid-vapor envelope stability of the pure component attractive Yukawa model which is also discussed in the text. In addition, details about the equivalence between continuous and discontinuous molecular dynamics simulations are given, in the Appendix, for Yukawa and Lennard-Jones potentials.

A non-polarizable model of water that yields the dielectric constant and the density anomalies of the liquid: TIP4Q.

A four-site rigid water model is presented, whose parameters are fitted to reproduce the experimental static dielectric constant at 298 K, the maximum density of liquid water and the equation of state at low pressures. The model has a positive charge on each of the three atomic nuclei and a negative charge located at the bisector of the HOH bending angle. This charge distribution allows increasing the molecular dipole moment relative to four-site models with only three charges and improves the liquid dielectric constant at different temperatures. Several other properties of the liquid and of ice Ih resulting from numerical simulations with the model are in good agreement with experimental values over a wide range of temperatures and pressures. Moreover, the model yields the minimum density of supercooled water at 190 K and the minimum thermal compressibility at 310 K, close to the experimental values. A discussion is presented on the structural changes of liquid water in the supercooled region where the derivative of density with respect to temperature is a maximum.

Liquid-vapor interfacial properties of vibrating square well chains.

Liquid-vapor interfacial properties of square well chains are calculated. Surface tension, orthobaric densities, and vapor pressures are reported. Spinodal decomposition with a discontinuous molecular dynamics simulation program is used to obtain the results which are compared to previously published data for orthobaric densities and vapor pressures. In order to analyze the effect of the chain stiffness results for near tangent and overlapping linear chains as well as angled chains are obtained. Properties are calculated for linear chains of 2, 4, and 8 spheres for intramolecular distances of 0.97, 0.6, and 0.4 as well as for angled chains of 4 and 8 spheres and intramolecular distances of 0.4. The complete series of fully flexible near tangent square well chains is also studied (chains of 2, 4, 8, 12, and 16 particles with intramolecular distances of 0.97). The corresponding states principle applies to most of the systems considered. Critical properties values are reported as obtained from orthobaric densities, surface tensions, and vapor pressures. For the near tangent chains the critical temperatures increase with chain length but the rate of increment tends to zero for the longest chains considered. When the stiffness of the chain increases (intramolecular distance from 1 , 0.6, and 0.4) this saturation effect is either not present or reverses itself. The surface tension increases with the length of the chain while the width of the interface decreases.

Molecular association of heteronuclear vibrating square-well dumbbells in liquid-vapor phase equilibrium.

Molecular aggregates are formed by heteronuclear vibrating square-well dumbbells. In a recent article [G. A. Chapela and J. Alejandre, J. Chem. Phys., 132(10), 104704 (2010)], it is shown that heteronuclear vibrating square-well dumbbells with a diameter ratio between particles of 1/2 and interacting potential ratio of 4 form micelles of different sizes and shapes which manifest themselves in both the liquid and vapor phases, up to and above the critical point. This means that micellization and phase separation are present simultaneously in this simple model. These systems present a maximum in the critical temperature when plotted against the potential well depth of the second particle ε(2). In the same publication, it was speculated that the formation of micelles was responsible for the appearance of the maximum. A thorough study on this phenomena is presented here and it is found that there is a threshold on the size of the second particle and its corresponding depth of interaction potential, where the micelles are formed. If the diameter and well depth of the second particle are small enough for the first and deep enough for the second, micelles are formed. For σ(2)/σ(1) between 0.25 and 0.65 and ε(2)/ε(1) larger than 5.7, micelles are formed up to and above the critical temperature. Outside these ranges micelles appear only at temperatures lower than the critical point. There is a strong temperature dependence on the formation and persistence of the aggregates. For the deepest wells and large enough second particles, a gel interconnected aggregate is obtained. In this work, the micelles are formed at temperatures as low as the triple point and as high as the critical point and, in some cases, persist well above it. The presence of these maxima in critical temperatures T(c) when plotted against ε(2) as follows. At lower values of ε(2), an increase of T(c) is obtained as is expected by the increase of the attractive volume as indicated by the principle of corresponding states. As ε(2) increases further, the formation of molecular aggregates produce a saturation effect of the deepening of the potential well by encapsulating the particles of the second kind inside the micelles, so the resulting T(c) represents a new poly disperse system of molecular aggregates and not the original heteronuclear vibrating square-well dumbbells. The surface tension is also analyzed for these systems, and it is shown that decreases with increasing attraction due to the formation of molecular aggregates.

Discrete perturbation theory applied to Lennard-Jones and Yukawa potentials.

Discrete perturbation theory (DPT) is a powerful tool to study systems interacting with potentials that are continuous but can be approximated by a piecewise continuous function composed of horizontal segments. The main goal of this work is to analyze the effect of several variables to improve the representation of continuous potentials in order to take advantage of DPT. The main DPT parameters chosen for the purpose are the starting location and size of the horizontal segments used to divide the full range of the potential and its maximum reach. We also studied the effect of having each segment aligned to the left, to the right, or centered on the continuous function. The properties selected to asses the success of this strategy are the orthobaric densities and their corresponding critical points. Critical parameters and orthobaric densities were evaluated by DPT for each of an ample set of variables and compared with their values calculated via discontinuous molecular dynamics. The best sets of DPT parameters are chosen so as to give equations of state that represent accurately the Lennard-Jones and Yukawa fluids.

Surface tension and orthobaric densities for vibrating square well dumbbells. I.

Surface tensions and liquid-vapor orthobaric densities are calculated for a wide variety of vibrating square well dumbbells using discontinuous molecular dynamics simulations. The size of the vibration well, the elongation or bond distance of the two particles of the dumbbell, the asymmetry in size (and interaction range) of the two particles, and the depth of the interaction well are the variables whose effects are systematically evaluated in this work. Extensive molecular dynamics simulations were carried out and the orthobaric liquid-vapor densities are compared with those obtained previously by other authors using different methods of simulation for rigid and vibrating square well dumbbells. Surface tension values are reported for the first time for homonuclear and heteronuclear vibrating square well dumbbells as well as for all the simulated series. The molecular dynamics results of tangent homonuclear dumbbells are compared with those from Monte Carlo simulations also obtained in this work, as a way of checking the order of magnitude of the molecular dynamics results. The size of the vibration well is shown to have a small influence on the resulting properties. Decreasing elongation and the size of the second particle increase critical temperatures, liquid densities, and surface tensions. Moderate increases in the depth of the interaction well have the same effect. For larger asymmetries of the depth of the interaction well on the dumbbell particles, a strong association phenomenon is observed and the main effects are a maximum on the critical temperature for increasing well depth and a decrease in the surface tension.

The surface tension of TIP4P/2005 water model using the Ewald sums for the dispersion interactions.

The liquid-vapor phase equilibria and surface tension of the TIP4P/2005 water model is obtained by using the Ewald summation method to determine the long range Lennard-Jones and electrostatic interactions. The method is implemented in a straightforward manner into standard simulation programs. The computational cost of using Ewald sums in dispersion interactions of water is estimated in direct simulation of interfaces. The results of this work at 300 K show a dramatic change in surface tension with an oscillatory behavior for surface areas smaller than 5x5sigma(2), where sigma is the Lennard-Jones oxygen diameter. The amplitude of such oscillations substantially decreases with temperature. Finite size effects are less important on coexisting densities. Phase equilibria and interfacial properties can be determined using a small number of water molecules; their fluctuations are around the same size of simulation error at all temperatures, even in systems where the interfaces are separated a few molecular diameters only. The difference in surface tension of this work compared to the results of other authors is not significant (on the contrary, there is a good agreement). What should be stressed is the different and more consistent approach to obtain the surface tension using the Ewald sums for dispersion interactions. There are two relevant aspects at the interface: An adsorption of water molecules is observed at small surface areas and its thickness systematically increases with system size.

The short range anion-H interaction is the driving force for crystal formation of ions in water.

The crystal formation of NaCl in water is studied by extensive molecular dynamics simulations. Ionic solutions at room temperature and various concentrations are studied using the SPC/E and TIP4P/2005 water models and seven force fields of NaCl. Most force fields of pure NaCl fail to reproduce the experimental density of the crystal, and in solution some favor dissociation at saturated conditions, while others favor crystal formation at low concentration. A new force field of NaCl is proposed, which reproduces the experimental phase diagram in the solid, liquid, and vapor regions. This force field overestimates the solubility of NaCl in water at saturation conditions when used with standard Lorentz-Berthelot combining rules for the ion-water pair potentials. It is shown that precipitation of ions is driven by the short range interaction between Cl-H pairs, a term which is generally missing in the simulation of ionic solutions. The effects of intramolecular flexibility of water on the solubility of NaCl ions are analyzed and is found to be small compared to rigid models. A flexible water model, extending the rigid SPC/E, is proposed, which incorporates Lennard-Jones interactions centered on the hydrogen atoms. This force field gives liquid-vapor coexisting densities and surface tensions in better agreement with experimental data than the rigid SPC/E model. The Cl-H, Na-O, and Cl-O pair distribution functions of the rigid and flexible models agree well with experiment. The predicted concentration dependence of the electric conductivity is in fair agreement with available experimental data.

The Wolf method applied to the liquid-vapor interface of water.

The Wolf method for the calculation of electrostatic interactions is applied in a liquid phase and at the liquid-vapor interface of water and its results are compared with those from the Ewald sums method. Molecular dynamics simulations are performed to calculate the radial distribution functions at room temperature. The interface simulations are used to obtain the coexisting densities and surface tension along the coexistence curve. The water model is a flexible version of the extended simple point charge model. The Wolf method gives good structural results, fair coexistence densities, and poor surface tensions as compared with those obtained using the Ewald sums method.

Effect of flexibility on surface tension and coexisting densities of water.

Molecular dynamics simulations of pure water at the liquid-vapor interface are performed using direct simulation of interfaces in a liquid slab geometry. The effect of intramolecular flexibility on coexisting densities and surface tension is analyzed. The dipole moment profile across the liquid-vapor interface shows different values for the liquid and vapor phases. The flexible model is a polarizable model. This effect is minor for liquid densities and is large for surface tension. The liquid densities increase from 2% at 300 K to 9% at 550 K when the force field is changed from a fully rigid simple point charge extended (SPCE) model to that of a fully flexible model with the same intermolecular interaction parameters. The increases in surface tension at both temperatures are around 11% and 36%, respectively. The calculated properties of the flexible models are closer to the experimental data than those of the rigid SPCE. The effect of the maximum number of reciprocal vectors (h(z) (max)) and the surface area on the calculated properties at 300 K is also analyzed. The coexiting densities are not sensitive to those variables. The surface tension fluctuates with h(z) (max) with an amplitude larger than 10 mN m(-1). The effect of using small interfacial areas is slightly larger than the error in the simulations.