Simulation of phase equilibria and interfacial properties of binary mixtures on the liquid-vapour interface using lattice sums

Molecular dynamics simulations of Lennard-Jones binary mixtures were performed to obtain phase equilibria and thermodynamic properties for the liquid—vapour interface. The dispersion interactions were handled using the lattice sum method where the full interaction is obtained and there is no requirement for any long range correction to the properties. The application of the method using the Lorentz—Berthelot combining rule for unlike interactions is discussed. The coexisting densities, adsorption of molecules at the interface and surface tension are the main results of this work. Coexisting properties were compared with Gibbs ensemble Monte Carlo results and with those of the grand canonical Monte Carlo method combined with the histogram reweighting technique, and good agreement was found. The lattice sum method results were compared with those of the spherically truncated and shifted potential to analyse the truncation effect. The adsorption of molecules at the interface and surface tension increase with interaction.     

Monte Carlo simulations of neon and argon using ab initio potentials

Gibbs ensemble Monte Carlo simulations of neon and argon have been performed with pair potentials taken from literature as well as with new ab initio potentials from just above the triple point to close to the critical point. The densities of the coexisting phases, their pair correlation functions, the vapour pressure and the enthalpy and entropy of vaporization have been calculated. The influence of the potential choice and of the addition of the Axilrod-Teller (AT) three-body potential on the above mentioned properties have been investigated. It turns out that an accurate ab initio two-body potential in connection with the AT potential yields very good results for thermodynamic properties of phase equilibria.     

Comprehensive study of the vapour–liquid coexistence of the truncated and shifted Lennard–Jones fluid including planar and spherical interface properties

Vapour–liquid equilibria of the Lennard–Jones potential, truncated and shifted at 2.5σ, are studied using molecular dynamics simulations, an attractive option for studying inhomogeneous systems. Comprehensive simulation data are reported for three cases: no interface, a planar interface, and a spherical interface between the coexisting phases, covering a wide range of temperatures. Spherical droplets are also studied for a range of radii between 5 and 16σ. The size dependence of the surface tension, based on the Irving–Kirkwood pressure tensor, and other properties is quantified for spherical interfaces. All simulation results are correlated with a consistent set of empirical equations. A comparison with the results of other authors as well as with experimental data for noble gases and methane is also presented.     

Liquid–vapour equilibrium of n -alkanes using interface simulations

Molecular Dynamics simulations were performed to calculate liquid–vapour coexisting properties of n-alkane chains up to 16 carbon atoms using interface simulations. The lattice sum or Ewald method on the dispersion forces of the Lennard–Jones potential was applied to calculate the full interaction. The liquid and vapour coexisting densities were obtained for two flexible force field models, NERD and TraPPE-UA, where the intermolecular interactions are of the Lennard–Jones type. We have recently shown [P. Orea, J. López-Lemus, and J. Alejandre, J. Chem. Phys. 123, 114702 (2005)] that the liquid–vapour densities for simple fluids do not depend on interfacial area and therefore it is possible to use a small number of molecules in a simulation. We show that the same trend is found on the simulation of these hydrocarbon molecules. The phase diagram of ethane/n-decane binary mixtures is also obtained at 410.95 K for the NERD model. The simulation results from this work were compared with those obtained using methods with interfaces using large cut-off distances and with methods without interfaces for the same potential model. In both comparisons, excellent agreement was found. The results of liquid density from the TraPPE-UA model are in good agreement with experimental data while those from the NERD model are underestimated at low temperatures. Our findings are consistent with results published by other authors for small hydrocarbons.     

A simple effective pair potential for the molecular simulation of the thermodynamic properties of ammonia

A new optimized effective pair potential model is proposed, which is appropriate for the prediction of thermodynamic properties of fluid ammonia including vapour—liquid coexistence data. The phase behaviour is determined using a recently developed version of the Gibbs ensemble Monte Carlo method. Furthermore, liquid structure characteristics, the dielectric constant and supercritical properties are determined by Monte Carlo simulations in the isothermal—isobaric ensemble. The second virial coefficient of the pair potential model is calculated over a broad range of temperature. All properties are compared with experimental data or results of a multi-parameter equation of state for ammonia. The new model is found to yield coexistence properties and second virial coefficients in good agreement with experimental data and the results of the equation of state, respectively.     

Vapour-liquid equilibria of the two- and three-dimensional monoatomic classical fluids interacting via double Yukawa potential

We have carried out Monte Carlo simulations in Gibbs ensemble for two-and three-dimensional double Yukawa fluid. We have compared liquid-vapour equilibrium curve with that of Lennard-Jones, when parameters occurring in double Yukawa potential are chosen to fit Lennard-Jones potential. The results are in good agreement. The role of repulsive and attractive contributions for the potential on the liquid-vapour coexistence region as well as on critical temperature and critical density has been studied. The critical temperature is found to be more sensitive than the critical density to the variation in repulsive and attractive parts of the potential. Also, the range of the attractive interaction directly influences range of the liquid vapour coexistence region. It has been found that smaller the values of the attractive parameter, larger is the coexistence region.     

The phase behaviour of a fluid in a slitlike pore with permeable walls

The confinement of a lattice fluid in a set of slitlike pores separated by semipermeable walls with a finite width has been studied. The walls are modelled by a square-well repulsive potential with a finite height. The thermodynamic properties and the phase behaviour of the system are evaluated by means of Monte Carlo simulations. For some states theoretical calculations have been made using a mean-field-type theory. These investigations confirm previous findings for confined Lennard-Jones fluids, obtained from a density functional approach. For intermediate and low potential barriers that separate the pores, the isotherms exhibit two hysteresis loops and the liquid-vapour coexistence curve divides into two branches describing condensation inside the pore and inside the permeable wall. These two branches are separated by a triple point. At temperatures lower than the triple point temperature, the condensation takes place instantaneously in both the pore and inside the permeable wall. It was found that when the temperature is scaled by the bulk critical temperature, the phase diagram emerging from this simple mean-field treatment is close to the phase diagram obtained from simulation.     

Solution of lattice gas models in the generalized ensemble on the Bethe lattice

We present the exact Bethe lattice solution for a lattice gas Potts model defined in the generalized ensemble which was previously studied in elucidating the anomalous thermodynamic properties of water. For this model the locus of density maxima (TMD), the locus of isothermal compressibility extrema, (TEC), the spinodal curve, and the percolation curve for four hydrogen bonded molecules are calculated using the Bethe lattice solution. The results confirm qualitative relationships between the TMD, the TEC, and the percolation curve obtained previously from a mean field calculation.     

Equation of state for the Lennard-Jones truncated and shifted fluid with a cut-off radius of 2.5 σ based on perturbation theory and its applications to interfacial thermodynamics

ABSTRACT

An equation of state is presented for describing thermodynamic properties of the Lennard-Jones truncated and shifted (LJTS) potential with a cut-off radius of 2.5 σ. It is developed using perturbation theory with a hard-sphere reference term and labelled with the acronym PeTS (perturbed truncated and shifted). The PeTS equation of state describes the properties of the bulk liquid and vapour and the corresponding equilibrium of the LJTS fluid well. Furthermore, it is developed so that it can be used safely in the entire metastable and unstable region, which is an advantage compared to existing LJTS equations of state. This makes the PeTS equation of state an interesting candidate for studies of interfacial properties. The PeTS equation of state is applied here in two theories of interfaces, namely density gradient theory (DGT) and density functional theory (DFT). The influence parameter of DGT as well as the interaction averaging diameter of DFT are fitted to data of the surface tension of the LJTS fluid obtained from molecular simulation. The results from both theories agree very well with those from the molecular simulations.     

Structural and Thermodynamic Peculiarities of Core-Shell Particles at Fluid Interfaces from Triangular Lattice Models

A triangular lattice model for pattern formation by core-shell particles at fluid interfaces is introduced and studied for the particle to core diameter ratio equal to 3. Repulsion for overlapping shells and attraction at larger distances due to capillary forces are assumed. Ground states and thermodynamic properties are determined analytically and by Monte Carlo simulations for soft outer- and stiffer inner shells, with different decay rates of the interparticle repulsion. We find that thermodynamic properties are qualitatively the same for slow and for fast decay of the repulsive potential, but the ordered phases are stable for temperature ranges, depending strongly on the shape of the repulsive potential. More importantly, there are two types of patterns formed for fixed chemical potential—one for a slow and another one for a fast decay of the repulsion at small distances. In the first case, two different patterns—for example clusters or stripes—occur with the same probability for some range of the chemical potential. For a fixed concentration, an interface is formed between two ordered phases with the closest concentration, and the surface tension takes the same value for all stable interfaces. In the case of degeneracy, a stable interface cannot be formed for one out of four combinations of the coexisting phases, because of a larger surface tension. Our results show that by tuning the architecture of a thick polymeric shell, many different patterns can be obtained for a sufficiently low temperature.     

Monte Carlo simulations of nitrogen using an ab initio potential

A new ab initio pair potential for nitrogen has been calculated at CCSD(T) level with aug-cc-pVDZ and -pVTZ correlation consistent basis sets. The results were extrapolated to approximate the basis set limit. This potential was used within Gibbs ensemble Monte Carlo (GEMC) simulations to obtain the densities of the coexisting phases, the vapour pressure and the enthalpy of vaporization from 70 K to close to the critical point. The influence of several 3-body interactions (an approximate anisotropic triple dipole potential derived by Stogryn, the isotropic triple dipole potential by Axilrod and Teller (AT), and a 3-body induction potential on the above mentioned properties was investigated. Satisfactory agreement with experimental data was observed. To determine whether the remaining deviations between experimental and computed data are due to inaccuracies in the 2-body or 3-body potential, the 2-body potential was rescaled to reproduce experimental 2nd virial coefficients accurately, and some of the calculations were repeated with the new potential. It turns out that an accurate 2-body potential only in connection with the AT potential yields accurate results for the thermodynamic properties phase equilibria.     

Temperature and density extrapolations in canonical ensemble monte carlo simulations

We show how to use the multiple histogram method to combine canonical ensemble Monte Carlo simulations made at different temperatures and densities. The method can be applied to study systems of particles with arbitrary interaction potential and to compute the thermodynamic properties over a range of temperatures and densities. The calculation of the Helmholtz free energy relative to some thermodynamic reference state enables us to study phase coexistence properties. We test the method on the Lennard-Jones fluids for which many results are available.     

Equilibrium thermodynamics and thermodynamic processes in nonlinear systems

A general method for the calculation of thermodynamic quasi-equilibrium processes by molecular dynamics (MD) simulation in canonical ensemble is developed. The method is suitable for classical systems with arbitrary interaction potentials. Though this MD method does not allow to calculate directly partition function and entropy, it is possible to calculate necessary partial derivatives which enter into the expressions for the full derivatives dT/dV and d β/dV for adiabitic and isobaric processes. Namely the solutions of these ordinary differential equations define the corresponding thermodynamic processes. The adiabatic process for the 1D Toda lattice is analyzed in details. The usage of the Toda potential allows to perform all analytical calculus up to accurate answers and to compare numerical and analytical results. Exact analytical expressions for the thermodynamics of 1D lattices with few types of nearest neighbor interactions are obtained as a necessary interim solutions. MD-simulation of quasi equilibrium processes in canonical ensemble demands the achievement of thermodynamic equilibrium, thus the thermalization kinetics is briefly discussed.     

Atomistic simulations of liquid water using Lekner electrostatics

Equilibrium molecular dynamics simulations have been performed for liquid water using three different potential models in the NVT and NPT ensembles. The flexible SPC model, the rigid TIP4P model and the rigid/polarizable TIP4P-FQ potential were studied. The Lekner method was used to handle long range electrostatic interactions, and an efficient trivariate cubic spline interpolation method was devised for this purpose. A partitioning of the electrostatic interactions into medium and long range parts was performed, and the concomitant use of multiple timestep techniques led to substantially enhanced computation speeds. The simulations were carried out using 256 molecules in the NVT ensemble at 25°C and 997 kg m^?3 and in the NPT ensemble at 25°C and 1 bar. Various dynamic, structural, dielectric, rotational and thermodynamic properties were calculated, and it was found that the simulation methodologies performed satisfactorily vis-à-vis previous simulation results and experimental observations.     

Effects of long-range interactions on the dynamics of ions in aqueous solution

Molecular dynamics simulations have been carried out for a Br⁻ ion in aqueous solution in order to establish the effect of truncation of long-range interactions on the dynamical properties of the ion. Simulations using smooth truncation of the potential at different cutoff radii were carried out and compared to results using the Ewald summation method. It is shown that when small cutoffs are applied (i.e. R_c = 8Å), the calculations yield low ionic diffusion coefficients relative to experiment, as well as short-time dynamical behavior which is inconsistent with the Ewald calculations. As the cutoff is increased, the results approach both the Ewald and the experimental results. In contrast to the results with the truncated potential, the short-time dynamical behavior of the hydrated bromide ion obtained with the Ewald method can be described by simple Langevin dynamics.     

Modelling of mass-transfer induced instabilities at liquid–liquid interfaces based on molecular simulations

Interfaces and especially mass transfer across interfaces are of great importance in many fields of chemical engineering. Interfacial convection, which is generally called the Marangoni effect, may improve mass transfer across interfaces quite drastically and has not been investigated adequately in detail. In order to investigate the influence of mass transfer on a liquid–liquid interface molecular computer simulations have been performed. Since many molecules have to be considered for a significant modelling of the interface, cubic lattice systems have been chosen for the simulation which proceeds according to the Monte-Carlo scheme. The parameters that describe the thermodynamic and transport properties resemble those of realistic standard EFCE test systems for extraction. Results of various Monte-Carlo simulations show that under certain conditions mass transfer across interfaces induces the formation of nano droplets in the close vicinity of the interface. The different combinations of the nano droplet behaviour due to attractive or repulsive long-range forces together with the characteristics of coalescence may lead to different macroscopic interfacial instabilities such as spontaneous emulsification or eruptions. Based on diffusive and thermodynamic properties of the chosen lattice system a first stability criterion which allows the prediction of the onset of nano droplet formation is developed. The theoretical results compare well with experimental observations at a single drop and in a two-phase cell where the instabilities are investigated optically via Schlieren optics.     

Microcanonical equilibrium properties of chiral liquid crystals—a Monte Carlo study

Chiral liquid crystals have been investigated by means of a multicanonical Monte Carlo approach in order to characterize their phase behaviour by microcanonical equilibrium properties. The liquid crystals were described by three-dimensional lattice systems with intermolecular interactions given by the chiral Lebwohl-Lasher potential. Self-determined boundary conditions have been applied in order to enable the formation of chiral phases with equilibrium pitch. Selected thermodynamic properties, e.g. microcanonical entropy, temperature, heat capacity and a set of order parameters have been determined with dependence on microcanonical total energy. A cholesteric phase with temperature-induced helix inversion could be proven where the helical superstructure of the single component system studied changed its handedness through an infinite-pitch system. The thermodynamical behaviour in the microcanonical ensemble was found to be very similar to the behaviour in the canonical ensemble. The study of microcanonical equilibrium properties by means of multicanonical Monte Carlo simulations was shown to be a powerful tool for the study of the phase behaviour of model liquid crystals.     

Effect of Chemical Potential Shift on Thermodynamical Properties of the Mixed Valence Compounds

Starting from the SU(N_d) Anderson lattice model in the slave boson formalism, we study the effect of the chemical potential shift on the thermodynamic properties of the mixed valence lattice system by using the Green's function technique. In the mean field approximation, the self-consistent equations of the mean field parameters and the chemical potential are obtained. The average number off electrons, the magnetic susceptibility and the specific heat are calculated. The numerical studies show that the shift of the chemical potential has a strong effect on the thermodynamic properties.     

Heat capacity of ZnO with cubic structure at high temperatures

The heat capacities at constant pressure and constant volume, and thermal expansivity are calculated for ZnO with rocksalt-type and zinc-blende-type cubic structures over a wide range of temperatures using molecular dynamics simulations with interactions due to effective pair-wise potentials which consist of the Coulomb, dispersion, and repulsion interaction. It is shown that the calculated structural and thermodynamic parameters including lattice constant, thermal-expansion coefficient, isothermal bulk modulus and its pressure derivative at ambient condition are in good agreement with the available experimental data and the latest theoretical results. At extended pressure and temperature ranges, lattice constant and heat capacity have also been predicted. The structural and thermodynamic properties of ZnO with cubic structure are summarized in the 300-1500 K temperature ranges and up to 100 kbar pressure.