Sergey P. Protsenko

Metastable extension of the liquid-vapor phase equilibrium curve and surface tension

The method of molecular dynamics has been used to calculate the parameters of liquid-vapor phase equilibrium and the surface tension in a two-phase system of 4096 Lennard-Jones particles. Calculations have been made in a range from the triple point to near-critical temperature and also at temperatures below the triple point corresponding to the metastable equilibrium of a supercooled liquid and supersaturated vapor. To determine the surface tension, along with a mechanical approach a thermodynamic one has been used as well. The latter was based on calculation of the excess internal energy of an interfacial layer. It has been shown that in accuracy the thermodynamic approach is as good as the more sophisticated mechanical one. Low-temperature asymptotics of the phase-equilibrium curve and also of liquid and vapor spinodals have been considered in the Lennard-Jones and the van der Waals models. The behavior of the surface tension and the excess internal energy of an interfacial layer at T-->0 is discussed.

Effect of the cut-off radius of the intermolecular potential on phase equilibrium and surface tension in Lennard-Jones systems

Abstract We present the molecular dynamic simulation results for the liquid–vapour interface of the pure Lennard–Jones fluid. The thermodynamical properties, the surface tension, the effective thickness of interfacial layer and the mean-square amplitude of capillary waves are determined. Calculations have been performed at cut-off radii of the intermolecular potential r c 1 =2.6 σ and r c 2 =6.78 σ . It is shown that the cut-off radius of the interaction potential in the two-phase systems should be chosen to be larger than that in the one-phase systems for an adequate representation of properties.

Temperature dependence of the crystal-liquid interfacial free energy and the endpoint of the melting line

The crystal-liquid interfacial free energy γ has been calculated as a function of the crystal orientation in a molecular dynamics experiment in a system of Lennard-Jones (LJ) particles with a cutoff radius of the potential rc(*)=rc/σ=6.78 at a triple-point temperature Tt(*)=kBTt/ε=0.692 and temperatures above (in the region of the stable coexistence of liquid and solid phases) and below (metastable continuation of the coexistence curve of liquid and solid phases) the temperature Tt(*). At T(*)=Tt(*), for determining γ use was made of the method of cleaving potential. The temperature dependence of γ on the crystal-liquid coexistence curve has been determined by the Gibbs-Cahn thermodynamic integration method. In the region of stable phase coexistence (T(*)>Tt(*)) good agreement with the data of Davidchack and Laird [J. Chem. Phys. 118, 7651 (2003)] has been obtained with respect to the character of the temperature dependence of γ and the orientation anisotropy. In the region of metastable phase coexistence (T(*)<Tt(*)) at the approach to the endpoint of the melting line (TK(*)=0.529) (the existence of which was established first by Baidakov and Protsenko [Phys. Rev. Lett. 95, 015701 (2005)]) the interfacial free energy decreases, approaching at T(*)=TK(*) the orientation-averaged value γ0K(*)=γ0Kσ(2/ε)=0.365. The paper discusses the behavior of the excess interfacial energy, excess interfacial entropy and excess interfacial stress on the metastable extension of the melting line and close to T(*)=TK(*).

Metastable Lennard-Jones fluids. I. Shear viscosity.

Molecular dynamics methods have been employed to calculate the coefficient of shear viscosity η(s)* of a Lennard-Jones fluid. Calculations have been performed in the range of reduced temperatures 0.4 ≤ k(B)T/ε ≤ 2.0 and densities 0.01 ≤ ρσ(3) ≤ 1.2. Values of η(s)* have been obtained for 217 states, 99 of which refer to metastable liquid and gas regions. The results of calculating η(s)* for thermodynamically stable states are in satisfactory agreement with the data of earlier investigations. An equation has been obtained which describes the temperature and density dependence of the coefficient of shear viscosity in stable and metastable regions of the phase diagram up to the boundaries of spontaneous nucleation. The behavior of the coefficient of shear viscosity close to the spinodal of a superheated liquid and supersaturated vapor is discussed and the applicability of the Stokes-Einstein relation at high supercoolings of the liquid phase is examined.

Computer simulation of nucleation in a gas-saturated liquid

Molecular dynamics methods have been used to investigate the kinetics of the liquid-gas phase transition in a two-component Lennard-Jones system at negative pressures and elastic stretches of the liquid to values close to spinodal ones. The molecular dynamics system consists of 2048 interacting particles with parameters of the Lennard-Jones potential for argon and neon. Density dependences of pressure and internal energy have been calculated for stable and metastable states of the mixture at a temperature T* approximately 0.7+/-0.01 and three values of the concentration. The location of mechanical and the diffusion spinodals has been determined. It has been established that a gas-saturated mixture retains its stability against finite variations of state variables up to stretches close to the values near the diffusion spinodal. The statistic laws of the process of destruction of the metastable state have been investigated. The lifetimes of the metastable phase have been determined. It is shown that owing to the small height of the potential barrier that separates the microheterogeneous from the homogeneous state a system of finite size has a possibility to make the reverse transition from the microheterogeneous into the homogeneous state. The lifetimes of the system in the microheterogeneous state, as well as the expectation times of the occurrence of a critical nucleus, are described by Poissonian distributions.

Metastable Lennard-Jones fluids. III. Bulk viscosity

The method of equilibrium molecular-dynamics simulation in combination with the Green-Kubo formula has been used to calculate the bulk viscosity of a Lennard-Jones fluid. Calculations have been made at temperatures 0.4 ≤ k(B)T/ɛ ≤ 2.0 and densities 0.0075 ≤ ρσ(3) ≤ 1.2 at 116 stable and 106 metastable states of liquid and gas. The depth of penetration into the region of metastable states was limited by spontaneous nucleation. In the region of stable states the data obtained are compared with the results of previous investigations. It has been established that the system transition across the lines of liquid-gas and liquid-crystal phase equilibrium and penetration into the metastable regions of liquid and gas are connected with increasing bulk viscosity. The behavior of bulk viscosity close to the spinodal of a superheated liquid and supersaturated vapor is discussed.

Metastable Lennard-Jones fluids. II. Thermal conductivity

The method of equilibrium molecular dynamics with the use of the Green-Kubo formalism has been used to calculate the thermal conductivity λ in stable and metastable regions of a Lennard-Jones fluid. Calculations have been made in the range of reduced temperatures 0.4 ≤ T* = k(b)T/ε ≤ 2.0 and densities 0.01 ≤ ρ* = ρσ³ ≤ 1.2 on 15 isotherms for 234 states, 130 of which refer to metastable regions: superheated and supercooled liquids, supersaturated vapor. Equations have been built up which describe the dependence of the regular part of the thermal conductivity on temperature and density, and also on temperature and pressure. It has been found that in (p, T) variables in the region of a liquid-gas phase transition a family of lines of constant value of excess thermal conductivity Δλ = λ - λ0, where λ0 is the thermal conductivity of a dilute gas, has an envelope which coincides with the spinodal. Thus, at the approach to the spinodal of a superheated liquid and supersaturated vapor (∂Δλ/∂p)T → ∞, (∂Δλ/∂T)p → ∞.

Surface free energy of the crystal-liquid interface on the metastable extension of the melting curve

The surface free energy γ, excess surface energy e, and excess surface stress τ at the crystal-liquid interface of a Lennard-Jones system have been determined by molecular dynamics simulation. The calculations have been performed for temperatures both above and below the triple-point temperature for the region where each of the coexisting phases is metastable and is at a negative pressure. The asymptotic behavior of γ, e, and τ has been analyzed near the endpoint of the melting curve, which is a point of the contact of the metastable extension of the melting curve and the spinodal of the stretched liquid [V.G. Baidakov and S.P. Protsenko, Phys. Rev. Lett. 95, 015701 (2005)]. It has been found that γ, e, and τ at this point are finite and the excess surface entropy is zero.

Thermodynamic approach to calculating the surface tension of single-component liquids by computer simulations

A thermodynamic method for computing the surface tension at a flat liquid-vapor interface by the Monte Carlo or molecular dynamics methods over a wide temperature range was proposed. The approach is based on the Gibbs separating surface method; it does not require information on the mechanical state of the surface layer.

Evaluation of metastable region boundaries for liquid and solid states in MD simulations

An automatic method based on MD simulations was developed for detecting and tracing the boundaries of metastable states of superheated crystal and supercooled liquid. The main criterion of the detection of early nucleation of new phase is the self-diffusion coefficient temperature dependence. The scanning for nucleation events is performed at continuous temperature change. The set of independent nucleation events at a given pressure allows evaluation of temperature dependence of specific nucleation frequency. The collection of a large number of these calculations allows accurate approximation of pressure and temperature dependence of the specific nucleation frequency in both directions between phases. This dependence allows estimating the behavior of the free energy in the region between superheating and supercooling curves. In addition, dependence of nucleation frequency on pressure and temperature provides an opportunity to integrate the probability of nucleation under dynamic loading and subsequent release and thus to determine the likelihood of the crystallization and melting. The technique was applied to tin. MD simulation was carried out with the help of the EAM interatomic potential, well reproducing the properties of BCC phase.