Molecular dynamics simulation of the equilibrium liquid–vapor interphase with solidification

The equilibrium structure of the finite, interphase interfacial region that exists between a liquid film and a bulk vapor is resolved by molecular dynamics simulation. Argon systems are considered for a temperature range that extends below the melting point. Physically consistent procedures are developed to define the boundaries between the interphase and the liquid and vapor phases. The procedures involve counting of neighboring molecules and comparing the results with boundary criteria that permit the boundaries to be precisely established. Two-dimensional radial distribution functions at the liquid and vapor boundaries and within the interphase region demonstrate the physical consistency of the boundary criteria and the state of transition within the region. The method developed for interphase boundary definitions can be extended to nonequilibrium systems. Spatial profiles of macroscopic properties across the interphase region are presented. A number of interfacial thermodynamic properties and profile curve-fit parameters are tabulated, including evaporation/condensation coefficients determined from molecular flux statistics. The evaporation/condensation coefficients away from the melting point compare more favorably with transition state theory than those of previous simulations. Near the melting point, transition theory approximations are less valid and the present results differ from the theory. The effects of film substrate wetting on evaporation/condensation coefficients are also presented.     

Kinetic evaporation and condensation rates and their coefficients

The origins and properties of evaporation and condensation coefficients are described, and results of their measurement are surveyed for water and liquid metals. Contrasts are drawn as to whether their values are likely to limit practical transfer rates at plane surfaces and on aerosols, and between evaporation and condensation. Existing theories which express condensation and evaporation rates in terms of the coefficients are described. Their failure to satisfy energy and momentum conservation as well as mass conservation at the interface is remedied by constructing a new theory which also starts with vapor molecules in Maxwell-Boltzmann distributions. The resulting rates are shown to be close to those predicted by more accurate theories in which the Boltzmann transport equation is solved.     

Competing evaporation and condensation processes during the boiling of methane

The atomistic mechanism of the boiling of methane is explored from molecular dynamics simulations. The liquid --> vapor transition is initiated by local density fluctuations resulting in a nanometer-sized domain that exhibits both liquid and vapor characteristics. Though the rates of evaporation and condensation events increase dramatically in this area, the overall balance exhibits only a marginal net rate of evaporation. Growth of the precritical domain leads to the nucleation of a vapor phase in which isolated methane molecules are confined by a liquid-vapor interface. After crossing the transition state, the system experiences progressive destabilization of the liquid phase and the evaporation processes clearly outnumber the condensation events.     

Monte Carlo simulations of Lennard-Jones nonionic surfactant adsorption at the liquid/vapor interface

We present Monte Carlo simulations of nonionic surfactant adsorption at the liquid/vapor interface of a monatomic solvent. All molecules in the system, solvent and surfactant, are characterized by the Lennard-Jones (LJ) potential using differing interaction parameters. Surfactant molecules consist of an amphiphilic chain with a solvophilic head and a solvophobic tail. Adjacent atoms along the surfactant chain are connected by finitely extensible harmonic springs. Solvent molecules move via the Metropolis random-walk algorithm, whereas surfactant molecules move according to the continuum configurational bias Monte Carlo (CBMC) method. We generate quantitative thermodynamic adsorption and surface tension isotherms in addition to surfactant radius of gyration, tilt angles, and potentials of mean force. Surface tension simulations compared to those calculated from the simulated adsorbed amounts and the Gibbs adsorption isotherm agree confirming equilibrium in our simulations. We find that the classical Langmuir isotherm is obeyed for our LJ surfactants over the range of head and tail lengths studied. Although simulated surfactant chains in the bulk solution exhibit random orientations, surfactant chains at the interface orient roughly perpendicular and the tails elongate compared to bulk chains even in the submonolayer adsorption regime. At a critical surfactant concentration, designated as the critical aggregation concentration (CAC), we find aggregates in the solution away from the interface. At higher concentrations, simulated surface tensions remain practically constant. Using the simulated potential of mean force in the submonolayer regime and an estimate of the surfactant footprint at the CAC, we predict a priori the Langmuir adsorption constant, KL, and the maximum monolayer adsorption, Gammam. Adsorption is driven not by proclivity of the surfactant for the interface, but by the dislike of the surfactant tails for the solvent, that is by a "solvophobic" effect. Accordingly, we establish that a coarse-grained LJ surfactant system mimics well the expected equilibrium behavior of aqueous nonionic surfactants adsorbing at the air/water interface.     

Capillary rise of a meniscus with phase change

The Lucas-Washburn equation, describing the motion of a liquid body in a capillary tube, is extended to account for the effect of phase change - evaporation or condensation. The system is found to always possess a stable equilibrium state when the temperature jump across the interface is confined to a certain range. We show that phase change affects the equilibrium height of the meniscus, the transition threshold from monotonic to oscillatory dynamics, and the frequency of oscillations, when present. At higher mass transfer rates and/or large capillary radii, vapor recoil is found to be the dominant factor. Evaporation lowers the equilibrium height, increases the oscillation frequency and lowers the transition threshold to oscillations. For condensation, two regimes are identified: at high mass transfer rates similar trends to those of evaporation are observed, whereas the opposite is found for low mass transfer rates, resulting in an increased equilibrium height, lower oscillation frequencies and a shift of the transition threshold toward monotonic dynamics.     

Molecular dynamics study on evaporation and condensation of n-dodecane at liquid-vapor phase equilibria

Molecular dynamics simulations are performed to study the evaporation and condensation of n-dodecane (C(12)H(26)) at temperatures in the range 400-600 K. A modified optimized potential for liquid simulation model is applied to take into account the Lennard-Jones, bond bending and torsion potentials with the bond length constrained. The equilibrium liquid-vapor n-dodecane interface thickness is predicted to be ~1.2-2.0 nm. It is shown that the molecular chains lie preferentially parallel to the interface in the liquid-vapor transition region. The predicted evaporation/condensation coefficient decreased from 0.9 to 0.3 when temperature increased from 400 to 600 K. These values can be used for the formulation of boundary conditions in the kinetic modeling of droplet heating and evaporation processes; they are noticeably different from those predicted by the transition state theory. We also present the typical molecular behaviors in the evaporation and condensation processes. The molecular exchange in condensation, typical for simple molecules, has never been observed for n-dodecane molecular chains.     

Some consequences of high temperature water vapor spectroscopy: water dimer at equilibrium

It is shown that the evolution of water vapor spectra in the 2500-5000 cm(-1) range recorded at 650 K and pressures up to 130 atms after subtraction of monomer contribution may be interpreted qualitatively well on the basis of experimental data on water dimer and trimer obtained from cold molecular beams and in He droplets. The proposed spectroscopic model considers water vapor as a mixture of nonideal monomers, dimers, and trimers at chemical equilibrium. The effect of line mixing is taken into account in the monomer spectrum modeling. Decomposition of the high temperature spectra allowed determining a dimer equilibrium constant that was compared with the previously known values. The contribution of water trimer is assessed. The performed analysis indicates that the number of bound dimers in water vapor is quite large, even at such a high temperature.     

Multicomponent dynamical nucleation theory and sensitivity analysis

Vapor to liquid multicomponent nucleation is a dynamical process governed by a delicate interplay between condensation and evaporation. Since the population of the vapor phase is dominated by monomers at reasonable supersaturations, the formation of clusters is governed by monomer association and dissociation reactions. Although there is no intrinsic barrier in the interaction potential along the minimum energy path for the association process, the formation of a cluster is impeded by a free energy barrier. Dynamical nucleation theory provides a framework in which equilibrium evaporation rate constants can be calculated and the corresponding condensation rate constants determined from detailed balance. The nucleation rate can then be obtained by solving the kinetic equations. The rate constants governing the multistep kinetics of multicomponent nucleation including sensitivity analysis and the potential influence of contaminants will be presented and discussed.     

Monte Carlo simulation of mixed lennard-jones nonionic surfactant adsorption at the liquid/vapor interface

New Monte Carlo simulations are presented for nonionic surfactant adsorption at the liquid/vapor interface of a monatomic solvent specifically investigating the roles of tail attraction and binary mixtures of different tail lengths. Surfactant molecules consist of an amphiphilic chain with a solvophilic head and a solvophobic tail. All molecules in the system, solvent and surfactant, are characterized by the Lennard-Jones (LJ) potential. Adjacent atoms along the surfactant chain are connected by finitely extensible harmonic springs. Solvent molecules move via the Metropolis random-walk algorithm, whereas surfactant molecules move according to the continuum configurational bias Monte Carlo (CBMC) method. We generate thermodynamic adsorption and surface-tension isotherms and compare results quantitatively to single-surfactant adsorption (Langmuir, 2007, 23, 1835). Surfactant tail groups with attractive interaction lead to cooperative adsorption at high surface coverage and higher maximum adsorption at the interface than those without. Moreover, adsorption and surface-tension isotherms with and without tail attraction are identical at low concentrations, deviating only near maximum coverage. Simulated binary mixtures of surfactants with differing lengths give intermediate behavior between that of the corresponding single-surfactant adsorption and surface-tension isotherms both with and without tail attraction. We successfully predict simulated mixture results with the thermodynamically consistent ideal adsorbed solution (IAS) theory for binary mixtures of unequal-sized surfactants using only the simulations from the single surfactants. Ultimately, we establish that a coarse-grained LJ surfactant system is useful for understanding actual surfactant systems when tail attraction is important and for unequal-sized mixtures of amphiphiles.     

Experimental studies of the vapor phase nucleation of refractory compounds. VI. The condensation of sodium

In this paper we discuss the condensation of sodium vapor and the formation of a sodium aerosol as it occurs in a gas evaporation condensation chamber. A one-dimensional model describing the vapor transport to the vapor/aerosol interface was employed to determine the onset supersaturation, in which we assume the observed location of the interface is coincident with a nucleation rate maximum. We then present and discuss the resulting nucleation onset supersaturation data within the context of nucleation theory based on the liquid droplet model. Nucleation results appear to be consistent with a cesium vapor-to-liquid nucleation study performed in a thermal diffusion cloud chamber.     

Condensation of a vapor bubble in submicrometer container

Condensation of a spherically symmetric submicrometer size vapor bubble is studied using diffuse interface hydrodynamic model supplemented by the van der Waals equation of state with parameters characteristic for argon. The bubble, surrounded by liquid, is held in a container of constant volume with temperature of the wall kept fixed. The condensation is triggered by a sudden rise of the wall temperature. We find that in the same container and subjected to a similar increase of the wall temperature the condensation process is totally different from the opposite process of droplet evaporation. In particular, the rapid change of the wall temperature excites the wave, which hits the interface and compresses the bubble, leading to a considerable increase of the temperature inside. The condensation of the submicrometer size bubble takes tens of nanoseconds, whereas evaporation of the same size droplet lasts roughly 50 times longer. In contrast to evaporation the condensation process is hardly quasistationary.     

Complete thermodynamically consistent kinetic model of particle nucleation and growth: numerical study of the applicability of the classical theory of homogeneous nucleation

A complete thermodynamically consistent elementary reaction kinetic model of particle nucleation and growth from supersaturated vapor was developed and numerically evaluated to determine the conditions for the steady-state regime. The model treats all processes recognized in the aerosol science (such as nucleation, condensation, evaporation, agglomerationcoagulation, etc.) as reversible elementary reactions. It includes all possible forward reactions (i.e., of monomers, dimers, trimers, etc.) together with the thermodynamically consistent reverse processes. The model is built based on the Kelvin approximation, and has two dimensionless parameters: S0-the initial supersaturation and Theta-the dimensionless surface tension. The time evolution of the size distribution function was obtained over the ranges of parameters S0 and Theta. At low initial supersaturations, S0, the steady state is established after a delay, and the steady-state distribution function corresponds to the predictions of the classical nucleation theory. At high initial supersaturations, the depletion of monomers due to condensation on large clusters starts before the establishing of the steady state. The steady state is never reached, and the classical nucleation theory is not applicable. The boundary that separates these two regimes in the two dimensionless parameter space, S0 and Theta, was determined. The model was applied to several experiments on water nucleation in an expansion chamber [J. Wolk and R. Strey, J. Phys. Chem. B 105, 11683 (2001)] and in Laval nozzle [Y. J. Kim et al., J. Phys. Chem. A 108, 4365 (2004)]. The conditions of the experiments performed using Laval nozzle (S0=40-120) were found to be close to the boundary of the non-steady-state regime. Additional calculations have shown that in the non-steady-state regime the nucleation rate is sensitive to the rate constants of the initial steps of the nucleation process, such as the monomer-monomer, monomer-dimer, etc., reactions. This conclusion is particularly important for nucleation from supersaturated water vapor, since these processes for water molecules at and below the atmospheric pressure are in the low pressure limit, and the rate constants can be several orders of magnitude lower than the gas kinetic. In addition, the impact of the thermodynamic inconsistency of the previously developed partially reversible kinetic numerical models was assessed. At typical experimental conditions for water nucleation, S0=10 and Theta=10 (T=250 K), the error in the particle nucleation rate introduced by the thermodynamic inconsistency exceeds one order of magnitude.     

Chemical reaction equilibrium in nanoporous materials: NO dimerization reaction in carbon slit nanopores

We present a molecular-level simulation study of the effects of confinement on chemical reaction equilibrium in nanoporous materials. We use the reaction ensemble Monte Carlo (RxMC) method to investigate the effects of temperature, nanopore size, bulk pressure, and capillary condensation on the nitric oxide dimerization reaction in a model carbon slit nanopore in equilibrium with a bulk reservoir. In addition to the RxMC simulations, we also utilize the molecular-dynamics method to determine self-diffusion coefficients for confined nonreactive mixtures of nitric oxide monomers and dimers at compositions obtained from the RxMC simulations. We analyze the effects of the temperature, nanopore width, bulk pressure, and capillary condensation on the reaction equilibrium with respect to the reaction conversion, fluid structure, and self-diffusion coefficients. We show that the influence of the temperature, nanopore size, and capillary condensation on the confined reaction equilibrium is quite dramatic while the effect of the bulk pressure on the reaction equilibrium in the carbon slit nanopore is only moderate. This work is an extension of previous work by Turner et al. [J. Chem. Phys. 114, 1851 (2001)] on the confined reactive nitric oxide system.     

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.     

Synthesis of Novel Symmetric Porphyrin Schiff Base Dimers by Solid–Liquid Reaction Methodology

A new convenient solid–liquid condensation reaction procedure for the synthesis of novel asymmetric and symmetric meso‐tetraarylporphyrin and metalloporphyrin Schiff bases is reported. The condensation reaction between β‐formyl porphyrin or metalloporphyrins and aromatic amines was carried out at solid–liquid interface by using neutral alumina powder as a solid support for β‐formyl porphyrin or metalloporphyrins and absolute ethanol as the carrier solvent for aromatic amines. Six different asymmetric porphyrin/metalloporphyrin Schiff bases were synthesized via solid–liquid interface reaction methodology. The same solid–liquid synthetic methodology was applied for the synthesis of six novel symmetric Schiff base porphyrin/metalloporphyrin dimers. The comparison of UV–visible spectra of porphyrin Schiff base monomers and dimers revealed that some degree of electronic perturbation has occurred upon dimerization as the Soret bands of the monomers underwent peak broadening along with red shifts. Column chromatography and crystallization were used to purify the compounds. Fourier transform infrared, UV–visible, elemental analysis, ¹H NMR, and mass spectrometry were used to characterize the newly synthesized compounds.     

Molecular dynamics simulation of potassium along the liquid-vapor coexistence curve

The applicability of pair potential functions to liquid alkali metals is questionable. On the one hand, some recent reports in the literature suggest the validity of two-parameter pair-wise additive Lennard-Jones (LJ) potentials for liquid alkali metals. On the other hand, there are some reports suggesting the inaccuracy of pair potential functions for liquid metals. In this work, we have performed extensive molecular dynamics simulations of vapor-liquid phase equilibria in potassium to check the validity of the proposed LJ potentials and to improve their accuracy by changing the LJ exponents and taking into account the temperaturedependencies of the potential parameters. We have calculated the orthobaric liquid and vapor densities of potassium using LJ (12–6), LJ (8.5–4) and LJ (5–4), effective pair potential energy functions. The results show that using an LJ (8.5–4) potential energy function with temperature-independent parameters, ε and σ, is inadequate to account for the vapor-liquid coexistence properties of potassium. Taking into account the temperature-dependencies of the LJ parameters, ε(T) and σ(T), we obtained the densities of coexisting liquid and vapor potassium in a much better agreement with experimental data. Changing the magnitude of repulsive and attractive contributions to the potential energy function shows that a two-parameter LJ (5–4) potential can well reproduce the densities of liquid and vapor potassium. The results show that LJ (5–4) potential with temperature-dependent parameters produces the densities of liquid and vapor potassium more accurately, compared to the results obtained using LJ (12–6) and LJ (8.5–4) potential energy functions.     

Interfacial transport of evaporating water confined in nanopores

A semianalytical, continuum analysis of evaporation of water confined in a cylindrical nanopore is presented, wherein the combined effect of electrostatic interaction and van der Waals forces is taken into account. The equations governing fluid flow and heat transfer between liquid and vapor phases are partially integrated analytically, to yield a set of ordinary differential equations, which are solved numerically to determine the flow characteristics and effect on the resulting shape and rate of evaporation from the liquid-vapor interface. The analysis identifies three important parameters that significantly affect the overall performance of the system, namely, the capillary radius, pore-wall temperature, and the degree of saturation of vapor phase. The extension of meniscus is found to be prominent for smaller nanoscale capillaries, in turn yielding a greater net rate of evaporation per unit pore area. The effects of temperature and ambient vapor pressure on net rate of evaporation are shown to be analogous. An increase in pore-wall temperature, which enhances saturation pressure, or a decrease in the ambient vapor pressure result in enhancing the net potential for evaporation and increasing the curvature of the interface.     

The special features of molecular transport in nanosized channels

The molecular theory of the transport of pure substances and mixtures of molecules of different shapes in narrow slit-like pores, in which the potential of surface forces creates a strongly anisotropic distribution of molecules across pores and thereby makes the hydrodynamics equation inapplicable, is considered. The new microhydrodynamic approach is based on the lattice gas model, which takes into account the intrinsic volume of molecules and intermolecular interactions in the quasi-chemical approximation. Self-consistent calculations of dissipative coefficients taking nonlocal fluid properties into account were performed on the basis of the transition state model including information about equilibrium adsorbate distribution. Changes in fluid concentrations from the gaseous to liquid state and a broad temperature range, including the critical region, are analyzed. This allows vapor, liquid, and vapor-liquid fluid flows to be considered in the presence of capillary condensation. An increase in the size of pores transforms the equations of the theory into hydrodynamic transfer equations for gas or liquid flows, while preserving the relation of transfer coefficients to intermolecular potentials. The use of microhydrodynamic approach equations in numerical calculations and the possibility of applying this approach are discussed.     

Behavior of evaporating droplets at nonsoluble and soluble surfaces: Modeling with molecular resolution

Liquid droplets in equilibrium with vapor are simulated at solidlike surfaces using the cooperative motion algorithm (CMA). These droplets behave like real droplets, i.e., the densities of the coexistent liquid and vapor phases obey empirical relations such as rho l - rho v proportional, variant (1 - T/Tc)(1/3). Droplet evaporation was studied under various interaction conditions, i.e., nonsoluble and soluble substrates. In the last case, substrate particles migrate toward the liquid-vapor interface to minimize the droplet surface energy. This leads to the formation of a microwell surrounded by a ringlike deposit on the substrate surface. It is shown that the ring formation in the first stages of evaporation results in pinning of the droplet contact area.