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.     

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.     

Evaporation of Lennard-Jones fluids

Evaporation and condensation at a liquid/vapor interface are ubiquitous interphase mass and energy transfer phenomena that are still not well understood. We have carried out large scale molecular dynamics simulations of Lennard-Jones (LJ) fluids composed of monomers, dimers, or trimers to investigate these processes with molecular detail. For LJ monomers in contact with a vacuum, the evaporation rate is found to be very high with significant evaporative cooling and an accompanying density gradient in the liquid domain near the liquid/vapor interface. Increasing the chain length to just dimers significantly reduces the evaporation rate. We confirm that mechanical equilibrium plays a key role in determining the evaporation rate and the density and temperature profiles across the liquid/vapor interface. The velocity distributions of evaporated molecules and the evaporation and condensation coefficients are measured and compared to the predictions of an existing model based on kinetic theory of gases. Our results indicate that for both monatomic and polyatomic molecules, the evaporation and condensation coefficients are equal when systems are not far from equilibrium and smaller than one, and decrease with increasing temperature. For the same reduced temperature T/T(c), where T(c) is the critical temperature, these two coefficients are higher for LJ dimers and trimers than for monomers, in contrast to the traditional viewpoint that they are close to unity for monatomic molecules and decrease for polyatomic molecules. Furthermore, data for the two coefficients collapse onto a master curve when plotted against a translational length ratio between the liquid and vapor phase.     

Electrical processes upon the evaporation and condensation of water and ice

A mathematical model of electrical processes that take place upon the evaporation of water and sublimation of ice, as well as the condensation growth of water and ice phases from vapor, is proposed. The transfer of the main charge carriers, such as (i) protons and hydroxide ions (in ice, water, and vapor and (ii) orientational defects (in ice and water) is taken into account. Upon the evaporation of water and the sublimation of ice, the first carriers are accumulated before the phase front and cause positive charges in the surface of the water and ice, while the second carriers are depleted (their concentration becomes lower than the thermodynamic value) and impart a negative charge to water and ice. The contribution of protons and hydroxide ions dominates at a low rate of evaporation. In the condensation of vapor and relevant growth of water and ice phases, the polarity of surface charge is opposite to that observed upon evaporation. The values of interfacial current and signs of phase charges upon sublimation, evaporation, and condensation that are predicted in the model comply with experimental data.     

Temperature and structural changes of water clusters in vacuum due to evaporation

This paper presents a study on evaporation of pure water clusters. Molecular dynamics simulations between 20 ns and 3 micros of clusters ranging from 125 to 4096 molecules in vacuum were performed. Three different models (SPC, TIP4P, and TIP5P) were used to simulate water, starting at temperatures of 250, 275, and 300 K. We monitored the temperature, the number of hydrogen bonds, the tetrahedral order, the evaporation, the radial distribution functions, and the diffusion coefficients. The three models behave very similarly as far as temperature and evaporation are concerned. Clusters starting at a higher temperature show a higher initial evaporation rate and therefore reach the point where evaporation stop (around 240 K) sooner. The radius of the clusters is decreased by 0.16-0.22 nm after 0.5 micros (larger clusters tend to decrease their radius slightly more), which corresponds to around one evaporated molecule per nm(2). The cluster temperature seems to converge towards 215 K independent of cluster size, when starting at 275 K. We observe only small structural changes, but the clusters modeled by TIP5P show a larger percentage of molecules with low diffusion coefficient as t-->infinity, than those using the two other water models. TIP4P seems to be more structured and more hydrogen bonds are formed than in the other models as the temperature falls. The cooling rates are in good agreement with experimental results, and evaporation rates agree well with a phenomenological expression based on experimental observations.     

The kinetics of condensation behind the shock front

The growth and evaporation of clusters is considered in the frame of a quasichemical model of condensation. The rate coefficients of growth and evaporation reactions are calculated using the molecular dynamics method. Condensation of supersaturated Fe vapor behind the shock front is studied. For an explanation of known experimental data the chemical mechanism of dimer formation is considered. Probabilities of dimerization are calculated using the molecular dynamics method. Calculated values of the characteristic time of condensation are in satisfactory agreement with experiment.     

Water diffusion through hydrogel membranes: A novel evaporation cell free of external mass-transfer resistance

A novel evaporative cell is used to measure steady-state gradient-driven diffusion rates of water through hydrogel membranes in the absence of external mass-transfer resistance. In this cell, the bottom surface of a hydrogel membrane is exposed to pure water vapor at known activity (a_w) less than unity, while a sealed liquid-water reservoir bathes the upper membrane surface. Induced by the chemical-potential gradient between the two surfaces, the water evaporation rate is monitored by the rate of weight loss of the water reservoir.Results at ambient temperature are compared with those from measured water flux through soft-contact-lens (SCL) materials and with other published experimental results. Concentration-dependent water diffusivities are obtained by interpreting measured water fluxes for 0.11 ≤ a_w ≤ 0.93 with extended Maxwell–Stefan (EMS) diffusion theory. Thermodynamic non-ideality is taken into account through Flory–Rehner polymer–solution theory. Shrinking/swelling is modeled by conservation of the total polymer mass assuming volume additivity. In spite of correction for thermodynamic non-ideality, EMS–water-diffusion coefficients increase with the water volume fraction, especially strongly for those hydrogel materials with low liquid-saturated water contents. The evaporation cell described here provides a simple robust method to establish water transport rates through soft-contact-lenses and other hydrogel membranes without the need to correct for external mass-transfer resistance.     

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.     

Flow-rate dependence of gel permeation chromatography

Analysis of polystyrene standards by gel permeation chromatography over a wide range of flow rates revealed two sources of error in volume measurement. These errors arise from solvent evaporation in the siphon chamber and from solvent continuing to flow into the siphon during discharge. Appropriate corrections are discussed, and a vapor feedback loop to eliminate the solvent evaporation error is described. The flow rate dependence of the GPC calibration curve, expressed in the corrected elution volumes, appears different from that reported in the literature. The corrected flow rate dependence of peak elution volumes is in agreement with the expectation of diffusion and exclusion theories.     

Evaporation of two solution droplets and a droplet located near a flat liquid surface

The mutual influence of two moderate-sized droplets of a dilute nonvolatile substance solution on the processes of their evaporation or condensation is theoretically analyzed under the assumption of a uniform concentration distribution inside the droplets. The conditions for the applicability of this approach are revealed. The evaporation or condensation of a droplet near a flat liquid surface is considered as a limiting case. The fluxes of water molecules to and from the surface of aqueous glycerol solution droplets occurring in air are numerically estimated depending on the droplet radii, distances between their surfaces, and air humidity. Analogous estimates are obtained for an aqueous glycerol solution droplet growing near a flat water surface.     

Gas adsorption in mesoporous micelle-templated silicas: MCM-41, MCM-48, and SBA-15

This paper reports a molecular simulation and experimental study on the adsorption and condensation of simple fluids in mesoporous micelle-templated silicas MCM-41, MCM-48, and SBA-15. MCM-41 is described as a regular cylindrical silica nanopore, while SBA-15 is assumed to be made up of cylindrical nanopores that are connected through lateral channels. The 3D-connected topology of MCM-48 is described using a gyroid periodic minimal surface. Argon adsorption at 77 K is calculated for the three materials using Grand Canonical Monte Carlo simulations. Qualitative comparison with experiments for nitrogen adsorption in mesoporous micelle-templated silicas is made. The adsorption isotherm for SBA-15 resembles that for MCM-41. In particular, capillary condensation and evaporation are not affected by the presence of the connecting lateral channels. In contrast, the argon adsorption isotherm for MCM-48 departs from that for MCM-41 having the same pore size. While condensation in MCM-41 is a one-step process, filling of MCM-48 involves two successive jumps in the adsorbed amounts which correspond to condensation in different domains of the porosity. The condensation pressure for MCM-48 is larger than that for MCM-41. We attribute this result to the morphology of the MCM-48 surface (made up of both concave and convex regions) that differs from that for MCM-41 (concave only). Our results suggest that the pore connectivity affects pore filling when the size of the connections is comparable to that of the nanopores.     

Layering, condensation, and evaporation of short chains in narrow slit pores

The phase behavior of short-chain fluids in slit pores is investigated by using a nonlocal-density-functional theory that takes into account the effects of segment size, chain connectivity, and van der Waals attractions explicitly. The layering and capillary condensation/evaporation transitions are examined at different chain length, temperature, pore width, and surface energy. It is found that longer chains are more likely to show hysteresis loops and multilayer adsorptions along with the capillary condensation and evaporation. Decreasing temperature favors the inclusion of layering transitions into the condensation/evaporation hysteresis loops. For large pores, the surface energy has relatively small effect on the pressures of the capillary condensation and evaporation but affects significantly on the layering pressures. It is also observed that all phase transitions within the pore take place at pressures lower than the corresponding bulk saturation pressure. The critical temperature of condensation/evaporation is always smaller than that of the bulk fluid. All coexistence curves for confined phase transitions are contained within the corresponding bulk vapor-liquid coexistence curve. As in the bulk phase, the longer the chain length, the higher are the critical temperatures of phase transitions in the pore.     

Sol‐to‐Gel Transition in Fast Evaporating Systems Observed by in Situ Time‐Resolved Infrared Spectroscopy

The in situ observation of a sol‐to‐gel transition in fast evaporating systems is a challenging task and the lack of a suitable experimental design, which includes the chemistry and the analytical method, has limited the observations. We synthesise an acidic sol, employing only tetraethylorthosilicate, SiCl₄ as catalyst and deuterated water; the absence of water added to the sol allows us to follow the absorption from the external environment and the evaporation of deuterated water. The time‐resolved data, obtained by attenuated total reflection infrared spectroscopy on an evaporating droplet, enables us to identify four different stages during evaporation. They are linked to specific hydrolysis and condensation rates that affect the uptake of water from external environment. The second stage is characterized by a decrease in hydroxyl content, a fast rise of condensation rate and an almost stationary absorption of water. This stage has been associated with the sol‐to‐gel transition.     

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.     

Multi-Monte Carlo method for coagulation and condensation/evaporation in dispersed systems

A new multi-Monte Carlo (MMC) method is promoted to consider general dynamic equation (GDE) for particle coagulation and condensation/evaporation. MMC method introduces the concept of a "weighted fictitious particle" and is based on time-driven Monte Carlo technique, constant number of fictitious particles technique, and constant volume technique. MMC method for independent coagulation, for independent condensation/evaporation, and for simultaneous coagulation and condensation/evaporation are validated by some special cases in which analytical solutions exist, in which numerical results agree with corresponding analytical solutions well. Furthermore, the computation cost of MMC method is low enough to be applied in engineering computation and general scientific quantitative analysis.     

Strong effect of minor impurities in a gas on the rate of evaporation of solid surfaces

Evaporation of surfaces of quartz, corundum, and germanium monoxide precipitates in a flow of nitrogen and air was studied by the method of molecular nuclei of condensation, which makes it possible to determine extremely low concentrations of molecules from 10² to 10⁸ per I cm³ of a gas. The appreciable effect of low concentrations of gas impurities on the rate of evaporation of solid surfaces was found and studied in the region of low evaporation rates. Equations describing the dissimilar effects of the retention of molecules of impurities on the surface on the rates of evaporation and reverse condensation were proposed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 808–813, April, 1996.     

A Mathematical Model of the Carbon Arc Reactor for Fullerene Synthesis

A mathematical model of the carbon arc process for the synthesis of fullerenes (C ₆₀ , C ₇₀ ) is developed. The two-dimensional model solves for the velocities, temperature, and total concentration of carbon species. The net emission coefficient method is used for the radiation term. The carbon species conservation equations consider the evaporation of carbon from the anode, cathode surface deposition, and carbon condensation. The thermodynamic and transport properties are calculated as a function of temperature and carbon mass fraction, using the method of Chapman–Enskog. Erosion rates used by the model are determined experimentally. Calculated fields of the velocities, temperatures, carbon mass fraction and current intensity are presented. Comparison is made of the behavior of the arc at 1 and 4 mm interelectrode gaps, and between operation in argon and in helium. The results of simulations provide a justification for the higher yields observed in helium compared to the argon case.     

Interface film resistivities for heat and mass transfers-integral relations verified by non-equilibrium molecular dynamics

Integral relations that predict interface film transfer coefficients for evaporation and condensation have recently been derived. According to these relations, all coefficients can be calculated for one-component systems, using the thermal resistivity and the enthalpy profile through the interface. The integral relations were tested in this work using nonequilibrium molecular dynamics simulations for argon-like particles and n-octane molecules. The simulations confirm the integral relations within the accuracy of the calculation for both systems. Evidence is presented for the existence of an excess thermal resistivity on the gas side of the surface, and the fact that this property is decisive for interface heat and mass transfer coefficients. The integral relations were used to predict the mass transfer coefficient for n- octane as a function of surface tension. The findings are important for modeling of one-component phase transitions.     

Temperature dependence of the evaporation coefficient of water in air and nitrogen under atmospheric pressure: study in water droplets

The evaporation coefficients of water in air and nitrogen were found as a function of temperature by studying the evaporation of a pure water droplet. The droplet was levitated in an electrodynamic trap placed in a climatic chamber maintaining atmospheric pressure. Droplet radius evolution and evaporation dynamics were studied with high precision by analyzing the angle-resolved light scattering Mie interference patterns. A model of quasi-stationary droplet evolution accounting for the kinetic effects near the droplet surface was applied. In particular, the effect of thermal effusion (a short-range analogue of thermal diffusion) was discussed and accounted for. The evaporation coefficient alpha in air and in nitrogen were found to be equal. The alpha was found to decrease from approximately 0.18 to approximately 0.13 for the temperature range from 273.1 to 293.1 K and follow the trend given by the Arrhenius formula. The agreement with condensation coefficient values obtained with an essentially different method by Li et al. [Li, Y.; Davidovits, P.; Shi, Q.; Jayne, J.; Kolb, C.; Worsnop, D. J. Phys. Chem. A. 2001, 105, 10627] was found to be excellent. The comparison of experimental conditions used in both methods revealed no dependence of the evaporation/condensation coefficient on the droplet charge nor the ambient gas pressure within the experimental parameters range. The average value of the thermal accommodation coefficient over the same temperature range was found to be 1 +/- 0.05.     

Capillary condensation as a morphological transition

The process of capillary condensation/evaporation in cylindrical pores is considered within the idea of symmetry breaking. Capillary condensation/evaporation is treated as a morphological transition between the wetting film configurations of different symmetry. We considered two models: (i) the classical Laplace theory of capillarity and (ii) the Derjaguin model which takes into account the surface forces expressed in terms of the disjoining pressure. Following the idea of Everett and Haynes, the problem of condensation/evaporation is considered as a transition from bumps/undulations to lenses. Using the method of phase portraits, we discuss the mathematical mechanisms of this transition hidden in the Laplace and Derjaguin equations. Analyzing the energetic barriers of the bump and lens formation, it is shown that the bump formation is a prerogative of capillary condensation: for the vapor-liquid transition in a pore, the bump plays the same role as the spherical nucleus in a bulk fluid. We show also that the Derjaguin model admits a variety of interfacial configurations responsible for film patterning at specific conditions.