E. S. Zaitseva

Surface tension of different sized single-component droplets, according to macroscopic data obtained using the lattice gas model and the critical droplet size during phase formation

Size dependences of the surface tension of spherical single-component droplets are calculated using equations of the lattice gas model for 19 compounds. Parameters of the model are found from experimental data on the surface tension of these compounds for a macroscopic planar surface. The chosen low-molecular compounds satisfy the law of corresponding states. To improve agreement with the experimental data, Lennard-Jones potential parameters are varied within 10% deviations. The surface tensions of different sized equilibrium droplets are calculated at elevated and lowered temperatures. It is found that the surface tension of droplets grows monotonically as the droplet size increases from zero to its bulk value. The droplet size R0 corresponding to zero surface tension corresponds to the critical size of the emergence of a new phase. The critical droplet sizes in the new phase of the considered compounds are estimated for the first time.

Times of metastable droplet relaxation to equilibrium states

Times of metastable droplet relaxation to their equilibrium state are calculated at saturated vapor pressures, depending on the droplet size. It is shown that for small droplets with radius R = 6 molecular diameters (or ~2 nm) the relaxation times are ~1 ns (which is comparable to the characteristic flight times of rarefied gas molecules). For large droplets with radius R ~ 800 molecular diameters, the relaxation times are as long as 10 μs. At a fixed droplet radius (6 ≤ R ≤ 800), the range of variation in relaxation time from the melting point to the critical temperature does not exceed one order of magnitude: the lower the temperature, the slower the relaxation process.

Calculating the surface tension of binary solutions of simple fluids of comparable size

A molecular theory based on the lattice gas model (LGM) is used to calculate the surface tension of one- and two-component planar vapor–liquid interfaces of simple fluids. Interaction between nearest neighbors is considered in the calculations. LGM is applied as a tool of interpolation: the parameters of the model are corrected using experimental surface tension data. It is found that the average accuracy of describing the surface tension of pure substances (Ar, N2, O2, CH4) and their mixtures (Ar–O2, Ar–N2, Ar–CH4, N2–CH4) does not exceed 2%.

Analysis of the linear tension of two-dimensional droplets on heterogeneous adsorbents

A procedure for analyzing the formation processes of two-dimensional droplets of an adsorbate on a rigid adsorbent support is considered. The molecular theory is based on data on the potential functions between adsorbent atoms and adsorbate molecules. Interactions between nearest neighbors are considered in the quasi-chemical approximation. The internal motions of adsorbent atoms and adsorbate molecules are ignored. Problems of describing the formation of droplets on heterogeneous adsorbents are associated with calculations for binodals (illustrated with the simplest example of two different homogeneous crystal faces) due to the choice of methods for calculating linear tension and the structural model of the region of the liquid–vapor transition. The dependence of the characteristics of droplets in the layered structural model on the method for determining the reference lines of the tension is shown for their metastable and equilibrium states. It is found that for a number of structural parameters, the thermodynamic determination of the line of tensions of metastable droplets can result in nonmonotonic dependences of the linear tension on their radii. The characteristics of two-dimensional liquid–vapor interfaces are compared for two structural models: coordination sphere and layered. It is found that the coordination sphere model allows the exclusion of the structural parameter of the layered model, but both models need refinement at small radii.

Fundamentals of numerical analysis of linear tension of two-dimensional drops

Fundamentals of numerical analysis of linear tension of two-dimensional drops of molecules adsorbed on uniform crystal faces have been developed. A lattice-gas model has been applied for description of adsorption. Molecular distributions have been computed in a quasi-chemical approximation, allowing for the effects of direct correlations of interacting particles. Differences in the algorithms of calculation of linear tension on a two-dimensional vapor–liquid interface connected with the effect of the transition region structure, taking into account metastability of coexisting small phases, and a variation in methods of determining line tension at a curved interface according to the material balance condition (equimolecular line) or mechanical equilibrium condition. This has allowed us to compute the equilibrium molecular distribution in small two-dimensional drops and the linear tension value at the interface as a function of the drop size and temperature.

Simulating the Surface Relief of Nanoaerosols Obtained via the Rapid Cooling of Droplets

An approach is formulated that theoretically describes the structure of a rough surface of small aerosol particles obtained from a liquid droplet upon its rapid cooling. The problem consists of two stages. In the first stage, a concentration profile of the droplet–vapor transition region is calculated. In the second stage, local fractions of vacant sites and their pairs are found on the basis of this profile, and the rough structure of a frozen droplet surface transitioning to the solid state is calculated. Model parameters are the temperature of the initial droplet and those of the lateral interaction between droplet atoms. Information on vacant sites inside the region of transition allows us to identify adsorption centers and estimate the monolayer capacity, compared to that of the total space of the region of transition. The approach is oriented toward calculating adsorption isotherms on real surfaces.

Polylayer Adsorption on Rough Surfaces of Nanoaerosols Obtained via the Rapid Cooling of Droplets

An approach is developed for studying polymolecular adsorption on the modeled rough surface of a small aerosol obtained from a liquid droplet on its rapid cooling. A way of estimating the specific surface of adsorbent droplets with rough surfaces is proposed, and the temperature and size dependences of the specific surface are established. Isotherms of N2 and Ar polymolecular adsorption on a heterogeneous surface of small spherical particles of SiO2 are derived. The possibility of using this approach to describe an experiment is demonstrated. Comparison to the experimental isotherms reveals agreement with isotherms of argon and nitrogen on silica surfaces, with an error of up to 4.5%.

Calculation of the Surface Tension of Droplets of Binary Solutions of Simple Fluids and the Determination of Their Minimum Size

To describe the surface tension of vapor–liquid interfaces of one- and two-component simple fluids, a molecular theory based on the lattice gas model is applied. The surface tension of mixtures of simple fluids are calculated in a quasi-chemical approximation of an accounting of the intermolecular interactions of the nearest neighbors. The model parameters previously found from experimental data on bulk surface tensions enable calculation of the surface tension of vapor–liquid interfaces of one- and two-component droplets with different sizes as the function of their radius. The minimum size of thermodynamically stable small droplets with the properties of a homogeneous phase inside is estimated.

Molecular basis for calculating the surface tension of binary droplets

A procedure for calculating the surface tension of droplets consisting of two components in the vapor phase is considered. The calculations are performed using the lattice gas model in the quasi-chemical approximation with allowance for the correlation effects of the nearest interacting molecules. A layered model of the structure of a vapor–liquid interface is used. Ways of calculating the surface tension of droplets with different radii are considered. They are based on different thermodynamic definitions of reference surfaces. Typical dependences of the surface tension of metastable and equilibrium droplets on the droplets’ radii are analyzed for four types of phase diagram. It is found that if the energy of interaction between the components of one type exceeds by 150% the energies of interaction between components of another type and between particles of different types, and if the component with the highest energy of interaction predominates in a droplet, this results in a nonmonotonic profile of the component with the lowest energy of interaction in the region of transition. Mixture components are distributed in the region of transition such that the component with the highest energy of interaction is concentrated on the liquid side and the other component is concentrated on the vapor side. The surface tension of equilibrium droplets is less than that of metastable droplets.

The effect of system volume limitation on the surface tension of a vapor–liquid interface

The effect of the system volume limitation on the thermodynamic characteristics of a vapor–liquid interface, that is, the phase states of a substance and the surface tension, is considered. The molecular theory is used based on the lattice gas model, which describes the two-phase state of a vapor–liquid system. To simplify the calculations, the molecular characteristics of the spherical interface of a drop inside a spherical region of vapor having a single dimensional parameter, namely, the radius of the system, are assessed. It is found that, when the radius of the system decreases, the critical temperature decreases, while the internal pressure, the chemical potential, and the surface tension increase.