F. M. Kuni

Role of surface forces in heterogeneous nucleation on wettable nuclei

Abstract The condition has been formulated and the role of the surface forces at a solid-liquid interface has been established for the barrierless heterogeneous formation of a droplet on a macroscopic wettable insoluble solid nucleus in supersaturated vapour. The threshold value of the vapour supersaturation starting from which heterogeneous nucleation occurs as a barrierless process and all thermodynamic characteristics of heterogeneous formation of a droplet which are necessary for kinetic description of phase transition below the threshold have been found as a function of parameters of the exponential and the power-law approximations to the work of wetting of the nucleus associated with the surface forces and size of condensation nuclei: the coordinates and the half-widths of the potential hump and the potential well in the curve of the work of heterogeneous formation of a droplet; the activation barrier which droplets have to overcome by fluctuations in the process of formation of the stable phase.

The microphysical effects in nonisothermal nucleation

The role of microphysical effects in the ability of a small new phase nucleus to emit molecules into the vapor is revealed on a thermodynamic basis. It is shown that dependence of the surface tension of a nucleus on its temperature and the dependence of the vaporisation heat on the nuclear surface curvature are insignificant in nonisothermal nucleation. The meaning of the quantities used in the one-dimensional theory of isothermal nucleation has been clarified from the point of the two-dimensional nonisothermal theory. Statistical and kinetic treatment of the microphysical effects in the emitting rate of a nucleus has been performed. An association of the microphysical effects with deviation of the kinetic equation of nonisothermal nucleation from the Fokker–Planck form has been examined.

Thermodynamic Characteristics of Micellization in the Droplet Model of Surfactant Spherical Molecular Aggregate

The dependence of the work of the molecular aggregate formation on the aggregation number and surfactant monomer concentration in solution that has the key role for the theory of micellization was studied on the basis of a simple realistic droplet model of spherical aggregate composed of surfactant molecules (the o/w micelle type). Analytical formulas were derived for the coordinates of maximum and minimum of aggregate formation work on the aggregation number axis arising with an increase in the concentration of micellar solution. Model calculations of the thermodynamic characteristics of the kinetics of micellization were performed for premicellar and micellar regions of aggregate sizes within a wide range of solution concentration including the critical micellization concentration.

Stages of steady diffusion growth of a gas bubble in strongly supersaturated gas-liquid solution

Gas bubble growth as a result of diffusion flux of dissolved gas molecules from the surrounding supersaturated solution to the bubble surface is studied. The condition of the flux steadiness is revealed. A limitation from below on the bubble radius is considered. Its fulfillment guarantees the smallness of fluctuation influence on bubble growth and irreversibility of this process. Under the conditions of steadiness of diffusion flux three stages of bubble growth are marked out. Taking into account Laplace forces in the bubble, intervals of bubble size change and time intervals of these stages are found. The trend of the third stage towards the self-similar regime of the bubble growth, when Laplace forces in the bubble are completely neglected, is described analytically.

Study of nonsteady diffusional growth of a droplet in a supersaturated vapor: Treatment of the moving boundary and material balance

A new mathematical treatment of the problem of droplet growth via diffusion of molecules from a supersaturated vapor is presented. The theory is based on a semiquantitative analysis with good physical arguments and is justified by its reasonable predictions. For example it recovers the time honored growth law in which, to a high degree of approximation, the droplet radius increases with the square root of time. Also, to a high degree of approximation, it preserves material balance such that, at any time, the number of molecules lost from the vapor equals the number in the droplet. Estimates of the remaining approximational error are provided. On another issue, we show that, in contrast, the conventional treatment of droplet growth does not maintain material balance. This issue could be especially important for the nucleation of another droplet in the vicinity of the growing droplet where the rate of nucleation depends exponentially on supersaturation. Suggestions for further improvement of rigor are discussed.

Thermodynamic and Kinetic Foundations of the Micellization Theory: 5. Hierarchy of Kinetic Times

The characteristic kinetic times of micellization in the solution of a nonionic surfactant: the times of establishment of quasi-equilibrium concentrations of molecular aggregates in micellar, subcritical, and overcritical regions, times of establishment of quasi-equilibrium concentrations of molecular aggregates in the near-critical region of their sizes, the average time between two successive acts of emission of surfactant monomers by a micelle, the average value of micelle lifetime, the time of establishment of quasi-stationary mode of matter exchange between the solution and molecular aggregate, as well as the times of fast and slow relaxation in a solution were analyzed. The hierarchy of these times disclosing complex multistage kinetic process of micelle formation and decomposition and the establishment of equilibrium in the micellar solution was revealed. It was shown that this hierarchy is provided by the small parameters of the kinetic theory. The inverse problem of micellization kinetics was discussed; this problem allows us to find the characteristics of the formation work for micellar aggregate from the experimental data on the relaxation time of micellar solution.

Thermodynamic and Kinetic Foundations of the Micellization Theory: 4. Kinetics of Establishment of Equilibrium in a Micellar Solution

A system of the kinetic equations of the material balance for the concentrations of surfactant monomers and micelles in a micellar nonionic surfactant solution was formulated. The equilibrium state of a materially isolated micellar solution was analyzed. The system of the kinetic equations of the material balance of a micellar solution was solved. The total time of the establishment of equilibrium in a micellar solution was determined. It was shown that this time increases or (typically) decreases with an increase in micelle concentration, depending on the degree of micellization.

On the theory of the mechanochemical sorption-striction phenomenon in nanoporous bodies with dispersion forces

The soption-striction phenomenon is a change in the dimensions of a porous body in the course of sorption due to the strain caused by the action of molecular forces. The formulation of the theory of the phenomenon includes the following problems: the statistical-mechanical calculation of the pressure tensor in the pore interior as a function of the pore shape and size; the analysis of the role of surface tension in the mechanical equilibrium condition at the pore wall and producing strain at various mechanisms (physical or chemical) of sorption; the calculation of the body strain within the theory of elasticity. The calculation of the pressure tensor was performed for spherical, cylindrical, and flat (slit-like) pores using asymptotic relations for ordinary dispersion forces (in the context of the nano-scaled pore size) and dispersion forces with electromagnetic retardation (for micropores of larger dimensions), with the pair potential exponents −6 and −7, respectively. The results obtained consider both an initial contraction of a porous body in a vacuum and an additional contraction, if any, or the body expansion on the initial stage of the gas sorption. The exact calculation of strain is given for a cylindrical and spherical pore. The role of surface tension is shown to be reduced, first, to the initial contractive strain of a porous body in a vacuum and, second, to the body dilatation in the course of the gas sorption. A small additional contraction of a porous body on the initial stage of sorption (that, as is shown, cannot be caused by surface tension) is explained by the peculiarities of the sorbate pressure tensor in a pore. The effect is more pronounced the smaller the pore size and the lower the temperature, and is typical for nanoporous bodies. A general consideration based on the Irving-Kirkwood pressure tensor qualitatively confirms the regularities established for any kind of molecular interaction.

Nanostructural Models of Micelles and Primicellar Aggregates

For the case of direct spherical micelles, two nanostructural models of molecular aggregates have been discussed: the classical drop model implying flexibility of hydrocarbon chains of molecules and their full immersion into the hydrocarbon core of an aggregate, and a quasi-drop model allowing partial outcropping of the chains in the strainless state from the core. For the sake of simplicity, a solution is assumed to contain only a single surfactant whose molecules possess only one, unbranched hydrocarbon radical. Within the frames of the models, the behavior of the chemical potential of surfactant molecules in a primicellar and micellar molecular aggregate has been analyzed, as well as the work of formation of the molecular aggregate as a function of the aggregation number and the solution concentration.

Thermal effects accompanying stationary binary condensation of vapors into overcritical droplet

A set of equations is derived to calculate the stationary temperature and concentration of a solution in a overcritical droplet with regard to the heat release accompanying the condensation of a binary mixture of vapors in a diffusion or free-molecular regime. In the approximation of an ideal solution, relations are found for the stationary temperature of droplet growing under the conditions of strong and weak thermal effects. For the general case and the cases of strong and weak thermal effects, the temperature and concentration of the droplet and the coefficient of the thermal deceleration of the droplet growth are calculated as functions of the density of a passive gas. The influence of the condensation heat values of the first and second components of the mixture on the stationary temperature and concentration of the solution in the growing droplet is investigated separately.