A. P. Grinin

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.

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.

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.

Kinetics of fast relaxation of cylindrical micelles

On the basis of the kinetic description of stepwise aggregation upon the release and absorption of surfactant monomers by micelles, the complete spectrum of relaxation times is found for relatively fast establishment of a quasi-equilibrium distribution of cylindrical micelles. These times also include the time required for the establishment of the corresponding quasi-equilibrium concentration of surfactant monomers. The resultant times are compared to an earlier diffusion estimate for the characteristic time of the establishment of quasi-equilibrium state of cylindrical micelles in a solution with a surfactant concentration much higher than the second critical micellization concentration CMC2.

Theory of nonstationary diffusion growth of gas bubble in the supersaturated solution of gas in liquid

General theory of nonstationary diffusion growth of gas bubble in the supersaturated solution of gas in liquid is constructed using the ideas of similarity and self-similar solutions. The balance between the number of gas molecules in solution and in the bubble that displaces incompressible liquid solvent with an increase in bubble size is taken into account at the material isolation of the solution and the bubble. The dependences of the rate of growth of bubble radius on the solubility of gas and the supersaturation of solution are found. The nonstationary effect of a rapid increase in the rate of bubble growth with an increase in the product of gas solubility and solution supersaturation is elucidated. The upper limit of this product at which bubble growth can be considered as isothermal process is established. The theory is constructed at the arbitrary gas solubility.

Study of Relaxation in Micellar Solution by the Numerical Experiment

A numerical simulation of the relaxation process of surfactant micellar solution to a new equilibrium state is performed using model analytical representations for the main characteristics of micellar aggregates. Relaxation stages of molecular aggregate size distribution in the typical regions of aggregation number variations predicted by the analytical theory in two-flux approximation are revealed. Good agreement between the predicted values of the relaxation times of micellar solution and those obtained in numerical simulation is disclosed within the domain of applicability of two-flux approximation. Numerical algorithm proposed in this work makes it possible to study the relaxation process of micellar solution even in the case when two-flux approximation becomes inapplicable. The realization of numerical algorithm can be considered as a kind of experiment for studying the relaxation process of a model micellar solution.

Self-similar solution to the problem of vapor diffusion toward the droplet nucleated and growing in a vapor-gas medium

The problem of vapor diffusion toward a droplet nucleated and growing in the diffusion regime is exactly solved using the similarity theory. The surface motion of droplets is taken into account in the solution. The constructed nonstationary concentration field of vapor satisfies the diffusion equation, the boundary condition of equilibrium on the surface of growing droplet, and the initial homogeneous condition. According to the found solution, the radius of a droplet is proportional to the square root of the time of its growth. Far from the critical point, at a low ratio between the densities of excess vapor and a liquid droplet, the proportionality coefficient coincides with that resulting from an approximate solution. The balance between the numbers of molecules removed from vapor and those composing a growing droplet exactly corresponds to the obtained solution.