Thermodynamic Characteristics of a Spherical Molecular Surfactant Aggregate in a Quasi-Droplet Model

The model of spherical molecular aggregate of nonionic surfactant is proposed. This model allows for the maximal (in accordance with packing rules) penetration of water molecules into an aggregate and is an alternative to the droplet model of molecular aggregate. Necessary conditions for the applicability of a model named quasi-droplet model are formulated. Based on this model, the dependence of the work of molecular aggregate formation on the aggregation number and surfactant monomer concentration in solution that plays the key role for the theory of micellization is studied. The equation is 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 are performed. The approximation of the work of molecular aggregate formation allowing for the analytical study is constructed.     

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.     

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.     

Statistical Approach to the Description of Homogeneous Nucleation in the Vapor-Gas Medium: Effects of the Heat of Phase Transition

The effect of the heat release of phase transition is included in the formalism of the statistical approach in order to allow for the depletion of a substance comprising the metastable phase in the kinetics of the homogeneous nucleation of supersaturated vapor. The diffusion regime of the exchange of molecules between the vapor and the growing droplets is considered on the assumption of instantaneous creation of the initial vapor supersaturation. The time-dependent boundary condition on the surface of a sphere with a fixed radius and a center coinciding with the center of a growing droplet is used in the problem of heat conductivity that allowed us to provide the heat balance of phase transition. The main characteristics of the nucleation stage are calculated for the representative vapor-gas systems. It is shown that the allowance for the effects of the heat release of phase transition resulted in a rather notable change in the kinetics of nucleation even at a sufficiently high concentration of the passive gas.     

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.     

Kinetic description of the relaxation of surfactant solutions containing spherical and cylindrical micelles

Monotonically decaying relaxation of a materially isolated nonionic surfactant solution containing spherical and cylindrical micelles at the arbitrary heights of the first and second potential barriers of aggregation work is kinetically substantiated. The realistic situation, where the height of second potential barrier is at least slightly higher (by the relative value) than that of the first barrier, is studied. Analytical expressions for two relaxation times of materially isolated surfactant solution are calculated. The shortest of these times corresponds to the relatively fast establishment of the mutual quasi-equilibrium of spherical and cylindrical micelles, beginning with relatively small cylindrical micelles. The longest of relaxation times corresponds to the relatively slow establishment of the total equilibrium of surfactant solution. It is shown that this time (the only significant for the establishment of the final equilibrium of materially isolated surfactant solution) is determined by the height of the first potential barrier of aggregation work and is by no means dependent on the height of the second potential barrier about which not much is known. Variations (with time) of the total concentrations of spherical and cylindrical micelles, surfactant monomer concentration, and the total amount of the substance in cylindrical micelles in the approach of solution to the final equilibrium state are described analytically. It is shown that theoretically admitted small relative deviations of the concentrations of spherical and cylindrical micelles from their values in the final equilibrium state are fully measurable in experiment. Calculated relaxation time of surfactant solution can also be measured experimentally together with the aforementioned values. It is elucidated that this time is approximately proportional to the overall solution concentration, if the second critical micellization concentration (CMC2) by the order of magnitude exceeds the first critical micellization concentration (CMC1), and is virtually independent of the overall solution concentration, if the CMC2 exceeds the CMC1 by two orders of magnitude. The characteristic time of the establishment of quasi-equilibrium distribution of cylindrical micelles throughout the region of their sizes is estimated, thus allowing us to establish the lower limit of the height of the first barrier of aggregation work.Translated from Kolloidnyi Zhurnal, Vol. 67, No. 1, 2005, pp. 47–56.Original Russian Text Copyright © 2005 by Kuni, Shchekin, Grinin, Rusanov.