V. S. Kuznetsov

Electrostatic interactions in micellar solutions of sodium n-alkyl sulfates and applicability of the poisson-boltzmann equation for their calculation

By the example of four even members in a homologous series of sodium n-alkyl sulfates (decyl-, dodecyl-, tetradecyl-, and hexadecyl sulfate) and with the use of the Debye-Hueckel theory of strong electrolytes the parameters are calculated that determine electrostatic interactions in micellar solutions of surfactants. Calculation results for the Gibbs electrostatic energy of micellization are compared to those obtained from one of the approximate solutions of the Poisson-Boltzmann equation and also to the results of its numerical integration for spherical micelles. Applicability conditions of the Debye-Hueckel theory are determined with respect to the micelle concentration and size and the number of carbon atoms in a surfactant molecule. It is shown that the Debye-Hueckel theory in the proposed version enables an efficient and quite accurate calculation of all electrostatic properties of micelles and ionic micellar solutions for surfactants with a number of carbon atoms in a molecule starting from 10 and more and at concentrations up to 0.15 mol/dm3.

The gibbs energy, chemical potential, and state parameters of the surface of an ionic micelle in the form of an ellipsoid of revolution

A molecular-thermodynamic model of an ionic micelle in the form of an ellipsoid of revolution was suggested. Equations for the chemical potential of an ellipsoidal micelle, the work of transfer of ions from solution volume into the micelle, and the state parameters of the surface of the micelle (fraction of free hydrophobic surface, surface tension coefficient, and surface charge density) were obtained. The Gibbs energy, chemical potential, work of transfer, and state parameters of an ellipsoidal micelle were determined as depending on the form factor of the corresponding ellipsoid. The model was verified for the example of sodium decyl sulfate micelles. The calculated parameters were close to the thermochemical data on the asymmetrization of spherical micelles in a solution of sodium decyl sulfate. The equilibrium ion-micellar solution composition was estimated.

Surface tension anisotropy in the mechanics of ellipsoidal micelles

Expressions for the calculation of the surface tension at any point of ellipsoidal micelle surface in the directions of the main axes have been derived within the framework of the droplet model of molecular aggregates. It has been established that the anisotropy of the surface tension of an ellipsoid of revolution-shaped micelle depends on the ellipsoid shape factor and the polar angle. At low shape factors, the anisotropy is low in the vicinity of points with maximum and minimum curvatures and it reaches its maximum value at angles of ≈π/4. The maximum is shifted toward larger polar angles with an increase in the shape factor.

Structural, electrostatic and thermodynamic properties of the surface of spherical micelles in solutions of sodium n-alkyl sulfate homologues. I. Structural characteristics

Using the aggregation numbers of micelles and the effective sizes of hydrated surfactant ions and counterions of the first coordination sphere, we calculated the average geometric characteristics of the surface layer of ionic spherical micelles in solutions of the sodium n-alkyl sulfate homologues with nC = 8, 10, 12, and 14 carbon atoms in the molecule; in particular, we established 1) the size of the micelle core; 2) the thickness of the electrical double layer on the surface; 3) the mutual arrangement parameters of hydrophilic and hydrophobic ions; 4) the number of “free” water molecules and showed their dependence on the homologue number and the degree of binding of counterions.

Thermodynamic Study of Sodium Decyl Sulfate Solutions in the Region of Second Critical Micelle Concentration: 2. Thermodynamic Functions of Polymorphic Micellar Transition and Components of Its Gibbs Energy

Temperature dependences of the thermodynamic functions of polymorphic micellar transition in the region of second critical micelle concentration are calculated based on data on heat capacities of sodium decyl sulfate solutions obtained previously by scanning calorimetry. Equilibrium constants and fractions of surfactant molecules aggregated into spheroidal and cylindrical micelles are calculated. Using the models of the ellipsoid of revolution and cylinder, components of the equilibrium Gibbs energy of intermicellar transition are calculated.

Thermodynamic study of sodium decyl sulfate solutions in the region the second critical micellization concentration: 1. Volumetric and heat capacity properties

Densitometry and precision adiabatic scanning calorimetry are used to reveal a number of volumetric and heat capacity properties of sodium decyl sulfate in the region of the second critical micelle concentration. Heat capacities are established in a wide temperature range. The coefficients of thermal expansion, apparent and partial mole expandabilities, volume, heat capacities, and excess partial mole heat capacities are calculated. The analysis of variations in these thermodynamic properties occurring upon variations in concentration and temperature makes it possible to identify the structural variations in sodium decyl sulfate micelles that are relevant to the transition of micelles from globular to cylindrical forms.

Packing conditions of ionic surfactant molecules in ellipsoidal micelles

Relations between the main parameters characterizing the structure of ellipsoidal micelles of ionic surfactants in aqueous solutions and the geometric sizes of micelles are derived and analyzed within the framework of the model of the two-axial ellipsoid of revolution. Conditions of the existence of “continuous” and hollow ellipsoidal micelles are discussed using the generalized Gibbs-Curie principle. Shape factors of spherical, ellipsoidal, and cylindrical micelles are compared. Results are verified using micelles of sodium decyl sulfate in aqueous solutions as examples.

Thermodynamics of the surfaces of nonionic spherical micelles with relatively large extensions of the interfacial layer

The structural properties of nonionic spherical micelles with relatively large extensions of the interfacial layer are investigated, and the size dependences of their adsorption, interfacial tension, and chemical potential are obtained. Such familiar thermodynamic relationships as the Gibbs and Laplace equations, the differential equation for the chemical potential, and the concept of hydrophilic–lipophilic balance are used. The method is applied to micelles formed in surfactant solutions of a homologous series of tetraethylene glycol alkyl ethers. The region of the existence of micellar solutions and the structural characteristics of the interfacial layer of micelles are determined. The interfacial tension minimum corresponding to ideal hydrophilic–lipophilic balance in the micelle interfacial layer is detected. The chemical potential is negative over the range of the homologous series, and its derivative with respect to the tension radius is also negative.

Structural, electrostatic, and thermodynamic properties of the surface of spherical micelles in solutions of sodium n-alkyl sulfate homologues. II. Electrostatic and thermodynamic characteristics

The structural characteristics of micelles from our previous work (Part I) are used to calculate the electrostatic energy of ions in the electric double layer on the surface of spherical ionic micelles in solutions of sodium n-alkyl sulfate homologues with the following number of carbon atoms in the molecule: nC = 8, 10, 12, and 14. This energy is found to depend on the thickness of the electric double layer and its average radius on the surface of a micelle, the aggregation number, the degree of binding of counterions, and the dielectric constant. The developed semi-empirical method is used to calculate interfacial tensions in spherical micelles for the said homologues in solutions at their critical micellar concentrations and T = 303 K. These values are split into the contributions from the hydrophobic and electrostatic components. The electrostatic component of the interfacial tension in spherical micelles is compared with the expression for the ion–ion repulsion energy to obtain the values of static permittivity (dielectric constant) in the surface layer of micelles.

Dielectric permittivity in a dense layer of the hydration shell of an ion in a strong-electrolyte solution

Based on the experimental data on the dielectric dispersion and the static dielectric permittivity of solutions of strong electrolytes, the effective value of the latter in the dense layer of the hydration shell of an ion has been calculated. The calculations have been carried out in terms of the three-layer model of the hydration complex. The calculations have shown that for the solutions of strong electrolytes the value of the static dielectric permittivity (dielectric constant) in the dense layer of the hydration shell of an ion proves to be close to 2 and is almost independent of the concentration and temperature.