Dynamic surface tension of micellar solutions studied by the maximum bubble pressure method. 1. Experiment

The effect of the micelles on the dynamic surface tension of micellar surfactant solutions is studied experimentally by means of the maximum bubble pressure method. Different frequencies of bubbling ranging approximately between 1 and 30 s^–1 are applied. The time dependence of the surface tension is calculated using a dead time correction. Water solutions of two types of surfactants with different concentrations are investigated: sodium dodecyl sulfate and nonylphenol polyglycol ether. The surface tension relaxes more quickly in the presence of micelles. The characteristic times of relaxation of the surface tension seem to be in the millisecond range. The time constants observed experimentally are explained in terms of the theory of surfactant diffusion affected by micellization kinetics.     

Electrolyte screening effect on the photoprotolytic cycle of excited photoacid in ice

Time-resolved emission was used to measure the photoprotolytic cycle of an excited photoacid as a function of temperature, both in liquid water and in ice, in the presence of an inert salt. The inert salt affects the geminate recombination between the transferred proton with the conjugate base of the photoacid. We used the Debye-Hückel theory to express the screening of the Coulomb electrical potential by the inert salt. We find that in the liquid phase the measured screening effect is small and the Debye-Hückel expression slightly overestimates the experimental effect. In ice, the screening effect is rather large and the Debye-Hückel expression under estimates the measured effect. We explain the large screening in ice by the "salting-out" effect in ice that tends to concentrate the impurities to confined volumes to minimize the ice crystal energy.     

Ionic Strength Effect on the Stability of the V(V) + IDA Complex

In this research the interaction of dioxovanadium(V) with iminodiacetic acid has been considered at 25 °C and pH=1.00–2.50 in an ionic strength range of 0.1 to 1.0 mol⋅dm⁻³ of NaClO₄ by UV spectrophotometric and potentiometric techniques. Only one species, VO₂H₂L⁺, was assumed on the basis of two stoichiometric models. The extended Debye-Hückel theory predicts the first order effects in simple electrolyte solutions. Interactions between the reacting species and the ionic medium are taken into account in the specific ion interaction model. Parabolic, specific ion interaction, and extended Debye-Hückel models have been compared and it has been shown that the parabolic model with two coefficients is satisfactory for this complexation reaction. The results have also been compared with the literature values.     

Osmotic and Activity Coefficients of Trimethyloctylammonium Bromide and Decyltrimethylammonium Bromide in Aqueous Solutions as a Function of Temperature

Osmotic coefficients of aqueous solutions of trimethyloctylammonium bromide and decyltrimethylammonium bromide were measured by the isopiestic method at the following temperatures: 298.15, 293.15, 288.15 and 283.15 K. Activity coefficients of the solutes were calculated from the osmotic coefficients. The results were compared with the Debye-Hückel limiting law and analyzed according to their variation with the alkyl chain length of the cation and with the change in temperature.     

Use of the concentration dependences of hydration numbers for calculating the gibbs energies and activities of strong electrolytes

The expression for the Gibbs energy (G) of electrolytes derived in terms of the Debye-Hückel theory is modified so as to describe the experimentally observed dependence of the hydration numbers of electrolyte ions on their concentration by minimizing G. It is shown that the activity coefficients of electrolyte solutions determined from this expression are in good agreement with experimental data over a wide concentration range.     

A new equation for calculating the enthalpies of dilution of solutions of nonassociated electrolytes

An equation for determining the enthalpies of dilution of solutions of nonassociated electrolytes was derived on the basis of the results obtained by Kuznetsova. The enthalpies of dilution calculated by this equation are compared with those obtained using the known equation based on the Debye-Hückel theory.     

Micelle–monomer equilibria in solutions of ionic surfactants and in ionic–nonionic mixtures: A generalized phase separation model

On the basis of a detailed physicochemical model, a complete system of equations is formulated that describes the equilibrium between micelles and monomers in solutions of ionic surfactants and their mixtures with nonionic surfactants. The equations of the system express mass balances, chemical and mechanical equilibria. Each nonionic surfactant is characterized by a single thermodynamic parameter — its micellization constant. Each ionic surfactant is characterized by three parameters, including the Stern constant that quantifies the counterion binding. In the case of mixed micelles, each pair of surfactants is characterized with an interaction parameter, β, in terms of the regular solution theory. The comparison of the model with experimental data for surfactant binary mixtures shows that β is constant — independent of the micelle composition and electrolyte concentration. The solution of the system of equations gives the concentrations of all monomeric species, the micelle composition, ionization degree, surface potential and mean area per head group. Upon additional assumptions for the micelle shape, the mean aggregation number can be also estimated. The model gives quantitative theoretical interpretation of the dependence of the critical micellization concentration (CMC) of ionic surfactants on the ionic strength; of the CMC of mixed surfactant solutions, and of the electrolytic conductivity of micellar solutions. It turns out, that in the absence of added salt the conductivity is completely dominated by the contribution of the small ions: monomers and counterions. The theoretical predictions are in good agreement with experimental data.     

Re-evaluation of the Thermodynamic Activity Quantities in Pure Aqueous Solutions of Chlorate, Perchlorate, and Bromate Salts of Lithium, Sodium or Potassium Ions at 298.15 K

The Hückel equation used to correlate the experimental activities of dilute alkali metal chlorate, perchlorate or bromate solutions up to a molality of about 1.5 mol⋅kg⁻¹ contains two electrolyte-dependent parameters: B {that is related closely to the ion-size parameter (a ^∗) in the Debye–Hückel equation} and b ₁ (this parameter is the coefficient of the linear term with respect to the molality, which is related to hydration numbers of the ions of the electrolyte). In more concentrated solutions up to 7 mol⋅kg⁻¹, an extended Hückel equation was used, it contains additionally a quadratic term with respect to the molality, and the coefficient of this term is the parameter b ₂. Parameters for the Hückel equations were evaluated from isopiestic data for LiClO₃, LiBrO₃, LiClO₄, NaClO₃, NaBrO₃, NaClO₄, KClO₃, and KBrO₃. In these estimations, the Hückel parameters determined recently for NaCl solutions were used. The resulting parameter values were tested with the vapor pressure and isopiestic data available in the literature for solutions of these salts. Most of these data were reproduced within experimental error by means of the Hückel or extended Hückel equations, at least up to a molality of 3.0 mol⋅kg⁻¹, for all salts considered. Reliable activity and osmotic coefficients for solutions of these salts can, therefore, be calculated by using the new Hückel equations, and they are tabulated here at rounded molalities. The activity and osmotic coefficients obtained from these equations were compared to the values reported in several previous tabulations.     

Hückel theory applied to large linear and cyclic conjugated π-systems

By use of rotational symmetry (C_n-symmetry) a lower limit to the frontier orbital (HOMO-LUMO) gap in large molecules with linear and cyclic conjugated π-systems containing simple repetitive units has been calculated within the Hückel approxmation. The frontier orbitals are shown to be the same in series of cyclic oligomers and liner polymers containing the same repetitive units. The orbital gap is calculated from the repetitive units closed on themselves to give a ring of Hückel or, alternatively, Möbius topology depending on the number of conjugated π-electrons in a liner array between the ends of the repetitive unit. For 4n (4n+2) systems the small ring of Hückel (Möbius) topology will give the frontier orbitals.     

Two-dimensional hückel molecular orbital theory

The conventional Hückel molecular orbital (HMO) theory is extended to include hydrocarbons with sp-hybridized C atoms in addition to the sp²-hybridization. MOs are constructed as linear combinations of 2p-orbitals in two dimensions perpendicular to each other. The resulting two parts of the π system (viz. π′ and π″) are assumed to be independent. The total π-bond order is assumed to be obtained by the addition of contributions from π′ and π″. The two-dimensional HMO theory covers hydrocarbons with acetylenic (CC) bonds and cumulated CC bonds. The theory is applied to vinylacetylene, diacetylene, allene, butatriene and divinylacetylene. CC bond lengths calculated from the theoretical π-bond orders are compared with experimental data. Agreements between calculated and observed bond lengths within ±0.03 Å are found.     

The Enthalpies of Solution of Tetraethyl- and Tetrabutylammonium Bromides in Aqueous Solutions of Hexamethylphosphorus Triamide at 328.15 K

The heats of solution of Et₄NBr and Bu₄NBr in water and aqueous solutions of hexamethylphosphorus triamide (HMPT) at 328.15 K were measured in a variable-temperature isothermic-shell calorimeter. The standard enthalpies of solution were calculated using the Debye-Hückel second-order theory. The enthalpy parameter of electrolyte—amide pair interactions was determined in terms of the McMillan-Mayer formalism. The processing of the data obtained in this work and previously led us to conclude that heat capacity changes caused by pair interactions of Et₄NBr and Bu₄NBr with HMPT were negative and independent of temperature over a wide temperature range. The methyl and methylene groups interacted with HMPT without heat capacity changes and, consequently, the enthalpies and entropies of their interactions with HMPT were constant over a wide temperature range.     

Measurement of the Diffusivity of Cesium Ion in Aqueous Rubidium Chloride Solution

For the first time cesium diffusivity in aqueous solutions of rubidium chloride is being reported here in the concentration range from 0.001 to 4.00 mol⋅dm⁻³. The measurement use a radioactive tracer technique employing a sliding cell mechanism. These diffusivity values were utilized to understand the transport mechanism of Cs ion in the RbCl–H₂O system using the Onsager-Gosting-Harned equation and the extended Debye-Hückel equation. The observed deviation between the theoretical and experimental diffusivities are explained by introducing the concept of Field-Dielectric-Gradient forces and energies that exist around an ion, which takes care of the finite size of the ion, ion-water interaction and the ion-ion interaction in a continuum basis.     

Partial molal compressibilities of salts in aqueous solution and assignment of ionic contributions

Apparent molal adiabatic compressibilities of a number of 1:1, 2:1, 3:1, and 4:1 electrolytes have been accurately determined in the concentration range 0 to 1 m at 25°C. Debye-Hückel limiting-law behavior is observed in the low concentration region, and a scale of individual ionic compressibilities is proposed in terms of semiempirical calculations based on assessment of the contributions of the various types of solute-solvent interaction in the Frank and Wen model for a series of alkali halides. On this scale, K _s ^o (Cl^?, 25°C)=?17×10^?4 ml-mole^?1 bar^?1. Isothermal compressibility values also have been calculated for a number of the salts studied, and specific effects of hydrophobic interaction and hydrogen bonding on compressibility are indicated.     

Madelung-like attractions in colloidal crystals

The Debye-Hückel (Derjaguin-Landau-Verwey-Overbeek) two-sphere interaction potential is discussed in relation to the dissociative electrical double layer (DEDL) theory. The DEDL theory provides new electrostatic models to investigate the origin of attractions in colloidal crystals. Three Maxwellian models of two, three, and four interacting spheres are suggested. It is estimated that at least four spheres are needed to obtain Madelung-like attractions that are brought about by co-ion exclusion.     

Study on osmotic pressure of non-ionic and ionic surfactant solutions in the micellar and microemulsion regions

To investigate the osmotic pressure of non-ionic and ionic surfactant solutions in the micellar and microemulsion regions, a potential of mean force including hard-core repulsion, van der Waals attraction and electric double layer repulsion is proposed to describe the interactions between micelles and between microemulsions. Both van der Waals attraction and electric double layer repulsion are represented using Yukawa tails. The explicit analytical expression of osmotic pressure derived from the first-order mean spherical approximation is implemented by accounting for the Donnan membrane effect. The proposed theory has been applied to micelle solutions of the non-ionic surfactant, n-dodecyl hexaoxyethylene monoether, the cationic surfactant, cetylpyridinium chloride, the anionic surfactant, sodium dodecyl sulfate, and spherical oil-in-water microemulsion system. Successful comparison is made between the proposed theory and the experimental osmotic pressure data for the studied surfactant solutions. Theoretical results show that the long-range electric double layer repulsion dramatically influences the osmotic pressure of both cationic and anionic surfactant solutions in the micellar region. The regressed model parameters such as effective micelle diameter, the mean aggregation number and effective micellar charge are in good agreement with those from static light scattering studies in the literature.     

Point excesses in the theory of ordinary and micellar solutions

Point excesses of substances and thermodynamic properties and the role they play in the solvation and binding of counterions in solutions of electrolytes, including micellar systems, are analyzed. A complete system of fundamental thermodynamic equations for point excesses is formulated. Statistical mechanics equations that relate point excesses of substances to the electrochemical potentials and concentrations of components are derived. For ionic micellar systems, a relation between point excesses and charges and concentrations of ions and micelles is obtained. The results are substantiated by direct calculations of point excesses with the use of the Debye-Hückel method.     

Impurity-vacancy interactions in the alkali halides

The interaction energies of vacancies with divalent impurities are calculated using recently developed efficient computer simulation methods. The results show that nearest neighbour and next nearest neighbour complexes are roughly equally bound, thus emphasising the importance of including both types of defect pair in analyses of spin resonance and other experimental data on doped alkali halides. We also find that a simple Coulomb expression for defect interactions gives energies close to those obtained by the full calculation, for all but the nearest neighbour complex. This result encourages the use of Debye-Hückel treatments of defect activities in alkali halide crystals.     

Excited stateπ-electron polarizabilities for some condensed aromatic molecules

Excited state π-electron polarizabilities are calculated with Hückel molecular orbitals where the β parameter is calibrated to electrochromic effect data for some condensed aromatic systems. The excited state parameter is found to beβ_c=3.6 eV as compared to the ground state value of β_g=7.5 eV. Our results are about the same as calculations with PPP orbitals and agreement with experimental data is generally good.