Photophysical characterization of mixed micelles of n-butanol/SDS and n-hexanol/SDS. A study at low alcohol concentrations

 The effect of the addition of n-butanol (BuOH) and n-hexanol (HexOH) on the micellization of sodium dodecylsulfate (SDS) has been investigated using fluorescence quenching methods. The binding constants were calculated using an expression which relates the total concentration of alcohols and the micelle concentration. The values of K were 4.67 and 17.6 M^-1 for BuOH/SDS and HexOH/SDS, similar to values obtained by other methods. The cmc of SDS decreases on addition of alcohols and goes through a minimum for the BuOH/SDS system. Micellar aggregation numbers (N) were determined from linear plots of Ln (I ⁰/I) against [Quencher] at low alcohol concentrations. For 15 mM SDS, in the presence of BuOH the N values decrease on addition of alcohol up to 0.2 M. For HexOH, N can be assumed to be constant up to 4.8 mM, after which N decreases. The polarity of the micellar core containing alcohol was evaluated from the I ₁/I ₃ ratio of monomeric pyrene. The effect of addition of the alcohol causes a decrease in the I ₁/I ₃, which corresponds to a decrease in the polarity of the pyrene solubilization site. Received: 28 October 1996 Accepted: 10 January 1997     

Symmetry numbers and chemical reaction rates

This article shows how to evaluate rotational symmetry numbers for different molecular configurations and how to apply them to transition state theory. In general, the symmetry number is given by the ratio of the reactant and transition state rotational symmetry numbers. However, special care is advised in the evaluation of symmetry numbers in the following situations: (i) if the reaction is symmetric, (ii) if reactants and/or transition states are chiral, (iii) if the reaction has multiple conformers for reactants and/or transition states and, (iv) if there is an internal rotation of part of the molecular system. All these four situations are treated systematically and analyzed in detail in the present article. We also include a large number of examples to clarify some complicated situations, and in the last section we discuss an example involving an achiral diasteroisomer.     

Evaluation of single-ion conductances in nonaqueous solvents at 25°C by the use of tetrabutylammonium tetrabutylboride as a reference electrolyte

Precise conductances for tetrabutylammonium tetrabutylboride (Bu₄NBBu₄) at 25°C have been measured in a number of nonaqueous solvents, and the data have been analyzed by the 1957 Fuoss-Onsager conductance equation. Limiting ion conductances for the Bu₄N⁺ ion at infinite dilution ₀(Bu ₄ N ⁺) in various solvents have been evaluated by dividing ₀ values of the salt into two equal parts. The ₀(Bu ₄ N ⁺) values so obtained are in fairly good agreement (within±0.1–3.5%) with the corresponding values determined from direct transference number measurements in these solvents.     

On the determination of polarity parameters of silica by means of solvatochromic probe dyes

Empirical solvent parameters of silica surfaces are determined by means of solvatochromic dyes, e.g., Cu(tmen) (acac)⁺ ClO ₄ ^– /B(C₆H₅) ₄ ^– , Fe(phen)₂(CN)₂, and Michlers Ketone dissolved in 1,2-dichloroethane or cyclohexane. The values obtained by UV/VIS-measurements are compared with both the polarity scales of Kamlet and Taft and with Gutmann's donor and acceptor numbers. Kamlet and Taft's -parameter (the hydrogen-bond donation capacity of a solvent) is determined independently by means of salicylideneaniline. The ^* of silica is determined using 5-N,N-dimethylamino-5-nitro-2,2-bithiophene and the complex of tetracyanoethylene with Michlers Ketone, respectively. Further on the reliabilities of the obtained Kamlet-Taft parameters , , and ^* are checked by comparism with experimental and calculated values of theE _T(30)-parameter of silica by means of multi-parameter regression analysis. The surface properties of silica are influenced mainly by HBD-properties (75%) and dipolarity/polarizability ^* (20%), but hardly by the HBA-properties (<5%). UV/VIS-measurements were carried out in a special equipment with glass fiber optics, A drawing of the apparatus is given.     

Oscillations of certain second order nonlinear differential equations

A second order nonlinear differential equation

Electrophysical characteristics and stability of solid apatite-like electrolytes La x Si6O12 + 1.5x and La x Ge6O12 + 1.5x

Oxygen-ion conduction in apatite-like compounds based on silicates and germanates of lanthanum La _x A₆O_{12 + 1.5x} (A = Si, Ge; x = 9.11–10.22) is studied. The compounds are shown to be purely ionic conductors at 600–900°C and partial oxygen pressures 10^?16 to 10⁵ Pa. The electroconductivity of the best conducting specimens of La _x A₆O_{12 + 1.5x} (A = Si, Ge; x = 9.77–10) exceeds that of electrolyte YSZ at moderate temperatures. The electroconductivity of lanthanum germanate is substantially greater than that of lanthanum silicate, specifically, 7.85 × 10^?2 and 2.35 × 10^?2 S cm^?1, respectively, at 800°C. An inflection is discovered at ～750°C in the temperature dependences of electroconductivity of La _x Ge₆O_{12 + 1.5x} (x = 9.77–10.22). A dilatometric examination points to a second-kind phase transition that may be due to the oxygen sublattice disordering. The behavior of apatite-like electrolytes La _x A₆O_{12 + 1.5x} (A = Si, Ge) during long exploitation periods in the interval of working temperatures of electrochemical devices is studied for the first time ever. The electrolytes’ aging at 800°C in air for 1000 h was investigated by the electroconductivity method. The electroconductivity of lanthanum germanates decayed with time by 5% and that of lanthanum silicates, by 9.5%. The steady-state values of electroconductivity of all compounds studied is reached after 600–700 h. The compounds studied form a class of materials that hold some promise as solid electrolytes for medium-temperature fuel cells and other electrochemical devices.     

Evaluation of mean and variance integrals without integration

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential calculus. The general nature of the technique has potential for wider applications.     

Motzkin numbers out of Random Domino Automaton

Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton.     

Open problems in pluripotential theory

We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold setting.