The unusual importance of activity coefficients for micelle solutions illustrated by an osmometry study of aqueous sodium decanoate and aqueous sodium decanoate + sodium chloride solutions.

Freezing-point and vapor-pressure osmometry data are reported for aqueous sodium decanoate (NaD) solutions and aqueous NaD + NaCl solutions. The derived osmotic coefficients are analyzed with a mass-action model based on the micelle formation reaction qNa(+) + nD(-) = (Na(q)D(n))(q-n) and Guggenheim equations for the micelle and ionic activity coefficients. Stoichiometric activity coefficients of the NaD and NaCl components and the equilibrium constant for micelle formation are evaluated. Illustrating the remarkable but not widely appreciated nonideal behavior of ionic surfactant solutions, the micelle activity coefficient drops to astonishingly low values, below 10(-7) (relative to unity for ideal solutions). The activity coefficients of the Na(+) and D(-) ions, raised to large powers of q and n, reduce calculated extents of micelle formation by up to 15 orders of magnitude. Activity coefficients, frequently omitted from the Gibbs equation, are found to increase the calculated surface excess concentration of NaD by up to an order of magnitude. Inflection points in the extent of micelle formation, used to calculate critical micelle concentration (cmc) lowering caused by added salt, provide unexpected thermodynamic evidence for the elusive second cmc.

Dalton's disputed nitric oxide experiments and the origins of his atomic theory.

In 1808 John Dalton published his first general account of chemical atomic theory, a cornerstone of modern chemistry. The theory originated in his earlier studies of the properties of atmospheric gases. In 1803 Dalton discovered that oxygen combined with either one or two volumes of nitric oxide in closed vessels over water and this pioneering observation of integral multiple proportions provided important experimental evidence for his incipient atomic ideas. Previous attempts to reproduce Dalton's experiments have been unsuccessful and some commentators have concluded the results were fraudulent. We report a successful reconstruction of Dalton's experiments and provide an analysis exonerating him of any scientific misconduct. But we conclude that Dalton, already thinking atomistically, adjusted experimental conditions to obtain the integral combining proportions.

Activity coefficients and free energies of nonionic mixed surfactant solutions from vapor-pressure and freezing-point osmometry.

The thermodynamic properties of mixed surfactant solutions are widely investigated, prompted by numerous practical applications of these systems and by interest in molecular association and self-organization. General techniques for measuring thermodynamic activities, such as isopiestic equilibration, are well-established for multicomponent solutions. Surprisingly, these techniques have not yet been applied to mixed surfactant solutions, despite the importance of the free energy for micelle stability. In this study, equations are developed for the osmotic coefficients of solutions of nonionic surfactant A + nonionic surfactant B. A mass-action model is used, with virial equations for the activity coefficients of the micelles and free surfactant monomer species. The equations are fitted to osmotic coefficients of aqueous decylsulfobetaine + dodecylsulfobetaine solutions measured by vapor-pressure and freezing-point osmometry. Equilibrium constants for mixed-micelle formation are calculated from the free monomer concentrations at the critical micelle concentrations. The derived activity coefficients of the micelles and free monomers indicate large departures from ideal solution behavior, even for dilute solutions of the surfactants. Stoichiometric activity coefficients of the total surfactant components are evaluated by Gibbs-Duhem integration of the osmotic coefficients. Relatively simple colligative property measurements hold considerable promise for free energy studies of multicomponent surfactant solutions.

Coupled mutual diffusion in solutions of micelles and solubilizates.

The coupled diffusion of micelles and solubilizates has been studied by measuring ternary mutual diffusion coefficients (D(ik)) for aqueous solutions of dodecylsulfobetaine (SB12) with added butanol, pentanol, or hexanol. SB12 micelles solubilize alcohols, so diffusing SB12(1) might be expected to co-transport alcohol(2). Negative values of cross-coefficient D(21) indicate, however, that the diffusion of SB12 drives substantial counterflows of alcohol. To help interpret the results, measured decreases in critical micelle concentrations with added alcohol (ROH) are used to evaluate equilibrium constants for the formation of (SB12)(m)(ROH)(n) mixed micelles. Increasing the concentration of SB12 along a diffusion path raises the concentrations of micelles and solubilized alcohol while lowering the concentration of free alcohol. The resulting flux of relatively mobile free alcohol molecules up SB12 concentration gradients is larger than the flux of solubilized alcohol down SB12 gradients, producing net countercurrent coupled fluxes of alcohol. The measured D(ik) coefficients are in close agreement (+/- 0.05 x 10(-5) cm(2) s(-1)) with predictions using self-diffusion coefficients (D(i)*) for SB12 and alcohol in solutions at thermodynamic equilibrium and the relations D(ik) = partial differential(C(i)D(i)*)/ partial differentialC(k) proposed recently for mutual diffusion in non-equilibrium solutions of associating solutes. Mutual diffusion coefficients for coupled surfactant-solubilizate diffusion are used to evaluate equilibrium constants for the formation of surfactant-solubilizate mixed micelles.

A comparison of diffusion coefficients for ternary mixed micelle solutions measured by macroscopic gradient and dynamic light scattering techniques.

Taylor dispersion is used to measure ternary mutual diffusion coefficients (D(ik)) for aqueous solutions of decylsulfobetaine (SB10) (1) + dodecylsulfobetaine (SB12) (2), SB10 (1) + SB14 (2), and SB12 (1) + SB14 (2) mixed zwitterionic micelles. Cross-coefficient D(21) for the coupled flow of surfactant 1 produced by a concentration gradient in surfactant 2 is relatively small for these solutions, but D(12) reaches values as large as the main D(ii) coefficients. The results are interpreted by using the equation D(ik) = partial differential(C(i)D(i))/ partial differentialC(k) to relate the ternary mutual diffusion coefficients to the concentration-weighted average diffusion coefficients D(i) of the micellar and free-monomer forms of the surfactants. The macroscopic-gradient Taylor measurements are compared with diffusion coefficients measured by dynamic light scattering (DLS), which monitors microscopic concentration fluctuations. At most compositions, the intensity autocorrelation function G(tau) is a single exponential decay in D((2)), the smaller eigenvalue of the mutual diffusion coefficient matrix. A contribution from D((1)) is identified at high solute fractions of surfactant 1. The DLS results are consistent with contributions to G(tau) from uncoupled fluctuations in the concentrations of eigencomponents defined as the linear combinations of surfactants 1 and 2 that diagonalize the D(ik) matrix. A procedure for the rapid and convenient DLS measurement of ternary mutual diffusion coefficients, including the cross-coefficients for coupled diffusion, is suggested, using the Onsager reciprocal relation together with the eigenvalues and pre-exponential factors from G(tau).

Nernst-Planck analysis of propagating reaction-diffusion fronts in the aqueous iodate-arsenous acid system.

Propagating fronts can be generated in solution by combining diffusion and chemical reactions with an autocatalytic feedback mechanism. Front propagation is usually analyzed in terms of the rate equations for the chemical reactions and Fick's laws of molecular diffusion. In practice, however, reaction-diffusion fronts are known mainly for aqueous electrolyte solutions. A more accurate description of front propagation in these systems is developed by using Nernst-Planck (NP) transport equations. This treatment includes diffusion fluxes driven by the concentration gradients and, for the ionic species, the migration fluxes driven by the electric field which is generated internally by the diffusion of ions of different mobility. NP equations are used to describe propagating fronts for the iodate oxidation of aqueous arsenous acid. The analysis provides a detailed picture of front structure and propagation, including concentration profiles, reaction rate profiles and velocity profiles for the solution species. After a short induction period, fully-developed fronts reach steady velocities and the profiles across the fronts transformed from laboratory coordinates to the frame of reference moving with the front become time-independent. The velocities of the autocatalytic I(-) ions ahead of the fronts are nearly identical to the steady front velocities. Electric fields generated by ionic diffusion across the fronts reach maximum strengths of about 0.4 V cm(-1), producing ion migration velocities as large as 50% of the front velocities.

Taylor dispersion monitored by electrospray mass spectrometry: a novel approach for studying diffusion in solution.

This work describes a novel approach for monitoring analyte diffusion in solution that is based on electrospray ionization mass spectrometry (ESI-MS). A mass spectrometer at the end of a laminar flow tube is used to measure the Taylor dispersion of an initially sharp boundary between two solutions of different analyte concentration. This boundary is dispersed by the laminar flow profile in the tube. However, this effect is diminished by analyte diffusion that continuously changes the radial position, and hence the flow velocity of individual analyte molecules. The steepness of the resulting dispersion profile therefore increases with increasing diffusion coefficient of the analyte. A theoretical framework is developed to adapt the equations governing the dispersion process to the case of mass spectrometric detection. This novel technique is applied to determine the diffusion coefficients of choline and cytochrome c. The measured diffusion coefficients, (11.9 +/- 1.0) x 10(-10) m(2) s(-1) and (1.35 +/- 0.08) x 10(-10) m(2) s(-1), respectively, are in agreement with the results of control experiments where the Taylor dispersion of these two analytes was monitored optically. Due to the inherent selectivity and sensitivity of ESI-MS, it appears that the approach described in this work could become a valuable alternative to existing methods for studying diffusion processes, especially for experiments on multicomponent systems.