Liquid interfaces concentrations from bulk solution

For example, in the dissolution of a solid into a liquid, the solute diffuses from the saturated solution at the interface to the bulk solution. In crystallization the solute diffuses from the supersaturated bulk solution to the saturated solution at the interface. The relevant diffusivity that should be used in an analysis of these two processes, therefore, is the integral diffusivity, which covers the range of concentration from equilibrium saturation to that in the bulk solution. 

Precipitation of soiid particies, which are poorly wetted by the liquid, can adsorb at the interface and cause foam stability. Precipitated solid particles may also reduce the surfactant concentration by adsorption from bulk solution. This would reduce the effectiveness of the Gibbs - Maragoni effect... 

Figure Bl.22.8. Sum-frequency generation (SFG) spectra in the C N stretching region from the air/aqueous acetonitrile interfaces of two solutions with different concentrations. The solid curve is the IR transmission spectrum of neat bulk CH CN, provided here for reference. The polar acetonitrile molecules adopt a specific orientation in the air/water interface with a tilt angle that changes with changing concentration, from 40° from the surface nonnal in dilute solutions (molar fractions less than 0.07) to 70° at higher concentrations. This change is manifested here by the shift in the C N stretching frequency seen by SFG [ ]. SFG is one of the very few teclnhques capable of probing liquid/gas, liquid/liquid, and even liquid/solid interfaces.

On account of the very great difficulty of measuring the extremely small amounts of adsorbed substance at a liquid/gas or liquid/liquid interface, very few experiments are available for testing Gibbs s equation. Zawidski(13) (1900) pointed out that the concentration of the foam of a solution should be different from that of the latter in bulk, and Miss Benson (14> (1903) by the analysis of a solution of amyl alcohol in water found... 

Phosphoric acid ester was used as a model for the estimation of concentration of a reagent in an adsorbed layer by optical measurements of the intensity of a beam reflecting externally from the liquid-liquid interface. The refractive index of an adsorbed layer between water and organic solution phases was measured through an external reflection method with a polarized incident laser beam to estimate the concentration of a surfactant at the interface. Variation of the interfacial concentration with the bulk concentration estimated on phosphoric acid ester in heptane and water system from the optical method agreed with the results determined from the interfacial tension measurements... 

Fig. 15 Two of the simplest theories for the dissolution of solids (A) the interfacial barrier model, and (B) the diffusion layer model, in the simple form of Nemst [105] and Brunner [106] (dashed trace) and in the more exact form of Levich [104] (solid trace). c is the concentration of the dissolving solid, cs is the solubility, cb is the concentration in the bulk solution, and x is the distance from the solid-liquid interface of thickness h or 8, depending on how it is defined. (Reproduced with permission of the copyright owner, John Wiley and Sons, Inc., from Ref. 1, p. 478.)...

The interfacial barrier theory is illustrated in Fig. 15A. Since transport does not control the dissolution rate, the solute concentration falls precipitously from the surface value, cs, to the bulk value, cb, over an infinitesimal distance. The interfacial barrier model is probably applicable when the dissolution rate is limited by a condensed film absorbed at the solid-liquid interface this gives rise to a high activation energy barrier to the surface reaction, so that kR kj. Reaction-controlled dissolution is somewhat rare for organic compounds. Examples include the dissolution of gallstones, which consist mostly of cholesterol,... 

What characterizes surfactants is their ability to adsorb onto surfaces and to modify the surface properties. At the gas/liquid interface this leads to a reduction in surface tension. Fig. 4.1 shows the dependence of surface tension on the concentration for different surfactant types [39]. It is obvious from this figure that the nonionic surfactants have a lower surface tension for the same alkyl chain length and concentration than the ionic surfactants. The second effect which can be seen from Fig. 4.1 is the discontinuity of the surface tension-concentration curves with a constant value for the surface tension above this point. The breakpoint of the curves can be correlated to the critical micelle concentration (cmc) above which the formation of micellar aggregates can be observed in the bulk phase. These micelles are characteristic for the ability of surfactants to solubilize hydrophobic substances in aqueous solution. So the concentration of surfactant in the washing liquor has at least to be right above the cmc. 

The simplest way to treat an interface is to consider it as a phase with a very small but finite thickness in contact with two homogeneous phases (see Fig. 16.1). The thickness must be so large that it comprises the region where the concentrations of the species differ from their bulk values. It turns out that it does not matter, if a somewhat larger thickness is chosen. For simplicity we assume that the surfaces of the interface are flat. Equation (16.1) is for a bulk phase and does not contain the contribution of the surfaces to the internal energy. To apply it to an interface we must add an extra term. In the case of a liquid-liquid interface (such as that between mercury and an aqueous solution), this is given by 7 cL4, where 7 is the interfacial tension - an easily measurable quantity - and A the surface area. The fundamental equation (16.1) then takes on the form ... 

On the basis of the above experimental results, the expected conformations of polymer-surfactant complexes at the oil-water interface are depicted in Fig. 2.19. In case I, the added polymer associates with excess surfactants present in the bulk solution, but the complexes prefer to remain in the bulk phase. Alternately, the polymer-surfactant complexes are unable to displace the adsorbed surfactant molecules from the liquid-liquid interface. Irrespective of the amount of polymer-surfactant concentration in the bulk, the experimental decay length values remain comparable to the Debye lengths, corresponding to the concentration of ion species in the bulk solution (Eq. (2.11)). This means that the force profile is... 

Solubility and diffusion in the liquid phase (Xsol). Consider the diffusion of a dissolved species in one dimension into the bulk solution from the interface region. The concentration of the species in the liquid will depend on time as well as on the distance from the interface. It is assumed first that no reaction is taking place in the aqueous phase. 

The composition boundary values entering into Eqs. (All) represent external values for Eqs. (A10). With some further assumptions concerning the diffusion and reaction terms, this allows an analytical solution of the boundary-value problem [Eqs. (A10) and (All)] in a closed matrix form (see Refs. 58 and 135). On the other hand, the boundary values need to be determined from the total system of equations describing the process. The bulk values in both phases are found from the balance relations, Eqs. (Al) and (A2). The interfacial liquid-phase concentrations xj are related to the relevant concentrations of the second fluid phase, y , by the thermodynamic equilibrium relationships and by the continuity condition for the molar fluxes at the interface (57,135). 

The lamellae in a foam contain two gas/liquid interfaces separated by a layer of fluid, thin film, each interface having a surface tension. For this reason the term film tension is sometimes used, the film tension being equal to twice the surface tension of the surfaces. It should be noted that, while the film tension is twice the surface tension of the surfaces, this is not necessarily the same as twice the surface tension of the bulk solution. In fact, the surface tension of a fluid film surface is similar to that of the bulk solution when the fluid film is thick, but departs from the bulk solution value as the fluid film thins. The situation is similar for the thin films between droplets in a concentrated emulsion. 

The liquid-liquid interface formed between two immissible liquids is an extremely thin mixed-liquid state with about one nanometer thickness, in which the properties such as cohesive energy density, electrical potential, dielectric constant, and viscosity are drastically changing from those of bulk phases. Solute molecules adsorbed at the interface can behave like a 2D gas, liquid, or solid depending on the interfacial pressure, or interfacial concentration. But microscopically, the interfacial molecules exhibit local inhomogeneity. Therefore, various specific chemical phenomena, which are rarely observed in bulk liquid phases, can be observed at liquid-liquid interfaces [1-3]. However, the nature of the liquid-liquid interface and its chemical function are still less understood. These situations are mainly due to the lack of experimental methods required for the determination of the chemical species adsorbed at the interface and for the measurement of chemical reaction rates at the interface [4,5]. Recently, some new methods were invented in our laboratory [6], which brought a breakthrough in the study of interfacial reactions. 

Fig. 3 Mechanism for the synthesis of a hexagonal silica thin film by dip coating. This is zoomed in at the substrate-bulk solution interface. The dotted line indicates the second critical micelle concentration, above which the micelles form cylindrical micellar rods. These rods then begin to assemble at the air-liquid interface and the liquid-substrate interface. (From Ref. l)...

Early studies were carried out at the liquid gas interface [22, 23]. Castro et al. [24] studied the adsorption of / -propyl-phenol from aqueous solutions at the air interface as a function of phenol concentration in the bulk. They showed that the square root of the second-harmonic intensity plotted against bulk phenol concentration followed a Langmuir isotherm with a standard Gibbs energy of adsorption equal to -24.3 kJmol Similar results were obtained for other alkylphenols and alkylanilines. In other work with phenols, the orientation of phenol at the water air interface was determined by studying the phase of the xfl component of the susceptibility. As expected, the OH was oriented toward the water phase [25] so that it could participate in the hydrogen-bonded structure of water. The same conclusion was reached for / -bromophenol and -nitrophenol. 

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