Interfacial concentration, solid-liquid

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,... 

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. 

Tliese results revealed that the liquid/liquid interface produced by agitation or stirring could catalyse the extraction rate by increasing the interfacial concentration of extractant and facilitating the interfacial complexation rate, similar to gas/solid or liquid/solid catalysis. 

For many purposes it is conducive to start analyses with thermodynamic considerations. In this way, it is often possible to find laws of general validity and to determine the boundaries between which models can be developed. For the study of (relaxed) double layers the Gibbs adsorption equation is the starting point. Although the interfacial tension of a solid-liquid interface cannot be measured, this equation remains useful because it helps to distinguish measurable and Inoperable variables, and because it can be used to correlate surface concentrations of different species (Including the surface ions), some of which may not be analytically accessible. 

Emulsion systems can be considered a subcategory of lyophobic colloids. Like solid-liquid dispersions, their preparation requires an energy input, such as ultrasonication, homogenization, or high-speed stirring. The droplets formed are spherical, provided that the interfacial tension is positive and sufficiently large. Spontaneous emulsification may occur if a surfactant or surfactant system is present at a sufficient concentration to lower the interfacial tension almost to zero. 

Diffusivity or viscosity Solid-liquid interfacial tension Water/solvent activity Boiling/melting point Solute activity (concentration)... 

Further, A5, Gb and Gi denote thermal conductivities and temperature gradients in the liquid and solid, and D the solute diffusivity in the liquid. m = dTjdCoo and k are volumetric latent heat of fusion, liquidus slope and interfacial distribution coefficient. G o is the concentration far from the interface and F = Tmlsi/Ly the Gibbs-Thompson parameter based on the solid liquid interfacial energy 7 / and melting temperature Tm is the solidification velocity and uj = 27t/A the wave number of a perturbation. 

A solute distribution exists in the melt because the solidification is carried out at a finite rate. For example, if k0 < 1, then solute is rejected and accumulates at the surface which is solidifying, and this creates solute gradients in the melt which tend to be relaxed by molecular diffusion and any convection which may exist. The interfacial distribution coefficient, k, refers to the solid to liquid solute concentration ratio at the interface. It is k which is used in transport calculations when one is trying to understand the dynamic behavior of zone refining systems. It usually is found that equilibrium exists locally at the solid-liquid interface, in which case k ko. 

The effect of the concentration of interfacial transfer catalysts in aprotic solvents in contact with solid salts (sodium 2,4-dinitrophenolate) has been investigated with regard to their effectiveness for reaching the solid-liquid equilibrium in benzene, chlorobenzene, dichloromethane and acetonitrile at 25 °C [185], Polyethylene glycols with 300, 600 and 2000 mol. wt., trianthrylmethylammonium chloride, dodecyldi-methylammonium chloride, tetrabutylammonium chloride and a crown ether, have... 

Figure 7 Plots of potential energy of interaction as a function of the distance H between the surfaces of identical spherical particles with radius a = I pm. Top clasHcal DLVO theory. Bottom Exterxled DLVO approach. The following values were used for the calculations = 30 mV 1 1 electrolyte concentration 10 - M Mamaker constant = 2 X lO J acid-base component of the solid-liquid interfacial toiuon — 10 mJ/ni See text for details.

Strictly speaking, equation 3.58 should be expressed in terms of solution activities rather than concentrations (Enustiin and Turkevich, 1960). Furthermore, it involves a number of assumptions that may not always be valid. For example, the solid-liquid interfacial tension (section 5.6) is implicitly assumed to be independent of particle size, and no account is taken of any ionization or... 

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