Solubility of small particles

Although the increase in solubility of small particles is unquestionably a real effect, using it quantitatively as a means of evaluating ySL is fraught with difficulties ... 

Rate of Solubility—The rath of solubility of small particles depends on a great number of variables. Eq (12-2) takes into account free surface energy (a) and particle surface (1 /d). These are purely surface considerations, and are scarcely complete in themselves. The shape of the surface and its physical state must also be specified, that is, its relative freedom from contamination which might influence the speed of reaction. The effect of packing density and the extent of agitation imparted to the particles are also important, particularly with regard to exposure of fresh surfaces and formation of possible gas pockets. The liquid and liquid-solid phases jointly are additional important considerations. The volume of the liquid, its temperature, and the amount of dissolved solid already in solution must enter into all calculations. Nor can we ignore the chemical nature of the substances involved in the... 

An enhanced solubility of small particles could not be expected to be an equilibrium condition. Even if all particles were uniform in size, the system would be metastable. If a slight dissolution of any particle occurred, the solution would become supersaturated with respect to all the other particles and tmsaturated with respect to the particle that had decreased in size, so that ultimately this particle would... 

They cause an important increase in the solubilities of small particles (an increase in a solid s AGf value) (cf. Langmuir and Whittemore 1971 Stumm and Morgan 1996). 

Knapp, L.F. (1922) The solubility of small particles and the stability of colloids. Transactions of the Faraday Society, 17, 457-465. 

One problem in calculating the solubility of small particles is that the surface energy is not accurately known. There are very few substances of which the solubility of particles of uniform size and less than 100 A diameter have been measured. According to Walton (174), a combination of these requirements has not previously been achieved, but recently using radiotracer measurements and the electron microscope, such measurements have been made on strontium sulfate particles, from which the solid-water interfacial energy was calculated to be 84 8 ergs cm". ... 

In multiphase equilibria in binary systems involving solid and liquid phases the solubility of small particles is increased. The effects of this increase have been described for the shifts in phase boundaries on binary T-X diagrams and for the phenomenon of particle coarsening. 

It is thus comparatively large solubility of small particles that can be considered iD be llie origin of the difficulty with which nuclei of a new phase are formed ... 

Fig. 3 Solubility (Cs r) of small particles of radius, r, compared with the solubility (Cs ) of large particles. The solid is assumed to have a molecular weight of 200 g/mol, a density of 2 g/cm3, and an interfacial free energy of 30 mJ/m2 (dyne/cm) at 298 K (25°C).

Thomson-Freundlich equation relates the solubility of a particle to its curvature radius (e.g., Swalin, 1962). Using this equation, Kirkaldy and Young (1987) show how periodic precipitation may result from the capillary resistance of the matrix to grow small precipitates. Formally, the conditions read... 

Such an explanation cannot however account for the abnormally high values of the adsorption of simple salts at a water-oil interface, as found by Lewis. If we are to accept these results (though the emulsion method is certainly the least satisfactory of those used for the present purpose) some secondary effect must be looked for, such as the increased solubility of oil in water when emulsified and in the form of small particles. (The mean radius in one experiment was found to be about 4 x 10 cms., a size at which Hulett and Ostwald (see page 166) found a notable increase in the solubility of calcium and barium sulphates.) It is probable however that the chief error introduced was the disturbance brought about by the effect on the surface tension of the free charges of the salt ions (Lewis, Zeit. Physikal. Chem. Lxxiii. 129, 1910). (See Ch. VII.)... 

C.4.2 Equilibrium Solubilities of Small Dispersed-Phase Particles... 

Hydrogen sulfide dissolves in water to give a solution that, as a result of its oxidation by dissolved air, slowly becomes cloudy as a result of the formation of a colloidal dispersion of small particles of sulfur. Hydrogen sulfide is a weak diprotic acid and the parent acid of the hydrogen sulfides (which contain the HS ion) and the sulfides (which contain the S2- ion). The sulfides of the s-block elements are moderately soluble, whereas the sulfides of the heavy p- and d-block metals are generally very insoluble. 

Nanoparticles are frequently used as a suspension in some kind of solvent. This is a two phase mixture of suspended solid and liquid solvent and is thus an example of a colloid. The solid doesn t separate out as a precipitate partially because the nanoparticles are so small and partially because they are stabilised by coating groups that prevent their aggregation into a precipitate and enhance their solubility. Colloidal gold, which has a typical red colour for particles of less than 100 nm, has been known since ancient times as a means of staining glass. Colloid science is a mature discipline that is much wider than the relatively recent field of nanoparticle research. Strictly a colloid can be defined as a stable system of small particles dispersed in a different medium. It represents a multi-phase system in which one dimension of a dispersed phase is of colloidal size. Thus, for example, a foam is a gas dispersed in a liquid or solid. A liquid aerosol is a liquid dispersed in gas, whereas a solid aerosol (or smoke) is a solid dispersed in a gas. An emulsion is a liquid dispersed in a liquid, a gel is liquid dispersed in a solid and a soils a solid dispersed in a liquid or solid. We saw in Section 14.7 the distinction between sol and gel in the sol gel process. 

The Kelvin equation can be applied to the solubility of spherical particles by replacing the ratio p/p0 by a/a0 where a0 is the activity of dissolved solute in equilibrium with a large flat surface and a is the activity in equilibrium with a small spherical surface. If we consider an ionic solute of formula MmXn,the activity of a dilute solution is related to the molar solubility S by ... 

Coarsening or Ostwald ripening is the solution and redeposition of small particles. The cause of this process is the higher solubility of convex surfaces, compared to concave surfaces. Therefore, the small particles are dissolved and redeposition on larger particles occurs. Also necks between particles will grow (figure 1.8) and small pores may be filled in. This results in an increase in the average pore size and a decrease in the specific surface area. 

Figure 1.8 A chain of small particles is converted to a fiber or rod by the laws of solubility of convex and concave surfaces.

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