Solubility: decrease with particle size

If the temperature dependence of the free-energy curves is considered in addition to the (3 particle size, a temperature-composition diagram for the system can be plotted. This is illustrated in Fig. C.7, which shows clearly the way in which the solubility of component B in a increases with decreasing (3 particle size. 

The solubility of any solid substance in a liquid phase is well known to be dependent on the size of its particles (crystals) which are in contact with the saturated solution. For substances existing in solutions in the molecular form, the dependence of their solubility against the particle size is expressed by the Ostwald-Freundlich equation (3.6.57). From this equation it follows, in particular, that an increase in the crystal (particle) dimensions results in a decrease in solubility. The oxide particles precipitated from concentrated solutions should be larger than those formed from more dilute solutions. The increase in the particle sizes in concentrated solutions of cations and oxide ions may be explained by ageing oxide, i.e. by the re-crystallization processes, whose rate increases with the concentration of the dissolved substance. 

Oligomers decline when inert polymer begins to appear. The reaction rate with molybdate decreases rapidly to 0.1 between 3.75 and 4.75 days. It is probably at this stage that nucleation of colloidal particles begins. The oligomers dissolve and the silica is deposited upon the nuclei. The nuclei grow and the concentration of monomer in equilibrium decreases. The particle size can then be calculated from the concentration of monomer. The proportion of monomer drops to 5% after 90 days, which is 5% of 4000, or 200 ppm. This corresponds to the solubility of 2 nm particles. 

In the RESS process, the rapid expansion of supercritical solutions, the target compound is dissolved in the supercritical solvent, that is, in supercritical carbon dioxide. Due to the apolar nature of the solvent, the solubility is limited nevertheless, the pressures of up to 300 bar allow for a solution of sometimes >2% at 50 °C. These solutions are rapidly expanded to subcritical conditions, that is, often ambient pressures. The cooling due to the adiabatic expansion limits the pressure ratio. As mentioned earlier, the solubility decreases with falling pressure, leading to a supersaturation and subsequently nudeation and growth of crystals. The expansion itself can be carried out very fast thus, very small crystalline particles are formed. In the case of benzoic acid, a mean particle size on the order of 100 nm can be achieved (Figure 12.7). 

The intrinsic solubility of a material is dependent on the particle size of the material. Smaller particles have a higher intrinsic solubility compared with their larger counterparts. This is aptly explained by the existence of a higher interfacial free energy on smaller particles resulting in a thermodynamically unstable system which is corrected by greater dissolution of the particles and production of a supersaturated solution. The increase in intrinsic solubility with decrease in particle size, however, ceases when the particles have a very small radius and any further decrease in particle size causes a decrease in intrinsic solubility. 

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