The effect of particle size on solubility

The melting point of 3 is lowered as the radius becomes smaller. 

The increase in solubility in the liquid may be quantified as follows. Consider the L—p equilibrium at temperature T. The chemical potential of component 2 in the liquid is related to its activity by Equation (6.69) for equilibrium with bulk p, 

The corresponding relation when the liquid is in equilibrium with P spheres of radius r is given by 

The difference between the two chemical potentials is thus given by 

Equality of the chemical potentials in coexisting bulk phases is given by 

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Figure 7.24c shows variation of the reaction free energy with particle size for the conversion of hematite to goethite. The stability relation depends on particle size. Figure 7.24b shows the effect of particle size on solubility of calcite. 

Ostwald ripening is the result of the difference in solubility S between small and large particles. Typically, smaller particles have a larger solubility than larger particles, and the effect of particle size on solubility can be described by the Kelvin equation [9],... 

The definition of solubility permits the occurrence of a single solid phase which may be a pure anhydrous compound, a salt hydrate, a non-stoichiometric compound, or a solid mixture (or solid solution, or "mixed crystals"), and may be stable or metastable. As well, any number of solid phases consistent with the requirements of the phase rule may be present. Metastable solid phases are of widespread occurrence, and may appear as polymorphic (or allotropic) forms or crystal solvates whose rate of transition to more stable forms is very slow. Surface heterogeneity may also give rise to metastability, either when one solid precipitates on the surface of auiother, or if the size of the solid particles is sufficiently small that surface effects become important. In either case, the solid is not in stable equilibrium with the solution. See (21) for the modern formulation of the effect of particle size on solubility. The stability of a solid may also be affected by the atmosphere in which the system is equilibrated. 

Many studies have been conducted to look at the effect of particle size on dissolution and the bioavailability of insoluble drugs [69-84], One study looked at the effect of surface area on the bioavailability of griseofulvin, which has an aqueous solubility of 0.014 mg/mL and an average dose of 500 mg. The authors showed that an approximately sixfold increase in the surface area led to a 2.5-... 

C.E. presumably affects also some experimental results on the ys. In particular, the effect of particle size on vapor pressure and solubilities, Sections III.6 and III.7, are related to C.E. more than to the true surface energy as already pointed out, small particles usually have a less perfect crystal lattice than do larger crystals. A more direct estimate of C.E. is afforded by the measurements of the heat of dissolution. 

The often important effect of particle size on. solubility can be estimated through the equation... 

Parameters describing the effect of particle sizes on the oxide- solubility changes in saturated solutions in the molten equimolar KCl-NaCl mixture at 700 °C... 

It was mentioned in Section 5.4 that the interfacial tension of a solid cannot be determined by direct measurement. The Ostwald equation gives, in principle, access to the interfacial tension of an S/L interface. However, although the effect of particle size on the solubility may be well measurable, evaluation of Ysl is not unambiguous because the surface tension of a solid particle is usually not uniform and the presence of more strongly curved areas (e.g., edges and protuberances) has an increasing effect on the solubility. 

The effect of particle size on the solubility of components from solid solution in a liquid... 

Bisrat et al. concluded that for sparingly soluble, suspended drugs, diffusional transport plays a major role in the dissolution kinetics [19]. They studied the effect of particle size and viscosity on dissolution rate and apparent diffusional distance (.h-App) of oxazepam and griseofulvin. The term apparent diffusional distance was used as a simplified measure of the distance over which diffusion dominates and was calculated as follows ... 

Kanobo, I.A.K. and Gilkes, R.J. 1988. The effect of particle size in North Carolina phosphate rock on it dissolution in soil and on levels of bicarbonate-soluble phosphorus. Fertilizer Research 15 137-145. 

The effect of particle size reduction on dissolution rate is one of exposure of increasing amounts of surface of the drug to the solvent. It is only when comminution reduces particle size below 0.1 m that there is an effect on the intrinsic solubility of the substance (see Chapter 5), and thus on its intrinsic dissolution rate. Very small particles have a very high surface/bulk ratio. If the surface layer has a higher energy than the bulk, as is the case with these small particles, they will interact more readily with solvent to produce higher degrees of solubility. 

This effect of particle size on dissolution rate of sparingly soluble drug substances has been demonstrated in many instances by the superior dissolution rates observed after size reduction. Examples of compounds studied in such work include methylprednisolone (Higuchi et al., 1963), l-isopropyl-7-methyl-4-phenylquinazolin-2(lH)-one (Kornblum and Hirschorn, 1970), griseofulvin (Ullah and Cadawader, 1971), monophenylbutazone (Habib and Attia, 1985), nitrofurantoin (Eyjolfsson, 1999), and piroxicam (Swanepoel et al., 2000). 

Figure VII-19 Effect of particle size on the solubility constant of Th02(cr) predicted with the equation of Schindler [1967SCH] and experimental data for microcrystalline Th02(cr, hyd), and X-ray amorphous Th02(am, aged, hyd) and Th02(am, fresh, hyd) or Th(OH)4(am) .

A subtler problem is the effect of particle-size segregation on salt analyses. The composition of salt is not uniform, and it is found in particular with rock salts that purity is a function of particle size. In a rock salt deposit, anhydrite is present as layers and as inclusions in particles of salt. It is less friable than salt, and so regions of high salt content tend to crush more easily and form finer particles. Whether these segregate from the associated insolubles is open to question, and Sutter [31] reports that screening has little effect on the insoluble impurity content of a sample. On the other hand, soluble impurities tend to be more concentrated in the finer salt. This phenomenon is less likely to be a problem with solar salt or processed grades. 

Gravimetric analysis was performed on Pr-powders precipitated from solvated Pr Oj and PrC030H and PitOH)j to determine the effects of particle size/powder preparation on the solubility of each species (Fig. 6.6). The Pr-powder precipitated at atmospheric conditions at 85 °C was the most soluble followed by the powder precipitated in the presence of at ambient temperature, and Ar at 85 °C, which were not statistically different as calculated by a t-test. The Pr-powder precipitated with COj at ambient temperature, Ar at ambient temperature, at 85 °C, CO ... 

E. K. Anderberg, M. Bisrat, C. Nystrom. Physicochemical aspects of drug release. VII. The effect of surfactant concentration and drug particle size on solubility and dissolution rate of felodipine, a sparingly soluble drug. Int. I. Pharm. 1988, 47, 67-77. 

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