Gibbs-Freundlich-Ostwald equation

It is noteworthy that the Gibbs-Freundlich-Ostwald equation, describing the size dependence of the solubility c(r) of drops or solid crystals is similar to eq.(1.15) ... 

Solubility is also affected by particle size, small crystals (<1 pm say) exhibiting a greater solubility than large ones. This relationship is quantified in the Gibbs-Thomson, Ostwald-Freundlich equation (see Mullin, 2001)... 

Changes in crystal dispersion due to surface effects are typically based on the Gibbs-Thomson equation (sometimes called the Ostwald-Freundlich equation), which describes the effects of particle size on equilibrium conditions (Hartel 2001). For solution systems, the equation is given as... 

As early as 1878, Gibbs concluded that the breakdown or growth of a crystal was not a continuous transformation, as the gas-liquid transition was considered to be. Thomson derived what has come to be known as the Gibbs-Thomson equation, relating the vapor pressure of liquid droplets to the size of the droplets. Ostwald extended the concept to the problem of solubility, but made a numerical error later corrected by Freundlich. Similar to the Gibbs-Thomson equation, the Ostwald-Freundlich equation was expressed by... 

The difference in thermodynamic equilibrium between crystals of different size is defined by the Gibbs-Thomson or Ostwald-Freundlich equation (Mullin 1993). The original Kelvin equation was written to describe droplets of liquid in a vapor in terms of vapor pressures around droplets of different size. However, in crystallization studies, the vapor pressure may be related, through the solution activity, to the equilibrium concentration in solution for crystals of different size, faking the assumption that concentration can be used directly fpr vapor pressure gives... 

Confusingly, but for understandable reasons, equation 3.58 is referred to in the literature by a variety of names such as the Gibbs-Thomson, Gibbs-Kelvin and Ostwald-Freundlich relation. For consistency, however, the designation Gibbs-Thomson will be used throughout this work. 

The Ostwald-Freundlich equation, applied to solubility (known as the Thompson-Gibbs effect), is as follows ... 

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