Ostwald–Freundlich equation

The Ostwald–Freundlich equation governs boundaries between two phases; specifically, it relates the surface tension of the boundary to its curvature, the ambient temperature, and the vapor pressure or chemical potential in the two phases.

The Ostwald–Freundlich equation for a droplet or particle with radius ${\displaystyle R}$ is:

${\displaystyle {\frac {p}{p_{\rm {eq}}}}=\exp {\left({\frac {R_{\rm {critical}}}{R}}\right)}}$

${\displaystyle R_{critical}={\frac {2\cdot \gamma \cdot V_{\rm {atom}}}{k_{\rm {B}}\cdot T}}}$

${\displaystyle V_{\rm {atom}}}$ = atomic volume

${\displaystyle k_{\rm {B}}}$ = Boltzmann constant

${\displaystyle \gamma }$ = surface tension (J ${\displaystyle \cdot }$ m⁻²)

${\displaystyle p_{\rm {eq}}}$ = equilibrium partial pressure (or chemical potential or concentration)

${\displaystyle p}$ = partial pressure (or chemical potential or concentration)

${\displaystyle T}$ = absolute temperature

One consequence of this relation is that small liquid droplets (i.e., particles with a high surface curvature) exhibit a higher effective vapor pressure, since the surface is larger in comparison to the volume.

Another notable example of this relation is Ostwald ripening, in which surface tension causes small precipitates to dissolve and larger ones to grow. Ostwald ripening is thought to occur in the formation of orthoclase megacrysts in granites as a consequence of subsolidus growth. See rock microstructure for more.