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
is: 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.
In 1871, Lord Kelvin (William Thomson) obtained the following relation governing a liquid-vapor interface:[1] where: In his dissertation of 1885, Robert von Helmholtz (son of the German physicist Hermann von Helmholtz) derived the Ostwald–Freundlich equation and showed that Kelvin's equation could be transformed into the Ostwald–Freundlich equation.
[2][3] The German physical chemist Wilhelm Ostwald derived the equation apparently independently in 1900;[4] however, his derivation contained a minor error which the German chemist Herbert Freundlich corrected in 1909.
[5] According to Lord Kelvin's equation of 1871,[6][7] If the particle is assumed to be spherical, then
; hence, Note: Kelvin defined the surface tension
In what follows, the surface tension will be defined so that the term containing
; hence, Assuming that the vapor obeys the ideal gas law, then where: Since
is the mass of one molecule of vapor or liquid, then Hence Thus Since then Since