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.
Contents
The Ostwald–Freundlich equation for a droplet or particle with radius
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.
History
In 1871, Lord Kelvin (William Thomson) obtained the following relation governing a liquid-vapor interface:
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. The German physical chemist Wilhelm Ostwald derived the equation apparently independently in 1900; however, his derivation contained a minor error which the German chemist Herbert Freundlich corrected in 1909.
Derivation from Kelvin's equation
According to Lord Kelvin's equation of 1871,
If the particle is assumed to be spherical, then
Note: Kelvin defined the surface tension
Since
Assuming that the vapor obeys the ideal gas law, then
where
Since
Hence
where
Thus
Since
Since
If
Hence
Therefore
which is the Ostwald–Freundlich equation.