The Gibbs–Thomson effect, in common physics usage, refers to variations in vapor pressure or chemical potential across a curved surface or interface.
The existence of a positive interfacial energy will increase the energy required to form small particles with high curvature, and these particles will exhibit an increased vapor pressure.
More specifically, the Gibbs–Thomson effect refers to the observation that small crystals that are in equilibrium with their liquid, melt at a lower temperature than large crystals.
In cases of confined geometry, such as liquids contained within porous media, this leads to a depression in the freezing point / melting point that is inversely proportional to the pore size, as given by the Gibbs–Thomson equation.
[1] This behaviour is closely related to the capillary effect and both are due to the change in bulk free energy caused by the curvature of an interfacial surface under tension.
[2][3] The original equation only applies to isolated particles, but with the addition of surface interaction terms (usually expressed in terms of the contact wetting angle) can be modified to apply to liquids and their crystals in porous media.
As such it has given rise to various related techniques for measuring pore size distributions.
However, simple cooling of an all-liquid sample usually leads to a state of non-equilibrium super cooling and only eventual non-equilibrium freezing.
To obtain a measurement of the equilibrium freezing event, it is necessary to first cool enough to freeze a sample with excess liquid outside the pores, then warm the sample until the liquid in the pores is all melted, but the bulk material is still frozen.
Then, on re-cooling the equilibrium freezing event can be measured, as the external ice will then grow into the pores.
[4][5] This is in effect an "ice intrusion" measurement (cf.
mercury intrusion), and as such in part may provide information on pore throat properties.
The melting event can be expected to provide more accurate information on the pore body.
For an isolated spherical solid particle of diameter
in its own liquid, the Gibbs–Thomson equation for the structural melting point depression can be written:[6]
where: Very similar equations may be applied to the growth and melting of crystals in the confined geometry of porous systems.
In cylindrical pores there is some evidence that the freezing interface may be spherical, while the melting interface may be cylindrical, based on preliminary measurements for the measured ratio for
[7] Thus for a spherical interface between a non-wetting crystal and its own liquid, in an infinite cylindrical pore of diameter
where: As early as 1886, Robert von Helmholtz (son of the German physicist Hermann von Helmholtz) had observed that finely dispersed liquids have a higher vapor pressure.
[11] By 1906, the German physical chemist Friedrich Wilhelm Küster (1861–1917) had predicted that since the vapor pressure of a finely pulverized volatile solid is greater than the vapor pressure of the bulk solid, then the melting point of the fine powder should be lower than that of the bulk solid.
[12] Investigators such as the Russian physical chemists Pavel Nikolaevich Pavlov (or Pawlow (in German), 1872–1953) and Peter Petrovich von Weymarn (1879–1935), among others, searched for and eventually observed such melting point depression.
[13] By 1932, Czech investigator Paul Kubelka (1900–1956) had observed that the melting point of iodine in activated charcoal is depressed as much as 100 °C.
[14] Investigators recognized that the melting point depression occurred when the change in surface energy was significant compared to the latent heat of the phase transition, which condition obtained in the case of very small particles.
[15] Neither Josiah Willard Gibbs nor William Thomson (Lord Kelvin) derived the Gibbs–Thomson equation.
[16] Also, although many sources claim that British physicist J. J. Thomson derived the Gibbs–Thomson equation in 1888, he did not.
[17] Early in the 20th century, investigators derived precursors of the Gibbs–Thomson equation.
[18] However, in 1920, the Gibbs–Thomson equation was first derived in its modern form by two researchers working independently: Friedrich Meissner, a student of the Estonian-German physical chemist Gustav Tammann, and Ernst Rie (1896–1921), an Austrian physicist at the University of Vienna.
In 1871, William Thomson published an equation describing capillary action and relating the curvature of a liquid-vapor interface to the vapor pressure:[23]
where: In his dissertation of 1885, Robert von Helmholtz (son of German physicist Hermann von Helmholtz) showed how the Ostwald–Freundlich equation
For example, in the case of some authors, it's another name for the "Ostwald–Freundlich equation"[29]—which, in turn, is often called the "Kelvin equation"—whereas in the case of other authors, the "Gibbs–Thomson relation" is the Gibbs free energy that's required to expand the interface,[30] and so forth.