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The technique is closely related to using gas adsorption to measure pore sizes, but uses the Gibbs–Thomson equation rather than the Kelvin equation.They are both particular cases of the Gibbs Equations of Josiah Willard Gibbs: the Kelvin equation is the constant temperature case, and the Gibbs–Thomson equation is the constant pressure case. [1]
Diagram of thermodynamic surface from Maxwell's book Theory of Heat.The diagram is drawn roughly from the same angle as the upper left photo above, and shows the 3D axes e (energy, increasing downwards), ϕ (entropy, increasing to the lower right and out-of-plane), and v (volume, increasing to the upper right and into-plane).
The Gibbs adsorption isotherm for multicomponent systems is an equation used to relate the changes in concentration of a component in contact with a surface with changes in the surface tension, which results in a corresponding change in surface energy. For a binary system, the Gibbs adsorption equation in terms of surface excess is
The Marangoni effect (also called the Gibbs–Marangoni effect) is the mass transfer along an interface between two phases due to a gradient of the surface tension. In the case of temperature dependence, this phenomenon may be called thermo-capillary convection [ 1 ] or Bénard–Marangoni convection .
Gibbs emphasized that for solids, the surface free energy may be completely different from surface stress (what he called surface tension): [14]: 315 the surface free energy is the work required to form the surface, while surface stress is the work required to stretch the surface. In the case of a two-fluid interface, there is no distinction ...
The discontinuity in , and other properties, e.g. internal energy, , and entropy,, of the substance, is called a first order phase transition. [12] [13] In order to specify the unique experimentally observed pressure, (), at which it occurs another thermodynamic condition is required, for from Fig.1 it could clearly occur for any pressure in the range .
When perfectly pure, the interface between fluids usually displays only surface tension. [1] The stress within a fluid interface can be affected by the adsorption of surfactants in several ways: Change in the surface concentration of surfactants when the in-plane flow tends to alter the surface area of the interface (Gibbs' elasticity). [2]
Surface stress was first defined by Josiah Willard Gibbs [1] (1839–1903) as the amount of the reversible work per unit area needed to elastically stretch a pre-existing surface. Depending upon the convention used, the area is either the original, unstretched one which represents a constant number of atoms, or sometimes is the final area ...