Disjoining pressure (symbol Πd), in surface chemistry, according to an IUPAC definition, arises from an attractive interaction between two surfaces. For two flat and parallel surfaces, the value of the disjoining pressure (i.e., the force per unit area) can be calculated as the derivative of the Gibbs energy of interaction per unit area in respect to distance (in the direction normal to that of the interacting surfaces). There is also a related concept of disjoining force, which can be viewed as disjoining pressure times the surface area of the interacting surfaces.
The concept of disjoining pressure was introduced by Derjaguin (1936) as the difference between the pressure in a region of a phase adjacent to a surface confining it, and the pressure in the bulk of this phase.
- Πd - disjoining pressure, N/m2
- A - the surface area of the interacting surfaces, m2
- G - total Gibbs energy of the interaction of the two surfaces, J
- x - distance, m
- indices T, V and A signify that the temperature, volume, and the surface area remain constant in the derivative.
- P - pressure in a film, Pa
- P0 - pressure in the bulk of the same phase as that of the film, Pa.
Disjoining pressure is interpreted as a sum of several interactions: dispersion forces, electrostatic forces between charged surfaces, interactions due to layers of neutral molecules adsorbed on the two surfaces, and the structural effects of the solvent.
- AH - Hamaker constant, J
- δ0 - liquid film thickness, m
- ω(ρ,z) - solid-liquid potential, J/m6
- Wtotal - , total system free energy including surface excess energy and free energy due to solid-liquid interactions, J/m2
- ζL - meniscus shape, m
- ζ'L - slope of meniscus shape, 1
In the theory of liquid drops and films, the disjoining pressure can be shown to be related to the equilibrium liquid-solid contact angle through the relation
where is the liquid-vapor surface tension and is the precursor film thickness.
- ""Disjoining pressure". Entry in the IUPAC Compendium of Chemical Terminology ("The Gold Book"), the International Union of Pure and Applied Chemistry, 2nd edition, 1997".
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