Disjoining force
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.
Disjoining pressure can be expressed as:
where:
Using the concept of the disjoining pressure, the pressure in a film can be viewed as:
where:
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.
Classic theory predicts that the disjoining pressure of a thin liquid film on a flat surface as follows,
where:
For a solid-liquid-vapor system where the solid surface is structured, the disjoining pressure is affected by the solid surface profile, ζS , and the meniscus shape, ζL
where:
The meniscus shape can be by minimization of total system free energy as follows
where:
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
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