Gibbs isotherm

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:

where

Different influences at the interface may cause changes in the composition of the near-surface layer Substances may either accumulate near the surface or, conversely, move into the bulk. The movement of the molecules characterizes the phenomena of adsorption. Adsorption influences changes in surface tension and colloid stability. Adsorption layers at the surface of a liquid dispersion medium may affect the interactions of the dispersed particles in the media and consequently these layers may play crucial role in colloid stability The adsorption of molecules of liquid phase at an interface occurs when this liquid phase is in contact with other immiscible phases that may be gas, liquid, or solid

Surface tension describes how difficult it is to extend the area of a surface (by stretching or distorting it). If surface tension is high, there is a large free energy required to increase the surface area, so the surface will tend to contract and hold together like a rubber sheet.

There are various factors affecting surface tension, one of which is that the composition of the surface may be different from the bulk. For example, if water is mixed with a tiny amount of surfactants (for example, hand soap), the bulk water may be 99% water molecules and 1% soap molecules, but the topmost surface of the water may be 50% water molecules and 50% soap molecules. In this case, the soap has a large and positive "surface excess". In other examples, the surface excess may be negative: For example, if water is mixed with an inorganic salt like sodium chloride, the surface of the water is on average less salty and more pure than the bulk average.

Consider again the example of water with a bit of soap. Since the water surface needs to have higher concentration of soap than the bulk, whenever the water's surface area is increased, it is necessary to remove soap molecules from the bulk and add them to the new surface. If the concentration of soap is increased a bit, the soap molecules are more readily available (they have higher chemical potential), so it is easier to pull them from the bulk in order to create the new surface. Since it is easier to create new surface, the surface tension is lowered. The general principle is:

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