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
− d γ = Γ 1 d μ 1 + Γ 2 d μ 2 , {\displaystyle -\mathrm {d} \gamma =\Gamma _{1}\,\mathrm {d} \mu _{1}+\Gamma _{2}\,\mathrm {d} \mu _{2},}
where
γ {\displaystyle \gamma } is the surface tension,
Γ i {\displaystyle \Gamma _{i}} is the surface excess concentration of component i,
μ i {\displaystyle \mu _{i}} is the chemical potential of component i.
Adsorption 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
Conceptual explanation of equation 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:
When the surface excess of a component is positive, increasing the chemical potential of that component reduces the surface tension. Next consider the example of water with salt. The water surface is less salty than bulk, so whenever the water's surface area is increased, it is necessary to remove salt molecules from the new surface and push them into bulk. If the concentration of salt is increased a bit (raising the salt's chemical potential), it becomes harder to push away the salt molecules. Since it is now harder to create the new surface, the surface tension is higher. The general principle is:
When the surface excess of a component is negative, increasing the chemical potential of that component increases the surface tension. The Gibbs isotherm equation gives the exact quantitative relationship for these trends.
Location of surface and defining surface excess
Location of surface In the presence of two phases (α and β), the surface (surface phase) is located in between the phase α and phase β. Experimentally, it is difficult to determine the exact structure of an inhomogeneous surface phase that is in contact with a bulk liquid phase containing more than one solute. Inhomogeneity of the surface phase is a result of variation of mole ratios. A model proposed by Josiah Willard Gibbs proposed that the surface phase as an idealized model that had zero thickness. In reality, although the bulk regions of α and β phases are constant, the concentrations of components in the interfacial region will gradually vary from the bulk concentration of α to the bulk concentration of β over the distance x. This is in contrast to the idealized Gibbs model where the distance x takes on the value of zero. The diagram to the right illustrates the differences between the real and idealized models.
Definition of surface excess In the idealized model, the chemical components of the α and β bulk phases remain unchanged except when approaching the dividing surface. The total moles of any component (Examples include: water, ethylene glycol etc.) remains constant in the bulk phases but varies in the surface phase for the real system model as shown below.
In the real system, however, the total moles of a component varies depending on the arbitrary placement of the dividing surface. The quantitative measure of adsorption of the i-th component is captured by the surface excess quantity. The surface excess represents the difference between the total moles of the i-th component in a system and the moles of the i-th component in a particular phase (either α or β) and is represented by:
… excerpt ends here. Continue reading the full article.
