Derivation of excess surface concentration
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Surface excess concentration
The surface excess concentration Γ is the area-related concentration of a surfactant at the surface or interface. It has the unit mol/m2.
Background
Due to the adsorption of a surfactant at the surface or interface, the surfactant concentration at this surface is very much higher than that of the volume phase. The surface tension s or interfacial tension correlates directly with this surface excess concentration Γ:

(R = Universal gas constant; T = Absolute temperature; σ = Surface tension; c = Molar surfactant concentration)
Strictly speaking, the surface excess concentration Γis the difference between the interfacial concentration ΓI and the concentration at a virtual interface in the interior of the volume phase ΓV :

However, as the surface excess concentration in surfactants is very much greater than ΓV, this is usually equated with the interfacial concentration.
The surface excess concentration can be calculated when measuring the CMC from the slope of the concentration-dependent region of the surface tension based on the equation given above. The result can be combined with results from bubble pressure tensiometer measurements in order to determine the adsorption coefficient.
Glossary
Pendant drop
The surface excess concentration Γ is the area-related concentration of a surfactant at the surface or interface. It has the unit mol/m2.
Background
Due to the adsorption of a surfactant at the surface or interface, the surfactant concentration at this surface is very much higher than that of the volume phase. The surface tension s or interfacial tension correlates directly with this surface excess concentration Γ:

(R = Universal gas constant; T = Absolute temperature; σ = Surface tension; c = Molar surfactant concentration)
Strictly speaking, the surface excess concentration Γis the difference between the interfacial concentration ΓI and the concentration at a virtual interface in the interior of the volume phase ΓV :

However, as the surface excess concentration in surfactants is very much greater than ΓV, this is usually equated with the interfacial concentration.
The surface excess concentration can be calculated when measuring the CMC from the slope of the concentration-dependent region of the surface tension based on the equation given above. The result can be combined with results from bubble pressure tensiometer measurements in order to determine the adsorption coefficient.
Glossary
Pendant drop
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