Tensiometric determination of Gibbs surface excess and micelle point: a critical revisit

Amphiphile adsorption at the air/water interface lowers the surface tension (γ) of the solution. After a critical surfactant concentration (C), γ becomes constant (with a break in the γ-logC plot), which is considered the critical micelle concentration (CMC). At very low amphiphile concentration, γ decreases slowly, forming a plateau, then decreases sharply and often nonlinearly by a co-operative adsorption process till the second plateau is reached at CMC. To get the Gibbs surface excess (Γ) of the amphiphile relative to water, a polynomial equation of appropriate degree needs to be used, since the drop in γ progresses with continuous changing slope, which maximizes at CMC and becomes zero afterward. Recent research has evidenced that a complete saturated Gibbs monolayer may not always form at CMC; there may be formation of multilayer of micelles below the Gibbs monolayer, which cannot be assessed by ST measurements. A method like neutron reflectometry (NR) can evaluate the Γ beyond CMC. A procedure for determining Γ(max) from tensiometric results is herein proposed. Amphiphiles do sometimes show a linear decline in γ with logC followed by a break with a plateau at CMC. There, a single slope leading to a single surface excess quantity is obtained for the Gibbs equation at all concentrations up to CMC. Possible reasons for such results are given. Current conflicting ideas and criticisms on the issue of Gibbs equation and determination of Γ and Γ(max) have been addressed.