Application of the Gibbs Equation to the Adsorption of Nonionic Surfactants and Polymers at the Air–Water Interface: Comparison with Surface Excesses Determined Directly using Neutron Reflectivity

Four recent papers by Menger et al. have questioned methods of analysis of surface tension (ST) data that use the Gibbs equation to obtain the surface excess (Γ) of a surfactant at the air–water interface. There have been two responses which challenge the assertions of Menger et al. and a response from Menger et al. We use directly determined values of Γ from a range of neutron reflectometry (NR) data to examine some of the issues that are relevant to these seven papers. We show that there is excellent agreement between NR measurements and careful ST analyses for a wide range of nonionic adsorbents, including surfactants and polymers. The reason it is possible to obtain good agreement near the critical micelle concentration (CMC) is that nonionic surfactants generally seem to saturate the surface before the CMC is reached and this makes it relatively easy to determine the limiting slope (and hence Γ) of the ST-log(concentration) plot at the CMC. Furthermore, there is also generally good agreement between ST and NR over the whole range of concentrations below the CMC until depletion effects become important. Depletion effects are shown to become important at higher concentrations than expected, which brings them into the range of many experiments, including techniques other than ST and NR. This is illustrated with new measurements on the biosurfactant surfactin. The agreement between ST and NR outside the depletion range can be regarded as a mutual validation of the two methods, especially as it is demonstrated independently of any model adsorption isotherms. In the normal experimental situation NR is less vulnerable to depletion than ST and we show how NR and a single ST measurement can be used to determine the hitherto undetermined CMC of the nonionic surfactant C18E12, which is found to be 1.3 × 10–6 M.