Limitations in the use of surface tension and the Gibbs equation to determine surface excesses of cationic surfactants.

Neutron reflection (NR) and surface tension (ST) are used to show that there are serious limitations in applying the Gibbs equation accurately to ST data of cationic surfactants to obtain the limiting surface excess, Γ(CMC), at the critical micelle concentration (CMC). Nonionic impurities in C12TABr and C16TABr have been eliminated by extensive purification to give ST - ln(concentration) (σ - ln c) curves that are convex with respect to the ln c axis around the CMC, which is characteristic of a finite micellization width. Because NR shows that the surface excess often continues to increase at and above the CMC, this finite width makes it impossible to apply the Gibbs equation to obtain Γ(CMC) without knowledge of the effect of aggregation on the activity. NR data made it possible to apply the integrated Gibbs equation to the ST below the onset of the convex region of the σ - ln c curve and show that for C12TABr the micellization width causes the ST to underestimate Γ(CMC) by 12%. Hexadecyltrimethylammonium (C16TA) sulfate is used to show that divalent ion impurities are not a significant problem. For cationic surfactants, further errors are associated with ST methods that rely on complete wetting. Measurements using ring, plate, and bubble shape analyses indicate that with ring and plate incomplete wetting occurs at or above the CMC and may extend to lower concentrations and also causes the ST-Gibbs analysis to underestimate the surface excess. In combination with ion association and preaggregation in cationic gemini surfactants, this can cause errors as large as 100% in Γ(CMC). Comparison of ellipsometry and NR for C16TAX in 0.1 M KX (X = F or Cl) shows that ellipsometry cannot, as yet, be quantitatively modeled accurately enough for surface excess determination independent of NR calibration.