*4.4. Time-Resolved Surface Potential*

The main feature we want to stress about the surface potential results is the existence of oscillations in ϕ during the adsorption process as shown in Figure 6. Despite the variability observed from each independent experiment, the qualitative behavior is always the same and for all surfactant concentrations. The several "relaxations" observed can be roughly fitted with exponentials:

$$
\phi = \phi\_0 + \Lambda \phi \exp\left(-\frac{t}{\tau}\right) \tag{8}
$$

Some of the results of those fittings are shown in the figures. The number of processes observed in surface potential experiments seem to be related to the several processes observed in dynamic surface tension. However, the times and characteristic times are different. The differences found in the time when the surface potential and surface tension change is probably due to the way in which time-resolved surface potential measurements are done. After the concentration impulse, there is a time delay, because of the concentration homogenization in bulk, before adsorption takes place. Despite that, it is clear that the large ϕ(*t*) oscillations are not replicated as large oscillations in surface tension. This is an indication that the behavior of ϕ is due to the reorganization of counterions at the interfacial region and not due to the migration of surfactant molecules into and out to the interface, at least in such amounts that could produce appreciable changes in the surface tension. We could rationalize the results as follows: First the G12-2-12 surfactant adsorbs onto the interface producing an increase of the surface potential from that of pure water. This process is fast and consistent with the decrease of the surface tension (see Figures 6 and 7). The drop in surface potential that follows, could be due to the reorganization, redistribution, and condensation of charges, resulting in a temporal decrease of the measured surface potential. After that, and because the condensation of counter ions, a decrease in the charge repulsion among surfactant molecules, at the interface, would allow more surfactant molecules to adsorb, thereby producing a subsequent increase of the surface potential, and a slow decrease of surface tension, until the final equilibrium value is reached. This last process lasts from hundreds to thousands of seconds. The characteristic times obtained from fittings with Equation (8), labelled as τend in Figures 6 and 7, span from 700 to 3500 s. It is worth mentioning here that these results help to explain the behavior of the surface step-compression rheology observed in these systems [11].

A final comment is needed about the apparent differences observed on the time-dependent surface potential curves of Figure 7. In those figures (see insets), we observe that the behavior for *c*s = 0.5 mM (and also for *c*s = 1mM in Figure 6) is different from those at lower surfactant concentrations. First note that, for *c*s = 0.1 and 0.2 mM, the change in the equilibrium surface potential goes through a maximum (Figure 8). This is probably because the interface is less saturated than for *c*<sup>s</sup> = 0.5 (see Figure 3b), therefore, the distances between charged heads are larger and the condensation of counterions onto the interface lower for *c*<sup>s</sup> = 0.1 and 0.2 (the distances between charges are larger than the Bjerrum length) than for *c*<sup>s</sup> = 0.5 mM. For this last concentration, the distances between charged surfactant heads at the interface are close to the Bjerrum length, thus, what we observe in the time-dependent surface potential after the first surfactant adsorption, could be a fast condensation of counterions onto

the interface, followed by a slow surfactant adsorption until equilibrium is reached, a behavior not observed for the two lower concentrations.
