The surface tension as a function of concentration is shown in Fig. 2. A break can be observed at concentration 6 × 10−2 mM with a certain levelling of the surface tension but still decreasing to complete levelling off around 1 × 10−1 mM. From the slope just before the first levelling at 6 × 10−2 mM the surface excess can be calculated according to the Gibbs adsorption isotherm in eqn. (8):where γ is the surface tension, c the bulk surfactant concentration, R the gas constant, T the absolute temperature. The parameter n is the effective number of dissociated species per molecule for solutions without added salt. In the case of 1010R surfactant n = 3; the cationic surfactant plus two chloride ions (see Fig. 1).
The experimental value of surface excess was 1.19 × 10−6 mol m−2. From the surface excess Γ, the area per molecule is obtained via Avogadro's number, eqn. (9).
The calculated area per surfactant molecule was 1.4 nm2. The consideration of smaller adsorbing species numbers would lead to smaller areas per molecule, i.e. 0.93 nm2 for n = 2 and 0.47 nm2 for n = 1.
The surface tension curve could be qualitatively described taking in consideration the ionisation of the surfactant and the concentration dependence on the relative concentration of species. See below for a more detailed discussion about the species in solution. At low surfactant concentration the dominant species would be the singly charged molecule, which, because of lower water solubility is expected to be more surface active than the doubly charged one. At high concentration the proportion of doubly charged species will dominate, producing a modest decrease of surface tension because of the adsorption of the additional chloride ion. The higher slope at very low concentration, if true, could be due to the adsorption of the non-charged species. However, the amount of this form in the acid–base equilibrium seems to be too low to justify this affirmation. The shallow minimum around 10−4 M could be due to the desorption of the lower charged species by competition with the higher charged species and their solubilisation in micelles, much in the same way the dodecanol present in dodecylsulfate solutions induce a minimum in the surface tension around the critical micellar concentration.
The pH as a function of surfactant concentration at 25 °C is shown in Fig. 3. Because the surfactant molecule can dissociate in several species, the concentration behaviour is relatively complex. The species in solution and the different equilibrium are shown in Scheme 1. The salt dissociation is expected to be a complete reaction.
Without taking into consideration the possibility of preferential adsorption of certain species or the aggregation in the bulk solution and assuming dilute ideal behaviour, we can solve the acid–base equilibrium equations resulting in eqn. (10):where Ca is the total concentration of surfactant, K1, K2 are the first and second dissociation constants and Kw the ionic product of water.
It should be mentioned that the water used does not have neutral pH; this acidity is usually attributed to CO2 solubilisation which makes the pH lower than 7. If we take this additional equilibrium into account, the results are very close to those obtained from eqn. (3) except for the lowest concentration. The dissociation constant of the guanidine group in the literature are of the order of 10−12.[29] By assuming K2 = 10−12 we can calculate K1. In Fig. 4 we show the calculated K1. It is clear that the dissociation constant is much higher that it could be assumed regarding the literature, the surfactant behaves as a weak acid (comparable to acetic acid), not as a very weak acid as expected for an ammonium group (the dissociation constant for protonated ethylamine is around 2.5 × 10−11). The variation of this dissociation constant with concentration could be due to the aggregation of the molecule (note the maximum apparent dissociation constant around 1 mM). For the surfactant to release more protons (higher dissociation constant) in the aggregated state would mean that the aggregation takes place preferably with the dissociated species (neutral species in the present case). We should also take into account how adsorption of the surfactant on the glass electrode could influence those results. On the one hand it is expected that adsorption at interfaces will be stronger for the lower charged molecules (the more dissociated ones with this surfactant). However, the positive charge on the surfactant could also imply the contrary effect, higher adsorption of the more charged species because of the usual free negative charges on glass surfaces. If the adsorption of neutral species is favoured, then the concentration of protons would be locally higher than in the bulk (see Scheme 1), explaining the relatively high dissociation constant found. If adsorption of the divalent cation was favoured then the concentration of protons would be lower than in the bulk, meaning that the apparent dissociation constant would be still higher than measured.
The higher than expected acid constant for this surfactant contrasts with the less acid than expected behaviour encountered in fatty acids.[30] The reason for this difference should lie in the different charges on the fatty acids (the neutral molecule is the acid form) and in 1010R where the neutral form is the dibasic species. Kanicky et al[30]. explain their results on the apparent pK of fatty acids with the argument that a monolayer with half the molecules ionised allow for the stabilisation of the acidic proton of one of the molecules in the pair. Following this argument with 1010R we should expect for the singly ionised and non ionised species to be favoured. This could explain the high acid constant. Letting pK1 and pK2 be adjustable parameters the best fit produces similar values for both constants (values around 5), however, the statistical error in their determination becomes quite high. Moreover, the pH-concentration curve for the same molecule acetylated in the amino group seems to indicate that the apparent pK of the guanidine group is also of the order of 5[31].
In Fig. 5 the scattered intensity at 90° is plotted as a function of concentration for the surfactant 1010R at 25 °C. Two changes of slope are apparent in this figure. The first one, at a concentration of about 4 × 10−2 mM is close to the c.m.c. detected by surface tension while the second one, around 5 × 10−1 mM, is close to the c.m.c. detected by conductivity and fluorescence.[5] The closed symbols in Fig. 5 show the detail of the low concentration samples, note that for those points the intensity has been magnified by a factor of 100. For reference, the level of our background water is shown as a horizontal line with the same scale as the lower concentrations. Although the reproducibility of the intensity data is not very good at very low concentrations, it is clear that, even at those low concentrations some aggregation must be present, the intensity before background subtraction, is, at least, double than the background intensity. For some of the concentrations the intensity as a function of the scattering angle was recorded and this effect was more pronounced at lower scattering angles.
In Fig. 6 we show a selection of the angular dependence of the scattered light for different concentrations. The concentration of 8 × 10−3 mM (Fig. 6a) is lower than the c.m.c. as obtained by surface tension. The 6 × 10−2 mM (Fig. 6b) sample lies between the c.m.c. obtained by surface tension and that obtained by conductivity. The sample 6 × 10−1 mM (Fig. 6c) lies around the c.m.c. detected by conductivity and that with 1.3 mM (Fig. 6d) is already above that value. In each plot three sets of points are shown, they correspond to the intensity, intensity multiplied by the scattering vector modulus q and intensity multiplied by the squared scattering vector modulus as a function of the squared scattering vector modulus. Those correspond to Guinier plots for globular, rod and lamella respectively. Linear plots are obtained if the objects have the corresponding geometry.[27] Although the scattering vector range is not large enough to directly prove the geometry, we can appreciate that changes are occurring at those concentrations. The triangles, which correspond to Iq2 (lamellar representation) have negative slope for 8 × 10−3 mM (Fig. 6a) and positive slope for 1.3 mM (Fig. 6d). Positive slopes are incompatible with the structure detected in this range. Therefore while 8 × 10−3 mM could correspond to globular aggregates, 1.3 mM can not correspond to lamellae. Moreover, the consideration of the apparent molecular weight calculated form the intensity at 45° and the apparent gyration radii obtained from the Guinier plot, eqn. (5), using the angles of 45, 60 and 75°, shows that a model of compact spheres is inconsistent. The molecular weight calculated from the gyration radii is always more than one order of magnitude bigger than the experimental value. We should also note that performing these calculations the condition of validity of eqn. (5) is not strictly accomplished and qRg ∼ 2 in the range of calculation. The structure that reconciles the overall intensity with its angular dependence is that of vesicles at low concentrations and ribbons at the higher concentration.
To further investigate this possible assignation we have tried to fit the form factor of vesicles and cylinders to the experimental data considering that the RDG approximation applies,[28] together with the absence of interparticle interaction due to high dilution. We have calculated the form factors analytically or by the Fourier transform of the pair distribution function of the corresponding object.[24–25]
We have further scaled the model to the absolute scattered scale to compare the goodness of the fit. The intensity and intensity multiplied by q and q2 are shown in Fig. 6. The intensity trend as a function of angle is quite well represented by the form factor of the ellipsoidal vesicles or cylinders with elliptical section. Because the scattering vector range is relatively small, the dependence of the intensity trend with bilayer thickness is very weak, and this parameter mainly depends on the absolute level of intensity.
The fitting parameters for ellipsoidal vesicles are shown in Table 1; a, b and c are the external axes of the ellipsoid and d is the thickness of the bilayer. For the cylindrical model (1.3 mM and 5 × 10−2mM at low pH) a corresponds to the length of the cylinder; b and d are the semiaxes of the elliptical section of the cylinder. For those two last samples the elliptical vesicles could not fit the experimental values even with extreme parameters. The aggregation number, molecular weight and area per surfactant molecule have been calculated taking into account a surfactant molecular volume of 1.1 nm3. The calculated area per surfactant molecules seem excessive, not just compared to the values we obtain from surface tension but with the usual values found for double chain surfactants.[32] We have to mention that the most concentrated sample can also be fitted by a flexible rod model with Gaussian statistics. In this case the fitted gyration radius corresponds to 78.6 nm and the molecular mass of the aggregate to 1.7 × 107, which is close to the value obtained from the elliptical section cylinder. It is clear from the data that the aggregation changes of this surfactant with concentration influences both the total mass of the aggregate and the form of the aggregate.
A slightly better quality of fit can be obtained by using a polydisperse population of vesicles with a Schultz distribution[33] for the radii and constant thickness. The fitted parameters are shown in Table 2. R and σ are the mean and width of the Schultz distribution, d is the bilayer thickness, Am the area per molecule in the aggregates and Mw the aggregate molecular weight. From this data it is clear that the global size of the aggregates decreases as the concentration of surfactant increases, as the distribution width is nearly constant the relative polydispersity increases. The vesicle thickness and, the calculated area per molecule of surfactant have been scaled to reach the measured absolute intensity. The vesicular thickness decreases as the concentration increases and the area per molecule increases. An increase in area per molecule is what could be expected from the consideration of the charge per molecule. This model also fails for the most concentrated sample; small vesicles very polydispersed with large thickness and small area per molecule would be obtained. The quality of the fit in this case is also clearly worse as can be observed from the large uncertainty of the parameters.
As the anisometry of the elliptical section cylinders is very large, the same quality of fit can be obtained by using a ribbon model. The parameters of this fit are given in Table 3 for a 1.3 mM sample and for the 5 × 10−2 mM sample in presence of HCl with a final acid concentration of 0.04 M. The fit of both samples give reasonable agreement with the same area per surfactant molecule of 1.2 nm2 reinforcing the trend of increasing area per molecule as the surfactant concentration increases or with decreasing pH.
The 1010R surfactant has a chiral carbon atom in the arginine residue (Fig. 1). In the literature some examples of ribbons formed by surfactants with a chiral carbon atom are described.[34,35] The ribbons in those papers preferably adopt a helical structure. In the range of our experiment this helical structure has not any noticeable influence if the period of the helix is moderate.
In parallel, quasielastic light scattering was performed on the most concentrated samples. Although these results were not obtained in ideal conditions (large aperture of the photomultiplier) they agree overall with these observations. When forcing the model to produce a single population, this was a very wide distribution centred around 99 nm and, when allowed to fit a bimodal distribution the peaks were centred at 59 and 205 nm respectively, agreeing with the dimensions of the ribbon model.
The transition from vesicular to cylindrical geometry could be caused by an increase in the area per surfactant molecule or a decrease of the hydrophobic tail length or a combination of both. Not much can be said about this point with the present data, only the trend is apparent. The concentration used in the calculations corresponds to the nominal concentration. We have to note that if the aggregation corresponds only to a part of the surfactant (as it occurs with classical surfactants for which the concentration of aggregates correspond to the nominal concentration minus the c.m.c). thickness and area per molecule could be different. However, to keep a constant bilayer thickness we would need a concentration dependent micellar concentration. This is not unreasonable in view of the acid–base behaviour of those surfactants. The higher the concentration of surfactant, the higher the proportion of the more charged species and higher the critical micellar concentration would be. Moreover, this interpretation could reconcile de widely different values of critical micellar concentration depending on the method used for its determination. It has been found that the values of critical micellar concentration are about one order of magnitude lower as obtained from surface tension measurements than that obtained from conductivity or fluorescence. Surface tension measurements will sense first the lower charged species; as the concentration increases the acid–base equilibrium favours the presence of more charged species, which will also adsorb and replace the lower charged species. Although, not very clear with the present data, this change could correspond to the very shallow minimum that is observed around 10−1 mM. The more charged species would then micellate. This explanation also agrees qualitatively with the observed intensity as a function of concentration. At very low concentration some non-negligible scattering occurs. This can be seen in Fig. 5, the closed symbols are a magnification of the open symbols and are compared with the level of the subtracted background, which has a magnitude a few times above the water background scattering. Between 10−3 and 10−1 mM the intensity starts growing with concentration and from 1 mM the intensity starts growing at a faster rate. In the very low concentration some aggregation of the non-charged species can be expected even at those very low concentrations. Increasing concentration the dominant species would be the singly charged species and at even higher concentrations the double charged species.
Additional proof of the effect of pH on the aggregation of this surfactant was obtained by adding a small amount of hydrochloric acid solution to a sample in which the preferred structure was vesicular. The changes observed are quite dramatic as it can be observed in Fig. 7. In this figure the scattered intensity as a function of dispersion modulus is plotted for a sample 5 × 10−2 mM and the same sample after addition of aqueous HCl solution with a final concentration of 0.04 M HCl. The intensity at 90° dropped by a factor of four and the curvature of the plot also changed. This is more easily seen by comparing the Iq curve for both samples. Without acid addition this curve has a clear negative slope in most of the range while the acidified sample presents a flat Iq behaviour. This change can be compared to the change observed between Fig. 6b and Fig. 6d.
The curves in Fig. 7 correspond to polydisperse vesicles for the original sample and a ribbon model for the acidified sample. The parameters of the fits are also shown in Tables 1, 2 and 3. Those parameters compare close to the sample of 6 × 10−2 mM and 1.3 mM respectively, with assigned vesicular and ribbon structures respectively. This shows that increasing concentration and decreasing pH have a similar effect on the aggregates and further strengthen the conclusion that the surfactant concentration influences the structure via a pH effect.