JOURNAL OF COSMETIC SCIENCE 62 Figure 2. Viscosity as a function of shear rate of formulations of 9 wt% SLES/3 wt% APB/2 wt% NaCl (pH 5.5) using different alkyl APBs. Formulations. For the rheological characterization of the surfactant mixtures, a simple model formulation consisting of 9 wt% SLES, 3 wt% betaine, and 2 wt% NaCl was used. The pH was adjusted to 5.5 using citric acid. Rheology. The shear viscosity of the formulations was measured using a MCR 302 rheom- eter (Anton Paar, Ostfi ldern, Germany) with a plate–plate geometry. The upper plate had a diameter of 50 mm. Oscillatory measurements as a function of frequency were con- ducted on a StressTech rheometer by Rheologica (formerly Lund, Sweden now available at TS RheoSystems, State College, PA) with a plate–plate geometry, with a diameter of 40 mm the applied stress was 0.2 Pa. All measurements were conducted at 25°C. RESULTS AND DISCUSSION INFLUENCE OF THE ALKYL CHAIN LENGTH DISTRIBUTION IN ALKYL APBs The alkyl APBs used in the fi rst part of this study were all a variation of CAPB, as can be seen in Table I: fi rst the pure lauryl APB12, then two variants with an average of 12.7 carbon atoms in the fatty acid chain, APB12/14 with a narrow distribution and APB8/10 + 12/18 with a broad distribution, were obtained by using a mixture of the corresponding fatty acids, and fi nally the “real” triglyceride–based CAPB with a typical alkyl chain distribution Table I Alkyl Chain Length Distributions of the Betaines Used (n = narrow b = broad) Name Average alkyl chain length C8 (%) C10 (%) C12 (%) C14 (%) C16 (%) C18 (%) APB12 12.0 100 APB12/14 12.7 (n) 70 30 APB8/10 + 12/18 12.7 (b) 10 8 47 17 9 9 APBcoco 12.8 8 8 48 17 8 11 AEBcoco 12.8 8 8 48 17 8 11 AB12/14 12.7 (n) 70 30

RHEOLOGICAL PROPERTIES OF SURFACTANT FORMULATIONS 63 Figure 3. Plot of storage modulus G′ and loss modulus G″ versus frequency of a formulation of 9 wt% SLES/3 wt% APB12/2 wt% NaCl (pH 5.5) the inset shows same data as Cole–Cole plot (the semicircle is a guide for the eyes). of hydrogenated coconut oil was obtained. The differences in the chain length might be small, but they have a signifi cant infl uence on the shear viscosity of the model formula- tions SLES/APB/NaCl as shown in Figure 2. In all cases, the behavior is typical of rod- like micelles: a plateau at low shear rates, followed by shear thinning at higher shear rates. The level of the plateau, however, is quite different, for the broad alkyl chain length distribution being the lowest. Considering there is no additional thickener in these model formulations, all their viscosities were remarkably high. To study the origin of these viscosities, oscillatory rheological measurements were per- formed to determine the storage and loss moduli G′ and G″ as a function of frequency. In case of a network of rod-like micelles, the slopes G′ and G″ in a plot versus frequency should be 2 and 1, respectively. Figure 3 shows such a Maxwell plot exemplarily for the model formulation with APB12. At low frequencies, the slopes of G′ and G″ are just as expected for rod-like micelles. The crossover point of G′ and G″—aka structural relax- ation time, a measure of the exchange kinetics of the surfactants—was 0.5 Hz. The initial shear modulus, the plateau value of the storage modulus at high frequencies, which is a measure of the network density, is about 190 Pa. The inset in Figure 3 shows the same data as Cole–Cole plot the data in the accessible sensitivity range are all on a semicircle, confi rming the interpretation given above (2). For the other alkyl APBs, these plots are in general quite similar, but there are quantita- tive differences concerning the specifi c values (Table II). The addition of C14-APB leads Table II Results of Oscillatory Rheological Measurements of Formulations Containing 9 wt% SLES/3 wt% of APB/2 wt% NaCl (pH 5.5) for Different Alkyl APBs Name Structural relaxation time (Hz) Initial shear modulus G′ (Pa) APB12 0.50 190 APB12/14 0.35 220 APB8/10 + 12/18 0.72 145 APBcoco 0.50 160