152 JOURNAL OF COSMETIC SCIENCE To more clearly describe the relative contributions of the monomeric SDS and the miceliar SDS to skin penetration, Figure 3(a-c) shows the total contributions of the monomeric and the miceliar fractions of SDS to Cs•i, for o• s = 1, 0.83, and 0.50 respectively, based on the regression data given above. Specifically, the SDS monomeric contribution to Cs•i, is a'C•,sos, and the three miceliar contributions to Cs•i, are b ß C(o• m = 1), c' C(o• m = 0.83), and d' C(o• m = 0.50). Figure 3(a-c) clearly shows that the SDS monomers make a contribution to Cs•i, that is larger than that of the miceliar SDS for the three o•s values examined, as seen by the empty bars (representing the monomeric contribution) always being larger than the solid bars (representing the miceliar contribution). It is only for o• = 1, the pure SDS case, that the micelies make a large contribution to Cs• , , particularly at the highest surfactant concentrations ex- amined (see Figure 3a). In Figures 3b and 3c, which correspond to the o• -- 0.83 and 0.50 surfactant mixtures, respectively, the miceliar contribution is almost non-existent. Indeed, considering the confidence interval for the coefficients c and d, it is apparent that the miceliar contributions include the possibility of a zero contribution to Cs• ,. There- fore, the monomer penetration model represents a reasonable approximation for the two SDS/C•2E 6 surfactant mixtures examined, where the miceliar SDS does not penetrate appreciably into the epidermis for the SDS concentrations examined (25, 50, and 100 raM). However, the reduction in Cs•i, observed with decreasing o• s, shown in Figures 1 and 2, results from both the reduction in the SDS monomer concentration and the reduction in the ability of the miceliar SDS to penetrate into the epidermis. Generalizing the observations made in the case of the SDS/C•2E 6 surfactant mixtures to other surfactant mixtures, it is plausible that the observed reduction in skin irritation upon mixing surfactants reported by several researchers occurs because both the toohomeric and the miceliar s•rfactant penetrations into the skin are diminished (6,24,26). At the high total surfactant concentrations commonly utilized in commercial surfactant products, the micellar contribution can be quite large, as demonstrated by the dose-dependent surfactant-induced skin irritation results reported in the literature (2,3,8,13,16,18). Consequently, any reduction in the ability of the micellar surfactant to penetrate into the skin, as reflected by lower values of the regression coefficients (such as b, c, and d), should have a significant impact on C_,• n at high total surfactant concentrations. In other words, reducing the miceliar contribution to Cs•i, should lead to a reduction in the skin irritation potential of the surfactant system contacting the skin. DYNAMIC LIGHT SCATTERING DETERMINATION OF SDS/C•2E 6 MIXED MICELLE SIZES In Figure 4, the hydrodynamic radii of the SDS/C•2E 6 mixed micelles are determined using DLS by extrapolating the effective hydrodynamic radii of these micelies to a zero micelie concentration. At the surfactant concentrations corresponding to Figure 4, O• m is predicted to be approximately equal to o•, and therefore, one can treat the micelies as having a constant O• m value over the entire surfactant concentration range examined (see Table I). This is important, because a change in o• m could lead to a change in the hydrodynamic radii of the micelies. (The hydrodynamic radii of the micelies determined using this method are reported in Table III.) According to the surfactant penetration model advanced in our recent paper (28), the size of the micelie determines its ability to penetrate into the SC. (Note that the discussion in the following section introduces the caveat that electrostatic interactions may also play a role.) The micelie penetration

PENETRATION OF MIXED MICELLES INTO THE EPIDERMIS 153 3.5 25 mMSDS 50 mMSDS 100 mMSDS 3.0 2.5 2.0 1.5 1.0 0.5 0.0 b 1.4 ! 25 mM SDS 50 mM SDS i 100 mM SDS 1.2 0.4 0.2 0.0 c I I 25 mM SDS 50 mM SDS 100 mM SDS Figure 3. The contribution of monomeric SDS (open bars) and miceliar SDS (solid bars) to Cj,•i,, calculated using the results of the multiple linear regression analysis for: (a) ots = 1, (b) ot• = 0.83, and (c) ors = 0.50. Adding up the contributions from the two bars yields the combined contribution of the SDS monomers and the miceliar SDS to Cs,•i ,. Note that the vertical axes in a-c are scaled differently.