EPIDERMAL PENETRATION OF SDS MICELLES 37 a b No Added PEO Only Free Micelies Some Added PEO Free and PEO-Bound Micelies c Excess Added PEO Only PEO-Bound Micelies Increasing PEO Concentration Figure 3. Schematic representation of the effect of increasing the PEO concentration in a SDS-PEO solution on the distribution of SDS in monomeric form, in free SDS micelies, and in PEO-bound SDS micelies at a fixed SDS concentration. (a) With no added PEO, only free SDS micelies and SDS monomers are present. (b) With intermediate concentrations of added PEO, there are both free SDS micelies and PEO-bound SDS micelies, as well as SDS monomers. (c) With excess added PEO, only PEO-bound SDS micelies and SDS monomers are present, as well as free PEO molecules. lOO 80 20 0.0 0.5 1.0 Wt% PEO 1.5 2.0 Figure 4. Predicted distribution of SDS in free SDS micelies (empty bars) and PEO-bound SDS micelies (solid bars) as a function of PEO concentration at 100 mM SDS (39). REGRESSION ANALYSIS OF THE CONTRIBUTIONS OF SDS MONOMERS, FREE SDS MICELLES, AND PEO-BOUND SDS MICELLES TO SDS PENETRATION INTO THE EPIDERMIS Figures 1, 2, and 5 indicate that there is a relationship between the concentration of SDS that is not bound to PEO and the amount of SDS that penetrates into the skin after five

38 JOURNAL OF COSMETIC SCIENCE 7 100 I I I •e 5 Some Free SDS Micelies i No Free SDS Miceli u•4 , • 2 ', 0.0 0.5 1.0 1.5 2.0 2.5 wt% PEO in the •D•-PEO Conicting •olution hours of skin exposure to an SDS+PEO solution. With this in mind, we wanted to quantify the relative contributions of SDS monomers, free SDS micelies, and PEO-bound SDS micelles in the contacting solution to the SDS concentration measured in the epidermis after five hours of exposure. A multiple linear regression was used for this quantification, using all the experimental data, prior to averaging, that was presented above relating the SDS concentration in the epidermis to the SDS concentration in the contacting solution. The simplest relationship among the three contributions to SDS penetration into the skin is a linear one since for Fickian diffusion from an infinite reservoir with a large concentration difference, the net permeant flux at a given time is directly proportional to the initial permeant concentration (47). This leads to the fol- lowing relation that formed the basis of our regression analysis: = a' C ............. + b'C& .... + ...... (3) where a, b, and c are weighting factors that were determined by the regression analysis (C• is the concentration of SDS in monomeric [i = monomers], free micellar [i = free micelies], or PEO-bound micellar [i = PEO-bound micelies] form) and Cj•i, , is the concentration of SDS in the dry epidermis, having units of mmols of SDS per gram of dry epidermis. For the regression analysis, C .............. was set to 8.7 mM, the CMC of SDS, when there were free SDS micelies, and to 5 mM, the CAC of SDS+PEO, when only PEO-bound SDS micelies were present, based on data for the CMC and the CAC of SDS in the presence of PEO (39). Cv•o_3o,,,•,,,i•.ezz• •. was determined using the predic- tive theory (39), and C/ ...... it,/& was determined from the mass balance on SDS (CsD S- Cv•O-3o,,,,,z,,i,-,/&-C ........... ), where Cso s is the total SDS concentration in the contacting solution.