116 JOURNAL OF COSMETIC SCIENCE concentration of radiolabeled SDS in the contacting solution did not change appreciably during the five-hour exposure to the skin. The concentration of radiolabeled SDS in the contacting solution was determined by using afproximately 100 µl of the contacting solution and assaying for the radioactivity of 1 C-SDS using the scintillation cocktail assay described above. Knowing the concentration of SDS in the contacting solution, C sos, the radioactivity of the contacting solution, C raddonor' the dry weight of the epidermis, m, and the radioac­ tivity of the epidermis, Crad kin ' we were able to determine the concentration of SDS in the dried epidermis, Csvs ,;, in ' using the following equation (11): crad,skin • Csvs CSDS,skin = C rad,donor • m DYNAMIC LIGHT-SCATTERING MEASUREMENTS (2) The aqueous SDS and SDS + 10 wt% glycerol solutions were prepared in Millipore­ filtered water with 100 mM of added NaCl. Note that 100 mM NaCl was added to screen potential electrostatic repulsions between the negatively charged SDS micelles while performing the dynamic light-scattering (DLS) measurements (11,34,36-39). After mixing, the solutions were filtered through a 0.02-µm Anotop 10 syringe filter (Whatman International, Maidstone, England) directly into a cylindrical scattering cell to remove any dust from the solution, and then sealed until use. Dynamic light scat­ tering (34) was performed at 25 ° C and a 90° scattering angle on a Brookhaven BI- 200SM system (Brookhaven, Holtsville, NY) using a 2017 Stabilite argon-ion laser (Spectra Physics) at 488 nm. The autocorrelation function was analyzed using the CONTIN program provided by the BIC dynamic light-scattering software (Brookhaven, Holtsville, NY), which determines the effective hydrodynamic radius, R h , of the scat­ tering entities using the Stokes-Einstein relation (3 5 ): - kBT R =- h 6m1D (3) where k8 is the Boltzmann constant, Tis the absolute temperature, 'YI is the viscosity of the aqueous salt solution, and D is the mean diffusion coefficient of the scattering entities. In order to measure the size of the SDS micelles in the aqueous SDS and in the SDS + 10 wt% glycerol solutions, while eliminating the effects of interparticle interactions, the effective hydrodynamic radii were determined at several different SDS concentrations, and then extrapolated to a zero micelle concentration, which corresponds to the CMC of SDS, 8.7 mM (11,34,36-39). Note that the viscosity of a 10 wt% glycerol aqueous solution is similar to that of water, and hence, viscosity effects did not play a significant role in these measurements. SURF ACE TENSION MEASUREMENTS We used surface tension measurements to determine the critical micelle concentration, CMC, of the SDS and of the SDS + 10 wt% glycerol aqueous micellar solutions. It is well known that as the surfactant concentration, X, is increased, both the hydrophobicity

SDS MICELLES IN SKIN BARRIER PERTURBATION 117 of the surfactant tails and the high water-air surface free energy promote the adsorption of the surfactant molecules onto the surface (40). The increase in the surface pressure due to surfactant surface adsorption leads to a lowering of the surface tension, er. Beyond a certain threshold surfactant concentration, the CMC, it becomes more favorable, from a free energy point of view, for the surfactant molecules added to the solution to form micelles, rather than to continue to adsorb at the surface. This is reflected in a negligible change in surface tension, er, with increasing surfactant concentration, X, beyond the CMC. The "break" in the er versus X curve, therefore, approximates the concentration at which micellization first takes place (40). In order to determine this "break," the equilibrium surface tensions of SDS in water and of SDS in water + 10 wt% glycerol were measured as a function of the logarithm of the SDS solution concentration using a Kruss K-11 tensiometer (Kruss, Charlotte, NC) with a platinum plate. Additional experimental details can be found in reference 41. The experimental uncertainty in the surface tension measurements was approximately 0.05 dyn/cm. The temperature was held constant at 25.0 ± 0.1 °C by a thermostatically controlled jacket around the sample. A plot of er as a function of the logarithm of the surfactant concentration, X, was generated using the procedure outlined above for the SDS and for the SDS + 10 wt% glycerol aqueous micellar solutions. Linear regression was used to determine the best fit line on either side of the break in the curve, and the value of the SDS concentration at the intersection of these two best-fit lines was taken as the experimental CMC value. THEORETICAL DETERMINATION OF THE RADIUS AND NUMBER DENSITY OF THE SKIN AQUEOUS PORES Tang et al. (7) have recently demonstrated the existence of a linear-log relationship between the mannitol skin permeability, PJ and the average skin electrical resistivity, R. Specifically, within statistical error, the following relation holds (7): log P = log C - log R (4) where C = (k B T/2z2Fc i00 e 0 )*(D H(},-p)/D: n H(A ion )) is a constant that depends on the average skin aqueous pore radius, r pore ' through H(A p ) and H(A ion ), as follows (7 ,8,42): 1 H(AJ = fll - 2.1044},.,. i + 2.089Af - 0.948A�), for Ai 0.4 (5) where i = p (permeant, in our case, mannitol) or ion, r p ore = pore radius, A i = r/r pore ' and pi (the partition coefficient of i) = (1 - A/. Note that equation 5 considers only steric, hard-sphere particle (p or ion)-pore wall interactions, and does not account for longer­ range interactions, such as electrostatic and van der Waals interactions (7). Although the ions (and the permeant molecules) in the contacting solutions may be charged, Tang et al. have shown that equation 5 is valid provided that the Debye-Hi.ickel screening length-the length scale associated with the screening of electrostatic interactions be­ tween the ions (or between the charged permeants) and the negatively charged skin aqueous pore walls-is much smaller than the average skin aqueous pore radius, r p ore (7). 1 Tt is noteworthy that the skin aqueous pores have a distribution of pore radii (9). In this paper, we imply the average pore radius to be the mean of this distribution of pore radii, and denote this as the radius of the aqueous pores.