548 JOUBNAL OF THE SOCIETY OF COSMETIC CHEMISTS this paper, sorption is inversely related to molecular weight. The uncharged hydroxyethylcellulose shows very little sorption, representing essentially only a monolayer coverage of the substrate. Sorption of Polymer JR as a Diffusion Process The relatively high amount of polymer uptake by stratum corneum shown in Fig. i to 3 invites speculation about the mechanism involved. In this con- nection, it is relevant to examine first the behavior of Polymer JR on impene- trable inorganic substrates. Adsorption of this polymer (JR-125) from 0.1 per cent aqueous solution onto cleaned glass was measured and yielded values of about 0.25/xg/cm 2. This level of deposition is reached in less than 5 min and does not change with time. Such adsorption corresponds to a covering of one monolayer, if the reasonable assumption is made that each anhydro- glucose unit has an effective area of 25 37, and the adsorbed polymer has a fiat orientation on the surface. In order to make a comparison with skin, the BET surface area of neonatal rat stratum corneum was determined and found to be 0.47 meg, compared to a geometric surface area of 0.113 m2/g. Mono- layer coverage of this substrate would require only about 0.9/xg polymer/mg. It is clear from the data of Fig. i to 3 that the actual uptakes greatly exceed this amount. Figure 4 gives a comparison of the adsorption on glass and stratum corneum on ,qn area basis. The qualitative difference between the two substrate types is striking. The absence of multilayers on glass is presumptive evidence that they do not occur on other substrates. Instead the shape of the sorption curve for neonatal rat stratum corneum suggests that the polymer is slowly being absorbed. In the dry state, neonatal rat stratum corneum has a density of about 0.7. This indicates considerable void space, since the basic keratin of this substrate has a density of 1.4. Additionally, upon immersion in water, the stratum corneum quickly takes up about three to five times its own weight of watery thus providing more aqueous free space for penetration of dissolved species. The data indicate that molecules as large as those of Polymer JR are able to enter the substrate in this way, but probably no further than a few microns in distance. The picture of sorption which emerges corresponds to a semiinfinite solid in contact with a bath containing a constant concentration Co of the diffusing polymer. This is described (8) by the partial differential equation: 0C 02C --D- Ot Ox • with conditions The solution is C = Coat x = 0 for t ) 0 C = Oatt = 0 for x ) 0 C = Co erfc (2•)

SORPTION BY STRATUM CORNEUM 549 where erfc (x) is the "error function complement:" erfc(x) = 1 •I x o The data obtained here do not correspond to concentrations at differing dis- tances in the substrate, but to total material absorbed at varying times. We thus need the integral of the above solution over unit surface of the mem- brane: Q= oC(x,t)dx=Co erfc(••dx o \ 2VDt / By virtue of this becomes rfc (u) du - Q = 2Co •J Dt This well-known formula was quoted without derivation in a classical pa- per (9) on the diffusion of small molecules in animal tissues. A test of the validity of this approach is that sorption should follow a square-root of time dependence. This was indeed generally found to be the case for the experiments reported here, at least for the first several hours. At longer times, particularly over i day, deviations from 5/• do occur. By using Hill's formula above, diffusion constants can be calculated from the slope of the initial, linear part of the Q versus 5/• curves. An area of 0.47 m2/g was assumed in all cases corresponding to the observed BET area rather than the calculated geometric areas. Calculations were made for some of the more interesting cases. For example, the data of Fig. i gave the fol- lowing table. Type of Stratum Corneum Diffusion Constant (cm2sec) Fetal Pig 9.6 x 10 -9 Neonatal rat 1.07 x 10 -•ø Human 7.8 x 10 -• The different grades of Polymer JR in neonatal rat stratum corneum at 0.1 per cent concentration (Fig. 2) led to the following table. Grade Diffusion Constant (cm2/sec) JR-125 1.07 x 10 -•ø JR-400 9.7 x 10 -• JR-30 M 1.2 x 10 -•"