PHYSICAL CHEMICAL ANALYSIS OF PERCUTANEOUS ABSORPTION PROCESS 91 In effect, for such systems we can look on the resistant barrier as being composed of two dissimilar layers, one largely lipoidal and the other effec- tively hydrous. Schematically we can represent such a system by a plot Hydrous Barrier / j Lipold Barrier • 7•ctivity Plot ? / _ _ I •% A p• D, SLOPE • ( 1,% I..,+ • •, P Figure i--Schematic diagram of permeation through a double barrier layer. as shown in Fig. 5. Mathematically such double and multi-layer systems would obey the relationship: clq aA dt (h•/P•) q- (h=/P=) for a double layer where h is the thickness and P = D/7 of the respective layers. And clq aA dt (h•/P•) q- (h2/P2) q- ... (h•/Pn) for an n-layer system. As one might expect these equations are quite analogous to electric cir- cuits where dq/dt is the current, and P is the conductivity. It is also evident that the layer having the lowest conductivity will have dispropor- tionate effects on the flux analogous to the common series-connected resist- ance circuits. If we assume that diffusion coefficients in the several phases are approxi- mately the same as is often practically the case, we find dq aAD -- dt h•'• q- h2v• q- ..

92 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS where D here refers to the effective mean diffusion coefficient h, the thick- ness of each layer and 3' the activity coefficient of the penerrant in that layer. For such a system and comparing a number of chemicals the pene- rrant which minimizes the summation shown in the denominator will penetrate the fastest. This may lead to selection of a compound having balanced hydrophilic lipophilic properties if the double bai'rier layer such as suggested above really exists. If the activity coefficients in the above equation were such that all except that in the hydrous layer. the deeper aqueous tissues underlying the normal barrier layer, were very small the rate of agent penetration would be expected to be a sensitive function of the rate of capillary blood flow. This assumes that the effective thickness of the hydrous barrier depends on the rate of flow of blood through it. One would thus predict that the rate of absorption of highly hydrophobic solvents and materials would be influenced by capillary dilation and blood flow. On the other hand for systems showing low activity coefficients in water, that is for penetrating materials which are at least partly hydrophilic in nature, the rate of per- fusion or capillary flow would have little or no effect. ß Influence of Moisture and Solvents. So far in our consideration we have assumed (1) that diffusion coefficients are constants independent of con- centration and (2) that activity coefficients likewise were constant through- out the penetration process. In special instances these are poor assump- tions. This is particularly true where we are concerned with penetration ot water molecules by a transepidermal route or any transepidermal pene- tration where there is concomitant imbibition of water. Since water is particularly well sorbed by protein and protein degradation products con- tained in the outer skin, the transfer properties of the several layers are probably strongly influenced by the presence of water. - This sort of behavior, while difficult to establish in vivo, can be readily followed in vitro with certain artificial membranes. In Fig. 6 is shown an experimentally determined permeability of glyceryl monostearate to mois- ture as a function of relative humidity. At very low humidity perme- ability (gm./cm. 2. hr. min. Hg) is relatively insensitive to relative humidity, whereas near 100 per cent, the rate of penetration is acutely dependent on water activity. This is attributed to imbibition of water by the barrier phase exposed to saturated water vapor and consequent changes both in the diffusion coefficient and activity coefficient. The large effect on permeability of small decreases in the thermodynamic activity of water is evident for leather. Common leather normally offers little resistance to penetration by water vapor. Addition of salt to the penetrating aqueous phase, however, greatly decreases the rate. Leather has been found to be practically impermeable when exposed to 2.5 normal sodium chloride solution (approximately 90% relative humidity).