JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS of the thermodynamic activity of the penetrating agent in its vehicle: dq _ a D•l __ (It •/ L where a is the thermodynamic activity of the drug in its vehicle and • is the effective activity coefficient of the agent in the skin barrier phase. The significance of the second relationship is apparent in Fig. 3 where both activity and concentration under steady state conditions of a hypo- thetical penetrating drug having a partition coefficient of 1/2 and 2 have been plotted as a function of depth. In the activity plot there is a discontinuity in the slope but not in the absolute value at the interphase. Whereas in the concentration plot there are usually sharp breaks in both. Since the driving force behind the drug movement is the difference in the thermodynamic potential between the vehicle and the deeper tissues, activity plots always show a decrease with depth. This is not necessarily true with concentration plots since favor- able partition coefficients may result in an increase as shown in one of the examples in Fig. 3. Conc. ' •oint. I / ibase •arr/er, lower, /2 I tissue9 / = ! oint. I ! base , skin ! lower iI•arr •5 . . Act. PENETI•ATION {effective depth) Figure 3.--Plots showing schematically the changes in concentration and ac- tivity with effective depth of penetration. Although for thermodynamic reasons the direction of flow is always in the direction of negative concentration gradient for passive systems, one may conceivably obtain a net flow against the gradient if there exists an energy transfer mechanism. If Buettner's contention that water is readily ab- sorbed through human skin from highly hypertonic solutions is correct, there must be a pump mechanism which will push water molecules against the gradient into body fluid. Thermodynamic ,4ctivity and Rate of Penetration. In equation 2 only the activity of the drug in its vehicle appears, the properties of the base itself seem to play no part. For such systems the rate of percutaneous penetra- tion measured for different ointment bases would be approximately con- stant provided the thermodynamic activity of the drug in the vehicles

PHYSICAL CHEMICAL ANALYSIS OF PERCUTANEOUS ABSORPTION PROCESS 89 was maintained constant. Thus all ointments containing finely ground suspensions of the drug (thermodynamic activity equal to that of the solid drug) will produce the same rate of penetration. This again presupposes that the rate determinining step is essentially in the passage of the barrier phase. For highly insoluble systems this would not be true as we will see later. In order to obtain the maximum rate of penetration it is evident that the highest thermodynamic potential possible for the penetrating substances must be used. For simple organic compounds the activity of the pure form of the material at environmental temperature places, however, an upper limit on the available thermodynamics activity. Any higher activity would represent supersaturation with respect to the form. With more complex compounds, however, different crystalline modifications may exist having different free energies, thus different thermodynamic activities, at room temperature. In such instances the selection of the most energetic species will result in fastest penetration. These systems are, however, metastable and may show a gradual change in properties. TABLE 1--LIMITING ACTIVITY COEffiCIENTS or $ARIN IN ORGANIC SOLVENTS AND WATER Perfluorotributylamine ........ 66.6 Hexadecane .................. 15.6 Water ....................... 14 Tributylamine ............... 10.4 Tetralin ..................... 4.3 2-Pyrrolidone ................ 2.8 Diethylene glycol ............. 2.4 Carbon tetrachloride .......... 2.4 Phenyl ether ................. 2.38 Diisooctyl adipate ......... 1.84 Methyl salicylate .......... 1.74 N-methylacetamide ........ 1.44 Dibutyl phthalate ......... 1.42 Butryolactone ............. 1.3l Isoamyl alcohol ........... 1.07 Ethyl lactate ............. 0. 536 Benzyl alcohol ............ 0. 446 m-Cresol ................. 0. 044 Since activities are important rather than any absolute concentration, it is obvious that, for a given concentration of the penetrating substance, vehicles which have lower affinity (poorer solvent power) will normally produce faster penetration. It is not commonly realized how dependent such activity coefficients are on solvents. In Table 1, I have listed values in some solvents for sarin, a nerve gas, which we determined a few years ago. It is evident that these values encompass three orders of magnitude. It is to be expected that the same degree of difference will be found in the rates of absorption of the fluorophosphate from these solutions. In practical language one might say that solutes held firmly by the vehicle will exhibit low activity coefficients and slow rates of penetration. Good pharmaceutical examples of this behavior are the relative rates of release (penetration) of phenols from mineral oil or petrolatum bases and from camphor or polypropylene glycol bases. The latter preparations are mild and bland whereas the former are quite corrosive at equal concentrations. This is due to the reduction in the thermodynamic activity of the phenols caused by the ketone or the polyethers. Such complex formations usually