J. $oc. Cosmet. Chern. 29 625-639 (1978) Water diffusion coefficients versus water activity in stratum oorneum: a oorrelation and its implioations M. STOCKDALE The Boots Company Limited, Consumer Products Development, Nottingham Received 27 April 1978 Synopsis Literature reports of rates of trans-epidermal water loss through skin exposed to differing external relative humidities have been used to generate water diffusion coefficients by means of Fick's law. These have been related, within a given series, to the diffusion coefficient at a standard average water activity to give relative water diffusion coefficients. These have been combined, together with literature values of water diffusion coefficients obtained by kinetic experiments on stratum comeurn exposed to various humidities, to yield a correlation between the average water activity of stratum corneum and the relative water diffusion coefficient over the full range of water contents. The asymptotic relationship derived shows that the diffusion coefficient increases rapidly as the water activity approaches its maximum. The im- plications of this relationship in terms of water activity profiles of stratum corneum are discussed. A theoretical analysis of the subject is presented and water activity profiles of model systems are derived. INTRODUCTION The importance of the water content of the stratum corneum in determining its ob- servable properties is well documented (1-4). Simple diffusion theory shows that the water content will be lower in the outer layers than in the inner layers under normal ambient conditions. This variation with position will be non-linear, since the water diffusion coefficient will vary with water content (5, 6). A formula correlating the diffusion co- efficient with the water content of the stratum corneum at that point would be useful and would enable a water content profile of stratum corneum under different external conditions to be derived. Although there are several reports of variations in trans-epidermal water loss (TEWL) with external relative humidities, no single set of experiments has been sufficient to derive an empirical relationship between diffusion coefficient and water content. By combining the data from several literature reports, a correlation has been derived between stratum corneum water activity and relative diffusion coefficient. DEFINITIONS Fick's Law has been used extensively and successfully in relation to diffusion processes in stratum corneum (7). This is the basic equation involved in the theoretical treatment of this topic. dC• J= Di• (1) dx 0037-9832/78/1000-O625 $02.00 ¸ 1978 Society of Cosmetic Chemists of Great Britain 625

626 M. Stockdale where J = water transfer rate (TEWL) (mg cm -•' h -x) Di = diffusion constant at point i (cm a h -x) Ci = water activity at point i (mg cm -a) x = distance from the edge of the stratum corneum (cm) Scheuplein and Blank (7) have shown that the water diffusion coefficient of the stratum corneum is the dominant factor in determining the permeability of whole skin and thus the great majority of the water activity differential across the skin will take place across the stratum corneum. For the purpose of this discussion, it will be assumed that any other water activity differential is negligible in comparison. The definition of Ci needs further amplification. The concentration of water vapour in air in equilibrium with the water at point i is a useful concept, but since the diffusion process in vivo is generally non-isothermal, it is necessary to define Cx, in relation to a standard state. This is normally saturated vapour at the temperature of point i. The following definition of Ci will be used in this correlation, 4.39 x 10 -a x R.H.i Ci = (mg cm -a) 100 where R.H.i = relative humidity in air, at the temperature of point i, which would be in equilibrium with the water at point i. (4.39 x 10 -a mg cm -a is the saturated water vapour concentration at body temperature (8), i.e. Cint,rna•). Several investigators have reported values of TEWL at different external relative humidities, either in vivo (9-11), or in vitro (4, 12). Diffusion coefficients are obtainable from these reports. (This requires an assumption to be made about stratum corneum thickness, but since the values used finally are relative to a standard state, the accuracy of that assumption does not affect the correlation.) These diffusion coefficients can then be plotted against the average water activity of the stratum corneum samples. In all cases the internal relative humidity was approxi- mately 100•o. If the initial assumption is made that the water activity profile is close to linearity, the average water activity is derived from the average of the internal and external humidities (a correction for the non-linearity of the water activity profile will be applied later). C = 4.39 x 10-a(R.H.interna! q-R.H.ext•rn• ) (mg cm -a) 200 In addition, E1-Shimi and Princen (13) have determined diffusion coefficients at different humidities from kinetic sorption, desorption experiments. In these the relative humidity was the same on both sides of the stratum corneum samples, and thus 4.39 x 10 -a x R.H. Ci = 100 (mg cm -a) The data from the above references were obtained using different sources of stratum corneum and under different experimental conditions. In order to attempt a correlation, it is necessary to convert the results to relative diffusion coefficients (relative to a standard water activity state). The reference state chosen for convenience was the common experimental conditions of R.H.interna! • 100•o, R.H.ext,rnal = 0•o (i.e. C= 0.5 x 4.39 x 10 -a mg cm-a). The diffusion coefficient for this condition is denoted by Do.