ALPHA-TOCOPHEROL ACETATE PERMEATION 95 (4) where Here, K has units of mass, and A 2 has units of reciprocal time. Values for Kand A can be obtained from a nonlinear regression using equation 3, allowing D d to be calculat­ ed as Dd = (�) 2 AC 0 (5) In some cases, when D dis large enough, the M-vs-t plot is linear over the entire course of the experiment, and dM!dt can be taken as nearly constant during that time interval. (This often happens when the donor is a liquid.) In this case, the method loses accuracy in calculating the actual values for D d· However, good estimates of the lowest value of D d that can account for the linearity can be obtained. However, D dis evaluated only to verify that equation 3 is valid, and this information is sufficient for use in this study. The estimation is done as follows: From equation 4, the release rate is given by Using the approximation dM!dt = APmCo, it can numerically be shown that dM!dt changes by less than 5 % when At 0.05 and less than 10% when At 0.1. For the 10% condition, which is the less restrictive one, this leads to (6) during the experiment. In practice, P rn is estimated from the dM!dt data and tis taken as the time of the last data point in the experiment (four hours in this study), leading to D d 40P 2• Estimating D d from viscosity measurements. In some cases, using the liquid medium (i.e., mineral oil and isopropyl myristate) as the receiver vehicle made diffusion experiments difficult to perform and/or assay. For these media, the cellulose release data was not used and D d was estimated from viscosity data, which gives values that are sufficiently accurate for use here. The basis of this method is the Stokes-Einstein equation (18), given as where k8 is Boltzmann's constant, T is the absolute temperature, Tl is the viscosity of the liquid medium (donor), and r is the effect radius of the diffusing drug molecule. For

96 JOURNAL OF COSMETIC SCIENCE the same drug and temperature, the ratio of the diffusion coefficients in two solvents is given by D1 11 2 Thus, knowing the diffusion coefficient in one medium D 1, it is possible to estimate the diffusion coefficient in another medium D 2 from the inverse ratio of the viscosities of the two media. In this study, the ratio of viscosities was obtained using a falling ball viscometer method (19) according to 111 (Pa - P 1 )t1 112 (pB - P2 )t2 where p8 is the density of the falling ball, p 1 and p 2 are the densities of the two solvents, and t 1 and t2 are the times required for the ball to fall a given distance L through each solvent after achieving its terminal velocity. MATERIALS AND METHODS CHEMICALS AND REAGENTS All chemicals were analytical grade or higher in quality. Alpha-tocopherol and alpha­ tocopherol acetate were purchased from Sigma Chemical, Co. (St. Louis, MO). Isopropyl myristate NF, light mineral oil, and phosphate-buffered saline ultrapure were from Spectrum Chemical Mfg. Corp. (New Brunswick, NJ). HPLC grade acetonitrile and water were from EM Science (Gibbstown, NJ). Ethanol USP was from AAPER Alcohol and Chemical Company (Shelbyville, KY). Klucel® was from Hercules Inc. (Wilming­ ton, DE). TOPICAL FORMULATIONS Three different solutions and two gel formulations, all containing 5 % alpha-tocopherol acetate, were used in this study. The solvents of the solutions were ethanol USP, isopropyl myristate, and light mineral oil. The gels consisted of 1 % and 3% Klucel®, respectively. Gel formulations were prepared by dispersing Klucel® powder in ethanol USP and mixing by means of a magnetic stirrer to prepare Klucel® gel. Mixing con­ tinued until all particles were thoroughly wet. Alpha-tocopherol acetate was weighed accurately and dissolved separately in 95% ethanol USP. Then the alpha-tocopherol acetate solution was introduced dropwise to the Klucel® gel and continuously stirred for four hours at room temperature by means of a magnetic stirrer so that the proper concentration of the gel was achieved. HPLC ASSAY Alpha-tocopherol and alpha-tocopherol acetate concentrations were determined by HPLC with a UV-detector according to the method described by Rangarajan and Zatz (20). The chromatographic apparatus consisted of a Hitachi 1-7250 programmable auto-