434 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS where J is the steady-state flux, D is the diffusivity of the solute in the membrane, PC is the membrane/vehicle partition coefficient, C o and C R are the donor and receptor con- centrations of permeant, and h is the membrane thickness. When sink conditions are maintained, as in these experiments, CR is effectively zero and flux is proportional to donor concentration, Co (Figure 3). Although Eq. 1 is written in terms of concentration, the permeant activity gradient is actually the driving force for mass transport. Flynn and Roseman (10) and Most (11) had noted a negative deviation in flux at higher concentrations of p-aminoacetophenone and ethyl p-aminobenzoate which was attributed to non-ideal solution behavior. Steady-state flux values were used for evaluating solvent effects and comparing perme- ation of different parabens from the same vehicle. Flux values for saturated solutions (constant activity source) of methylparaben in various solvents are collected in Table I. Despite considerable differences in solubility, there was essentially no difference in flux from solution in water, glycerin, polyethylene glycol 400, propylene glycol, and mix- tures of the polyols with water (Figure 4). Less extensive studies with the other parabens led to the same conclusions. Flux comparisons for two donor liquids are shown in Figure 5. From partition data obtained on specially synthesized fillerless membranes, the concen- tration of paraben per unit volume of polymer was calculated. Within experimental error, these values were the same for a given paraben, independent of solvent for satu- rated systems in water, glycols, and aqueous glycol mixtures. z 0 0 20 40 60 80 100 PERCENT SATURAT I ON Figure 3. Steady-state flux of methylparaben as a function of aqueous donor concentration expressed as a percent of saturation.

PARABEN PERMEATION THROUGH MODEL MEMBRANES 435 Table I Permeation of Methylparaben Through Polydimethysiloxane Membranes From Non-Interactive Solvents Vehicle Flux Diffusion Solubility (mole/cm2/hr Partition Coefficient Solvent b (mg/ml) X 106) Coefficient (cm2/sec X 106) Water 3.53 0. 589 0. 156 1.49 Propylene Glycol 259. 0.639 0.00186 1.63 Propylene Glycol:Water, 60:40 88.8 0.617 0.00619 1.57 Propylene Glycol:Water, 40:60 31.6 0. 596 0.0174 1.54 Propylene Glycol:Water, 20:80 7.80 0.625 0. 0704 1.59 Polyethylene Glycol 400 334. 0.619 0.00164 1.58 PEG 400:Water, 60:40 232. 0.647 0.00237 1.65 PEG 400:Water, 40:60 138. 0.620 0.00398 1.58 PEG 400:Water, 20:80 14.1 0.644 0.0389 1.64 Glycerin:Water, 40:60 4.96 0. 595 0.111 1.52 Glycerin:Water, 20:80 4.18 0.622 0.131 1.59 Means: 0.619 1.58 STD Deviation: 0. 020 0.05 Data for commercial membranes of 0. 0254-cm thickness. Solvent ratios are w/w. Steady-state paraben flux through commercial (filled) membranes from saturated solu- tions can be described (12) by: J = (PC D qb• Cs)/(h x) (Eq. 2) 1.0 .@ .6 .4 - [] iI ß ß _- _- - [] I [] 0.0 • • I • • 0.0 .5 1.0 1.5 2.0 2.5 LOG SOLUBILITY (m•/cm a) Figure 4. Influence of methylparaben solubility in the donor on steady-state flux from saturated systems.