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.

436 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS x .35 - .28 .21 .14 .07 IvlETHYL- PROPYL- PARABEN BUTYL- •-'•J AOUEOUS J• P.G. 40% Figure 5. Effect of donor composition on steady-state flux from saturated aqueous and propylene glycol 40% w/w/systems. where PC is the polymer/solvent partition coefficient, (bl is the volume fraction of polymer, Cs is the saturation concentration, and ? is the tortuosity due to filler. Filler present in the commercial membranes reduces steady-state flux by increasing the effective thickness of the membrane (tortuosity) and decreasing the volume fraction of the polymer (diffusion medium). The volume fraction of polymer was calculated from the known weight fraction of filler (0.234) and densities of filler (2.2 g/cm 3) and polymer (0.97 g/cm3). A value of 0.88 was calculated for the polymer volume fraction. The tortuosity of the filled membranes was determined from permeation studies using custom-made filled and fillerless membranes. These membranes were from the same batch of polymer and were identically cured. The tortuosity is given by: ß = J'/(J/0O (Eq. 3) where J' is the flux from the fillerless membranes. The tortuosity was experimentally found to be 1.15 --+ 0.08 which is in agreement with a calculated value of 1.1 from the data of Most (11). Flynn and Roseman (12) evaluated the influence of filler on the apparent membrane solubility. Their data indicated that the adsorption of both ethyl p-aminobenzoate and p-aminoacetophenone was proportional to the solute concentration in the polymer phase. Adsorption to filler present in commercial membranes increases the total con- centration of solute present and can be described by: C T = Cp 01 -}- Cp 02 Z (Eq. 4)