12 JOURNAL OF COSMETIC SCIENCE with rough surfaces (5). This is important because the optical transmission of an ab- sorbing film of uniform thickness is lower than the transmission of a corresponding inhomogeneous film of the same average thickness. This effect can be quite dramatic and has been formulated mathematically by O'Neill using a step film model (9). In this model the step film structure is defined by two parameters that characterize the fraction of the thin and thick parts of the film and their difference in thickness. In the present paper the step film parameters of the O'Neill model are adjusted in such a way that the model optimally reproduces the i, vivo SPF values of three sunscreen standards that are known with accuracy to be above average. Knowing the UV filter content of a given sunscreen formulation and the spectral characteristics of the individual filters, the investigator can use the calibrated step film model to estimate the SPF of the formulation without any further measurement. For that reason, it can be a helpful tool for the sunscreen formulator. EXPERIMENTAL CHEMICALS For spectroscopic measurements ethanol (p.a., Merck) and bidistilled water were used as solvents. The UV absorbers used in this work are listed below. After the chemical name the INCI name is given in parenthesis followed by the abbreviation and the supplier name: © 2-Propenoic acid, 3-(4-methoxyphenyl)-2-ethylhexyl ester (octyl methoxycinnamate, OMC) from Ciba Specialty Chemicals Inc. (Tinosorb © OMC) © 2-Phenylbenzimidazole-5-sulfonic acid (2-phenylbenzimidazole-5-sulfonic acid, PBSA) from Merck (Eusolex © 232) © 1,7,7-Trimethyl-3-(p-methyl phenyl methylene)-bicyclo-[2.2.1]-heptane-2-one (4- methylbenzylidene camphor, MBC) from Merck (Eusolex © 6300) © 4-t-Butyl-4'-methoxydibenzoyl methane (butyl methoxydibenzoyl methane, BMDBM) from Givaudan-Roure (Parsol © 1789) © 2-Ethylhexyl-2-cyano-3,3-diphenyl-2-propenoate (Octocrylene, OC) from BASF (Uvinul © N539) © Trianilino-(p-carbo-2'-ethylhexyl-l'-oxi)-l,3,5-triazine (Octyl Triazone, OT) from BASF (Uvinul © T150) © Titanium dioxide (TiO2) from Merck (Eusolex © T2000) © 2-Hydroxy-4-methoxy benzophenone (Oxybenzone) from Ciba Specialty Chemicals Inc. (Tinosorb © B3) © 2-Ethylhexyl p-dimethylaminobenzoate (Padimate O) from Merck (Eusolex © 6007) © 2,4-Bis-|[4-(-2-ethyl-hexyloxi)-2-hydroxy]-phenyl}-6-(4-methoxyphenyl)-( 1,3,5 )- triazine (his ethylhexyloxyphenol methoxypphenyl triazine, BEMT) from Ciba Spe- cialty Chemicals Inc. (Tinosorb © S) © 2,2'-Methylene-bis-(6-(2H-benzotriazole-2-yl)-4-(1,1,3,3-tetramethylbutyl)-phenol (methylene bis-benzotriazolyl tetramethylbutylphenol, MBBT) from Ciba Specialty Chemicals Inc. (Tinosorb © M) MEASUREMENTS OF UV SPECTRA UV spectroscopic transmission measurements were carried out using a Perkin Elmer

STEP FILM MODEL FOR SPFs 13 Lambda 16 spectrometer. UV transmission spectra of particulate UV absorbers were recorded with the same instrument using an integration sphere attachment (Labsphere B009-4012). The UV spectra of the oil-soluble filters OMC, OC, OT, BEMT, BMDBM, Oxybenzone, and Padimate O were measured quantitatively in highly diluted ethanolic solutions (concentrations typically between 10 -6 and 10 -5 M) with optical cuvettes of 1 cm optical pathlength. The UV spectrum of PBSA was measured in the same way with bidistilled water as solvent. The UV spectra of these UV absorbers are shown in Figures 1 and 2. MBBT is an organic particulate UV absorber delivered as a 50% dispersion in water. The spectra of MBBT and of TiO 2 were measured quantitatively using concentrations of the UV absorber between 0% and 3% and an optical pathlength of 0.0008 cm (optical cells manufactured by Hellma, Germany). In this case, at each concentration ten measure- ments were carried out and the results were averaged. As shown in Figure 3, the Lambert Beer law is obeyed. The spectra of MBBT and TiO 2 are depicted in Figure 4. All spectra shown in Figures 2-4 are given in terms of molar decadic extinction coefficients. Table I summarizes some characteristic features of the spectra, including the extinctions El, 1 at the wavelength X ..... calculated for an optical pathlength of 1 cm and a concentration of 1% (weight per volume). 120000 90000 60000 30000 • OMC --o-- PBSA • MBC • Padimate O --m-- OT 300 320 340 360 380 400 Wavelength / nm Figure 1. UV spectra of some UVB absorbers: PBSA measured with distilled water as solvent OMC, MBC, Padimate O, and OT with ethanol as solvent.