STEP FILM MODEL FOR SPFs 15 2.0 1.5 1.0 0.5 ß TiO 2 (•.max = 291 nm) O MBBT (•.max= 360 nm) Linear regressions .0 ! ! 0 I 2 3 % (w/v) Partiulate UV-Absorber Figure 3. Lambert-Beer law functionality of particulate UV absorbers dispersed in distilled water at realistic concentrations. © PI: 2.7% OMC, in vivo SPF = 4.2 (+0.2) © P3: 3.0% OMC, 0.5% BMDBM, 2.78% PBSA, in vivo SPF = 15.5 (+1.5) © P4: 5.0% OMC, 10% MBBT (active ingredient), in vivo SPF = 35.7 (+3.2) The formulations of P1 and P3 are given in the literature (12). The in vivo SPF study of P4 was carried out twice according to the COLIPA protocol (12) so that total number of volunteers in this case was 20, resulting in a rather small confidence interval (+9%), similar to that of the P3 standard. The formulation of standard P4 is given in Appendix I. All confidence intervals given with the in vivo SPF values are based on a significance level of 95%. THEORETICAL ASPECTS AND CALCULATIONS TRANSMISSION OF A STEP FILM The derivation of the step film model presented by O'Neill (9) starts with a homoge- neous film of absorbing material of a certain thickness d and a horizontal extension of 1. The derivation of the model is visualized in Figure 5 as a two-dimensional sketch. A portion of the homogeneous film given by the horizontal extension g and the thickness

16 JOURNAL OF COSMETIC SCIENCE 40000 30000 20000 10000 --•-- MBBT --0-- Ti02 300 320 340 360 380 400 Wavelength / nm Figure 4. UV spectra of particulate UV absorbers dispersed in distilled water. Table I Characteristic UV Spectroscopic Parameters of the UV Absorbers Used in This Study Molecular weight k ...... e(k ...... ) UV Absorber (tool/g) (nm) (1' tool -• ß cm -•) E•.•(X ...... ) OMC 290.00 310 23980_+ 480 827_+ 17 PBSA 274.00 299 25390 _+ 500 926 _+ 19 MBC 254.00 299 22780+ 460 897 + 18 Padimate O 277.00 310 26880 + 540 970 +_ 19 OT 823.06 314 124700 _+ 2500 1515 _+ 30 BMDBM 310.00 357 34130_+ 680 1101 _+22 OC 361.00 303 12190_+ 240 338_+ 7 BEMT 627.80 342 48970 _+ 980 780 _+ 16 Oxybenzone 228.25 287 13970 _+ 280 612 _+ 12 MBBT (dispersion) 658.86 360 38500 _+ 2700 584 _+ 41 TiO2 79.9 291 6170_+ 430 772_+ 54 The error ranges are indicated for e(X .... ) and E•,•(X .... ) as confidence limits with 95% level of significance. f' d is removed from its original position and added to the remaining thicker part of the film. This results in two film fractions of different thicknesses d' and (l-f)' d, with horizontal extensions (l-g) and g, respectively. The transformation of the film geometry is carried out under the condition that the amount of absorbing material stays constant. The expression for d' is then: