MIE-SCATTERING MONTE CARLO SIMULATIONS 201 even relatively common materials such as Ti02 vary widely in the literature here we used theoretical RI values (13) for white, red, and green pigments, and measured RI values for soot for the black pigment (14). The components of the eight mixtures are summarized in Table I. In order to investigate the effect of adding different components together, we fixed the concentrations of the individual components while only manipulating whether or not a given component was added to the formulation. Although the formulations were strictly hypothetical, the volume loadings were on the order of those used in base foundations for the face. Note that transmission, reflection, and absorption values were dependent on the particle size (distribution), loading percentage, and RI of the matrix. In Figure 7 the absorption spectra of single-pigment formulations are plotted, corre- sponding to formulations 2 through 5 summarized in Table I. In these simulations, the concentration of white pigment was an order of magnitude larger than other pigments, causing the effects of the white pigment to dominate. By default, the pigments were dispersed in an oil-in-water emulsion where the oil droplets were 1 micron in diameter and constituted 10% of the volume. While the fact of selective absorption by different pigments is obvious, use of the described simulation tool demonstrates how these effects can be quantified, as shown in Figure 7. The data in Figure 7 clearly show that the pigments selectively absorbed certain wavelengths of light. The white pigment absorbed light in the violet region (recall that there was an order of magnitude more white pigment in the formulation compared to the other pigments), but absorbed very little light at all at wavelengths above 500 nm. The lack of absorption over a wide range of wavelengths contributed to its white appearance. In contrast, the black pigment absorbed light over all the wave- lengths. The red pigment absorbed a large percentage of light at the lower wavelengths, with the percentage of light absorbed decreasing as the wavelength got closer to red light at 650 nm. The green absorption curve, to which the axis on the right side in Figure 7 applies exclusively, is bow-shaped, with a minimum in absorption at the wavelength of green light. The absorption curves in Figure 7 indicate the percentage of light, of any given wave- length, that is absorbed by the formulation. These results, however, do not take into account the intensity distribution of light incident on the sample. For example, in Table I Proportions of Various Components for Eight Hypothetical Coating Formulations Oil drops White Red Red Green Black (1-micron (600-nm (100-nm (1-micron (100-nm (100-nm diameter, 10% diameter, 2% diameter, 0 .1 % diameter, 0.1 % diameter, 0.2% diameter, 0.1 % volume load) volume load) volume load) volume load) volume load) volume load) ✓ 2 ✓ ✓ 3 ✓ ✓ ✓ 4 ✓ ✓ 5 ✓ ✓ 6 ✓ ✓ ✓ ✓ 7 ✓ ✓ ✓ ✓ 8 ✓ ✓ ✓ ✓ ✓

202 JOURNAL OF COSMETIC SCIENCE 50 10 .:ii:: 40 8 � � -D- \Nhite C in_ 30 C 0 6 .# e • Red i. =-m L 6� • Black 0 ar 20 4 u, I u, .c .c Green cc 10 2 cc 0 a 400 500 600 700 'Wavelength Figure 7. Absorption spectra of single pigments dispersed in oil-in-water suspension. Figure 7 we see that white pigment absorbed a great deal of light at 400 nm, but what is not considered is the fact that the contribution of violet light within the daylight spectrum is relatively small. By multiplying the intensity distribution of the incident light source by the transmission, reflection, or absorption curves, the appearance of a formulation under certain lighting conditions can be calculated. Figure 8 shows the reflected intensity distributions of mixed-pigment formulations when CIE standard illuminant D65 was incident on the sample. Formulations 2 and 6-8 from Table I are represented in the plot. � tll C m 40 30 -cs 20 m m 1( 400 H 500 " I 600 'Wavelength (nm) H � 700 -a- Form. 2 • Form. 6 -,w,..-Form. 7 ----Form. 8 Figure 8. Reflected intensity distributions of formulations illuminated by D65 lamp.