-5 -4 -3 - -2 log C• (M) Figure 9. Comparison of theoretical and experimental plots of log Co/log Cw. Curves A, B, and C: theoretical lines for Poisson distribution NPEi•, NPE•, and NPE• (O, O, [•): experimental values for commercial NPEi•, NPE•, and NPE•. 12 o J=•0 9 o 8 •- m 7 6 (B) (C) i i I I I I I 0 1 2 3 4 5 6 7 Surfactant Concentration (wt. %/water) Figure 10. Average EO chain length of the micelie-forming components in the cyclohexane-water (1:1 volume) system as a function of surfactant concentration at 25øC. Curves A, B, and C are the calculated lines for Poisson distribution NPEi•, NPE•, and NPEg, respectively.

128 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS tion. This explains the observed results in Fig. 5 that the PITs of emulsions stabilized with mixed surfactants increase with decreasing concentration and that broadly distributed nonionics exhibit higher PITs compared to homogeneous ones at low concentrations. Furthermore, for the mixtures of homogeneous NPE4 and NPE•0, the • values of micelie-forming components were calculated as a function of composition of the mixtures for different concentrations. The calculated lines are shown in Fig. 11, from ø•10 'E 8 •-uo 7 0.•_ I,aJ O Q• , a 5 c 4 NPE4 NPE•0 0 0.2 0.4 0.6 0.8 1.0 Weight Fraction of NPE•o Figure 11. Plot of average EO chain length of the micelie-forming components in the cyclohexane-water (1:1 volume) system against the composition of the mixtures of homogeneous NPE 4 and NPE•0 at 25øC. Concentrations of the mixed surfactants: a, 2% b, 3% c, 4%/water. which it is apparent that the lower the concentration, the greater becomes the deviation of the • values of micelie-forming components from the weight average of the individual EO chain lengths in the total system. Thus, the deviations of HLB numbers of emulsifier blends from weight average can be attributed to the changes in composition of the mixed micelies formed in the oil-water system with total emulsifier concentration and/or mixing ratios of the constituent emulsifiers. REFERENCES (1) W. C. Griffin, Classification of surface-active agents by "LB," J. $oc. Cosmet. Chem., 1, 311-26 (1949).