SINGLE FIBER DEPILATORY STUDIES 47 1 Active Range 0.25-0.75M TGA pH Range 9.5-11.5 GuHCI Range 0-2.0M T95% = 67.45 4- HF- 39.47x [TGA] - 29.59 X [GuHCI] -4.44XPH 4- 5.77 X [TGA] 2 4- 2.81 X [GuHCI] 2 4- 6.00 X [TGA] X [GuHCI] 4- 2.0 X [TGA] X pH 4- 1.64 X pHX [GuHCI] for Hair:C/= 1 HF - 0 for Hair½2 HF -- 0.11 r 2 = .955 Only one residual time (Actual-Predicted) was greater than one min. Figure 8. Central composite response equation. ment in a central composite design format, which allows the construction of a regres- sion equation to predict the response to any set of conditions. From this regression equation may be obtained the single variables and variable interactions which statisti- cally significantly influence hair tensile weakening. Furthermore, by inspection of the equation, the T95 % response can be minimized with respect to all variables or to fewer variables when the remaining ones are fixed at given values. A central composite test of the response of T95 • to calcium thioglycolate concentration from 0.25 to 0.7 5 M, pH from 9.5 to 11.0, and GuHC1 concentration from 0 to 2.0 M was run. The complete response equation is shown in Figure 8. In order to run enough conditions to adequately define the response equation, fifteen 1.5-cm sections from each of two hairs were used. This results in the small hair-to-hair correction factor, HF. The fit to the model was excellent, with no measured time being different from the pre- dicted time by more than 1 minute. Figure 9 illustrates the calculated response surface for the response of T95 % to thioglycolate and GuHC1 concentration at pH 10.5. The thioglycolate and GuHC1 axes run from 0.25 to 0.75 M and from 0.0 to 2.0 M respec- tively. T95 % ranges from 16.5 to 6.5 minutes. While the equation in Figure 8 is useful for prediction of response within the range of the test, it should be pointed out that the equation cannot be extrapolated outside of the measured range of any of the parameters because bizarre results, such as prediction of negative values for T95 %, may occur. CONCLUSIONS The SFTK method is useful for the laboratory evaluation of depilatory systems. The

472 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS z x ø/ce/trtio/ Figure 9. Predicted T95v• response to TGA and GuHCI concentration at pH 10.5. Y method provides reproducible results that have been shown to correlate with in vivo performance with two commercial depilatory systems. The T95 % parameter can be ob- tained rapidly enough to allow convenient screening of a wide range of formulations. Central composite designs can be used to predict the response to multiple-treatment variables. Factors shown to increase the rate of TGA-induced stress decay as evaluated by T95 %, are: 1. Increased pH 2. Oxidative pretreatment of the hair at high pH 3. Incorporation of TGA into the water phase of an oil-in-water emulsion, thereby increasing the effective concentration