PERMANENT WAVING AND PERM CHEMISTRY 121 DISCUSSION The previously mentioned fi ndings clearly lead to more questions than answers. Wickett frequently referred to “reaction-controlled” and “diffusion-controlled” conditions—with this designation primarily relating to the linear response of plots involving experimental data to the two mathematical mechanisms. Staining experiments apparently provide a clearer designation based on the presence (or absence) of reaction “fronts” within fi bers as a function of different treatment conditions. Yet, our reduced time analysis of data from an experimental situation that did not yield such a front (and therefore indicates “reac- tion-controlled” conditions) did not abide by the fi rst-order mechanism. Similarly, data from circumstances that yielded a reaction front (and therefore suggest “diffusion-con- trolled” conditions) did not abide by Wickett’s moving boundary model. It is theorized that rather than being specifi c mechanisms, the descriptors “diffusion controlled” and “reaction controlled” represent a fi rst line of classifi cation for a variety of mathematical models that fall under each category. Again, there is clearly the need for additional math- ematical modeling work to derive new mechanisms that adequately describe the experi- mental data. It should be noted that other curve shapes have been obtained during performing this reduced time analysis on experimental SFTK data. The behaviors outlined earlier Figure 17. Reduced time plots for single-source Asian hair reacting with 0.42 M cysteamine as a function of pH.

JOURNAL OF COSMETIC SCIENCE 122 (experimental and theoretical) all have their highest rate of transformation (at or near to) to the beginning of the process. In solid-state kinetics, these are termed decelera- tion mechanisms because the rate decreases over most of the process. However, it is not uncommon to fi nd experimental reduced time curves with a distinctly sigmoidal behavior (see Figure 18). This implies that there is some induction period during which the rate of transformation progressively builds, but then another factor would appear to gradually dominate and the rate subsequently decreases. It is again noted that the analysis approach described herein is commonly used in the fi eld of heterogeneous kinetics, where a variety of mathematical models have already been de- rived based on underlying conditions such as diffusion, order, and/or geometric con- straints (25,29). Some examples of reduced time curves derived from diffusion- and geometry-based equations are shown in Figures 19 and 20. As an aside, this author has also used the same kinetic approach in modeling the rate of water adsorption by hair as a function of changing humidity conditions, wherein the applicability of these same fi rst- order and diffusion-based models has been identifi ed (30). ADDITIONAL VARIABLES IN SFTK EXPERIMENTS This section began by highlighting a number of concerns and seemingly questionable assumptions pertaining to the SFTK approach. Despite these issues, it is observed that Figure 18. Example of experimentally derived sigmoidal reduced time plot.