EFFECT OF CURLING IRONS 241 250 200 150 i5 •oo E (,3 50 -50 135 ß I nterm ittent [] Continuous ! , , 145 155 165 175 185 Temperature (øC) Figure 11. Combing work difference as function of temperature for fibers subjected to 3 min of thermal treatment using intermittent (15-s intervals) and continuous modes of treatment. in the range of 0.03 to 0.12 (min -1) and an estimated activation energy of 6.6 kcal/mol. The products of Trp oxidation, which emit light in the visible range (400-500 nm), were found to undergo decomposition in unpigmented types of hair (white, Piedmont, and bleached). Thermal treatments were also found to produce discoloration of hair, especially unpigmented hair, which becomes yellow (white or Piedmont hair) or dark-

242 JOURNAL OF COSMETIC SCIENCE colored (bleached hair). In addition to this, combing measurements demonstrated the damage to hair as reflected by an increase in combing forces. APPENDIX: HEAT TRANSFER CALCULATIONS In order to complement the experimental results, which investigated the differences between continuous and intermittent modes of thermal treatment, we have performed calculations for the temperature distribution as a function of time and distance through a fiber assembly. This was achieved by utilizing the heat-transfer solution for the semi-infinite solid model proposed by Carlsaw et al. (22,33). For illustration, we have included Figure 12, which depicts the arrangement of fibers in an ideal assembly. The arrangement of fibers in a cubic lattice provides a fiber (79%) and air (21%) contribution to the composite semi-infinite solid. In addition to this, a 15% contribution of H20 to the fiber itself was also considered. For the calculations, it is assumed that heat transfer, via conduction, flows through each fiber and into the next fiber while in perfect contact with one other. In practice, the fibers would not assume a position of perfect thermal contact nor would conduction be the only mode of heat transfer. The presence of air in the fiber assembly could decrease heat transfer by conduction while increasing it by convection. Also, the effect of water evaporation is neglected in the calculations. For the purposes of this model, we will only consider conductive heat transfer and not the combined effects of convection or water evaporation. One-dimensional heat transfer through a semi-infinite slab, representing a fiber assem- bly with no internal heat generation and constant thermal conductivity, is given by the Fourier equation: qx IRON SURFACE Figure 12. A series of cylinders representing an ideal hair fiber assembly.