2010 TRI/PRINCETON CONFERENCE 279 sorption or desorption step. The apparent diffusion coeffi cients (D) for hair are calculated from Fick’s diffusion model applied to a cylindrical geometry: Mt/Mf = 4(Dt/πr2)1/2 where D is the apparent diffusion coeffi cient, Mt is the vapor concentration at time t, Mf is the vapor concentration at equilibrium, and r is the radius of the hair fi ber. If the frac- tional absorbed or desorbed water, Mt/Mf, is plotted against the square root of the absorp- tion or desorption time, the points should form a straight line: Mt/Mf = 4/π1/2 r((D)1/2 (t)1/2. The apparent diffusion coeffi cient of moisture for sorption or desorption can be cal- culated from the slope as 2 2 ( /16)( ) D r slope c/s2m = π In Figure 9b, the apparent diffusion coeffi cient plots calculated from the isotherm data show that the thermally damaged hair has a much higher water diffusion coeffi cient on desorption during drying than the non-thermally-treated hair, i.e. water comes out of the damaged hair fi bers much faster than the unheated hair during drying. The difference is more pronounced at the higher humidity at which water is multi-layer absorbed. There- fore the heat damaged hair has increased permeability. On the sorption process, the ther- mally treated hair or thermally damaged hair has a slower water uptake rate than the unheated hair, though the difference is much smaller, compared with the desorption pro- cess. This is because sorption takes place in the dry and un-swollen fi bers in which diffu- sion is more diffi cult than desorption, which starts from wet and swollen hair fi bers experienced from the lengthy sorption process (12). At low humidity less than 30% RH, the water diffusion rate for both thermally treated and untreated hair fi bers are similar because at low humidity (relative humidity less than 25%), water molecules are princi- pally bonded water to hair (14). Figure 9b shows that polymer pretreatment of hair by polyquaternium-55 reduces the water diffusion coeffi cient on desorption compared with untreated and heated control samples, indicating that the polymer pretreatment slows down the loss of moisture from hair during drying. In Figure 10b, the diffusion coeffi cient plots of virgin hair with and without PQ-55 treatment are almost identical, again, suggesting that the reduced water diffusion coeffi cient on desorption by PQ-55 pretreatment for the thermally treated hair in Figure 9b is due to the protective effect of the polymer on hair protein structure. Fig- ure 11 shows the water sorption and desorption isotherm of thermally treated hair fi bers pretreated with PEC versus untreated control sample. The PEC-treated hair and the un- treated hair are the two split halves from the same tress to avoid variation among different hair samples. The PEC-pretreated hair after heating has a much higher water regain than the untreated control samples. The increased water regain on sorption, faster vapor sorption rate and slower vapor de- sorption of hair from the polymer pretreatment will, in turn, help to provide heat control to hair during repeated hot fl at ironing. This will have the effect of reducing further ther- mal damage. In order to evaluate the heat control effect of polymer pretreatment, the hair tempera- ture during hot fl at ironing was measured in three different heating schedules. Figure 12 shows the hair temperature of hair samples during hot fl at ironing at 232°C with and without polymeric pretreatments. The lowest temperatures are seen after the fi rst

JOURNAL OF COSMETIC SCIENCE 280 heating cycle (each cycle is three 5-second strokes). Seven cycles of continuously re- peated heating result in much higher measured temperatures. However, another seven cycles of heating with an overnight interval between cycles at 60% RH, to allow the hair samples to have a chance to rehydrate, show much lower temperatures as expected. These results indicate that the water restoration of hair contributes to heat control on hot fl at ironing. The thermal protective polymers tested in this study shown in the shaded box reduce hair temperatures signifi cantly. The temperature reduction of hair pretreated with PEC increases signifi cantly with the increasing level of PEC used from 1% to 4%, supporting the critical role of the polymer barrier in protecting the hair from thermal damage. Figure 12. Hair temperatures of hair samples during hot fl at ironing at 232°C with and without cosmetic pretreatment. Figure 11. Water sorption and desorption isotherms of thermally treated hair fi bers pretreated with PEC. Dark brown European hair.