HUMAN HAIR MOISTURIZATION WITH COSMETIC PRODUCTS 317 U sing the surface area (0.4 m2/g) and the total pore volume (0.000689 cm3/g) of hair from reference 12, we can calculate the number of molecular layers adsorbed on the BET surface area. The average thickness t of the adsorbed water fi lm is given by t he following equation: q q 21 18 0.000689 10 0.4 10 1.723 nm. t The geometric thickness of a water molecule based on the density and the Avogadro’s number is ~0.33 nm. This leads to the number of adsorbed molecular layers to be about 5. This apparently looks reasonable, considering the surface energy of hair which is quite low (about 30–40 mJ/m2) (14). However, the sorption isotherm tells a completely differ- ent story. For example, the amount of water sorbed in untreated hair is ~4% at 20% RH. Assuming the density of water as 1.0 g/cm3, the volume of water sorbed is 0.04 cm3/g. This is nearly 58 times the BET pore volume (0.04/0.000689 = ~58). This discrepancy suggests that a large part of water is not held in the nanoporous regions of hair, which are Figure 10. Hysteresis plot s of hair treated with products 1 and 2 along with that of the control hair. Product 1 (x) product 2 (¡) untreated (). Table IV Hysteresis Loop Areas from Figures 7–9 in the 10–60% RH Range Loop area 10–60% RH Product 1 Untreated Product 2 ¦Hi (%) 14.23 10.0 5.84 HR 1.42 1.0 0.58

JOURNAL OF COSMETIC SCIENCE 318 accounted for by the BET surface area. The large pores which contribute very little to the BET surface area hold a much larger fraction of water. These could be the regions covered by the medulla, CMCs, and intermacrofi brillar materials (15), which are known to be less keratinous (more hydrophilic). Ro wen and Blaine (16) from the National Bureau of Standards have compared the BET pore surface areas determined by sorption of water and nitrogen on a series of materials. For wool, their data are 206 and 0.96 m2/g for water and nitrogen, respec- tively. Similar data for nylon are 45 and 0.31 m2/g, respectively. However, for tita- nium dioxide (TiO2), the corresponding values are 7.0 and 7.9 m2/g, respectively. This clearly shows that the BET surface areas given by water sorption depend on the swellability of the substrate. Keratin fi bers swell ~15%, whereas nylon swells only ~4% and TiO2 does not swell. No nuniform distribution of water in keratin fi bers has been known from earlier studies of Spei and Zahn (17). These authors observed that the swelling of the matrix between in- termediate fi laments by X-ray diffraction was only 5.5% compared with the diametral swelling of 16% of the entire fi ber. In further studies of the distribution of water in hair using D2O and small angle neutron scattering (SANS), Murthy et al. (18) found that the amount of water sorbed into the amorphous matrix between intermediate fi laments (nanoporous region) was relatively small compared with the total volume of water which was held in the fi ber. These are as- sumed to be the smallest pores. The exact distribution in the larger pores in the fi ber still remains unknown. The analysis of sorption data presented earlier seem to confi rm the X-ray and the SANS results. CO NCLUSIONS Th is work has shown that the strength of interaction of water with hair can be studied by sorption and desorption of water into hair by DVS as a function of relative humidity. S-D isotherms yield a hysteresis loop, the area of which is related to the intensity of water–hair interaction. Thermodynamic origin of this interaction leads to irreversibility of the sorption–desorption process. Increase in entropy is related to the formation of a Table V Hysteresis Data for Untreated Hair Used in This Study RH (%) Hysteresis, H (%) Average H 95% confi dence level S1 S2 S3 S4 S5 10 0.88 0.95 0.9 1.01 0.92 0.93 0.063 20 1.2 1.31 1.22 1.32 1.26 1.26 0.066 30 1.49 1.49 1.45 1.54 1.47 1.49 0.042 40 1.88 1.82 1.83 1.72 1.67 1.78 0.107 50 2.22 2.24 2.32 2.08 1.9 2.15 0.205 60 2.33 2.45 2.73 2.24 2.07 2.36 0.306 70 1.28 1.4 1.92 1.29 1.43 1.46 0.326 80 0.55 0.65 0.71 0.51 0.59 0.60 0.099 90 0.17 0.34 0.19 0.05 0.20 0.19 0.128 ¦Hi 12.00 12.65 13.27 11.76 11.51 12.24 0.894