HUMAN HAIR MOISTURIZATION WITH COSMETIC PRODUCTS 305 T HERMODYNAMIC ORIGIN OF SORPTION HYSTERESIS T he following discussion is based on the work of W. P. Bryan (4) on sorption hysteresis. The nature of the DVS experiment lends itself conveniently to thermodynamic analysis. If the sorbent (hair) and the sorbate gas (water vapor) are confi ned to a cylinder with a piston, then sorption and desorption, respectively, can be carried out by reversibly com- pressing and expanding the sorbate. If the amount of moisture (sorbate) in the hair is determined and plotted as n (moles) vs lnP (P = partial pressure of water vapor), then we get the sorption and desorption isotherms. If the sorption and desorption process is re- versible, then the sorption–desorption isotherms will be coincident, and the overall work carried out is zero (W = 0). On the other hand, if the process is irreversible, then applying the second law of thermodynamics, the compression–expansion path gives a loop. The work that needs to be carried out on the system is given by the area of the loop and will be negative as seen in equation 1: ¨ ¨ 0 ln ln ln , D n low P S P W pdV RT n d P (1) w here R is the gas constant, T absolute temperature, nD and nS are moles of sorbate in the sorbent during desorption and sorption, respectively, P0 is the saturation vapor pressure of the pure sorbate, and Plow is the pressure between 0 and P0. W = -RT (area of the constant temperature hysteresis loop). For this purpose, the isotherm needs to be plotted as (moles of water sorbed) vs lnP. How ever, in this work, S-D data are plotted in terms of regain% vs RH. The region sur- rounded by the isotherms is the hysteresis loop. We have arbitrarily quantifi ed hysteresis H at a given humidity as fol lows: . D S H M M (2) T o correct for this change, we can express equation (2) as H = K (MD–MS). Using H, we can express equation (1) as a fi nite summation as œ 1"n i W RT K H i (3) Eq ua tion (3) can be used to interpret moisturizing ability of actives from cosmetic formu- lations on hair. Irrev ersibility of the S-D process also leads to an increase in the entropy of the system given by equation (4). ¨ 0 ln ln ln . low P D S P dS R n n d P (4) 'S = R (area of the constant temperature hysteresis loop). Increase in entropy refl ects the change in the fi ber structure as a result of sorption of water and consequent swelling. Rosenba um (5) has examined the applicability of Flory–Huggins polymer solution the- ory to sorption of water into keratin and has found that the theory agrees with the iso- therm only at high vapor pressures. Agreement at lower vapor pressures improves with

JOURNAL OF COSMETIC SCIENCE 306 the consideration of volume change with sorption of water, something similar to the transition occurring in polymers at the glass transition temperature. QUANTIF ICATION OF MOISTURIZATION Moistur ization as understood in the cosmetic industry can be loosely defi ned as the ability of a cosmetic product to enhance the retention of water in hair or skin. Because both hair and skin naturally have the ability to retain water to a certain extent with- out the application of any product, we need to defi ne moisturization with reference to the untreated hair or skin. Change in sorption hysteresis as a result of product ap- plication enables us to defi ne a hysteresis ratio of the hair treated with the product to that of the untreated hair. A hysteresis ratio higher than 1 (can be expressed as a percentage) indicates the ability of the product to absorb and retain water (Wtr Wuntr). A ratio lower than 1 indicates that the treatment with the product facilitates evaporation of water from treated hair (Wtr Wuntr). We defi ne this ratio as HR (hys- teresis ratio): (Area o f the hysteresis loop of treated hair in a given RH range/Area of the corresponding loop for untreated hair in the same RH range). . R tr untr H W W (5) Fr om eq uation (2), H = K (nD - nS) where K is a constant, then assuming the constants to be the same for treated and untreated hair, and replacing the integrals in equation (1) with fi nite summation, we can express equation (5) as follows (because all other factors cancel): , œ œ R tr untr i,tr i,untr H W W H H (6) (i = 1… n), n being the number of RH steps selected over the 'P interval. ¦Hi is the area of the hysteresis loop in the selected range of RH. From a practical point of view, it is suggested that the higher (70–95% RH) and the lower (0–10% RH) segments of the isotherm should not be included in this calculation. Including these regions in the calcu- lation can skew the result, limiting its usefulness. It is this strong interaction between water and the protein component in the mid-humidity range which gives rise to an increase in entropy and the moisturizing effect. RESULTS AND D ISCUSSION SORPTION HYST ERESIS Typical outco me of a DVS experiment conducted at a constant temperature (in this work, all experiments were carried out at 25°C) are a pair of isotherms forming a loop (S-D loop). To check the reproducibility of the measurement, we ran three experiments from a single sample of hair. The average moisture contents in each of the experiments in the S-D mode are given in Table I, and the S-D loops are plotted in Figure 1. The S-D iso- therm loops clearly show the accuracy of the instrument and excellent reproducibility of