2010 TRI/PRINCETON CONFERENCE 141 In the context of studying water-set, Wortmann and collaborators connected this experi- mental geometry (a single loop curl) to quantities that can be connected to a thermody- namic description of the problem (4). In Figure 1, the curl geometry and the relation of the evolving curl shape to the set and fade time are illustrated. The images are analyzed using software written by the authors in three stages. First, each image is sectioned to produce a single, time-stamped frame for each tress. Second, each tress image is further sectioned into fi ve slices of varying temperatures. Third, the diameter of the tress’ single curl is computed using the visible height of the tress (Figure 1b-c). When the fi ber tips are not visible, the diameter of curvature is simply the tress height. When the tress opens far enough that the bottom of the tress is the tip of the fi ber, we use the geometry shown in Figure 1c, which leads to the relation L/d = sin(Lm/πd) where Lm is the length of the straightened hair to determine the curl diameter d. The diameter data are converted to thermodynamically relevant quantities using the pro- cedure of Wortmann et al. (4,5). The set S is the diameter of the rod (1 inch) divided by the diameter of the curl. The initial set S0 is measured from the fi rst image after removal of the hair from the rod. Recovery is described by R = 1 − S = 1 − d rod /d. DAMAGE ASSESSMENTS Damage is assessed by several methods including mechanical and chemical assessments. Tensile properties of the fi bers are measured using the Diastron MTT-675 Fibers are clamped between brass ferules, which are used by the robot to handle the fi ber. The fi ber cross section is measured using a laser scanning micrometer (Mitutoyo LSM 6100. The fi bers are extended to breaking and each force extension curve is analyzed to extract the elastic (Young’s) modulus, the post-yield modulus and the break stress. The complex shear modulus is determined using a torsional pendulum. An L = 3 cm length of fi ber with a 5 g weight of moment M = 8.85119e-8 kg-m2 is held in the auto- mated pendulum. First the fi ber dimensions are scanned using a Mitutoyo LSM6100, then the pendulum is wound 360° and released. The major and minor axes are a and b. The period of the pendulum’s motion T is used to extract the shear modulus G = 16πLM/ T2(a3b + ab3) The speed of the pendulum is measured by the time it takes for a white stripe on the weight to pass in front of a photodetector. On each oscillation, the pendu- lum slows and the ratio of the velocity on one cycle to the next is used to extract tanδ. EXPERIMENTAL DESIGN Bleached and Virgin hair prepared in each of three moisture conditions (wet, 65% and 20% RH) are curled for 15, 30, or 60 seconds on the gradient iron. All temperatures be- tween 100°C and 225°C were tested. From these tresses, single fi bers were selected for damage assessment. RESULTS The temperature gradient curling iron was used to collect effi cacy data for bleached and virgin hair over a wide range of conditions. We see the overall effects and the range in

JOURNAL OF COSMETIC SCIENCE 142 Figure 2 where recovery is plotted as a function of time after 60 second treatments for a variety of initial conditions and temperatures. A few trends are immediately obvious. First, every curve shows the same qualitative behavior - an initial rapid relaxation fol- lowed by a very slow, stable phase in which curl can hold essentially all day. Initial water content is a critical factor, especially for bleached hair. But for treatments above 180°C initial conditions matter less. Also, irons are far more effective at lower temperatures on wet than dry hair and there is very little temperature dependence for wet heating in either bleached or unbleached hair. Turning in Figure 3 to a more detailed look at the initial set, we see that heating is det- rimental for bleach-damaged hair. For the dry hair, or any hair, higher temperatures provide little improvement in initial set. Above 200°C, there is no benefi t and in some cases the added heat actually produces worse results. Duration of hold is the one quantity that consistently improves with increasing temper- ature (Figure 4). This effect is clear and also large, producing factors of two difference in hold time between 200°C and 100°C as hold times vary from fractions of an hour to nearly two hours. The fi nal hold (Figure 5) shows the most compelling result on effi cacy. There is little temperature dependence. Again wet, bleached hair is an exception. But even in this case, heating to just 150°C seems suffi cient. Heating above 200°C seems counterproductive. We also investigated the effects of treatment time on effi cacy, but found little of note and do not display these data here. Turning to the measurement of damage we detect this damage from a single treatment. In other papers on hair damage it is common to perform multiple cycles of damage rep- resenting the accumulated effects over time (1–3,6). Extensional stiffening coupled with a drop in break stress is observed for bleached hair, but not for virgin hair. The loss of plasticity seen through the decrease in log-decrement in Figure 6 is a sign that bound Figure 2. Effi cacy results showing recovery vs. time for many combinations of temperature and initial mois- ture for bleached and virgin hair.