JOURNAL OF COSMETIC SCIENCE 264 the droplet to wick into the hair layer was recorded. On virgin hair, the droplet did not wick, due to high hydrophobicity (t 5 min). In contrast, on “relaxed hair, wicking oc- curred in 6 s, indicating that the hair surface was hydrophilic and signifi cantly damaged due to the relaxation process. On the 4X bleached hair sample, the hair was slightly dis- colored, but the water droplet did not wick within a 5-minute period, indicating a mild level of surface damage. HAIR VOLUME EXPERIMENT It is well known that curly hair assembly displays a signifi cant increase of volume in high humidity. In the present experiment, the objective was to use this property to investigate the role of hair fi ber–fi ber interaction on the volume increase and shape retention of the hair assembly. The experimental design is shown in Figure 2. Prior to treatment with silicones, clean, curly tresses and relaxed tresses were placed for an hour in an environmental chamber at 25°C and 75% RH, and then a picture was taken of the untreated tresses. The tresses were then treated with silicones, as indicated in section 2.3. The treated tresses were placed for an hour in an environmental chamber at 25°C and 75% RH, for an hour and then a picture was taken of the treated tresses. Volume of the treated tresses was compared to the control (tress before treatment). Thereafter, fi bers were taken from the curly tress and mounted to form pairs of parallel fi bers for the in- cline plane hair loop measurement. Fibers were also taken from the relaxed tresses to create the hair loops. THEORY Sliding a block down an inclined plane is a very old method of measuring static friction (5). If the surface is inclined at a small angle, θ, a component of the gravitational force acts downward along the surface of the inclined plane (Figure 3a). The magnitude of this component is mg sin θ. If the block does not slide, it is acted on by the static frictional force, fs. If the surface is inclined to the degree that the tangential component of the gravitational force exceeds fs, then static friction is overcome and the block begins to Figure 2. Experimental design.

2008 TRI/PRINCETON CONFERENCE 265 slide. At the angle where the block is just on the verge of slipping, fs is equal to mg sin θ and the force balance leads to: f mg fs m g s − = ⇒ = sin sin θ θ 0 (1) N mgcos N mg − = ⇒ = cos θ θ 0 (2) Note that the sin θ represents a frictional force, normalized by the weight of the block. The usual static coeffi cient of friction, which is defi ned by the relation fs = μN, can be readily deduced from the sliding angle and is equal to μ = tan θ. The hair loop experiment is similar to the sliding block experiment except that the loop is in contact with the inclined plane at only four points. Equations 1 and 2 apply to the loop center of mass. The dimensional force can be derived by multiplying sin θ by the weight loop (20 μN). Because the weight of the loop is so light, the adhesion forces created by some of the silicone material allow the loop to stick to the parallel fi bers. The parallel fi bers can be inclined at angle higher than 90°. For angle higher than 90°, the force balance corresponds to a free fall problem involving adhesion forces (Figure 3b). The tangential and normal component of the force exerted on the loop are also described by equations 1 and 2. In that case, cos θ represents the normalized normal adhesion, whereas sin θ is the normalized tangential adhesion. RESULTS FIBER–FIBER INTERACTIONS Untreated hair. The histograms of angle values for untreated virgin hair, bleached hair and relaxed curly hair are shown in Figure 4. A summary of the analytical data is shown in Table I. For untreated hair, the distribution was narrow and the average sliding angle was quite low (~26°), indicating weak hair fi ber–fi ber interactions. The variations of angle may be due to the variations of contact area for each sliding event (one or few cuticle Figure 3. Force balance. (a) Hair loop sliding down an inclined plane with sliding angle θ 90°. (b) Free fall of a hair loop held by adhesion forces θ 90°.