BENDING OF HAIR AND PERMANENT WAVING 125 o) b) hook sample fo aspirafor new solut'lon funnel fop pipeire f bending • device • freafment' soluhon Figure 1. a. Illustration of the device for the measurement of the bending stiffness of human hair, built according to the description by Scott and Robbins (5). b. Sketch of the solution exchange system to vary the treatment conditions during a bending relaxation measurement. attached to both ends of the specimen were carefully chosen, depending on the reducing conditions and on the fiber diameter. Prior to the experiment, the fiber was laid in a petri dish in distilled water for 20 min and then suspended on the hook of the bending device placed in a beaker filled with distilled water. After allowing 30 s for the fiber to stabilize, the measurements of the horizontal distances between the fiber ends were started and continued for each hair specimen through a sequence of the following treatment conditions: 1. Distilled water for 30 min 2. Reduction by thioglycollic acid (TGA) solution with an appropriate concentration and pH for 20 min 3. Rinse in distilled water for 20 min 4. Reoxidation by 2.3% hydrogen peroxide at neutral pH for 20 min 5. Rinse in distilled water for 20 min In processes 3 and 5, the solution exchange system was driven every five minutes for four cycles. To determine fiber bending set, hair specimens were carefully wound around PVC cylinders with 12-mm diameter under a load of 200-mg, keeping the hair perpendic- ular to the axis of the cylinder. The ends of the fiber were fixed with small drops of nail polish. The cylinders were suspended in a beaker and treated in the same sequence of conditions as during the bending measurements. After the final rinse, the cylinders were taken out from the beaker. The hair loops were cut and dropped into a petri dish filled with distilled water, where without delay the diameters of the loops were mea- sured with a ruler within one minute.

126 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Both the data for the bending stiffness and for fiber bending set were obtained on a total number of 89 hairs, i.e., 178 paired samples under a wide range of reducing condi- tions. The concentration of TGA was varied from 0.025 M to 1.0 M, and the initial pH of the solution was altered between pH 7.5 and pH 9.7 using appropriate amounts of 25 % ammonia solution. The testing procedure ensures a basically infinite liquor/hair ratio and, therefore, con- stant conditions during any one treatment step. It has to be pointed out, though, that under practical conditions this ratio rarely exceeds 2:1 (1). DEFINITIONS AND GEOMETRICAL CONSIDERATIONS As Scott and Robbins (5,6) have shown, the time-dependent bending stiffness B(t) of a hair under the conditions of the balanced fiber method is directly proportional to the square of the time-dependent, horizontal distance, that is the width w(t), between the suspended fiber ends (see Figure la): B(t) = F w2(t)/8 (1) where t is the time and F the force applied to each fiber leg. Due to the experimental procedure, allowing the fiber 30 s to stabilize on the device before the first measurement is taken, the initial width w(0) and hence the initial bending stiffness B(0) = Bo are not directly accessible but are estimated by extrapola- tion of the curve, e.g., for B(t), to t = 0. Figure 2 shows a typical curve for the change of the relative bending stiffness B(t)/Bo during a treatment cycle (0.3 M TGA at pH9) as well as the experimental definitions of the variables to be used below. The experimental results show that, as a rule, rinsing following reduction stops the decay of the fiber bending stiffness at a level termed B•e, where the subscript, in accor- dance with the terminology used in reference 4, refers to "reduced." B•o is the bending stiffness that a fiber, left straight during the treatment sequence, would exhibit after- wards. The suffix "ro" stands for "reoxidized." As indicated in Figure 2, B•o is expected to be a little smaller but close to Bo (3,4). Parallel to the balanced fiber experiments, fiber bending set was determined on hair loops from paired samples, applying the procedure reviewed by Gershon et al. (1) in the version described in reference 4. Set S is generally defined as S = e/e o (2) where E o is the strain imposed on the fiber during the treatment sequence and • the strain remaining after release. Recovery R is correspondingly given by R = ! - S (3) It is readily shown that, neglecting fiber diameter and taking into account that setting one fiber on a cylinder gives numerous loops, set after cutting the loops is given by s e = d•/• (4)