124 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS However, while DeJong (3) found that the extensional fiber stiffnesses accurately ac- count for the extensional set of wool induced by hot water or urea/bisulfite treatments, we observed systematic deviations between prediction and experiment when trying to predict fiber bending set from extensional hair fiber stiffnesses after reduction and reox- idation (4). This result was interpreted not so much as an indication for the invalidity of the rules of linear viscoelasticity for the prediction of fiber set, but rather as a phenom- enon generated by a distribution of degrees of reduction and hence of Young's moduli in a reduced fiber. In consequence, the present study is directed at the measurement of the bending prop- erties of human hair during reduction and reoxidation, to prove, on the basis of the bending performance of a hair and of the principles of linear viscoelasticity, that fiber bending set can accurately be predicted. The source of the differences between the bending and the extensional properties, that is a distribution of Young's modulus in a reduced hair fiber, is discussed on the basis of model calculations. EXPERIMENTAL All experiments were carried out on chemically untreated Japanese hair [taken from the head of one of the authors (N.K.)] at room temperature. 2-cm lengths were cut from the tip and root ends of the sample hairs that were subsequently rinsed in methylene chloride, in distilled water, and then allowed to dry in air. Virtually straight fibers were chosen and cut into halves. For each set of experiments, one of these paired spec- imens was subjected to the measurement of bending stiffness and the other one to that of bending set. The bending stiffness of hair specimens was measured by applying the balanced fiber method described by Scott and Robbins (5,6) using the simple device shown in Figure la. The body of the device was made of PVC, and both the hook and the weights were made of 1-mm diameter stainless steel. To read the horizontal width between the legs of a suspended fiber, denoted as w (see Figure la), a piece of plastic ruler, cut to 30-mm length, was glued to the main stand of the device. For the continuous measurement during a succession of different treatment conditions, the solution exchange system, shown in Figure lb, was used. The bending device was placed in a beaker of 60-ml volume, and two pipettes were attached inside the beaker with their fine tips down. A funnel of 70-ml volume was connected through a tap to the wide tip of one of the pipettes, where the fine tip was fixed at about 1-cm from the bottom of the beaker. To the wide tip of the other pipette, the fine end of which was attached just a little below the edge of the beaker and at the position of the intended surface level of the solutions, an aspirator was connected. The exchange of the solution was carried out by suction at the surface in parallel with an inflow of new solution from the funnel at the bottom of the beaker. The rate of one complete exchange was set empirically to about 30 s, to take place without any serious pertubations of the fiber that would affect the measurement. Before the bending measurement, the diameter of a hair specimen was determined microscopically in water. To give reasonably sized readings and in order to keep the bending strain averaged for the cross-section of the fiber always below 1%, the weights

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.