QUASI-STATIC TORSIONAL DEFORMATION OF SINGLE HAIR FIBERS 387 MATERIALS AND METHODS PREPARATION OF THE HAIR Dark brown European hair was obtained from International Hair Importers and Prod- ucts (Glendale, NY). Before any treatments, the swatches were washed with a 14% solution of sodium laureth sulfate (SLES), rinsed, and allowed to dry under controlled environmental conditions. For the studies requiring bleached hair, the swatches were bleached using a basic commercial bleach powder and 12% hydrogen peroxide for 60 min at 30°C before rinsing with warm water and dried with a hair drier set to 55°C. The swatches were allowed to equilibrate at 20°C and 50% relative humidity (RH) for 2 h in between bleaching cycles. The swatches were either bleached for two or three cycles dependent on the study. Individual fi bers were selected at random from the swatch and mounted between two 2-part plastic tabs to give a gauge length of 30 mm. A plastic torsion tab of length 14 mm was mounted and attached to the central section of the fi ber leaving two 8-mm test length sections. For the studies carried out on double bleached hair treated with a market leading com- mercial shampoo and conditioner system, the swatches were fi rst washed with 0.2 g of shampoo per gram of hair and rinsed for 30 s. This was followed by applying 0.1 g of the conditioner per gram of hair for 60 s and rinsed for 30 s. For the studies carried out on double bleached hair treated with Abyssinian oil (Crambe Abyssinica Seed Oil, Elementis), the premounted fi bers (without the central torsion tab) were immersed in the oil for 5 min taking care not to immerse the end tabs in the oil. The fi bers were then rinsed for 60 s in deionized water and then washed with a 5% SLES solution to remove any excess oil. For both treatments, the specimens were allowed to dry overnight under controlled environmental conditions. FIBER DIMENSIONAL ANALYSIS After sample preparation at equilibration at 50% RH and 20°C, the fi ber dimensions were measured with an automated Dia-Stron FDAS770. Six data slices, one rotation per slice, were collected for each specimen with three slices being taken on either side of the cen- trally mounted torsion tab. The maximum and minimum fi ber diameters per slice are obtained, with the averages across each slice being used in the calculations. TORSIONAL EXPERIMENTS The torsional properties of each fi ber were measured using an automated Dia-Stron FTT950. The fi bers were subjected to a pretension force of 10 g at a linear extension rate of 10 mm/min. From this, it is possible to obtain the tensile elastic modulus, although this was not recorded for all of these studies. A torsional gauge force of 2 mg was applied and the fi ber specimens were rotated through an angle of 90° at a rate of 5°/s. All fi bers were equili- brated at the required environmental conditions for at least 2 h before the measurements were taken.

JOURNAL OF COSMETIC SCIENCE 388 RESULTS AND DISCUSSION TORSIONAL MODULUS RELATIONSHIP WITH FIBER GEOMETRY Torsional modulus measurements on European virgin hair fi bers with cross-sectional areas ranging between 2,000 and 6,500 μm2 were recorded (Figure 3). This large data set, enabled by the use of the automated system, provided a diverse range of dimensions. Our data confi rms the fi ndings in previous publications (12,23) that the torsional modulus decreases with increasing fi ber dimensions or polar moment of inertia. The polar moment of inertia of an ellipse is described by equation 4, where a and b are the major and minor axis radii, respectively. ʌ 3 3 = + 4 p I a b ab (4) This effect was further exemplifi ed by additional measurements that were conducted on fi ner hair fi bers obtained from a European juvenile. These results clearly demonstrate that the storage modulus of hair is not a material property but is highly dependent on fi ber dimensions, particularly for fi ner fi bers (12). As mentioned earlier, the torsional stress is the greatest at the periphery of the fi ber, where the cuticle layers are found. The cuticle thickness does not substantially change as the whole fi ber diameter increases but the cuticle to cortex ratio does change. As the whole fi ber diameter increases, the cuticle to cortex ratio decreases. This observed relationship between torsional storage modulus and diameter, as shown by our data and others, is sug- gestive that the outer layers of the cuticle are dominating the measurement (12). Figure 3. Plot of torsional modulus G as a function of the polar moment of inertia, Ip, for both virgin normal and virgin fi ne European hair.