QUASI-STATIC TORSIONAL DEFORMATION OF SINGLE HAIR FIBERS 391 force required to twist the hair fi bers with increased RH. The initially linear relationship between measured force and twist angle begins to plateau as the twist angle increases for both virgin and bleached (Figure 5) hair fi bers. It is noteworthy that an increased moisture level results in the plateauing effect occurring at a smaller twist angle potentially indica- tive that the fi bers are being twisted beyond the elastic region into the yield region. This apparent transition occurs between 40° and 50° which is considerably lower than the angle of twist which is often used in the pendulum methods. For this reason, an analysis angle of 45° was applied to ensure that only the elastic torsional deformation is analyzed. When hair fi bers undergo bleach treatment, the disulfi de bonds of the cystine residues are oxidized diminishing the stability of the structure (30) compared with virgin fi bers but Figure 6. P lot of the torsional modulus G as a function of RH of virgin and 3 × bleached hair. Figure 7. Plo t of the torsional modulus as a function of RH for the calculated torsional modulus values for the cuticle and cortex components.

JOURNAL OF COSMETIC SCIENCE 392 as a result also increases the potential for both inter and intramolecular hydrogen bond- ing. In high humidity environments, disruption of these hydrogen bonds in addition to the cleaved disulfi de bridges results in a more deformable fi ber and thus a lower elastic modulus than undamaged, virgin fi bers. As the humidity decreases, the increase in hy- drogen bonding stiffens bleached fi bers to a greater extent than virgin fi bers. Studies by Harper and Kamath (14) showed that the torsional modulus of bleached hair at low humidity is higher than that of virgin hair. At high humidity this effect is reversed, with the crossover point occurring at around 55–60% RH. Our data show a similar rela- tionship with a marked difference between virgin and 3 × bleached hair at the lowest humidity (Figure 6), most likely because of the increase in hydrogen bonding due to the harsh bleaching. Separation of the cuticle and cortex contributions to the torsional modulus using the mod- eling approach described previously (Figure 7, Table II), hypothetically illustrates the increased stiffness of the cuticle at low humidity, particularly for the bleached hair. This is likely because of an increased amount of hydrogen bonding within the endocuticle and the matrix or an increase in electrostatic interactions. Although this modeling approach may account for the potential signifi cant contribution of the cuticles to the overall torsional modulus, it does not make any allowance for the role in which the matrix plays in torsional Table III Means Values for the Tensile and Torsional Elastic Moduli for Virgin, 2 × Bleached and Treated Hair Fibers Treatment Tensile modulus, E (GPa) Torsional modulus, G (GPa) Virgin 4.43 (b) 2.58 (a) 2 × Bleached 4.86 (b) 3.07 (b) 2 × Bleached, shampoo + cond. 5.35 (a) 2.83 (c) 2 × Bleached + oil 4.79 (b) 2.18 (d) Measurements were all conducted at 20% RH. A one-way analysis of variance was used to identify any sig- nifi cant differences between the tensile modulus groups. Post hoc analysis was conducted using the Tukey Honesty Signifi cant Difference (HSD) test. Groups that do not share a letter are signifi cantly different at the 95% confi dence level. The same analysis was conducted for the torsional modulus test groups. Table II Means for the Experimental Torsional Storage Modulus of Virgin European and 3 × Bleached Hair at 20, 50, and 80% RH RH (%) Experimental Predicted G (GPa) GCuticle GCortex Virgin 20 1.50 2.32 1.20 50 1.34 2.24 1.01 80 0.81 1.39 0.60 3 × Bleached 20 1.96 4.33 1.09 50 1.84 3.27 1.33 80 0.62 1.35 0.35 The theoretical values of GCuticle and GCortex have been calculated using the approach described in (23) based on a sample size of 45.