JOURNAL OF COSMETIC SCIENCE 60 determine, namely, the precision of the measurements. The potential of the method to detect the effects of cosmetic processes and products was assessed for perm-waving com- bined with bleaching as a harsh cosmetic process to impart hair damage, as well as for the further application of a shampoo. Specifi cally, in investigations of the torsional storage modulus G′, a substantial vari- ability of this parameter was observed for human hair, e.g., by Harper and Kamath (3), which impacts negatively on the ability of the method to discriminate between differ- ent samples an d treatments. A substantial part of this variability can be traced to the fact that the storage modulus for hair is in fact not a material property, but shows a signifi cant dependence on fi ber geometry, e.g., a decrease with fi ber diameter (2). This phenomenon has been observed over the whole range of humidities (2) and intro- duces a systematic error, which in turn creates obvious problems with the analysis of the data (4). This systematic error of G′, deriving from the violation of the assumption of fi ber geom- etry invariance, is determined for a set of data for virgin as well as cosmetically treated hair and analyzed on the basis of the cortex/cuticle structure of hair. This leads to a largely improved discriminative power of hair torsional measurements for the infl uences of cos- metic processes and products, as well as to values for the torsional storage moduli of the two morphological components. MATERIALS AND METHODS PRINCIPLES AND APPLICATION OF THE TORSIONAL PENDULUM METHOD All experiments on hair fi bers were conducted on a single fi ber torsion pendulum appara- tus (TRI/Princeton, NJ) as described by Persaud and Kamath (2). For the measurements, so-called brass crimps with an internal silicone polymer tube (Dia-Stron, Andover, United Kingdom) were attached to both ends of a 5-cm-long hair fi ber, leaving an effective test- ing length of 3 cm. One crimp of a fi ber was introduced into the upper clamp of the in- strument, while to the other, a cylindrical torsional weight (weight: 5 g) was attached. The geometry of the cylinder and thus its moment of inertia were chosen such as to pro- vide a frequency of the torsional oscillation of about 0.1 Hz for the chosen hair material. For the test, the fi ber was twisted through 360° and released. The machine monitored the torsional oscillation movement of the cylinder and determined frequency and amplitudes. The instrument was enclosed in a chamber, which provided controlled environmental conditions (22°C, 22% RH). This low humidity was chosen, since it was expected to provide the best discrimination between cosmetic treatments (3). Twisting angle and the torsional weight impart only low shear and tensile strains, well within the linear visco- elastic region of a hair fi ber (5,6). Pre-conditioning and storage conditions were chosen such as to avoid effects of physical ageing (7,8). One primary parameter determined by the test is the torsional storage modulus G′: JlX2 G I ′ (1)

TORSIONAL PERFORMANCE OF HUMAN HAIR 61 where J is the moment of inertia of the pendulum, l the length of the fi ber, I the polar moment of inertia of the fi ber, and ω the frequency of oscillation, with: X 2Q T (2) where T is the time taken for one oscillation. Equation 1 applies if the damping of the torsional oscillation, i.e. , the dissipation of torsional oscillation as frictional energy, is low. Though hair is inherently a viscoelastic material, it is consistently below its glass transition temperature for low to medium relative humidities (9), showing in conse- quence long relaxation times and thus little damping (7,10,11). The specifi c cross-sectional shape of a human hair, though irregular along its length, is generally assumed to be elliptical, so that the polar moment of inertia is given by: Q¬  ž ­ ž ⋅ ( ) 3 3 4® I a b ab (3) where a is the long and b the short semi-axis of the ellipse, respectively. Arithmetic means for G′ were determined from individual values for T, as determined along the oscillation curve and according to Equations 1 and 2. Five repeat measurements were conducted for each fi ber, averaged and taken as the G′-value for that fi ber. Values for fi bers tested for a sample were further summarized by their arithmetic mean, variance, standard error (S.E.), and the limiting value for the 95% confi dence range (1.96 S.E.) (4). Data sets were compared using the Fisher least signifi cant difference (LSD) test (12). This is essentially a multiple t-test and as such very non-conservative (4). It therefore appears generally well suited for testing in the context of cosmetic products and processes. Also separate t-tests for specifi c pairs of samples were conducted. CHARACTERIZATION OF HAIR GEOMETRY All tests and treatments were conducted on dark brown, commercial, Caucasian hair (In- ternational Hair Importers & Products Inc., Glendale, NY). The fi bers were washed with 3% sodium lauryl sulfate (BASF, Duesseldorf, Germany), rinsed thoroughly with warm water, and allowed to air-dry under ambient conditions. To determine the cross-sectional shape of a fi ber, the assumption of general ellipticity was made. For each fi ber, prepared for torsional testing, the smallest and largest diameters were determined at fi ve equidistant positions of a 3-cm-long fi ber through a 360° rota- tion by means of a Laser Scan Micrometer (LSM-500, Mitutoyo, Kanagawa, Japan), as implemented by Dia-Stron Ltd., United Kingdom. At each point along the fi ber, the smallest and largest diameter was determined. The arithmetic means of the measurement data were used to calculate the overall short and the long axis of the elliptical fi ber cross section. Diameter measurements were conducted under conditions of constant, but ambi- ent laboratory climate (approximately 22°C, 55% RH). The diameter data thus obtained