J. Cosmet. Sci., 65, 59–68 (March/April 2014) 59 Analysis of the torsional storage modulus of human hair and its relation to hair morphology and cosmetic processing FRANZ J. WORTMANN, GABRIELE WORTMANN, HANS-MARTIN HAAKE, and WOLF EISFELD, School of Materials, University of Manchester, Manchester M13 9PL, United Kingdom (F.J.W., G.W.), and BASF Personal Care and Nutrition GmbH, 40589 Duesseldorf, Germany (H.-M.H., W.E.) Accepted for publication February 7, 2014. Synopsis Through measurements of three different hair samples (virgin and treated) by the torsional pendulum method (22°C, 22% RH) a systematic decrease of the torsional storage modulus G′ with increasing fi ber diameter, i.e., polar moment of inertia, is observed. G′ is therefore not a material constant for hair. This change of G′ implies a systematic component of data variance, which signifi cantly contributes to the limitations of the tor- sional method for cosmetic claim support. Fitting the data on the basis of a core/shell model for cortex and cu- ticle enables to separate this systematic component of variance and to greatly enhance the discriminative power of the test. The fi tting procedure also provides values for the torsional storage moduli of the morphological components, confi rming that the cuticle modulus is substantially higher than that of the cortex. The results give consistent insight into the changes imparted to the morphological components by the cosmetic treatments. INTRODUCTION Mechanical tests on human hair are essential tools to determine their properties as guides for product research and development (1). In extension, all morphological components contribute to the parameter values according to their fractions in the cross-s ectional area, while a very strong bias towards the outside layers will occur for bending and torsion. Therefore, a strong infl uence by the surface layer of a hair, i.e., by the cuticle, can be ex- pected for the latter tests. These tests should thus be especially suitable to detect changes on or near the hair surface through cosmetic processes and products, which may pass un- detected in tensile testing. Applying analytical technology described by Persaud and Kamath (2), the torsional properties of European human hair at condition s of low humidity were investigated to Address all correspondence to Franz J. Wortmann at franz.wortmann@manchester.ac.uk. This paper was presented in specifi c parts at the 4th International Conference on Applied Hair Science, TRI Princeton, October 5–6, 2010.

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)