J. Cosmet. Sci., 61, 31–38 (January/February 2010) 31 Modeling the time-dependent water wave stability of human hair F.-J. WORTMANN, M. STAPELS, and L. CHANDRA, Textiles & Paper, School of Materials, University of Manchester, PO Box 88, Manchester M60 1QD, UK (F.-J.W.), DWI e. V. and ITMC, RWTH Aachen, Pauwelsstrasse 8, D-52056 Aachen, Germany (M.S.), and Unilever R&D, Port Sunlight, CH63 3JW Wirral, UK (L.C.). Accepted for publication June 15, 2009. Presented in specifi c parts at the 3rd International Conference on Applied Hair Science, TRI Princeton, September 15–16, 2008. Synopsis The viscoelastic bending recovery of human hair is described by a hydro-rheologically complex, two-phase model, where the humidity dependence of the pertinent parameters as well as the effects of physical aging are known. Model calculations are conducted to assess the consequences of the time- and humidity-dependent bending recovery of human hair for the formation and the stability of the water wave. It is shown that a hair fi ber that has been set in bending will achieve at 65% RH a recovery of about 50% after about ten times its storage time prior to release, if it is a non-aging material. However, aging drastically slows the recovery pro- cess so that it approaches an apparent “equilibrium,” fi nal recovery value of about 60%. The values of fi nal recovery decrease linearly with water content, vanishing as expected at maximum water content, where the hair fi ber is above its glass transition. The calculations further show that damage to the elastic modulus, attributed to the intermediate fi laments, is expected to reduce recovery and thus enhance fi ber set. The cal- culations demonstrate that it is in fact the phenomenon of physical aging that makes water waving a feasible and practically successful process for hair styling. INTRODUCTION In a recent investigations (1) we considered the recovery of human hair from bending deformation in an experimental context related to the formation and stability of a water wave. The bending recovery behavior was determined for a range of humidities and aging times and comprehensively analyzed on the basis of a two-phase fi lament/matrix model representing the complex morphology of hair. In this model the intermediate fi laments (IF) (2), or rather their α-helical fraction, are identifi ed as the fi lamentous phase in hair. The matrix in consequence contains as major components the amorphous IF-associated proteins (IFAP) (3) and also summarily the rest of the morphological components, such as cuticle, cell membrane complex, etc. (4). Address all correspondence to F.-J. Wortmann. The current address of M. Stapels is Kao Chemicals Gmbh, D-46446, Emmerich, Germany.

JOURNAL OF COSMETIC SCIENCE 32 The matrix of keratins is an amorphous protein that exhibits a strongly humidity-dependent glass transition (5,6). Under most practical conditions, such as 20°C and 65% relative humidity (RH), hair is a semi-crystalline, glassy polymer, for which the viscoelastic prop- erties change continuously due to physical aging (7,8). Furthermore, it was found that both the limiting, short-time elastic modulus of the matrix as well as the speed of the viscoelastic relaxation were affected by water, thus making hair a hydro-rheologically complex (HRC) material (1). These investigations now explore by model calculations the consequences that derive from the effects of humidity and physical aging on the time-dependent bending recovery of human hair, and which impact on the formation and the stability of the water wave. The results are meant to further contribute to our understanding of the daily consumer practice where bending deformation of hair, set, and recovery under conditions of varying temperature and humidity play an important role for the formation and stability of a hairstyle. EXPERIMENTAL, THEORETICAL, AND DATA BASIS The ring test procedure (9,10) was found (1) to be best suited to determine the bending recovery of single hair fi bers under various conditions of humidity and physical aging time. Tests, which are the basis of our considerations, were conducted on untreated Caucasian mixed hair. For the test, fi bers were wound around 10-mm-diameter glass cylinders and their ends fi xed. The cylinders were immersed in distilled water, dried, and subsequently stored for various aging times under controlled humidity conditions at 20°C. After this storage time, the fi bers were cut along a line parallel to the cylinder axis, yielding partially opened fi ber rings. The recovery of the fi ber segments from the rings toward a straight shape was determined by measuring the time-dependent diameters of the rings. Defi ning bending set as the retained fraction of initial bending deformation, it is readily shown (9) that the time-dependent set, S, of the fi ber at any point around the ring and the diameter, d, of the circle enclosing the partially opened ring are related by: 0 S(t) d d(t) (1) where d0 is the diameter of the cylinder on which the fi bers are initially wound and t represents time. Set is related to recovery, R, as the primary parameter to be used in this study: R(t) 1 S(t) (2) According to investigations by Chapman (11) and Denby (12), based on the general prin- ciples of the viscoelastic properties of polymers (13), the formation and time-dependent recovery of the hairs rings is determined by two antagonistic bending rigidities (stiff- nesses) according to: Z R(t) B(t)/B(t ) (3)