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)

VISCOELASTIC BENDING RECOVERY OF HAIR 33 B(t) is the time-dependent bending stiffness at any time after the initial deformation at t=0. The fi ber is released at t=ω, and B(t-ω) is accordingly the bending stiffness of the same fi ber if it had been bent at the time of release. B(t) relates to the straight fi ber and tends to re-straighten it, while B(t-w) derives from the bent state of the same fi ber and thus opposes re-deformation. Since both variables act on the same cross- sectional area and shape, R becomes a normalized parameter, for which diameter-related effects are canceled. Furthermore, it was established (1) that hair shows changes of relaxation behavior with aging time, tA, which are consistent with Struik’s (14) effective time principle and with an aging rate of μ=1 (see equation 10 below). That is, hair bending recovery curves shift on the log-time scale without changing their shape by one decade to higher times with every decade of increase in tA. In analogy to the case of extensional relaxation (8,15), time-dependent bending stiffness is described by: ' f B(t) B B (t) (4) with 0 'B f B B (5) B0 is the initial value of the bending rigidity at t=0. B∞ is the limiting, elastic stiffness reached by the fi ber after complete physical relaxation. Ψ is the relaxation function. In the context of the two-phase model, B∞ is the contribution of the elastic, partly α-helical fi laments, while ΔB is the limiting elastic contribution of the matrix, for which the vis- coelastic behavior is described by Ψ(t). A feasible choice for Ψ(t) is the stretched exponential of the Kohlrausch-Williams-Watts (KWW) function (1,16), given by: m ( ) exp[ (t/ ) ] W t (6) where τ is the characteristic relaxation time and m the shape factor, which give the posi- tion and the width of the function on the log-time scale, respectively. It was found (1) that the shape factor of the KWW function was independent of humidity and aging time, with a mean of m=0.28, which is close to the universal value of 1/3 (14). The relaxation of the matrix contribution to the overall fi ber bending stiffness is very fast in water (8,15), where hair is well above its humidity-dependent glass transition (6). This removes all effects of aging and yields effectively ΔB=0 after the wetting of the bent fi bers during the initial step of the experiment. A substantial rubber elastic contribution to ΔB, as is expected from the considerations of Hearle et al. (17), could experimentally not be verifi ed, namely by Feughelman and Druhala (18), and is thus neglected. Since this removes the time dependence of the numerator in equation 3, the combination of equations 3 and 4 simplifi es to: ( ) B ] '% f f /[B t t (7)