MORPHOLOGICAL CHANGES OF HUMAN HAIR 337 When the driving motion stops, the hair oscillates freely. During this stage, oscillation proceeds at its natural frequency f0 and is damped (8). Energy is stored as potential energy Epot and is transformed into kinetic energy Ekin, while dissipating through air and internal friction. Damped harmonic oscillation can be described as an exponentially decaying, periodic response, characterized by the logarithmic decrement -. The logarithmic decrement - is given by the natural logarithm of the ratio of the amplitudes A of two successive peaks at time t in the same direction (9): -=ln ( ) . ( ) n n+1 A t A t (3) MATER IALS HAIR STRANDS For the determination of the fi ber diameter, waviness and Youngs’ modulus and for the analysis of the in vitro hair movement, pigmented (color 7/0—medium brown) and non- pigmented hair strands (Caucasian hair) from Kerling International Haarfabrik GmbH (Backnang, Germany) are used. The in vitro analysis of the hair movement is performed on pigmented and nonpigmented, roundly bundled hair strands with a defi ned length (18.0 ± 0.1 cm) and weight (4.00 ± 0.02 g). STANDARD HAIR STRAND CLEANSING AND DRYING The hair strands are washed under tap water (V = 100 ± 20 ml/s T = 33 ± 2°C) for 2 min to remove coarse contaminants. Then, an aqueous solution (pH 5.5) of 12.5% (w/v) Figure 1. The sine function is an example of harmonic motion (7).

JOURNAL OF COSMETIC SCIENCE 338 sodium laureth sulfate is applied to hair (0.5 ml/1 g). The fi bers are rubbed against each other (shampooing) for 2 min. Afterward, the strand is rinsed under tap water for another 2 min. The processes of shampooing and rinsing are repeated once more. Finally, the hair strand is combed up to 15× by hand. After washing and combing, the hair strand is dried under standardized conditions (T = 21 ± 0.4°C relative humidity = 50% ± 3%) in a hanging position for 24 h. After 1 h, the strand is combed up to 15× by hand again. The weight of the dry hair strand is measured under standardized conditions after drying. VOLUNTEERS FOR THE IN VIVO METHOD The in vivo analysis comprises 41 Caucasian women, aged 9–67 years, with a ponytail length from 9 up to 54 cm and individual hair condition (independent hair cleansing and treatment 24 h before measurement, no styling products allowed). The amount of non- pigmented hair fi bers is determined for each volunteer and taken into account for the quantifi cation of the ponytail movement. Twenty-nine women have an amount of non- pigmented hair fi bers 5% (9–35 years) and 12 women an amount of nonpigmented hair fi bers ≥5% (27–67 years). METHODS HAIR THICKNESS MEASUREMENT The fi ber diameter of the hair strands is measured using a Laser Scan Micrometer LSM 6000 (Mitutoyo, Kanagawa, Japan). A hundred single hair fi bers are used per sample. The laser scan micrometer takes profi le width measurements as the fi ber is rotated through 360°. The circle equivalent fi ber diameter d is calculated by the cross-sectional area A of hair as follows: 2 = 2· . Q A d (4) QUANTIFICATION OF WAVINESS T he waviness of 50 pigmented and nonpigmented hair fi bers of the hair strands are mea- sured in a climate chamber (Binder KFB 720 Binder GmbH, Tuttlingen, Germany) at 21.0 ± 0.4°C and 50% ± 3% relative humidity in a hanging position. The percentage reduction of the fi ber length due to waviness is detected via laser (Dot laser LFD650-0.4-12, Picotronic GmbH, Koblenz, Germany) at the tip of the fi ber and serves as a measure for waviness. DETERMINATION OF THE YOUNGS’ MODULUS The Youngs’ modulus of the hair strands is analyzed by tensile strength measurements using the Stress-Strain-System MTT 686 with control unit UV 1000 (Dia-Stron Ltd.,