TRIBOELECTRIC CHARGING OF HAIR 197 10-sec intervals) of charge build-up on untreated keratin fibers for both modes of rubbing by various probes. All the materials except PMMA produced positive charges on the fiber surface when rubbing was in the direction from root to rip. When the direction of rubbing was changed to from rip to root, PC and ChA reversed the sign of rribocharges accumulated on the fibers. These data suggest that PC and ChA are characterized by work functions very close to that of hair, that PMMA has a lower value of the work function, and that other materials tested lie above hair in the rri- boelectric series. In Table I, literature values of the work functions of the insulators and metals employed in this study are collected. Unfortunately, there is a considerable discrepancy between various sources, mainly due to the use of different experimental procedures and materials with varying degree of purity. However, the general trend is evident, qbt½•on© 0polyethylene, 0polypropylene, 0polystyrene, 0gold 0polycarbonate 4)PMMA 0polyamide, 0aluminum and is consistent with the data shown in Figure 3, with the exception of polyamide and aluminum which seem to possess a higher work function in relation to PMMA and PC than the one shown in Table I. It should also be noted that the values of work functions for polymers measured in air are usually higher than those found in vacuum experiments (Table I) though that does nor affect the relative position of a material in a rriboelecrric series. Since our measurements were carried our in an air atmosphere, the interpretation of the results should be based on the work function values given in the third column of Table I. Quantitative analysis of the kinetic rriboelecrrificarion data, as exemplified by the curves shown in Figures 2 and 3, by the use of Eq. 7 was attempted but did not yield consistent results. In many cases, charging curves were non-exponential, and so it was impossible to calculate the values of the parameters cr:• and k. Repeatability was also nor very good (in terms of numerical values of k and o-o•), probably because of mass transfer, surface contamination, and surface abrasion during sliding contact between the probe and fiber surface. This required frequent changes of probes and hair fibers in order to obtain reproducible measurements. Similar problems were encountered and reported by other authors working in this field [see for example (8)]. Additional information concerning the mechanism of fiber conductivity was derived from charge decay measurements. Figure 4 shows examples of discharge kinetic curves obtained for various initial charge densities in the range 1.16' 10 -9 to 5.41 ß 10 -9 C/cm 2 for unrreared fibers. It can be seen that the charge migration was insignificant for low initial charge densities and increased dramatically with the increase of initial sur- face potential. According to Watson (29), the time dependence of the parameter 1 dV 1 do. •--"" • dt (13) V• • dr 0.• where V, 0. are surface potential and surface charge density and the subscript 1 denotes the values of these quantities at time 0, provides a test for the type of discharge mechanism: (1) In the case of an ideal trap-free system (ideal dielectric), 1/O'12 d0'/dr should be constant with time for 0 t t•/2 , where tl/•, is the half-time of the decay. (2) In the case of insulators containing a large number of carrier traps, 1/0.• 2 d 0./dt should decrease with time. (3) In the case of dielectrics in which the conduction is due to ionic species, charge

198 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Table I Work Functions of Various Materials Material Work Function (eV) Measured in Vacuum Measured in Air Polymers Teflon © Polyethylene Polypropylene Polystyrene Polycarbonate Poly(methyl methacrylate) Polyamide (nylon©6,6) Metals Gold Aluminum 6.71 +- 0.28 (8) 5.75 (2) 4.26 (4) 5.24 -+ 0.24 (8) • 6.04 +_ 0.47 (8) 2 4.90 (2) 5.43 - 0.16 (8) • 5.49 -+ 0.34 (8) 2 4.77 +_ 0.20 (8) 4.8 (24) 3 3.85 +- 0.82 (8) 4.80 (2) 4.26 (4) 4.30 +- 0.29 (8) 4 4.70 (2) 4.1 (24) 3 4.08 (4) 4.3 - 4.5 (2) 5.2 (8) 5.45 (27) 5.30 - 5.38 (8) 5 4.0 - 4.9 (8) 5 4.3 (26) 5.1 (25) 3.7 +- 0.2 (8) 3.38 (28) 4.25 (28) Iron 3.91, 3.92, 4.62, 4.68 4.70, 4.72, 4.77 (28) Nickel 3.67, 4.06, 4.87 (28) 4.5 (26) 1.03 (8) 4.8 (8) • 7.2 (8) 2 9.1 (8) • (37.2) (8) 2 7.45 (8) 4.40 (8) 2.90 (8) 4 4.46 (28) • Low density 2high density 3calculated as the centroid energy E = (E d .... d- E .... ptor)/2, Ed .... = 6.1 eV for PMMAand 7.1 eV for PS andE .... ptor = 2.0 eV for PMMAand 2.5 eV for PS found in metal/ polymer contact-charge-exchange measurements 4termed "acrylic" in (8) 5range for the literature data quoted by (26). decay should be exponential so that 1/t• dt•/dt is constant (t•/2 should also be a constant independent of The data presented in Figure 4 clearly indicate that the charge density decays for untreated fibers are non-exponential (t•/2 decreases with the increase in cr•) and 1/cr• 2 dt•/dt is not constant for 0 t t•/2. Moreover, a high residual charge remains on