New Insight on the Friction of Natural Fibers. Effect of Sliding Angle

Article pubs.acs.org/Langmuir

New Insight on the Friction of Natural Fibers. Effect of Sliding Angle and Anisotropic Surface Topography Hiroyasu Mizuno,†,‡ Gustavo S. Luengo,*,§ and Mark W. Rutland*,†,∥ †

Surface and Corrosion Science, School of Chemical Science and Engineering, KTH Royal Institute of Technology, Drottning Kristinas vg 51, 100 44 Stockholm, Sweden ‡ L’Oréal, KSP Research and Innovation center, 3-2-1 Sakado, Takatsu, Kawasaki, Kanagawa, Japan § L’Oréal Research and Innovation, Aulnay-sous-Bois, France ∥ SP Technical Research Institute of Sweden, SP Chemistry, Materials and Surfaces, Box 5607, SE-114 86 Stockholm, Sweden ABSTRACT: The friction anisotropy of human hair has been investigated as a function of angle using AFM fiber probe measurements to evaluate the role of cuticle alignment. It is found that friction hysteresis, the difference in friction coefficients between sliding with or against the cuticle direction, is essentially nonexistent for native human hair. For damaged human hair, however, a clear friction hysteresis is observed, which appears to be a periodic function of the angle between the fibers. The implication is that antiparallel sliding is not in itself sufficient for friction isotropy but that lifting of the cuticle edges is required. A methodology to perform friction analysis independently for trace and retrace was therefore developed, which is applicable to any type of AFM lateral force measurement. It explicitly accounts for roll, noncircular cross section, and off-axis alignment as well as baseline drift, which allows real anisotropy in the friction coefficient to be deconvoluted from these artifacts.

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INTRODUCTION Hair is a roughly cylindrical natural biofiber 50−100 μm in diameter. The number of hairs covering a normal human head is between 120000 and 150000, which leads to a large surface area (typically ∼6 m2 for ∼20 cm long hairs). The cuticle forms the outer surface of hair. It has an overlapping scale (approximately 5 μm long and 0.5 μm thick) structure protecting the cortex, oriented from the root to the tip of the fiber and making a series of scale edges along the outer surface of the hair. A normal hair has about 6−8 overlapping cuticle cells in tight contact. In cosmetics, hairstyle and hair manageability depends on numerous parameters: geometry of the fibers (length, diameter, ellipticity, and degree of curl), emergence angle from the scalp, and fiber-to-fiber interactions. The combinations of all these parameters result in extremely different cosmetic properties. The cuticle controls in part fiber-to-fiber interactions, which play a major role in fiber-assembly behavior, such as bending and compression of fiber bundles. When a fiber assembly is subjected to deformation strains (combing, shaping, brushing, detangling, curling, and spinning and weaving in the case of wool), single fibers slip past one another at their contact points, thus minimizing the extent of deformation of individual fibers. The efficiency of the process depends largely on fiber-to-fiber friction that depends in turn on the adhesion at the contact points.1 The means whereby hair may adopt various three-dimensional shapes depends on the general physical problem of how hundreds of thousands of fibers interact among each other © 2013 American Chemical Society

while in motion. The understanding and prediction of the phenomena using sophisticated models are of importance, ranging from performance evaluation in the cosmetic and textile industries to character animation in the cinema and entertainment industries.2,3 The roof tile-like structure that hair shares with most mammalian fibers, results in anisotropy during interactions; hair fibers exhibit macroscopically what is known as a “differential friction effect” (i.e., friction is different when sliding “root-totip” versus “tip-to-root”. The friction coefficient is higher when sliding takes place from the hair end to the root (“against the scales”). Generally, a relatively characteristic stick−slip phenomenon is also observed.4 Recently, a technique has been developed to measure friction between single human hair fibers using atomic force microscopy (AFM).5,6 The objective of the work reported herein is 2-fold: first, to investigate the friction anisotropy effect between two hair fibers as a function of the angle between them. This in turn necessitates the modification of the experimental approach to permit the different sliding directions to be analyzed individually, since conventional nanotribology techniques for colloid and fiber probe measurements intrinsically assume friction isotropy.7 Received: February 3, 2013 Revised: April 8, 2013 Published: April 8, 2013 5857

dx.doi.org/10.1021/la400468f | Langmuir 2013, 29, 5857−5862

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EXPERIMENTS AND MATERIALS Native hair samples (from blond female Caucasian) were selected. Some of the hairs were treated with a standardized oxidative treatment, involving immersion in a 40 volume (12%) hydrogen peroxide (H2O2) solution for 10 min, in the presence of NH4OH. This bleaching treatment leaves the hair in a more hydrophilic physicochemical state (closer to that induced in vivo by natural weathering). Both “natural” and bleached human hair samples were sonicated in 1% aqueous sodium dodecyl sulfate (SDS) solution for 2 min, rinsed with copious amounts of filtered, deionized water, and then dried with nitrogen.8 Initial ∼200 μm cuts of the fibers were performed with ordinary household scissors. Etched tungsten wires attached to a micromanipulator (Eppendorf) were used to position the glue and the fiber pieces, respectively, on tipless AFM cantilevers under a stereomicroscope. The cantilevers used were of silicon (NSC12, μMASCH), with a specified normal spring constant of 0.65 N/m. The actual normal and torsional spring constants were calibrated using a technique based on the hydrodynamic damping of the intrinsic thermal noise.9 The actual values of the normal and torsional spring constants for the various cantilevers used ranged from 0.3 to 0.56 N/m and from 6.8 × 10−9 to 1.4 × 10−8 Nm/rad, respectively. After gluing the fiber on a cantilever, overhang of the fiber was trimmed using a focused ion beam, FIB (Figure 1), to obviate the problem of the hair end contacting the lower substrate.6 (The cantilever sits at an angle of 12°).

200 nN) during scanning and then reduced until the surfaces spontaneously separated. The lower fiber was rotated manually in the plane of its long axis relative to the hair probe to achieve different relative sliding angles. Irrespective of the angle of the lower fiber to the cantilever, the movement of the lower surface was normal to the long axis of the cantilever/upper fiber (see Figure 1). Measurements were performed at low humidity (25−30%) and high humidity (70−75%) levels, controlled by potassium chloride-saturated aqueous solution.10 The normal and torsional signal of the cantilever changed in response to the humid environment, due to expansion of the hair arising from moisture gain.11 Hence, experiments were not performed until after the signal had stabilized (typically 3 h). Friction Anisotropy Approach. If the shape of a probe is not perfectly cylindrical or if the probe is not precisely mounted at the center of the cantilever, the normal load applied to the probe in fact twists the cantilever even in the absence of sliding. For hair probes (which have a large diameter compared to the cantilever width), this induced torsion can be large. In fact, the value of the lateral voltage in the friction loop is the sum of the frictional contribution arising from rubbing against the second hair fiber and the load-induced twist of the cantilever due to asymmetry. Since the torsional deflection due to normal loading increases with load, it manifests as a baseline shift for each friction loop. This shift becomes an issue only in the case where the friction force is analyzed for each direction separately, since conventional analysis obtains the friction solely from the difference between trace and retrace.7 In the case of hair fibers, however, it is expected that there will be a difference between sliding “root-to-tip” and “tip-to-root”, so the assumption of isotropy cannot be made and a different analysis must be performed. To perform such a directional friction analysis, the voltage in the friction loop was first averaged over the sliding distance for each direction (shown as Vav), and the value was plotted as a function of applied load without taking into account baseline shift. Examples of this are shown in Figures 3a and 3b, where the linear change with load shows that the frictional behavior obeys Amontons’ law, F = μN

(1)

where μ is the friction coefficient. Figure 3a shows “conventional”, isotropic frictional behavior with the arms of the trace and retrace symmetrically displaced about the x axis and no apparent directional effect; it was obtained using a commercial silicon nitride tip sheared on a flat surface without any hair fibers attached to either surface. (While the friction force cannot be negative by definition, the measured voltage change is either positive or negative depending on the direction of sliding/twisting. Since the two lines have the same absolute gradient, the friction coefficient that would be extracted is the same). A “worst-case scenario” for hair friction is plotted in Figure 3b, where the baseline (or “undeflected voltage value”) shifted upward, causing trace and retrace voltages to have gradients with the same sign. This is clearly impossible, if the only reason for twist is frictional forces, and it indicates that the asymmetry-induced twist is in fact larger than the frictional force. In general, two different absolute values of the gradients of the trace and retrace are obtained, and these different gradients result from both the asymmetry induced twist due to loading and any directional effects in the sliding friction.

Figure 1. Diagram of the crossed hair fiber system viewed from above. θ is the angle between tips of the two hair fiber cuts and defines the sliding angle. Experiments have been performed with both, tip end and root end sections, attached to the cantilever. Inset: SEM image of hair probe attached to cantilever. The outer (left-hand, root end) cut is that performed with the FIB, and it is finer than the inner cut (right-hand) performed with ordinary scissors.

The force and friction experiments were performed using an Atomic Force Microscope (Nanoscope IIIa, Picoforce, VEECO, Santa Barbara, USA), according to protocols described in an IUPAC report.7 In short, each AFM experiment started with acquiring two normal force curves at a constant scan rate of 1 μm/s. Then, friction measurements were run at a sliding velocity of 10 μm/s with a scan size of 5 μm. The load was gradually increased from zero to the maximum value (typically 5858


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for 74% of the measurements, Δμ is within the range of ±0.05. This indicates that while in most cases, Δμ is positive (i.e., sliding against the cuticle direction involves higher friction), the directional effect is negligible for native hair at almost all angles. In an earlier report6 on the friction of hair at a fixed sliding angle, we remarked on the apparent absence of directional effects, which is thus now confirmed here and extends to other sliding angles. As argued in that paper, and more extensively by Adams et al.13, the large radius in comparison to cuticle height means that the mechanical interlock of the cuticles (the origin of directional effects) is only feasible for certain angles and conditions. For bleached hair, however, a very different behavior was observed. μagainst was systematically larger than μalong (Figure 6a), indicating that the directional effect and mechanical interlocking is significant with weathered hair. Furthermore, there appears to be a strong angular dependence of this effect (Figure 6b). We thus speculate that two mechanisms are involved in this phenomenon: (a) at all sliding angles, Δμ is enhanced due to lifted, ragged cuticles14 and (b) variation of Δμ with the sliding angle is associated with the probability of antiparallel cuticle−cuticle interaction. The latter contribution is expected to be a periodic function of the angle, and the data in Figure 6b support this contention. If one imagines any given cuticle on the upper hair probe, the number of cuticles sliding on the opposing hair during a scan, Nlower, can easily be calculated from (2)

Thus, to be able to isolate directional effects in sliding friction and to get independent friction coefficients for the two sliding directions, we need to accurately account for the asymmetry-induced twist. This was achieved in the following way: first, the variation of the torsional signal was obtained as a function of the applied load, in the absence of any lateral scanning (see Figure 4a). Then, the appropriate voltage was subtracted from the raw data at each load (for example each point seen in Figure 3b).

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RESULTS AND DISCUSSION The friction force measured by AFM is obtained from the cantilever torsion and the ensuing lateral photodiode response as the hair probe slides over the lower hair in a reciprocating way. Such a friction “loop” is shown in Figure 2. (In all cases it is the lower surface which is in motion.)

Nlower = D0 sin(θ )R 0

Figure 2. A friction loop for native hair at 103 nN and sliding angle of 135°. The upper and lower lines show the photodiode response to friction force measured as the hair probe slides along cuticle (trace) and against cuticle, respectively (retrace). The signal was averaged over 5 μm after removing the first and last 20 data points (corresponding to static friction) and converted to friction force using the equation F = kV/hδ, where h, k, and δ denote fiber diameter, torsional spring constant, and calibration factor, respectively.12 The dashed lines correspond to the averaged value for trace and retrace, respectively.

(2)

where D0 is the scan length, θ is the angle between the hairs, and R0 is the length density of cuticles (approximately 1 per 5 μm). The probability of mechanical interlocking of the cuticles will also depend on the angle at which they meet, however. For example, if we assume that the cuticles can be considered to be perfectly circular, with their radii perpendicular to the fiber length, the possibility of interlocking is zero when the angle is 90°; on the other hand, when the angle is 180°, the cuticles would be antiparallel, and the interlocking possibility would be maximized (Pmax). (However, in the latter geometry Nlower would be zero!) In order to account for both considerations, we need to calculate the “effective” interaction length of the given cuticle of the upper hair in the direction of crossing cuticle of the lower hair, which is

Figure 4b shows the friction-load relationship for the two sliding directions after correction for asymmetry, or baseline shift. Independent friction coefficients for the two sliding directions can be extracted from the data. The friction coefficients obtained this way for both native and bleached hair (70% RH) are shown in Figures 5 and 6. In the case of native hair (Figure 5), there appears to be only very slight, if any, dependence of μagainst and μalong on the sliding angle. Figure 5b shows how Δμ (μagainst − μalong) varies with the sliding angle;

Leff = L0 cos(θ)

(3)

Figure 3. Variation of frictional signal (V) with applied load (a) for a system with no asymmetry induced torsion or directional effect and (b) for native hair where the hair fiber was not centered on the cantilever and a significant twist of the cantilever consequently occurred during loading. 5859


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Figure 4. (a) Example of the variation of torsional signal with applied load in the absence of sliding for native hair probe (121° angle between fibers). The deflection on loading and unloading changes linearly with load, reflecting the baseline shift. Such a torsional deflection test was made for each friction experiment (every point at which a friction coefficient is obtained). The torsional signal arising purely from the asymmetry of loading was then subtracted from the torsional signal obtained under sliding (b), the same data as shown in Figure 3b corrected for the baseline shift associated with asymmetry of the hair probe mounting. Friction coefficients can be extracted independently from the gradients of the two arms and are not necessarily similar.

Figure 5. (a) Friction coefficient of native hair at different sliding angles at high RH and (b) difference in friction coefficients against versus along the cuticle. The average μagainst and μalong are 0.11 and 0.10, respectively.

Figure 6. (a) Friction coefficient of treated hair at different sliding angles at high RH and (b) the difference in friction coefficients when shearing against versus along the cuticle. The average μagainst and μalong are 0.42 and 0.20, respectively, for bleached hair.

where L0 denotes the total length of the cuticles (related to hair diameter). The interlocking probability arising from the crossing of cuticles will then be P = NlowerLeff = D0 sin(θ )R 0L0 cos(θ )

P = C sin(2θ )

(5)

where C is a constant, which is independent of orientation. Therefore, the highest probability that two cuticles both meet and interlock during sliding is at 45° and 135°, and the lowest probability is at 90°. In Figure 6b, which shows Δμ for bleached hair, it is possible to interpret two peaks on either side of a

(4)

which can thus be rewritten 5860


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of the probe and/or deviation from spherical behavior can be easily accounted for. This approach is general and is not restricted to fiber probes but should also be implemented for conventional colloid probe or, indeed, tip, lateral force measurement. Quantitative analysis of friction at various sliding angles can now be applied to other fiber systems. This is particularly useful to understand properties of fiber assemblies whose fibers interact at various angles (e.g., polyester fibers), the interfiber friction of which determines mechanical strength of the array. Finally, this kind of information will be essential for predicting the dynamic behavior of multifiber assemblies.

minimum as expected from the above treatment. Thus, though relatively simple, this treatment apparently explains the broad features of the angular dependence rather well. The experimental maxima are found at roughly 70° and 130°, and the minimum at around 100°. The angle of 130° is close to the predicted angle of the highest probability, but 70° is rather different from the other predicted maximum for reasons that remain unclear. It should also be considered that the cuticle directions are the same (parallel) at 45° and opposite (antiparallel) at 135°, which means that the impact of cuticle−cuticle interaction on Δμ is expected to be smaller at 45°, since mechanical interlocking should be larger for opposite cuticle directions. This is not observed. We can only conclude from that particular result that mechanical interlocking is not the primary cause of directional hysteresis. Damaged/lifted cuticles merely have to be involved in the sliding contact, and the extra friction sliding against the cuticle direction may well be due to deformation (“bending back”) of the cuticle. With undamaged hair, the cuticle lies “flush” with the fiber so that bending back is unlikely. Finally, we reiterate that the AFM technique developed here for angular dependence measurement always provides movement at right angles to the cantilever-mounted probe. Thus, the movement is not axial with the lower fiber. This geometry is essentially a constraint of the AFM device, but in fact, it is more representative of the type of moving contact typically formed by two hair fibers. The antiparallel arrangement, is an extremely unlikely conformation on, for example, a head of hair, but in the case of wool fibers in textiles, it is expected.

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AUTHOR INFORMATION

Corresponding Author

*M.W.R.: e-mail, [email protected]; G.S.L.: e-mail, gluengo@rd. loreal.com. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Rubén Alvarez Asencio for assistance with the Fine Ion Beam equipment and Lubica Macáková for useful discussion. M.R. and H.M. thank VR, the Swedish Research Council, and SSF, The Foundation for Strategic Research, for financial support of the program Microstructure for Friction and Corrosion control

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REFERENCES

(1) Kamath, Y. K.; Weigmann, H. D. Measurement of interfiber adhesion. J. Cosmet. Sci. 2000, 51, 351. (2) Ward, K.; Bertails, F.; Kim, T. Y.; Marschner, S. R.; Cani, M. P.; Lin, M. C. A survey on hair modeling: Styling, simulation, and rendering. IEEE Transactions on Visualization and Computer Graphics 2007, 13, 213. (3) Huang, F.; Li, K. C.; Kulachenko, A. Measurement of interfiber friction force for pulp fibers by atomic force microscopy. J. Mater. Sci. 2009, 44, 3770. (4) LaTorre, C.; Bhushan, B. Investigation of scale effects and directionality dependence on friction and adhesion of human hair using AFM and macroscale friction test apparatus. Ultramicroscopy 2006, 106, 720. (5) Max, E.; Häfner, W.; Wilco Bartels, F.; Sugiharto, A.; Wood, C.; Fery, A. A novel AFM based method for force measurements between individual hair strands. Ultramicroscopy 2010, 110, 320. (6) Mizuno, H.; Luengo, G. S.; Rutland, M. W. Interactions between Crossed Hair Fibers at the Nanoscale. Langmuir 2010, 26, 18909. (7) Ralston, J.; Larson, I.; Rutland, M. W.; Feiler, A. A.; Kleijn, M. Atomic force microscopy and direct surface force measurements. Pure Appl. Chem. 2005, 77, 2149. (8) Breakspear, S.; Smith, J. R.; Luengo, G. Effect of the covalently linked fatty acid 18-MEA on the nanotribology of hair’s outermost surface. J. Struct. Biol. 2005, 149, 235. (9) Green, C. P.; Lioe, H.; Cleveland, J. P.; Proksch, R.; Mulvaney, P.; Sader, J. E. Normal and torsional spring constants of atomic force microscope cantilevers. Rev. Sci. Instrum. 2004, 75, 1988. (10) Rockland, L. B. Saturated salt solutions for static control of relative humidity between 5 and 40°C. Anal. Chem. 1960, 32, 1375. (11) Robbins, C. R. Chemical and Physical Behavior of Human Hair, 4th ed.; Springer: New York, 2001. (12) Pettersson, T.; Nordgren, N.; Rutland, M. W.; Feiler, A. Comparison of different methods to calibrate torsional spring constant and photodetector for atomic force microscopy friction measurements in air and liquid. Rev. Sci. Instrum. 2007, 78, 093702. (13) Adams, M. J.; Briscoe, B. J.; Wee, T. K. The differential friction effect of keratin fibers. J. Phys. D: Appl. Phys. 1990, 23, 406.

CONCLUSION There are two significant aspects in this work. First, the variation of hair friction coefficient with both sliding angle and sliding direction was revealed. The friction coefficient of native hair is relatively independent of the sliding angle, and the directional effect is not clearly observed. On the other hand, bleached hair exhibits a clear directional effect at most sliding angles due to higher surface roughness and this is a periodic function of the angle. This finding is related to the likely cuticle−surface or cuticle−cuticle interaction between two hair fibers, and it is clear that cuticle lifting and serration (a result of oxidative damage) is a necessary requirement for directional effects between hair fibers to be observed. The directional effect has a symmetrical distribution with sliding angle (i.e., when sliding one cuticle against the other); it does not appear to matter whether cuticles are aligned parallel or antiparallel on the counter surface. This implies that frictional hysteresis may in fact be due to deformation (bending) of single lifted cuticle edges rather than mechanical interlocking of the cuticles as has previously been surmised. The question as to why such antiparallel or interlock effects are so widely reported, presumably lies in the fact that the weathering and damage of natural fibers in for example textiles is much greater than for that experienced by natural in vivo damage. The bending and deformation of fibers in woven materials leads to increased cuticle relief and such conditions have not been reproduced here. Finally, the maximum contact pressure in woven materials is expected to be larger than can be applied using an AFM cantilever (the spring constant of which is less than that of hair itself). Second, a modification of the approach for analyzing friction data is introduced, which allows directional effects to be quantified. The issue of “baseline drift” due to off-axis mounting 5861


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(14) LaTorre, C.; Bhushan, B. Nano tribological characterization of human hair and skin using atomic force microscopy. Ultramicroscopy 2005, 105, 155.

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New Insight on the Friction of Natural Fibers. Effect of Sliding Angle

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