**2.2.1 Typical curve obtained**

234 Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale

Fig. 1. Principle of simultaneous measurement of the normal and lateral forces; two

Fig. 2. (A) Normal reacting force (N) as well frictional force (Ff) acting on a surface with corrugations; (B) schematic presentation of the X, Y, and Z components of the forces acting

the apparatus which was found to be 40 nN/V. Friction coefficients were obtained by

Sized glass filaments were provided by Owens Corning in the form of multifilament rovings. One or several of the filaments which are cylindrical in shape, were fixed onto a double-face Scotch tape, perpendicularly to the scan direction (90°), so as to measure both topographical and frictional data. This perpendicular position enables one to see in the scope mode the exact position of the fiber with respect to the tip point. As the maximum of the piezodrive in the *z*  direction is limited to 5.9 µm, the fiber cannot be scanned wholly. So, only the most elevated part of the fiber, where the slope (or curvature) is minimum, was rastered. We shifted from a 6 x 6 to a 3 x 3µm2 surface by zooming the top of the fiber, in the image mode, in real-time.

scanning directions are possible (0° and 90°).

at the top of the cantilever

**2.1.3 Sample preparation** 

dividing the friction force by the normal applied force.

The experimental curve stick-slip curve obtained is quite irregular (see Fig. 3B). A detailed statistical analysis of the force curves was carried out using a computer program.

Fig. 3. (A) : Experimental set-up for friction measurement of two crossed glass fibers : the deflection angle of the vertical fiber connected to the microbalance is 2.3°, the horizontal fiber is fixed to a fiber-holder B) Stick-slip friction curve profile of fiber A (in dark line) and of fiber E (in grey line); the change in force is plotted against the vertical displacement of the horizontal fiber.

Static friction force values were obtained from the minimum values of the curve because, at the start, the microbalance platform was constrained to move upwards, and consequently static friction force values measured had negative values. So the signs of the friction force values were inverted. Moreover, before the vertical displacement of the platform, the balance was set to zero, while in practice, there was a load N at the extreme end of the vertical fiber. The real static (or dynamic) friction force measured was then (-Fs+ N).

## **2.2.2 Static friction coefficients**

Capstan method generally applied for yarn-yarn friction measured by the F-meter was used to calculate the static friction coefficients during fiber-fiber motion (Gupta, 1993):

$$
\mu = \frac{Ln\frac{T\_2}{T\_1}}{a} \tag{3}
$$

Atomic Force Microscopy – For Investigating Surface Treatment of Textile Fibers 237

surface. Fig. 5C shows that there is a great attraction of the tip by the sample before the former may be in contact with the fiber. This phenomenon may be explained by a higher surface energy of the clean desized glass fiber which is going to attract water molecules of the air very rapidly. Indeed, molecules of water form a film of water at the fiber surface, and

Fig. 4. Desized glass fiber: (A) topographic image; (B) scope-mode forward and backward

Fig. 5. (A) A normal contact force profile, (B) Contact force profile during scanning of fiber E

scanned AFM and LFM signals of section A–A'.

and of (C) the desized glass fiber

this acts as a lubricant—hence, the very weak value of the friction coefficient.

'T1 ' is the initial tension, that is the load applied to the vertical fiber + the fiber weight

'T2' is the real static force measured. (-Fs+ N). The wrap angle '' is equal to the deflection angle '' of the vertical fiber for small values of deflection angle (see Fig. 3A). The deflection angle of the vertical fiber was calculated for each vertical displacement 'Z' of the horizontal fiber before calculating the friction coefficient
