**1. Introduction**

Glass fibers, generally used to reinforce composite materials, readily suffer abrasion damage due to friction when glass filaments slide against each other. In manufacturing, glass fibers are coated with a size consisting of a coupling agent, a lubricant, a film former and other additives. While the coupling agent is used to increase adhesion between the fibers and the matrix, in glass fiber reinforced composite materials (P.Plueddeman, 1982), the complete size should improve the frictional performance of contacting fibers surfaces during their processing and their uses (e.g.: spinning, weaving...). With the increasing demand for good sizing agents which have low friction values, it is important to study the frictional behavior of sized fibers.

#### **1.1 Theoretical background of frictional properties of fibers**

The frictional properties of polymer fibers deviate from the classical Amonton law. For polymers and fibers which are viscoelastic materials, the friction coefficient 'µ' depends on the temperature, speed, and more specifically on the applied load. The most striking characteristic is that the coefficient of friction 'µ' increases as the load 'N' is diminished, and at light loads, it can be very high. Indeed, other than deformation at asperities observed in the fiber, the radius of curvature of the fiber surface is an important parameter in determining friction. Gupta described the friction of fibers in empirical terms (Gupta, 1992):

$$\mathbf{F}\_{\mathsf{I}} = \mathbf{a} \mathbf{N}^{\mathsf{n}} \tag{1}$$

Atomic Force Microscopy – For Investigating Surface Treatment of Textile Fibers 233

(Meyer and Amer, 1990). Extensive reviews give detailed description of this apparatus and

AFM imaging was achieved in air under atmospheric conditions with a commercial scanning probe «Nanoscope III, from Digital inc.», in the contact mode at a constant force. The AFM measures the vertical deflection of a cantilever to which is fixed a microtip which scans the sample surface (see Fig. 1). In the contact mode, the normal deflection (due to intermolecular forces) of the cantilever is dependent on the distance between the tip and the sample, such that Fz= k. z, where : Fz= deflection force of the cantilever, k= spring constant

The fiber sample is placed onto a piezodrive, while the tip is in a fixed position. The normal deflection of the cantilever is monitored through the displacement of a laser beam reflected off the cantilever onto a segmented detector, during the scanning of the sample in x and y directions (Fig. 1). Any bending of the cantilever due to bumps or grooves on the sample surface induces an intensity difference between the lower and upper part of the segmented photodetector, and this in turn provides an error signal for the feedback of the piezo so as to maintain a constant preset force on the cantilever. The displacement of the piezodrive allows the reconstitution of a topographic image of the scanned surface. The lateral force images were obtained by measuring the torque imposed on the cantilever by the tip as a result of tangential forces experienced by the tip, when the sample is moved underneath. To measure normal and lateral forces simultaneously a four quadrant photodiode is used (Fig. 1). The normal bending of the cantilever is measured by the intensity difference ( I 1+2 - I 3+4 ) of the upper and lower segments of the diode, while the signal difference of the left and the right

Topographical 3-dimensional as well as scope mode images were obtained in the AFM and LFM modes. Scope mode images give trace and retrace profiles of the topography and of LFM signals in real time when the sample goes forward and backward underneath the tip (see Fig. 2). Lateral force signals are influenced by the surface topography (slopes of a surface feature for example). For a surface with friction as well as with corrugations (see Fig. 2A and B), like the glass fibers used in this study, the normal reacting force (*N*) as well the

N = Nx + Ny + Nz

Ff = Ffx + Ffy + Ffz In other words, the measured lateral force depends on the local slope as well and not only on frictional forces. The frictional force (*Ff*) is, of course, tangent to the slope (see Fig. 2B ) and acts in the opposite direction to the scan direction, and, therefore, by the reversal of the scan direction, each of the components of the frictional force (*Ff*) changes sign, while those due to the normal force do not. The difference between the forward and the reverse scans in the LFM scope mode gives twice the average friction force (Overney and Meyer, 1993) Baselt and Baldeschwielder, 1992). Full quantification of the frictional force is not yet possible, so scanning was carried out 90° (Fig. 1) to cancel the *y* and *z* components of the friction force. Friction forces in volts were converted to Newtons by determining the lateral sensibility of

therefore only a brief explanation of the method will be described in this paper.

of the cantilever, and z= the cantilever's deflection.

segments ( I 1+3 - I 2+4 ) provides torsional information.

frictional force (*Ff*) will have nonzero *x*, *y*, and *z* components, that is,

**2.1.2 Topographical and LFM images** 

with

$$
\mu = \text{aN}^{n \cdot 1} \tag{2}
$$

where 'a' and 'n' are constants, and 0<n<1.

The friction coefficient 'µ' reaches its maximum value at zero load where the friction forces due to adhesive forces are present. In order to initiate motion during sliding, a certain force called static friction force 'Fs' must be applied, which is greater than the kinetic friction force 'Fk' needed to maintain the sliding. This may result in stick-slip motion when one fiber slides on another one, and this intermittent motion can be generated even in the presence of the size (Gupta, 1985, 1992). Friction force is reported to be at its highest at the stick phase (Israelachvili, 1993).

#### **1.2 Static friction force and its relation to surface contact area and surface forces**

It is generally accepted that static friction depends on adhesion forces, and recently Israelachvili (Israelachvili, 1993) has demonstrated that the frictional energy required during the static phase is used partly to overcome adhesion and partly to overcome the load. At very small loads, as in our case (nanonewtons for the LFM and micronewtons for the microbalance), the influence of load is small but adhesion forces (Fad) are present. These forces depend on surface energy and on the apparent contact area. Surface energies are defined constants of materials, while the theoretical contact areas can be determined by contact mechanics theories. The first contact theory elaborated by Hertz concerns elastic solids for which the contact area for two contacting spheres, is a circle of radius 'a'. However in presence of adhesive forces, the contact areas may be altered and the two contact mechanics theories JKR (Johnson-Kendall-Roberts) (Johnson, 1971) and DMT (Derjaguin-Muller-Toporov) (Derjaguin, 1975) determine the real surface of contact.

The nature of fiber friction is known to be complex, and adequate theory describing it, is not available, though models have been provided to explain frictional behavior of fibrous materials (Gupta, 1992, 1993). The aim of this work was to use lateral force microscopy to investigate friction at nanoscale level and to relate the results to those obtained at a higher scale that is, during fiber-fiber friction, using an electronic microbalance.

#### **2. Experimental**

#### **2.1 Friction force measurements by Lateral force microscopy**

The atomic force microscopy/lateral force microscopy (AFM/LFM) invented by Bining & al. in 1986 (Binning, 1986) was used to obtain topographic image in the AFM mode, and lateral forces between a Si3 N4 tip and a fiber surface in the LFM (lateral force microscopy) mode (Meyer and Amer, 1990). Extensive reviews give detailed description of this apparatus and therefore only a brief explanation of the method will be described in this paper.

AFM imaging was achieved in air under atmospheric conditions with a commercial scanning probe «Nanoscope III, from Digital inc.», in the contact mode at a constant force. The AFM measures the vertical deflection of a cantilever to which is fixed a microtip which scans the sample surface (see Fig. 1). In the contact mode, the normal deflection (due to intermolecular forces) of the cantilever is dependent on the distance between the tip and the sample, such that Fz= k. z, where : Fz= deflection force of the cantilever, k= spring constant of the cantilever, and z= the cantilever's deflection.

The fiber sample is placed onto a piezodrive, while the tip is in a fixed position. The normal deflection of the cantilever is monitored through the displacement of a laser beam reflected off the cantilever onto a segmented detector, during the scanning of the sample in x and y directions (Fig. 1). Any bending of the cantilever due to bumps or grooves on the sample surface induces an intensity difference between the lower and upper part of the segmented photodetector, and this in turn provides an error signal for the feedback of the piezo so as to maintain a constant preset force on the cantilever. The displacement of the piezodrive allows the reconstitution of a topographic image of the scanned surface. The lateral force images were obtained by measuring the torque imposed on the cantilever by the tip as a result of tangential forces experienced by the tip, when the sample is moved underneath. To measure normal and lateral forces simultaneously a four quadrant photodiode is used (Fig. 1). The normal bending of the cantilever is measured by the intensity difference ( I 1+2 - I 3+4 ) of the upper and lower segments of the diode, while the signal difference of the left and the right segments ( I 1+3 - I 2+4 ) provides torsional information.

#### **2.1.2 Topographical and LFM images**

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

the temperature, speed, and more specifically on the applied load. The most striking characteristic is that the coefficient of friction 'µ' increases as the load 'N' is diminished, and at light loads, it can be very high. Indeed, other than deformation at asperities observed in the fiber, the radius of curvature of the fiber surface is an important parameter in determining friction. Gupta described the friction of fibers in empirical terms (Gupta, 1992):

Ff = aNn (1)

The friction coefficient 'µ' reaches its maximum value at zero load where the friction forces due to adhesive forces are present. In order to initiate motion during sliding, a certain force called static friction force 'Fs' must be applied, which is greater than the kinetic friction force 'Fk' needed to maintain the sliding. This may result in stick-slip motion when one fiber slides on another one, and this intermittent motion can be generated even in the presence of the size (Gupta, 1985, 1992). Friction force is reported to be at its highest at the stick phase

**1.2 Static friction force and its relation to surface contact area and surface forces** 

Muller-Toporov) (Derjaguin, 1975) determine the real surface of contact.

scale that is, during fiber-fiber friction, using an electronic microbalance.

**2.1 Friction force measurements by Lateral force microscopy** 

It is generally accepted that static friction depends on adhesion forces, and recently Israelachvili (Israelachvili, 1993) has demonstrated that the frictional energy required during the static phase is used partly to overcome adhesion and partly to overcome the load. At very small loads, as in our case (nanonewtons for the LFM and micronewtons for the microbalance), the influence of load is small but adhesion forces (Fad) are present. These forces depend on surface energy and on the apparent contact area. Surface energies are defined constants of materials, while the theoretical contact areas can be determined by contact mechanics theories. The first contact theory elaborated by Hertz concerns elastic solids for which the contact area for two contacting spheres, is a circle of radius 'a'. However in presence of adhesive forces, the contact areas may be altered and the two contact mechanics theories JKR (Johnson-Kendall-Roberts) (Johnson, 1971) and DMT (Derjaguin-

The nature of fiber friction is known to be complex, and adequate theory describing it, is not available, though models have been provided to explain frictional behavior of fibrous materials (Gupta, 1992, 1993). The aim of this work was to use lateral force microscopy to investigate friction at nanoscale level and to relate the results to those obtained at a higher

The atomic force microscopy/lateral force microscopy (AFM/LFM) invented by Bining & al. in 1986 (Binning, 1986) was used to obtain topographic image in the AFM mode, and lateral forces between a Si3 N4 tip and a fiber surface in the LFM (lateral force microscopy) mode

µ = aNn-1 (2)

with

(Israelachvili, 1993).

**2. Experimental** 

where 'a' and 'n' are constants, and 0<n<1.

Topographical 3-dimensional as well as scope mode images were obtained in the AFM and LFM modes. Scope mode images give trace and retrace profiles of the topography and of LFM signals in real time when the sample goes forward and backward underneath the tip (see Fig. 2). Lateral force signals are influenced by the surface topography (slopes of a surface feature for example). For a surface with friction as well as with corrugations (see Fig. 2A and B), like the glass fibers used in this study, the normal reacting force (*N*) as well the frictional force (*Ff*) will have nonzero *x*, *y*, and *z* components, that is,

$$\mathbf{N} = \mathbf{N\_x} + \mathbf{N\_y} + \mathbf{N\_z}$$

$$\mathbf{F\_f} = \mathbf{F\_{fx}} + \mathbf{F\_{fy}} + \mathbf{F\_{fz}}$$

In other words, the measured lateral force depends on the local slope as well and not only on frictional forces. The frictional force (*Ff*) is, of course, tangent to the slope (see Fig. 2B ) and acts in the opposite direction to the scan direction, and, therefore, by the reversal of the scan direction, each of the components of the frictional force (*Ff*) changes sign, while those due to the normal force do not. The difference between the forward and the reverse scans in the LFM scope mode gives twice the average friction force (Overney and Meyer, 1993) Baselt and Baldeschwielder, 1992). Full quantification of the frictional force is not yet possible, so scanning was carried out 90° (Fig. 1) to cancel the *y* and *z* components of the friction force. Friction forces in volts were converted to Newtons by determining the lateral sensibility of

Atomic Force Microscopy – For Investigating Surface Treatment of Textile Fibers 235

Samples were rastered at a constant force between 20 and 90 nN using a "J" head with scan area of 130 x 130 µm2 and conical-shaped ultralevers made from silicon nitride attached to the cantilever (180 µm long) with a spring constant k = 0.06 N/m. Topographic and lateral force

An experimental device was set up using an electronic microbalance to measure fiber-fiber friction. An electronic microbalance having a sensitivity of 10-8 N was used since friction forces measured for two monofilaments of diameter 11 µm sliding against each other are of the order of a few micronewtons. The microbalance was equipped with an inner chamber to protect test samples from contaminants and to perform experiments in specific environmental conditions (humidity of 45%, and 25°C). The data acquisition and control station allowed force measurements at the sample weighing position, as a function of the

During friction force measurements the vertical fiber was connected to the microbalance at the sample weighing position (see Fig. 3 A) and a load of 1 mg was applied at the other end of this fiber so as to maintain it in a vertical position. The horizontal fiber was fixed to a metallic holder, and brought into contact with the vertical fiber until the deflection angle of the vertical fiber was equal to 2.3°, which is also equal to the wrap angle of the horizontal fiber by the vertical one. The platform was then raised at a fixed speed of 2 µm/sec which induced sliding of one glass fiber against the other one. The force was recorded by the balance as a function of the vertical displacement of the platform. The total sliding distance

The experimental curve stick-slip curve obtained is quite irregular (see Fig. 3B). A detailed

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

statistical analysis of the force curves was carried out using a computer program.

images were obtained at a scan rate of 1.12 Hz with 512 samples per area scanned.

vertical displacement of the platform.

along the vertical fiber was fixed to 2 mm.

**2.2.1 Typical curve obtained** 

the horizontal fiber.

**2.2 Fiber-Fiber friction force measurements using an electronic microbalance** 

Fig. 1. Principle of simultaneous measurement of the normal and lateral forces; two scanning directions are possible (0° and 90°).

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 at the top of the cantilever

the apparatus which was found to be 40 nN/V. Friction coefficients were obtained by dividing the friction force by the normal applied force.

#### **2.1.3 Sample preparation**

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. Samples were rastered at a constant force between 20 and 90 nN using a "J" head with scan area of 130 x 130 µm2 and conical-shaped ultralevers made from silicon nitride attached to the cantilever (180 µm long) with a spring constant k = 0.06 N/m. Topographic and lateral force images were obtained at a scan rate of 1.12 Hz with 512 samples per area scanned.
