Contact area measurement

A second type of measurement that may be made on films, usually in conjunction with force-area measurements is that of the contact or surface potential. One essentially measures the Volta potential between the surface of the liquid and that of a metal probe. 

The often-cited Amontons law [101. 102] describes friction in tenns of a friction coefiBcient, which is, a priori, a material constant, independent of contact area or dynamic parameters, such as sliding velocity, temperature or load. We know today that all of these parameters can have a significant influence on the magnitude of the measured friction force, especially in thin-film and boundary-lubricated systems. 

Interfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell (52) are often operated with a flat Hquid—Hquid interface the area of which can easily be measured. In the single-drop apparatus, a regular sequence of drops of known diameter is released through the continuous phase (42). These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. 

The term a —xf was included as a measure of the surface area of the oxidizing salt and the term is associated with the reduction of contact area from product formation. 

The relationship between the increase in contact radius due to plastic deformation and the corresponding increase in the force required to detach submicrometer polystyrene latex particles from a silicon substrate was determined by Krishnan et al. [108]. In that study, Krishnan measured the increase in the contact area of the partieles over a period of time (Fig. 7a) and the corresponding decrease in the percentage of particles that could be removed using a force that was sufficient to remove virtually all the particles initially (Fig. 7b). 

Perhaps the most significant complication in the interpretation of nanoscale adhesion and mechanical properties measurements is the fact that the contact sizes are below the optical limit ( 1 t,im). Macroscopic adhesion studies and mechanical property measurements often rely on optical observations of the contact, and many of the contact mechanics models are formulated around direct measurement of the contact area or radius as a function of experimentally controlled parameters, such as load or displacement. In studies of colloids, scanning electron microscopy (SEM) has been used to view particle/surface contact sizes from the side to measure contact radius [3]. However, such a configuration is not easily employed in AFM and nanoindentation studies, and undesirable surface interactions from charging or contamination may arise. For adhesion studies (e.g. Johnson-Kendall-Roberts (JKR) [4] and probe-tack tests [5,6]), the probe/sample contact area is monitored as a function of load or displacement. This allows evaluation of load/area or even stress/strain response [7] as well as comparison to and development of contact mechanics theories. Area measurements are also important in traditional indentation experiments, where hardness is determined by measuring the residual contact area of the deformation optically [8J. For micro- and nanoscale studies, the dimensions of both the contact and residual deformation (if any) are below the optical limit. 

A series of force-distance curves for various materials pairs examined (gold/ nickel, diamond/graphite, diamond/diamond) are shown in Fig. 4 [39]. For an indentation, the unloading slope (dF/dr) of the force-displacement curve is a measure of the contact stiffness and can be used to determine the modulus if the contact area (A) is known using a variant of Eq. 3 below. 

The above measurements all rely on force and displacement data to evaluate adhesion and mechanical properties. As mentioned in the introduction, a very useful piece of information to have about a nanoscale contact would be its area (or radius). Since the scale of the contacts is below the optical limit, the techniques available are somewhat limited. Electrical resistance has been used in early contact studies on clean metal surfaces [62], but is limited to conducting interfaces. Recently, Enachescu et al. [63] used conductance measurements to examine adhesion in an ideally hard contact (diamond vs. tungsten carbide). In the limit of contact size below the electronic mean free path, but above that of quantized conductance, the contact area scales linearly with contact conductance. They used these measurements to demonstrate that friction was proportional to contact area, and the area vs. load data were best-fit to a DMT model. 

An example of interaction stiffness and force curves for a Si surface with a native oxide at 60% relative humidity (RH) is shown in Fig. 12 [104]. The stiffness and force data show an adhesive interaction between the tip and substrate. The hysteresis on retraction is due to a real change in contact area from surface oxide deformation and is not an experimental artifact. The adhesive force observed during retraction was consistent with capillary condensation and the surface energy measured from the adhesive force was close to that of water. 

Depth-sensing nanoindentation is one of the primary tools for nanomechanical mechanical properties measurements. Major advantages to this technique over AFM include (1) simultaneous measurement of force and displacement (2) perpendicular tip-sample approach and (3) well-modeled mechanics for dynamic measurements. Also, the ability to quantitatively infer contact area during force-displacement measurements provides a very useful approach to explore adhesion mechanics and models. Disadvantages relative to AFM include lower force resolution, as well as far lower spatial resolution, both from the larger tip radii employed and a lack of sample positioning and imaging capabilities provided by piezoelectric scanners. 

When selecting a lubricant, both the temperature at the contact area and the ambient temperature at important factors to be considered. Measuring the peak contact temperature is very difficult. The maximum rise in temperature of the oil leaving the gears and the maximum oil temperature are specified for various types of gears. For spur, bevel, helical and spiral level gears, the temperature rise should not normally exceed 30°C (86°F) with a maximum oil temperature of70°C (158°F). 

The Heterogeneity of Catalyst Surfaces for Chemisorption Hugh S. Taylor Alkylation of Isoparaffins V. N. Ipatieff and Louis Schmerling Surface Area Measurements. A New Tool for Studying Contact Catalysts P. H. Emmett... 

It is important to distinguish clearly between the surface area of a decomposing solid [i.e. aggregate external boundaries of both reactant and product(s)] measured by adsorption methods and the effective area of the active reaction interface which, in most systems, is an internal structure. The area of the contact zone is of fundamental significance in kinetic studies since its determination would allow the Arrhenius pre-exponential term to be expressed in dimensions of area"1 (as in catalysis). This parameter is, however, inaccessible to direct measurement. Estimates from microscopy cannot identify all those regions which participate in reaction or ascertain the effective roughness factor of observed interfaces. Preferential dissolution of either reactant or product in a suitable solvent prior to area measurement may result in sintering [286]. The problems of identify-... 

Fig. 24—Measured film thickness perturbation for square features passing through the contact area under different sliding condition, taken from Felix [54]. (a) Slip=0 (b) Slip=1.0 and (c) Slip=-1.0.

Contact ratio, a, is defined as the real contact area divided by the nominal contact zone, where the real contact area is referred to as the sum of all areas where film thickness is below a certain criterion in molecular scale. The contact area was measured by the technique of Relative Optical Interference Intensity (ROII) with a resolution of 0.5 nm in the vertical direction and 1 /xm in the horizontal direction [69]. 

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