Experiment 15 Measuring Hardness

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. 

For most substances used in the experiments an indentation force greater than 0.1 N leads to cracks or even lift-offs at the edges or the ends of the diagonals of the indentation produced by the Vickers pyramid. Therefore the values of the measured hardnesses have a large spread and usually are not reproducible. Most of the literature data were produced at a time where ultra-micro-hardness devices were not available, so that forces larger 5-10 N have been used. 

The experiments with H. M. employed a battery of tests. One set of experiments measured his sensitivity by means of a technique derived from signal detection theory (Corbit Engen, 1971), in which I asked H. M. to sniff 20 presentations of dilute odorant solution randomly interspersed with 20 presentations of odorless blank. The odor was so faint as to make it hard to tell it apart from blank. Figure 1 compares some of the data for H. M. with a male normosmic (P. D.) matched for age and race. After each presentation I asked H. M. whether he could smell an odor. His pattern of responding was the same as that of normosmics sometimes he gave affirmative responses to blanks (false alarms, symbolized by open symbols in fig. 14.1), but he did not always respond affirmatively to the dilute sample (correct affirmatives are symbolized by solid symbols in fig. 14.1). 

Prior to measurements sensors and amplifiers are calibrated with artificial sources on the surface, measurement parameters like threshold values are set and set-ups are tested. All these procedures need experience that hardly can be formalized. 

Another useful parameter in characterizing the stiffness of a gel network is hardness. Hardness is measured by indenting a probe into the gel at a specified velocity while measuring the force required for the indentation The force required to indent the gel to a certain depth is the hardness. While the measured hardness does depend strongly on the modulus of the gel, it also depends on many other measurement parameters such as the size and shape of the gel sample, probe size, speed, and indentation depth. Additionally, the applied strain field is very non-uniform. The strain and strain rate near the probe can be high, but because the gel is incompressible, the entire volume of the gel experiences deformation due to the displacement of gel by the probe. Thus hardness is at best a relative measure of gel material properties. However, since hardness is used by some common gel manufacturers to specify their materials, it is important to understand it in the context of other rheological characterization methods. 

Much of the fundaments we know about surface forces are based on experiments with the SFA. With the SFA, surface forces are measured between two atomically smooth mica surfaces. Distance is measured interferometrically, which allows absolute determination of separation distance with a resolution of typically 0.1 nm (with down to 25 pm achievable). Its absolute force sensitivity is not as high as in several other methods, but in terms of the usually more relevant force per unit area, its sensitivity is excellent. Lateral (friction) forces can be measured in addition to normal standard force versus distance measurements and have contributed much to our understanding of lubrication by thin films. Additional information such as refractive index and contact area can be obtained. The main reason for the limited number of groups using this instrument is the difficult operation of such a system that needs a very experienced and skillful expert. The large interaction areas demand a contamination-free surface preparation and can lead to significant hydrodynamic forces in highly viscous media, which could make equilibrium measurements hard to achieve. 

Heat transfer between gas and sohds is exceedingly hard to measure because it is so rapid. Although the coefficient is low, the available surface area and the relative specific heat of solid to gas are so large that temperature equilibration occurs almost instantaneously. Experiments on injection of argon plasmas into fluidized beds have shown quenching rates of up to fifty million degrees Kelvin per second. Thus, in a properly designed bed, gas to solids heat transfer is not normally a matter of concern. 

The shear viscosity, especially as measured with capillary rheometers characterized by high shear rates, is hardly sensitive to material structure since the investigator usually has to deal with the substantially destroyed structure in the molten sample. Melt stretching experiments would normally provide much more information [33]. 

It seems hard to support the above hypothesis on the basis of work function measurements for Hg in the presence of residual gases. Adsorption of water indeed reduces the work function and this is also the case with inert gases. There remains the possibility of surface oxidation by residual oxygen, but the values of Ayr measured with the Hg stream have been shown42,43 to be stable even in the presence of 02 impurities provided the gas flows rapidly, as was the case during the experiments. The same conclusion has been reached recently by measuring the work function of Hg in ambient gas.46... 

Bockris and Parry-Jones were the first to carry out experiments with a pendulum to measure the friction between a wetted substrate and the pivot upon which the pendulum swung. It should be noted that Rebinder and Wenstrom199 used such a device for an objective similar to that of Bockris and Parry-Jones, but they claimed that the characteristics of the pendulum oscillations reflected the hardness of the solid surface. The plastic breakdown determining this would be a function of v and this is a potential-dependent value.100, 01 More extensive determinations were made later by Bockris and Argade200 the theoretical treatment was given by Bockris and Sen.201 In the absence of adjustable parameters in the theory, a good agreement between theory and experimental data was assumed.201 The studies by Bockris and Parry-Jones indicated that the... 

At sufficiently low strain, most polymer materials exhibit a linear viscoelastic response and, once the appropriate strain amplitude has been determined through a preliminary strain sweep test, valid frequency sweep tests can be performed. Filled mbber compounds however hardly exhibit a linear viscoelastic response when submitted to harmonic strains and the current practice consists in testing such materials at the lowest permitted strain for satisfactory reproducibility an approach that obviously provides apparent material properties, at best. From a fundamental point of view, for instance in terms of material sciences, such measurements have a limited meaning because theoretical relationships that relate material structure to properties have so far been established only in the linear viscoelastic domain. Nevertheless, experience proves that apparent test results can be well reproducible and related to a number of other viscoelastic effects, including certain processing phenomena. 

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