Experimentally controllable parameters

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. 

It has already been mentioned that the properties of a dielectric sample are a function of many experimentally controlled parameters. In this regard, the main issue is the temperature dependence of the characteristic relaxation times—that is, relaxation kinetics. Historically, the term kinetics was introduced in the field of Chemistry for the temperature dependence of chemical reaction rates. The simplest model, which describes the dependence of reaction rate k on temperature T, is the so-called Arrhenius law [48] ... 

The experimental a versus x dependence for these samples, together with the fitting curves, are shown in Fig. 53. Note that in contrast to the previous example, these data are obtained at a constant sample composition. Now, Variations of the parameters a and x are induced by temperature variation. As mentioned above, the exponents a as well as the relaxation time x are functions of different experimentally controlled parameters. The same parameters can affect the structure or the diffusion simultaneously. In particular, both a and x are functions of temperature. Thus, the temperature dependence of the diffusion coefficient in (144) should be considered. Let us consider the temperature dependence of the diffusion coefficient D ... 

All measured quantities, namely a, G, and G were converted to the respective dimensionless quantities by multiplication with R /k T where Fr is the hydro-dynamic radius at the respective temperature. As already discussed above, the experimental control parameters yand co also were converted by 67irisRli/k T to the respective Peclet numbers. 

In the BZ reaction, malonic acid is oxidized in an acidic medium by bromate ions, with or without a catalyst (usually cerous or ferrous ions). It has been known since the 1950s that this reaction can exhibit limit-cycle oscillations, as discussed in Section 8,3. By the 1970s, it became natural to inquire whether the BZ reaction could also become chaotic under appropriate conditions. Chemical chaos was first reported by Schmitz, Graziani, and Hudson (1977), but their results left room for skepticism—some chemists suspected that the observed complex dynamics might be due instead to uncontrolled fluctuations in experimental control parameters. What was needed was some demonstration that the dynamics obeyed the newly emerging laws of chaos. 

In Fig. 4 (a) and (b) we compare, and contrast, the metal-insulator transition at r = 0 K in our divided metal with that of a macroscopic sample of a doped semiconductor. Si P. For the latter the average dopant separation, d, (and thus the electron carrier density) provides the key experimental control parameter separating the metallic [d < dc) and non-metallic d > dc) regimes. The metal-insulator tran-... 

The channel model of an arc includes three parameters to be determined plasma temperature Tm, arc channel radius ro, and electric field E. Electric current I and discharge tube radius R are experimentally controlled parameters. To find r, and E, the channel model has only two equations, (4-59) and (4-60). Steenbeck suggested the principle of minimum power (see Section 4.2.4) as the third equation to complete the system. The minimum power principle has been proved for arcs by Rozovsky (1972). According to the principle of minimum power, temperature and arc chaimel radius ro should minimize the specific discharge power w and electric field E = w/1 at fixed values of current 1 and discharge tube radius R. The minimization ( )/=const = 0 gives the third equation of the model ... 

In q versus 1. The intercept at t = 0 yields r Q = p/Cai, from which Cai is obtained, since qp is the experimentally controlled parameter. With C i known, Rp and jo can readily be obtained from tc-... 

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