Contact geometry

Compared witii other direct force measurement teclmiques, a unique aspect of the surface forces apparatus (SFA) is to allow quantitative measurement of surface forces and intermolecular potentials. This is made possible by essentially tliree measures (i) well defined contact geometry, (ii) high-resolution interferometric distance measurement and (iii) precise mechanics to control the separation between the surfaces. 

In accordance with equation (Bl.20.1). one can plot the so-called surface force parameter, P = F(D) / 2 i R, versus D. This allows comparison of different direct force measurements in temis of intemiolecular potentials fV(D), i.e. independent of a particular contact geometry. Figure B 1.20.2 shows an example of the attractive van der Waals force measured between two curved mica surfaces of radius i 10 nun. 

Well defined contact geometry and absolute cleanliness are crucial factors for a successfiil SFA experiment. Therefore, two curved sheets of mica are brought into contact in crossed-cylinder geometry. 

The well defined contact geometry and the ionic structure of the mica surface favours observation of structural and solvation forces. Besides a monotonic entropic repulsion one may observe superimposed periodic force modulations. It is commonly believed that these modulations are due to a metastable layering at surface separations below some 3-10 molecular diameters. These diflftise layers are very difficult to observe with other teclmiques [92]. The periodicity of these oscillatory forces is regularly found to correspond to the characteristic molecular diameter. Figure Bl.20.7 shows a typical measurement of solvation forces in the case of ethanol between mica. 

Let US now look at how this contact geometry influences friction. If you attempt to slide one of the surfaces over the other, a shear stress fj/a appears at the asperities. The shear stress is greatest where the cross-sectional area of asperities is least, that is, at or very near the contact plane. Now, the intense plastic deformation in the regions of contact presses the asperity tips together so well that there is atom-to-atom contact across the junction. The junction, therefore, can withstand a shear stress as large as k approximately, where k is the shear-yield strength of the material (Chapter 11). 

As is true for macroscopic adhesion and mechanical testing experiments, nanoscale measurements do not a priori sense the intrinsic properties of surfaces or adhesive junctions. Instead, the measurements reflect a combination of interfacial chemistry (surface energy, covalent bonding), mechanics (elastic modulus, Poisson s ratio), and contact geometry (probe shape, radius). Furthermore, the probe/sample interaction may not only consist of elastic deformations, but may also include energy dissipation at the surface and/or in the bulk of the sample (or even within the measurement apparatus). Study of rate-dependent adhesion and mechanical properties is possible with both nanoindentation and... 

Fig. 1. Contact geometry for a sharp indenter at (A) zero load, (B) maximum load and (C) complete unload. The residual penetration depth after load removal is given by h...

Fig. 11 —Nominal contact zone and real contact areas between rough surfaces in contact, (a) film thickness profile along the central line of contact, (b) a contour plot of the contact geometry where the white circular area and gray spots inside the circle correspond to the nominal and real contact area, respectively.

In the earliest SFG experiments [Tadjeddine, 2000 Guyot-Sionnest et al., 1987 Hunt et al., 1987 Zhu et al., 1987], a first-generation data acquisition method was used, and, because of the limited signal-to-noise ratios, IR attenuation by the electrolyte solution was a substantial handicap. So, in earlier SFG studies, as in IRAS studies, measurements were performed with the electrode pressed directly against the optical window [Baldelli et al., 1999 Dederichs et al., 2000]. With the in-contact geometry, the electrolyte was a thin film of uncertain and variable depth, probably of the order of 1 p.m. However, the thin nonuniform electrolyte layers can strongly distort the potential/coverage relationship and hinder the ability to study fast kinetics. 

The nature of the conductance families reported for single alkanedithiol junctions is still under debate. Current interpretations are based on different contact geometries [64, 115, 242], different molecular conformations [64, 244], substrate roughness [245], or the control of tip movement [252],... 

Independent of the contact geometry, the calculations also demonstrated that the introduction of gauche defects resulted in a decrease of the bridge conductance by a factor of 10, as compared to an all-trans alkanedithiol chain (see Fig. 14b, triangles). Due to variations in the number and positions of gauche defects, as well as various contact geometries, the molecular junctions can exhibit conductance values up to two orders of magnitude below the conductance values of an all-trans conformation of the alkyl chain. 

Fig. 20 (a) Experimentally measured conductances G/Go of the six biphenyl dinitriles N1-N6 as a function of cos2. (b) Computed conductances of N1-N6 as a function of cos2ip for the low-coordination (l.c., circles) contact geometry and the high-coordination h.c., squares) contact geometry [54]... 

The beauty of the differential UFM approach is that the absolute value of the contact stiffness of a nanoscale contact at a known force level F is directly measured in terms of the ultrasonic vibration amplitude and the applied force, and is practically independent of the adhesion or other contact parameters. The contact geometry would need to be known in order to determine the elastic stiffness of the sample. 

Equations (3.86) and (3.88) give some examples of the nonretarded van der Waals forces for ideal contact geometries. For retarded interactions, the exponent for the distance of separation increases by 1 with the change of the corresponding numerical coefficients. The preceding theory, assuming complete additivity of forces between individual atoms, is known as the microscopic approach to the van der Waals forces. 

Wear is not a direct property of polyurethane but is the result of a complex system of materials being in contact, geometry of contact, operating conditions, and environment (Mardel et al., 1995). Polyurethanes find successful... 

OFETs with wet-deposited films of 48 as the active layer in bottom contact geometry were fabricated on highly doped n-type silicon wafers with the organic semiconductor layer (ca. 50 nm) deposited from chloroform solution [70], OFETs made from 48 exhibited negative amplification, which is typical of... 

The review is organized as follows In Section 2 we present the multiscale equilibrium thermodynamics in the setting of contact geometry. The time evolution (multiscale nonequilibrium thermodynamics) representing approach of a mesoscopic level LmeSoi to the level of equilibrium thermodynamics Leth is discussed in Section 3. A generalization in which the level Leth is replaced by another mesoscopic level LmesoZ is considered in Section 4. The notion of multiscale thermodynamics of systems arises in the analysis of this type of time evolution. 

In this section we limit ourselves to equilibrium. The time evolution that is absent in this section will be taken into consideration in the next two sections. We begin the equilibrium analysis with classical equilibrium thermodynamics of a one-component system. The classical Gibbs formulation is then put into the setting of contact geometry. In Section 2.2 we extend the set of state variables used in the classical theory and introduce a mesoscopic equilibrium thermodynamics. 

The setting of contact geometry that we have used in the presentation following Hermann (1984) is very useful at least for three reasons (i) It puts the calculations involved in thermodynam ics on a firm ground. The formulation presented above remains in fact the same as the original Gibbs... 

We shall not enter here into the general formulation in the context of contact geometry. Instead, we shall only work out two examples. 

The zero-approximation in expansion of I(V) in d/l is the ohmic current considered by Sharvin [5]. From the Sharvin s formula the characteristic size d of the contact can be determined in the ballistic limit. The second derivative of the first approximation in expansion of I(V) in d/l is directly proportional to the spectral function of electron-phonon interaction (PC EPI) gpc w) = apc (w) F (w) °f the specific point-contact transport both in the normal and in the superconducting states [1, 6, 7], This term is the basis of the canonical inelastic point-contact spectroscopy (PCS). Here, ot2pC (oj) is the average electron-phonon matrix element taking into account the kinematic restriction imposed by contact geometry and F (oj) is the phonon density of states. 

Fig. 2 Typical contact geometries used for scratch testing. The average strain is proportional a to tan9 in the case of conical or pyramidal indentors and b to a/R in the case of spherical indentors...

The above result was obtained with front-side illumination geometry. As one would intuitively expect, carrier collection is most efficient close to the rear contact. Indeed, marked differences have been observed for photoaction spectra with the two irradiation (i.e., through the electrolyte side vs. through the transparent rear contact) geometries for Ti02, CdS and CdSe nanocrystalline films [319, 342]. Obviously, the relative magnitudes of the excitation wavelength and the film thickness critically enter into this variant behavior. 

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