Real Area

Thus, under conditions of plastic defonnation the real area of contact is proportional to the nonnal force. If the shear force during sliding is proportional to that area, one has the condition that the shear force is proportional to the nonnal force, thus leading to the definition of a coefficient of friction. 

Dry Sliding. When two surfaces mb, the real area of contact involves only sufficient asperities of the softer material so that their yield pressure balances the total load (3). As the initial load W increases, the real contact area illustrated in Figure 1 increases proportionately according to the relation... 

Yield pressurep of the asperities is about three times the tensile yield strength for many materials. The real area of contact is frequently a minute fraction of the total area. With a typical bearing contact stress of 3 MPa and a bron2e bearing asperity yield pressure of 500 MPa, for instance, less than 1.0% of the nominal area would involve asperity contact. 

So it follows that, if two surfaces are placed in contact, no matter how carefully they have been machined and polished, they will contact only at the occasional points where one set of asperities meets the other. It is rather like turning Austria upside down and putting it on top of Switzerland. The load pressing the surfaces together is supported solely by the contacting asperities. The real area of contact, a, is very small and because of this the stress P/a (load/area) on each asperity is very large. 

Obviously, if we double P we double the real area of contact, a. 

Fig. 2.1. Electrode potential during the oxidation of methanol and hydrogen on a platinized platinum electrode (real area = 130 cm2) at constant current i = 5 mA. Base electrolyte = 0.5 M H2S04, room temperature. 

Fig. 4.5. Mass spectroscopic detection of carbon dioxide during methanol adsorbate oxidation and Sn(IV) injection. Porous Pt electrode, real area 12.3 cm2. Procedure after methanol adsorption at 0.4 V from 10 2 M 13CH3OH/0.5 M H2S04, the electrolyte was exchanged with 0.5 M H2S04, then potential step to 0J was applied and Sn(lV) was added. Dashed line no tin added.

The net area of this intimate contact is called the real area of contact Areai. It is assumed that plastic flow occurs at most microscopic points of contact, so that the normal, local pressures correspond to the hardness aj, of the softer of the two materials that are in contact. The (maximum) shear pressure is given by the yield strength cry of the same material. The net load L and the net shear force Fs follow by integrating aj, and cry over the real area of contact Areai. That is, L = cs, Arca and Fs = ayAreai. Hence, the plastic deformation scenario results in the following (static) friction coefficient ... 

CI2 evolution reaction, 38 56 electrochemical desorption, 38 53-54 electrode kinetics, 38 55-56 factors that determine, 38 55 ketone reduction, 38 56-57 Langmuir adsorption isotherm, 38 52 recombination desorption, 38 53 surface reaction-order factor, 38 52 Temkin and Frumkin isotherm, 38 53 real-area factor, 38 57-58 regular heterogeneous catalysis, 38 10-16 anodic oxidation of ammonia, 38 13 binding energy quantification, 38 15-16 Haber-Bosch atrunonia synthesis, 38 12-13... 

The apparent surfaces of poly crystals, measured geometrically, are often 2—3 times smaller than the real area because the latter is relatively rough—it has hills and valleys that are invisible to unaided sight (see Fig. 7.32). Because various metals—and different samples of the same metal—may have different roughness factors ... 

Fig. 7.32. The real area of polycrystals is often 2-3 times larger than the apparent area because of hills and valleys.

The various methods of determining the real surface area usually agree only to about 25%. One of the advantages of single crystals with a well-defined face exposed is that the real area is a known property of the exposed crystal face (see Section 7.8.2 on Miller indices). 

The reader will sometimes find current and sometimes current density (A cm-2) used in the text (some texts use mA cm-2)- The relation between the current (amperes), passing through an electrode and the current density (i)(Acm-2), i, is I/A = i. Strictly speaking, A should be the real area (Section 7.5.3), but in practice many electrochemists use the geometric (or, visible ) area. Thus, one should refer to the real or apparent current density, respectively. 

F. P. Bowden and E. K. Rideal, Proc. Roy. Soc. London 120A 59 (1928). First real area measurements, first transients. 

When rubber is brought into contact with another surface it deforms elastically and the real area of contact will increase with increasing normal load and, hence, the coefficient of friction will decrease with increasing normal load. It is also apparent that the real contact area is dependent on the surface geometry of the test piece. It is, hence, desirable to measure the friction of rubber over the range of normal forces of interest and to test with the surface geometry to be used in service, which may mean using the product or part of it as the test piece. 

There are some (Heinze, 1996) to whom the polaron explanation of the ionic introduction of electronic conductivity in organic compounds is specious The roughness factor of 400 would limit the degree of penetration of ions into the interstices of the polymer. However, Li+ or even CIOJ is of course much smaller than the test molecules (large dye molecules) which are generally used to probe the real area. Thus, one might conceive of a model of the polymer that is all fibers, the intercalation being all pervasive. It is obvious that an Li+ ion adsorbed on the surface of a fiber will promote an electron that may indeed be free to move under a field, i.e., to conduct. 

Achieve a highly porous structure, resulting in a much greater real area per square centimeter. What one needs is a compressed powder so that in fact the apparent unit area turns out to be 100 or even 1000 cm2 internally per apparent external square meter. Some idea of what is needed on the porosity side can be seen from Fig. 13.54. 

Using an expression (low field approximation) for a membrane potential derived from this model calculate the membrane potential assuming that the difference of the reversible redox potentials of the reactions on either side of the membrane is 120 mV (i0)l = 10-4 A cm-2 (iQ)2 = 10-6 A cm-2 real area = 10 times the apparent area (0.2 cm2) and R = 104 ohms per sample of membrane. (Bockris)... 

Measurement of the area of solid surfaces. The measurement of the real area of a solid surface is obviously fundamental to a study of its properties, but is not at all easy. Even the definition of what is meant by the real area presents some difficulties if the surfaces are irregular, and some of the cracks in it narrow, all depends on the fineness of the measuring device employed, whether or no it can penetrate into the finest cracks. 

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