Sharp-kink approximation

Fig. 6. Coarse-grained description of a liquid-gas interface, where the intrinsic profile and local structure of the interface is disregarded, and one rather treats the interface as an elastic membrane at position z h(x, v) ( sharp kink -approximation for the interfacial profile).

This coarse-graining can also be used to justify the "drumhead model of an interface, cf. fig. 6, where on a more macroscopic scale the internal structure of the interface is disregarded, and one is more interested in large scale fluctuations of the local position z = h(x,y) of this interface. In this sharp kink approximation the interface is described similarly to an elastically deformable membrane. 

As the first example, we consider Ar adsorption in a slit pore with attractive walls made of amorphous hard sphere (HS) solid. Two different cases are considered. In the first case, the solid is modeled using a sharp-kink approximation for the solid density... 

The lattice gas model of Bell et al. [33] neither gave any detailed mechanism of the orientational ordering nor separated the contributions of the headgroup and the acyl chain. Lavis et al. [34] discussed Ref. 33 critically and concluded that the sharp kink point in the isotherm at transition was an artifact of the mean field approximation used. An improved correspondence to experimental data was claimed by the use of the real-space renormalization group method [35]. The same authors returned to the problem [35] and concluded that in addition to the orientation of the molecules, chain melting had to be included in a model which could interpret the phase transitions. 

Dislocation motion in covalent crystals is thermally activated at temperatures above the Einstein (Debye) temperature. The activation energies are well-defined, and the velocities are approximately proportional to the applied stresses (Sumino, 1989). These facts indicate that the rate determining process is localized to atomic dimensions. Dislocation lines do not move concertedly. Instead, sharp kinks form along their lengths, and as these kinks move so do the lines. The kinks are localized at individual chemical bonds that cross the glide plane (Figure 5.8). 

The other important and unusual feature observed in the magnetoresistance is the strange behavior of the background resistance. As can be seen in Fig. 4.10, first the resistance increases drastically in the applied magnetic field and then falls off gradually above 10T. At approximately 23 T a sharp kink structure occurs after which the oscillation amplitude starts to increase rapidly. The kink structure in resistivity has been mapped out in detail by different groups [294, 295] and is believed to be the indication for the field-induced phase transition from the SDW to the metallic state. 

In the spectrum of resinite from lignite there is also some loss of nonaromatic C-H groups that is shown particularly in the region below approximately 1250 cm. 1. The absorption at 1700 cm."1 becomes less sharp and widens on the low frequency side as oxidation proceeds. A distinct kink in the trace does develop at 1600 cm. 1, and it will be interesting to establish if broadening of the absorption band continues with prolonged oxidation and whether or not a separate band may eventually arise at the lower frequency. For com-... 

Following the pioneer work of Beebe et al. [168], the adsorption of krypton at 77 K has also been used for the determination of relatively small siuface areas, because its saturation vapor pressure is quite low (Pq near 267 Pa). Unfortunately, however, there are some complications in the interpretation of the adsorption isotherm. Thus, the working temperature is well below the triple point of bulk Kr (116 K approximately), but if the solid is taken as the reference state, the isotherm shows an xmusually sharp upward turn at the high-pressure end. Moreover, the BET plot is frequently not linear due to the kink produced by the phase change from a commensurate to an incommensurate structure. 

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