Curvature electricity

Fig, 3.13,1 Meyer s model of curvature electricity. The nematic medium composed of polar molecules is non-polar in the undeformed state ((a) and (< )) but polar under splay (b) or bend ([Pg.206]

D. Schmidt, M. Schadt and W. HeUrich, Liqnid-crystaUine curvature electricity the bending mode of MBBA, Z. Naturforsch. 27a, 277-280, (1972). 

A.G. Petrov, R.L. Ramsey and P.N.R. Usherwood, Curvature-electric effects in artificial and natural membranes studied using patch-clamp techniques, Eur. Biophys. J. 17(1), 13-17, (1989). doi 10.1007/BF00257141... 

The basic device is very simple. A tip of refractory metal, such as tungsten, is electrically heat-polished to yield a nearly hemispherical end of about 10" cm radius. A potential of about 10 kV is applied between the tip and a hemispherical fluorescent screen. The field, F, falls off with distance as kr, and if the two radii of curvature are a and b, the total potential difference V is then... 

When the curvature of the reaction vessel is too great for the efficient operation of the bar type magnetic stirrer, a miniature solenoid-operated reciprocating stirrer may be employed (Fig. XII, 2, 19). This stirrer may be easilj constructed from a telephone relay or electric bell. It is advisable to have a control for adjusting the stroke while running. 

Unless extremely high potentials are to be used, the intense electric fields must be formed by making the radius of curvature of the needle tip as small as possible. Field strength (F) is given by Equation 5.1 in which r is the radius of curvature and k is a geometrical factor for a sphere, k = 1, but for other shapes, k < 1. Thus, if V = 5000 V and r = 10 m, then, for a sphere, F = 5 x 10 V/m with a larger curvature of, say, Iff m (0.1 mm), a potential of 500,000 V would have to be applied to generate the same field. In practice, it is easier to produce and apply 5000 V rather than 500,000 V. 

E = electric potential (voltage) between the inner and outer ESA plates R= radius of curvature of the ion trajectory... 

A large electric potential applied to a needle provides a very intense field at its tip, where the radius of curvature is small. 

Similarly, a sharp edge (razor blade) or a very sharp curve can also provide an intense electric field. For any given electric potential, as the radius of curvature of a tip or edge becomes smaller, the electric field becomes increasingly stronger. 

By growing thin whiskers along a sharp edge or thin wire, the ends of the whiskers become regions of very small radius of curvature and, consequently, provide very intense electric fields. 

In field ionization (or field desorption), application of a large electric potential to a surface of high curvature allows a very intense electric field to be generated. Such positive or negative fields lead to electrons being stripped from or added to molecules lying on the surface. The positive or negative molecular ions so produced are mass measured by the mass spectrometer. 

The high potential and small radius of curvature at the end of the capillary tube create a strong electric field that causes the emerging liquid to leave the end of the capillary as a mist of fine droplets mixed with vapor. This process is nebulization and occurs at atmospheric pressure. Nebulization can be assisted by use of a gas flow concentric with and past the end of the capillary tube. 

The theory and appHcation of SF BDV and COV have been studied in both uniform and nonuniform electric fields (37). The ionization potentials of SFg and electron attachment coefficients are the basis for one set of correlation equations. A critical field exists at 89 kV/ (cmkPa) above which coronas can appear. Relative field uniformity is characterized in terms of electrode radii of curvature. Peak voltages up to 100 kV can be sustained. A second BDV analysis (38) also uses electrode radii of curvature in rod-plane data at 60 Hz, and can be used to correlate results up to 150 kV. With d-c voltages (39), a similarity rule can be used to treat BDV in fields up to 500 kV/cm at pressures of 101—709 kPa (1—7 atm). It relates field strength, SF pressure, and electrode radii to coaxial electrodes having 2.5-cm gaps. At elevated pressures and large electrode areas, a faH-off from this rule appears. The BDV properties ofHquid SF are described in thehterature (40—41). 

Brush discharge A nonuniform electric field between a charged dielectric and a conductor that has a moderate radius of curvature MIE <3 ml... 

Corona A corona is generated when a highly nonuniform electric field of sufficient strength terminates on a conductor that has a small radius of curvature (i.e., a point, wire, or knife-edge). The luminous... 

Fig. 12. Normalized dc electrical resistivity p(T) of single crystal KsCeo. The inset shows the p(T) behavior near the superconducting transition temperature Tc = 19.8 K [114]. The curvature in p(T) for T > Tc is due to the volume expansion of the sample [7, 4.3],...

At the end of the 1960s, Subba Rao et al. examined the influence of the interface on the CMC values [56]. They found a decrease in the CMC at the oil-water interface compared with the air-water interface. The CMC decreased by about 10% in the presence of heptane and by about 30-40% in the presence of benzene. The solubilization of the hydrocarbon in the micelle interior results in an increase in the micelle size and a slight change in the curvature of the micelle surface. The electrical potential and hence the electrical work of... 

In the theoretical section above, the nonlinear polarization induced by the fundamental wave incident on a planar interface for a system made of two centrosymmetrical materials in contact was described. However, if one considers small spheres of a centrosymmetrical material embedded in another centrosymmetrical material, like bubbles of a liquid in another liquid, the nonlinear polarization at the interface of a single sphere is a spherical sheet instead of the planar one obtained at planar surfaces. When the radius of curvature is much smaller than the wavelength of light, the electric field amplitude of the fundamental electromagnetic wave can be taken as constant over the whole sphere (see Fig. 7). Hence, one can always find for any infinitely small surface element of the surface... 

While the order parameters derived from the self-diffusion data provide quantitative estimates of the distribution of water among the competing chemical equilibria for the various pseudophase microstructures, the onset of electrical percolation, the onset of water self-diffusion increase, and the onset of surfactant self-diffusion increase provide experimental markers of the continuous transitions discussed here. The formation of irregular bicontinuous microstructures of low mean curvature occurs after the onset of conductivity increase and coincides with the onset of increase in surfactant self-diffusion. This onset of surfactant diffusion increase is not observed in the acrylamide-driven percolation. This combination of conductivity and self-diffusion yields the possibility of mapping pseudophase transitions within isotropic microemulsions domains. 

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