Chevrons instabilities

U.S. producers of benzene from petroleum and their approximate production capacities are shown in Table 5. These figures are inexact because the size of the market and instability of benzene prices causes frequent changes in capacity. Dow Chemical, with total annual benzene capacity of 8.3 x 105 t (250 million gallons) is the largest producer in the United States. Other companies with total domestic capacity of over 3.3 x 105 t (100 million gallons) per year are Amoco Corp., Lyondell, British Petroleum America, Chevron, Exxon Chemical, Occidental Petroleum, Shell Oil, and Mobil. These companies account for approximately 60% of total U.S. benzene capacity (65). 

Fig. 3.10.4. Threshold voltage of the AC instabilities versus frequency for MBBA. Sample thickness 100 / m. Region I conducting regime (stationary Williams domains) region II dielectric regime ( chevrons ). Full line is the theoretical The cut-off frequency / = 89 Hz. (After the Orsay Liquid Crystals Group. )...

Directing Convection Marangoni Convection/ Evaporation/Self- assembly Coffee rings, polygonal network structures, fingering instabilities, cracks, chevron patterns, etc. Nanometer to micrometer Marangoni convection and stick-slip motion can determine the final patterns observed [132-134]... 

FIGURE 5.10. Electrohydrodynamic instabilities in nematic liquid crystal with homogeneous initial orientation in the high-frequency regime (a > lJc)- (a) Domains when the voltage is slightly above the threshold voltage and (b) the Chevron pattern. 

The discrepancy between the calculated (0.2 fim) and observed (a few /xm) periods of instability may be caused by a nonuniform chevron structure of original bookshelf geometry. Chevron structures with smectic layers broken by a certain angle are often observed in smectic C liquid crystal cells. However, recently, they have been discovered in a certain temperature range for smectic A layers [111]. 

In the present multiscale approach, SAXS data analysis reveals that already at low deformations (lower than e(start)) the lamellar crystals oriented with their normal parallel to the tensile force, in order to alleviate compressive transversal stress, undergo buckling instability, with consequent formation of undulated chevron-like super-structures (Fig. 11.12b ). However, at deformations close to e(end) up to the breaking the effect of lamellar stacking and parallel orientation of the lamellar normal to the stretching direction on the SAXS intensity becomes buried by the large diffuse scattering localized on the equator due to cavitation (Fig. 11.12c"). 

Pawlak A, Galeski A (2005) Plastic deformation of crystalline polymers the role of cavitation and crystal plasticity. Macromolecules 38 9688-9697 Peterlin A (1971) Molecular model of drawing polyethylene and polypropylene. J Mater Sci 6 490 Popli R, Mandelkem L (1987) Influence of structural and morphological factors on the mechanical properties of the polyethylenes. J Polym Sci B Polym Phys 25 441 Read D, Duckett R, Sweeny J, Mcleish T (1999) The chevron folding instability in thermoplastic elastomers and other layered material. J Phys D Appl Phys 32 2087-2099 Resconi L, Cavallo L, Fait A, Piemontesi F (2000) Selectivity in propene polymerization with metallocene catalysts. Chem Rev 100 1253... 

Figure 31. Optical patterns accompanying different EHD processes, (a) Electrolytic mode for the homeo-tropic orientation of a nematic liquid crystal, (b) Ka-pustin-Williams domains (KWD) in homogeneously oriented nematic, (c) Anisotropic EHD mode for the planar texture of a cholesteric, (d) A chevron structure due to interference of two instabilities (KWD and inertial mode).

Figure 4. Threshold voltage of the AC instabilities for MBBA. Region I -conduction regime (Williams domains) Region II - dielectric regime (chevrons). Pull line from Dubois-Violette, de Gennes, and Parodi model. After Orsay Liquid Crystal Group [17, 23].

Figure 92. The shrinkage in smectic layer thickness due to the molecular tilt 0(T) in the SmC phase results in a folding instablity of the layer structure ( chevrons ). Even if the fold can he made to go everywhere in the same direction (in the figure to the right) to avoid invasive zigzag defect structures, the switching angle is now less than 2 9, which lowers brightness and contrast.

Y. Galerne, G. Durand, M. Veyssle, and V. Pontikis, Electrohydodynamic Instability in a Nematic Liquid Crystal Effect of an Additional Stabilizing ac Electric Field on the Spatial Period of Chevrons , Phys. Lett, Vol. 38A, p. 449 (1972). 

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