Phase calamities

E phases, calamities 12 edge disclinations, chiral nematics 354 Ehrlich magic bullet, chromonics 984 elastic constants 63, 79 ff... 

Calame JP, Myers RE, Binari SC, Wood FN, Garven M (2007) Experimental investigation of micro-channel coolers for the high heat flux thermal management of GaN-on-SiC semiconductor devices. Int J Heat Mass Transfer 50 4767-4779 Celata GP, Cumo M, Zummo G (2004) Thermal-hydraulic characteristics of single- phase flow in capillary pipes. Exp Thermal Fluid Sci 28 87-95 Celata GP (2004). Heat transfer and fluid flow in micro-channels. Begell House, N.Y. 

With an appropriate mobile phase pump and colorimetric detector, Tswett s method would not be out of place in any separations laboratory today. However, the intervening calamities of the first half of the twentieth century, the First World War, the Great Depression, and the Second World War, resulted in Tswett s work largely being forgotten. 

Monosubstitution, as in the case of conventional calamities, is expected to lead to a predominance of nematic and smectic A phases, with possibly nematic phases being favored because of the repulsive steric effects of the ferrocene unit causing a reduced ability of the molecules to pack in layers. Disubstitution, on the other hand, may be expected to lead to smectic polymorphism because the overall shape of the molecule can be extended and varied from being linear to being slightly bent. For instance, let us first consider disubstitution in one of the ferrocene rings. In... 

As mentioned earlier, we will obtain an omnidirectional transmitting (and thus also receiving) radiation pattern if all the elements are fed in phase. Basically this can be done by using an ordinary harness with simple T connectors as shown for example in Chapter 2, Section 2.12. However, as also shown there, we must prevent coupling between the elements through the feed network since this could lead to high backscatter return. Use of hybrids is a proven way to avoid the calamity. 

A polarizer is a device that transforms a linear polarized wave into a circular polarized wave, or vice versa. The common principle is simply to decompose the incident field into two components where the phase of one is advanced and the other is delayed such that their difference is 90° while their amplitudes are the same. It appears that Pakan [128] was the first to utilize this principle. Later improvements were introduced by Lemer [129]. These devices were not of the meander-line type, as will be discussed here. These seem to appear first in a paper by Young et al. [130] and were subsequently unproved by Epis [131]. Later, a paper by Terret et al. [132] discussed how to calculate the susceptance of a meander line. All of these contributions were primarily focused on normal angle of incidence while Chu and Lee [133] extended the calculation to include oblique angle of incidence. A recent contribution was supplied by Marino [134], It was apparent that meander-line polarizers gradually deteriorate for higher angles of incidence. The present appendix will demonstrate that introduction of a dielectric profile can greatly improve this calamity. 

There will also be a reflected field. The vertical and horizontal components have amplitudes and phases given simply by F and F , respectively. In general this reflected field will be elliptic polarized. What is of concern, however, is the fact that when a single meander-line sheet transmits a perfect circular polarized field, we readily see from the Smith chart that F = t = F = Tft. In other words A single meander-line sheet will produce a reflected field of the same amplitude as the transmitted field that is, the efficiency is only 50%. The remedy for this calamity is to use several meander-line sheets cascaded after each other as will be discussed in the next section. See also Problem C.l, where you are asked to consider a two-sheet meander-line polarizer. 

The nematic phase of nonlinear mesogens may be biaxial - a translationally disordered fluid phase with two directors n and o specifying the orientational order (Fig. 5.3). Biaxial order in a nematic is predicted to occur [29] if the shape anisotropy of the idealized molecule (discoid) representing the nonlinear meso-gen is appropriately intermediate between the prolate shape of calamities and the oblate shape of discotics. Discoid-shaped mesogens lend themselves to a variety of stratified phases. Ferroelectric (Sapp) and antiferroelectric (Sapa) layer motifs in the normal smectic phases of discoid-shaped mesogens are readily envisioned (Fig. 5.4), but less obvious is the possibility of generating chiral supramolecular structures from such achiral discoid-shaped mesogens (Fig. 5.5) [30]. 

One compound can exhibit more than one phase, but unlike calamities they do not obey a distinct sequence rule. For example, the Nj) phase can occur above the columnar phases as in the hexa-alkoxybenzoyloxytriphenylenes (15) —e.g., R = QHiiO PhCOj, K 186°C 193°C Vo 274°C / —or below the columnar phase... 

In both types of aggregation, it is possible for large amounts of thermal motion to be accommodated without destroying the structure of the phase. In particular, rotational motion about the long axes of calamities, and about the short axes of discotics, can occur without destroying the overall pattern of molecular alignment. 

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