T and R phases

A central issue in the field of surfactant self-assembly is the structure of the liquid crystalline mesophases denoted bicontinuous cubic, and "intermediate" phases (i.e. rhombohedral, monoclinic and tetragonal phases). Cubic phases were detected by Luzzati et al. and Fontell in the 1960 s, although they were believed to be rare in comparison with the classical lamellar, hexagonal and micellar mesophases. It is now clear that these phases are ubiquitous in surfactant and Upid systems. Further, a number of cubic phases can occur within the same system, as the temperature or concentration is varied. Luzzati s group also discovered a number of crystalline mesophases in soaps and lipids, of tetragonal and rhombohedral symmetries (the so-called "T" and "R" phases). More recently, Tiddy et al. have detected systematic replacement of cubic mesophases by "intermediate" T and R phases as the surfactant architecture is varied [22-24]. The most detailed mesophase study to date has revealed the presence of monoclinic. 

The classification here reported follows that proposed by Yashima et al. (1994a). The t- and r -phases correspond to the TZ° and TZ phases previously reported by Meriani (1985, 1989). b Defined as axial ratio da. 

Fig. 43. High-resolution HAADF micrograph of a (100) planar defect in edge-on orientation located between the dashed hnes, and superposed tilings for the T- and R-phases.

It is obvious that the core structure of the experimental [Figs 44(a) and 44(b)] and predicted [Fig. 42(d)] metadislocation are represented by the same tile. Hence they both have the same Burgers vector. However, they are connected to different types of planar defects. While the metadislocation in Fig. 42(d) is associated with six phason planes, the metadislocation in Fig. 44(b) is associated with a slab of R-phase. The phason elements on the left-hand side of the metadislocation core change the stacking sequence of the ideal T-phase structure A,B,A,B,A to a sequence A,A,A,B,B. These additional defects are required to accommodate the symmetrical metadislocation core into the structure and have to move along with the latter. In other words, the three phason lines act as escort defects to the metadislocation core, which move ahead and clear the way for the latter. Upon movement, the metadislocation locally transforms the T-phase structure, leaving a slab of modified R-phase in its wake. Different types of metadislocations in T- and R-phase structures and their modes of motion are discussed in Section 6.4. 

For the sake of mathematical simplicity wave motion was introduced before (1.3.2) as a one-dimensional problem. One of the most obvious features of waves, however, is their tendency to spread in all directions from the source of a disturbance. To represent such a wave in three dimensions requires two parameters, t and r, the distance from the source to any point in the medium, in a form like f(r — vt), in which v is the velocity at which the disturbance spreads, and the phase is r — vt. As the disturbance spreads it increases... 

Vrbaski, T., and R. J. Cvetanovic. A study of the products of the reactions of ozone with olefins in the vapor phase as determined by gas-liquid chromatography. Can. J. Chem. 38 1063-1069, 1960. 

Figure 4 shows a typical example of sustained kinetic oscillations occurring for particular conditions (pc0, p0r and T) during the catalytic CO oxidation on a Pt(llO) surface (40). The measurements were performed with an UHV system acting as flow reactor, where the C02 partial pressure is directly proportional to the rate. The simultaneously recorded CO pressure oscillates with the same period and with amplitudes of about 1%, whereby pco shows a minimum whenever the reaction rate is maximum. The work function A varies parallel to the rate R. This quantity is essentially determined by the oxygen coverage. Because under oscillatory conditions the rate is determined by oxygen adsorption (see above), it becomes plausible why A and R vary in phase. 

Kurnik, R. T., and R. C. Reid. 1982. Solubility of solid mixtures in supercritical fluids. J. Fluid Phase Equilib. 8 93. 

Associations within the bulk crystalline phase. The physical property of enantiomeric solids and their mixtures which is cited most often is melting point. Figure 18 gives the melting point versus composition diagram for mixtures of S( T-)- and R( — )-SSME. The solid-liquid coexistence line of... 

Herron, J. T., and R. E. Huie (1977). Stopped-flow studies of the mechanism of ozone-alkene reactions in the gas phase. Ethylene. J. Am. Chem. Soc 99, 5430-5435. 

Leu, M. T. and R. H. Smith (1981). Kinetics of the gas-phase reaction between hydroxyl and carbonyl sulfide over the temperature range 300-517 K. J. Phys. Chem. 85, 2570-2575. 

A pulsed perturbation of one species at a time is applied to an oscillatory system, often but not necessarily near a supercritial Hopf bifurcation. The phase of oscillation at which the perturbation is added and the amount of perturbant added are varied. It is determined whether each perturbation results in an advance or delay of the next oscillatory peak relative to the period of the unperturbed autonomous system. If we let t denote the time of the nth reference event (an easily followed feature of the oscillations, such as a sharp rise or fall in the concentration of a monitored species), the period of the unperturbed limit cycle is given by Tq = t - r i. A pulse perturbation is applied at some time ipert, between t and r +i, from which we define a phase of perturbation as y>pert = - r i)/ro. Another reference event of the same type... 

The formulation of transport processes requires the use of time and space variables t and r, in contrast with equilibrium thermodynamics which does not recognize time as a variable. The object of investigation is a phase with local inhomogeneities, composed of particles Xi, X2.Xi,..., molecules or ions, at particle num-... 

Any specimen will cause a phase change in the wavefront passing through it. The specimen has an optical thickness nt producing an optical path difference H- n- l)t and a phase retardation (27t/A)( - l)r. To make the phaseshift affect the image intensity, the retarded wave must be caused to interfere with another wave. The other wave must be coherent with that passing through the specimen. 

R. Hol5 t and R Oswald, Dislocations in uniaxial lamellar phases of liquid crystals, polymers and amphiphilic systems, Int. J. Mod. Phys. B, 9,1515 (1995]. 

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