Modulated layer phases

Recently fluorinated chains were also attached to amine based dendrimers, like PPI and poly(amido amine) (PAMAM), by means of ionic self assembly with semiperfluorinated alkanoic acids (Fig. 71, 216, 217). All dendrimer complexes 216 with perfluorinated alkanoic acids show SmA phases except the fifth generation dendrimer which shows a Colrec phase [378]. Also semiperfluorinated 4-alkoxybenzoic acids 217 [379] and mixed systems combining fluorinated and nonfluorinated alkanoic or benzoic acids (216, 217) have been reported [379-381]. In most cases layer structures (SmA) and for higher generation dendrimers also modulated SmA phases (Colrec phases) were observed. The layer thickness of the SmA phases of the mixed complexes 216 depends on the ratio of fluorinated and non-fluorinated acids, where smaller d values were observed for dendrimers with low Rp-content for Rp-rich dendrimers the more rigid Rp-chains provide... 

Both layers contain Pb and Bi atoms, and syntheses from these metals and sulphur suggest that the minor elements present in the natural material (Fe and Sb) are not essential for the formation of the structures. The sulphur atoms peripheral to the pseudo-hexagonal layers again complement the half-octahedral coordination of Pb and Bi in the surfaces of the T layers, the total coordination of which varies between deformed octahedral and bi-capped trigonal prismatic (which are also commonly observed in simpler Pb -I- Bi sulphosalt structures). Both sets of layers are sinusoidally modulated in phase with the periodic variation of coordination the period being slightly more than 5 T subcells (Fig. 18). 

The control module layer is the lowest level and defines how field devices (e.g., valves, pumps, controllers, etc.) interact with the process control system. Phases are at the next layer and describe small (often generic) sequences (e.g., fill, transfer, initiate temperature control, etc.) that operate on a unit. At the next layer up the hierarchy, phases may be combined into unit operations to perform more complex functions (e.g., distillation, crystallization, etc.). 

Solid waxes are a material class which is also compatible with liquid deposition processes. These can be heated in the printhead and deposited on the substrate held below the melting point of the material. Once the material prints it freezes-by taking advantage of the phase change there is no need for drying and no solvent evolution or underlayer dissolution. These liquid deposited waxes can be used as etch resists and affinity modulation layers for patterning. 

As described above, the kink in the molecular shape and the requirement to fill the space as effectively as possible are not compatible with a three-dimensional fluid order. In other words, when translating a bent-core molecule in the melt of the neighbouring bent-core molecules, it experiences a periodic potential with its periodicity determined by the length I of the molecules. To allow for fluidity at the macroscopic level, one needs to frustrate the bent-core structure so that they do not lock into smectic layers easily. Such a frustration can be introduced by some steric or electrostatic disturbance of the bare bent-core (or peeled banana ) shape, which has been seen in some modulated smectic phases.As discussed by Bailey and Jdkli,a steric or electrostatic inclusion in the core of the molecules leads to layer modulation, an SmCc structure and broken smectic layers that effectively correspond to a columnar phase, as the inclusions increase. Following this picture, here we postulate that bent-core nematics are probably more frustrated than the electrically unswitchable B7 (columnar) phases, in which the broken smectic ribbons are separated by melted fluid nematic regions. Such over-frustrated B7 materials are characterized... 

The classical picture of spheres, cylinders and lamellae was first challenged by the discovery of a new morphology in styrene/isoprene diblocks (Hasegawa et al. 1987) and styrene/isoprene star diblocks (Thomas et al. 1986). In the latter case the morphology has subsequently been identified as a so-called gyroid phase (Hajduk et al. 1995) this is a bicontinous nework with cubic symmetry that has now been identified in a number of different diblock systems (Schulz et al. 1994, Hajduk et al. 1995). Other non-classical phases have also been identified these include a perforated layer phase and a modulated lamellar phase (Bates et al. 1994). 

Polar Columnar (ColP) Phases In calamitic rod-shaped LCs, the frustration occurring in the layer organization of molecules due to steric and/or polar effects leads to form a variety of 2D density structures such as undulated layers, modulated layers (ribbons), and Cols. The situation for bent-core molecules with an ability to form macroscopic polar order is much more complex, and different types of modulated smectic and Col phases form. Since their 2D X-ray patterns, structural models, and nomenclature have been in great detail described in the two previous reviews [29, 32], in this section, the field-induced switching properties of polar columnar (ColP) phases are focused on. 

Modulated smectic phases are just one of a number of classes of frustrated smectic phases, all of which arise from the competition between different characteristic length scales but differ in the manner by which this frustration is relieved. In the incommensurate SmA phases the competing periodicities coexist along the layer normal and the first example of such a phase was observed for a nonsymmetric dimer, KI5 (see Fig. 1 g). In this phase the larger periodicity appears to correspond to the molec-... 

The Bj textures show characteristic helical filamentary growth in cooling from isotropic melt. i- 2 However they denote at least two distinct phases. X-ray measurements clarified that the original By materials, which form freestanding strands, - just like columnar liquid crystals of disc-shape molecules (see Chapter 2), indeed have a columnar phase (hereafter we will label them as Bj j). Other By-type materials (we call them Byu) were foimd to have modulated layer structures. We note that the By and B2 type banana-smectics also form strands of fibers. ... 

Figure 8-1. A cartoon of the nematic (left) and the smectic-A (right) phase. The nematic phase has only orientational order and no translational periodicity. The smectic-A phase exhibits, in addition, a sinusoidal density modulation ( layering ) in the direction of the oientational ordering this layering...

The fact that the most unstable mode of a lamellar phase is infinitely degenerate in the x-y plane can be used to show that, when the lamellar phase is driven into other ordered phases, the kinetics of the transition proceeds through a long-lived intermediate modulated-layered state that may correspond to the experimentally observed perforated layered structures. If one direction of the most unstable mode is excited, it will lead to the undulation of the layers that eventually form cylindrical structures (Figure 8.5). However, because of the degeneracy of the fluctuation modes, it is most likely that more than one direction of the fluctuation modes will be excited, leading to the formation of a perforated layered structure (Figure 8.6). 

The Maier-Saupe tlieory was developed to account for ordering in tlie smectic A phase by McMillan [71]. He allowed for tlie coupling of orientational order to tlie translational order, by introducing a translational order parameter which depends on an ensemble average of tlie first haniionic of tlie density modulation noniial to tlie layers as well as / i. This model can account for botli first- and second-order nematic-smectic A phase transitions, as observed experimentally. 

The transition from smectic A to smectic B phase is characterized by tire development of a sixfold modulation of density witliin tire smectic layers ( hexatic ordering), which can be seen from x-ray diffraction experiments where a sixfold symmetry of diffuse scattering appears. This sixfold symmetry reflects tire bond orientational order. An appropriate order parameter to describe tlie SmA-SmB phase transition is tlien [18,19 and 20]... 

The essential differences between sequential-modular and equation-oriented simulators are ia the stmcture of the computer programs (5) and ia the computer time that is required ia getting the solution to a problem. In sequential-modular simulators, at the top level, the executive program accepts iaput data, determines the dow-sheet topology, and derives and controls the calculation sequence for the unit operations ia the dow sheet. The executive then passes control to the unit operations level for the execution of each module. Here, specialized procedures for the unit operations Hbrary calculate mass and energy balances for a particular unit. FiaaHy, the executive and the unit operations level make frequent calls to the physical properties Hbrary level for the routine tasks, enthalpy calculations, and calculations of phase equiHbria and other stream properties. The bottom layer is usually transparent to the user, although it may take 60 to 80% of the calculation efforts. 

Although the above results again point towards a relation between the preeursing distortions and the martensite shuffles, detailed analysis of the neutron seattering data in the temperature region elose to Ms indieate that an intermediate phase may exist with an effective 6-layer periodieity. In this view the ISD modulations eould rather be preeursors to this intermediate phase than to the final martensite strueture. 

Smectic A and C phases are characterized by a translational order in one dimension and a liquid-like positional order in two others. In the smectic A phase the molecules are oriented on average in the direction perpendicular to the layers, whereas in the smectic C phase the director is tilted with respect to the layer normal. A simple model of the smectic A phase has been proposed by McMillan [8] and Kobayashi [9] by extending the Maier-Saupe approach for the case of one-dimensional density modulation. The corresponding mean field, single particle potential can be expanded in a Fourier series retaining only the leading term ... 

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