Structure periodic lamellar

Lattice models have been studied in mean field approximation, by transfer matrix methods and Monte Carlo simulations. Much interest has focused on the occurrence of a microemulsion. Its location in the phase diagram between the oil-rich and the water-rich phases, its structure and its wetting properties have been explored [76]. Lattice models reproduce the reduction of the surface tension upon adsorption of the amphiphiles and the progression of phase equilibria upon increasmg the amphiphile concentration. Spatially periodic (lamellar) phases are also describable by lattice models. Flowever, the structure of the lattice can interfere with the properties of the periodic structures. 

Fig. 8.3 SEM images of hexadecyl-functionalized magnesium phyllosilicate showing (A) intact spheroids (scale bar = 20pm) and (B) fractured spheroid with foam like interior (scale bar = 20pm). (C) TEM image of a wall fragment showing lattice fringes corresponding to a periodic lamellar structure (scale bar = 50 nm).

Figure 16.9 SEM images of the gratings cross section, which show the arrangement of a periodically lamellar layer a) 2-layer structure of Alq3 / Au and b) 4-layer structure of (Alq3 / Au / Alq3 / Au) on top of a 100 nm PR structure. Reprinted with permission from [Chiu et OPTICS EXPRESS. 15, 11608 (2007)]. Copyright 2007, Optical Society of America.

We have shown that they exhibit in dioxane concentrated solution (less than about 50 % of solvent) and in the dry state (after evaporation of dioxane at a slow rate) a periodic lamellar structure. 

When macromolecular cholesteric liquid crystals were imaged, a twisting of molecular orientation, which translated into a periodic lamellar structure in the materials, was foimd. Good agreement between afm and tern (transmission electron microscopy) was obtained in determining the widths of the lamellae. When the same polymer was processed from an isotropic solution, a homogeneous and nodular structure, lacking the periodicity of the cholesteric structure, was obtained (107). 

X-ray diffraction was also used to confirm the location of DNA within the supramolecular structure. The lamellar repeat period (d = 5.22 0.03 nm) and wide angle spacing (0.46 0.01) indicated the formation of ordered lamellar bilayers. These dimensions did not change upon addition of DNA (d = 5.31 0.14 and 0.46 0.01, respectively), which suggests that DNA was interacting with the liposome surface to form protective complexes, as opposed to being sandwiched between bilayers, which is often observed in lamellar lipoplexes. 

The classical theory of spinodal decomposition implies that a lamellar structure period is stipulated by nonlocal interaction intensity. The latter is taken into account in Gibbs potential density as a summand, proportional to the squared concentration gradient, that is. 

The scattering curves of samples of the gel region, shown in Fig. 9, show a more or less pronounced shoulder between 0.07 and 0.22 nm . This feature can be interpreted as a smeared correlation peak caused by periodic lamellar structures. It occurs in a similar range of Q values as the peaks observed for the more concentrated SDS/CA-SA/water system investigated by X-ray scattering [1]. For sample J3 the lamellar correlation peak corresponds to a periodic distance of 39.3 nm, which is higher than the value observed for the more concentrated system with a mixture of the alcohols CA and SA. There is no obvious trend in position or shape of the correlation peak for samples with different y. This may be due to the fact that the applied protocol of sample preparation does not ensure a fully reproducible structure of the samples. 

When comparable amounts of oil and water are mixed with surfactant a bicontinuous, isotropic phase is formed [6]. This bicontinuous phase, called a microemulsion, can coexist with oil- and water-rich phases [7,1]. The range of order in microemulsions is comparable to the typical length of the structure (domain size). When the strength of the surfactant (a length of the hydrocarbon chain, or a size of the polar head) and/or its concentration are large enough, the microemulsion undergoes a transition to ordered phases. One of them is the lamellar phase with a periodic stack of internal surfaces parallel to each other. In binary water-surfactant mixtures, or in... 

The period of the lamellar structures or the size of the cubic cell can be as large as 1000 A and much larger than the molecular size of the surfactant (25 A). Therefore mesoscopic models like a Landau-Ginzburg model are suitable for their study. In particular, one can address the question whether the bicontinuous microemulsion can undergo a transition to ordered bicontinuous phases. 

In this section we will discuss in some detail the application of X-ray diffraction and IR dichroism for the structure determination and identification of diverse LC phases. The general feature, revealed by X-ray diffraction (XRD), of all smectic phases is the set of sharp (OOn) Bragg peaks due to the periodicity of the layers [43]. The in-plane order is determined from the half-width of the inplane (hkO) peaks and varies from 2 to 3 intermolecular distances in smectics A and C to 6-30 intermolecular distances in the hexatic phase, which is characterized by six-fold symmetry in location of the in-plane diffuse maxima. The lamellar crystalline phases (smectics B, E, G, I) possess sharp in-plane diffraction peaks, indicating long-range periodicity within the layers. 

Dye structures of passive tracers placed in time-periodic chaotic flows evolve in an iterative fashion an entire structure is mapped into a new structure with persistent large-scale features, but finer and finer scale features are revealed at each period of the flow. After a few periods, strategically placed blobs of passive tracer reveal patterns that serve as templates for subsequent stretching and folding. Repeated action by the flow generates a lamellar structure consisting of stretched and folded striations, with thicknesses s(r), characterized by a probability density function, f(s,t), whose... 

Fig. 8 Various structure parameters appearing in the crystallization process of PET at 80 °C A, characteristic wavelength of SD D, dense domain size L, long period /p, persistence length Dc, lamellar stem length [19]...

An A-B diblock copolymer is a polymer consisting of a sequence of A-type monomers chemically joined to a sequence of B-type monomers. Even a small amount of incompatibility (difference in interactions) between monomers A and monomers B can induce phase transitions. However, A-homopolymer and B-homopolymer are chemically joined in a diblock therefore a system of diblocks cannot undergo a macroscopic phase separation. Instead a number of order-disorder phase transitions take place in the system between the isotropic phase and spatially ordered phases in which A-rich and B-rich domains, of the size of a diblock copolymer, are periodically arranged in lamellar, hexagonal, body-centered cubic (bcc), and the double gyroid structures. The covalent bond joining the blocks rests at the interface between A-rich and B-rich domains. 

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