Correlation mesophases

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

Relation (18) correlates Tgc with the thermal properties of matrix and mesophase. Obviously, more accurate expressions for the thermal expansion curves, or the thermal expansion coefficient of the composite may provide a better approach to Tgc than the above formula. However, in many cases, it was found that this relation applies with satisfactory accuracy. 

Two limiting cases chaos and order are determined here, but in addition one can also consider chaos with some correlation to particles localization (type 3, Table 9.3) type 4 assumes presence of some order, for example long-range order in silicate mesophases, or platinum particles in a xerogel, etc. One can also consider division of these types, which allow or disallow overlapping of particles. 

Unfortunately, these indices are difficult to determine. Furthermore, most vesicle dispersions contain a dispersed mesophase with particle sizes below 200 nm up to 1 pm. Therefore photon correlation spectroscopy (PCS), on the basis of laser light scattering, provides an appropriate method of investigation [18]. 

Note 3 By contrast with a smectic B mesophase, a crystal B mesophase has correlations of positional order (hexagonal) in three dimensions, i.e., correlations of position occur within and between layers. 

Note 2 A SmF mesophase is characterised by in-plane short-range positional correlations and weak or no interlayer positional correlations. 

Note 3 The in-plane positional correlations in a smectic I mesophase are slightly greater than in a smectic F mesophase. 

Mesophase in which disc-shaped molecules, the disc-shaped moieties of macromolecules or wedge-shaped molecules assemble themselves in columns packed parallel on a two-dimensional lattice, but without long-range positional correlations along the columns. 

Note 5 Distinct biaxial mesophases are created when the molecular centers of mass are correlated within the layers. Such mesophases have been proposed for board-like polymers and have been called sanidic mesophases. 

Comparson of the transitions observed by differential scanning calorimetry in membranes of M. laidlawii and in water dispersions of the lipids from the membranes support the concept that most of the lipids exist as a smectic mesophase in the membranes. The evidence for a bilayer structure is straightforward in this case. Lipid transition temperatures are a function of fatty acid composition and correlate well with biological properties. The calorimeter possesses advantages over high resolution NMR for M. laidlawii, and perhaps in many other systems, because the data can be interpreted less ambiguously. In M. laidlawii membranes the bilayer appears to be compatible with the same physical properties observed in other membranes—a red-shifted ORD, lack of ft structure in the infrared, reversible dissociation by detergents, and poorly... 

An artificial neural network (ANN) model was developed to predict the structure of the mesoporous materials based on the composition of their synthesis mixtures. The predictive ability of the networks was tested through comparison of the mesophase structures predicted by the model and those actually determined by XRD. Among the various ANN models available, three-layer feed-forward neural networks with one hidden layer are known to be universal approximators [11, 12]. The neural network retained in this work is described by the following set of equations that correlate the network output S (currently, the structure of the material) to the input variables U, which represent here the normalized composition of the synthesis mixture ... 

Short range order in liquid-like systems as well as long range order in crystalline domains are reflected in WAXS-patterns very dearly. Some examples of calculated X-ray patterns from PTFE (Phase I), a smectic LC-phase and even a PE melt, show that our model covers a wide range of macromolecular structures running the whole scale from crystalline systems over mesophases up to polymer melts. The range of intra- and intermolecular order can be estimated fairly well with the help of density correlation functions. 

T extures of lyotropic mesophases have been the object of numerous observations by optical (1,2,3) and electronic (4, 5, 6,7) microscopy. Except for the pioneering work of Lehmann (1) and Friedel (2) who intended to identify the various kinds of defects which constitute the textures, the purpose of these observations was to recognize the different existing phases—lamellar, hexagonal (or in the soaps language neat phase, median phase, etc.)—in correlation with x-ray data. 

In crystalline smectic phases the arrangement of the molecules within the layer is ordered in a hexagonal, orthorhombic or monoclinic fashion and the layers are correlated to each other. The in-plane order of the mesophase is indicated by the existence of sharp wide-angle reflection. The in-plane correlation is recorded by a small value of Full Width of Half Maximum (FWHM) and, in principle, by more than one wide-angle reflex. 

In discotic phases the orientation of the molecules is perpendicular to the molecular plane. Here, the columns can be arranged in a nematic or columnar manner. In the nematic phase the molecules possess a centre of gravity randomly ordered, but with the short molecular axis of each molecule more or less parallel. In the columnar phase, beside the preferable orientation of the short molecular axes, the disc-like molecules are ordered forming columns. Depending on the correlation strength between he columns these phases can be subdivided into ordered or disordered. A third possibility is to have a thermodynamically preferable position of the columns in the mesophase, like in a hexagonal cell. Additionally, a tilt of the columns is also possible. 

Cr Cub, Cubv d E G HT Iso Isore l LamN LaniSm/col Lamsm/dis LC LT M N/N Rp Rh Rsi SmA Crystalline solid Spheroidic (micellar) cubic phase Bicontinuous cubic phase Layer periodicity Crystalline E phase Glassy state High temperature phase Isotropic liquid Re-entrant isotropic phase Molecular length Laminated nematic phase Correlated laminated smectic phase Non-correlated laminated smectic phase Liquid crystal/Liquid crystalline Low temperature phase Unknown mesophase Nematic phase/Chiral nematic Phase Perfluoroalkyl chain Alkyl chain Carbosilane chain Smectic A phase (nontilted smectic phase)... 

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