Lamellar phase, scheme

This method has been devised as an effective numerical teclmique of computational fluid dynamics. The basic variables are the time-dependent probability distributions f x, f) of a velocity class a on a lattice site x. This probability distribution is then updated in discrete time steps using a detenninistic local rule. A carefiil choice of the lattice and the set of velocity vectors minimizes the effects of lattice anisotropy. This scheme has recently been applied to study the fomiation of lamellar phases in amphiphilic systems [92, 93]. 

The lamellar phase exists by virtue of the fact that amphiphilic molecules assemble into such a phase under given circumstances. One challenge is to relate properties of such a mesophase to macroscopic relevant properties, which was addressed in Section 9.2. In Section 9.3 a scheme has been given that was introduced by Israe-lachvili, which is useful in describing why certain amphiphiles form certain meso-phases. This scheme has been successfully applied to many amphiphilic systems. One of the challenges addressed in Section 9.3 is to see how that scheme may be also applied to the assembly of proteins, as another type of amphiphile, in particular how to explain recently observed phenomena of protein fibrillisation. 

Scheme 5.1 Schematic representation of the swelling of lamellar phase and vesicle precipitates with increasing glycerol. It demonstrates swelling of lamellar phase simply leads to an increase of the interlayer spacing, whereas swelling of MLV results in...

Fig. 10. (a) Scheme of lamellar self-organized phase typically achieved when a polyelectrolyte and an oppositely charged surfactant are com-plexed. (b) Long period as a function of alkyl chain length in the lamellar phase for sodium polystyrene sulfonate complexed with alkyltrimethylam-monium bromide. Adapted from M. Antonietti, J. Conrad, and A. Thiine-mann, Macromolecules 27,6007 (1994). 

The theory can be extended to three-dimensional systems [19, 22, 24]. Although the number of different structures increases, the bifurcation scheme is similar to the 2-D scheme. A 3-D body centered cubic structure involving six pairs of wavevectors and the 2-D hexagonal prismatic columns based on the same set as the 2-D hexagons come successively in a subcritical way (like the 2-D hexagons), losing stability far away from onset. Like stripes in 2-D systems, a 1-D lamellar phase bifurcates supercritically but becomes stable at some distance from onset. 

Whatever the precursor, the formation of an intermediate solid phase was always observed. It can be inferred from X-ray diffraction (Fig. 9.2.7) and infrared spectroscopy that this intermediate phase shows a lamellar, incompletely ordered structure (turbostratic structure) built up with parallel and equidistant sheets like those involved in the lamellar structure of the well-crystallized hydroxides Ni(OH)2 or Co(OH)2, these sheets are disoriented with intercalation of polyol molecules and partial substitution of hydroxide ions by alkoxy ions (29). The dissolution of this solid phase, which acts as a reservoir for the M(I1) solvated species, controls the concentration of these species and then plays a significant role in the control of the nucleation of the metal particles and therefore of their final morphological characteristics. For instance, starting from cobalt or nickel hydroxide as precursor in ethylene glycol, the reaction proceeds according to the following scheme (8) ... 

The synthesis of these materials is outlined in Scheme I. Transmission electron microscopy shows that the morphology of nearly equimolar compositions of the siloxane-chloromethylstyrene block copolymers is lamellar, and that the domain structure is in the order of 50-300 A. Microphase separation is confined to domains composed of similar segments and occurs on a scale comparable with the radius of gyration of the polymer chain. Auger electron spectroscopy indicates that the surface of these films is rich in silicon and is followed by a styrene-rich layer. This phenomenon arises from the difference in surface energy of the two phases. The siloxane moiety exhibits a lower surface energy and thus forms the silicon-rich surface layer. 

Fig. 4.10 Zone casting of a lamellar BCP thin film, (a) Taping mode AFM phase image (inset FT transform), and (b) GISAXS pattern of PODMA-i>-PtBA-h-PODMA block copolymer films prepared by zone casting at 40 °C. Arrow substrate withdrawal direction, (c) Scheme of the zone casting technique. Adapted with permission from ref. [98], J. Am. Chem. Soc. 2011, 133, 11802. Copyright 2011 American Chemical Society...

SAXS is a widely used method for the investigation of lamellar structure in the two phase systems. To obtain structural parameters, such as the average crystal separation and crystal thickness, the one dimensional elecbon density correlation function is often used. In syndiotactic poly(propylene) the one dimensional model calculation [24] can be applied since the amorphous phase and crystalline phase form one-dimensional stacks of crystalline lamellae. But in the case of monoclinic iPP, electron microscopy reveals the existence of unique cross-hatched lamellar stracture [25-30], and the applicability of the one dimensional model has been questioned by Albrecht and Strobl [31]. These researchers used SAXS and dilatometry to study structure development in PP, and presented a scheme to check for the feilure of the... 

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