Cubic phase involving

The supramolecular transformation from sphere to cylinder is supported by X-ray data indicating that the spherical polymers adopt a cubic phase, whereas the cylindrical polymers adopt a hexagonal phase [23b]. Further studies involving a library of dendritic macromonomers led to the conclusion that the effect of DP on polymer shape is a general phenomenon [24], More recently, scanning... 

Interpretation The results obtained for the cubic phase are less accurate than but generally consistent with the single crystal X-ray results.(4) The one obvious discrepancy involving the position of the Na(3) ions appears to be an artifact connected... 

The next section and the final section on polymeric cubic phases are intended for those readers who seek a more in-depth understanding of the microstmctures involved, including the geometrical aspects as well as the physics behind the self-assembly into these stmctures. These sections may be omitted by the more casual reader. 

A Monolayer Stmcture. One of Ae auAors (DMA) has proposed another structure of quite a different nature for a cubic phase occuring in ternary systems involving quaternary ammonium surfactants (16). and this cubic phase is Ae focus of much of... 

Siegel and Northrop provide X-ray powder evidence to show that the phase transition, observed for each of the solid hexafluorides of the second and third transition series, involves a low temperature orthorhombic form, evidently isomorphous with orthorhombic OsOF and a cubic high temperature from isomorphous with cubic OsOF. The equivalence of die Bravais lattices and the close similarity of the unit cell dimensions implies close structural similarity of the low temperature phases. The higher temperature, cubic phases, are on the X-ray evidence, body-centred cubic. 

Other detailed structural analyses of cubic phases of systems involving monoolein have been reported [14], and space groups observed that correspond to "asymmetric" or "unbalanced" surfaces of nonzero mean curvature, related to the "balanced" IPMS. If the channel systems on each side are different, or if the lipid bilayer contains constituent monolayers of different curv ature, an as5mtimetric (bicontinuous) cubic phase results. There are thus three other asymmetric (or imbalanced) Cd Cp or Cg structures. 

In 1980 it was pointed out that the prolamellar body is a perfect example of a Cp structure [4]. (Later, more detailed, analyses have revealed that it may also be a Cd structure cf. section 7.2.) Following work on the structure of cubic phases, it was also realised that two-dimensional analogues are possible. This in turn suggested that a phase transition involving changes in the intrinsic curvature of membranes might be possible [29, 30]. Such a mechanism has far reaching implications. Clear evidence for such transitions between bilayer conformations has been reported [9]. This membrane bilayer model will be described below. 

This membrane fusion process (outside the brain) is known to involve thousands of single membrane units, previously thought of as vesicles, assembled into units that have been termed "boutons". We have examined the EM texture of the boutons and found that they are in fact a cubic phase. The synaptic signal transmission can take place as frequently as hundreds of times per second. A fusion process involving a hyperbolic membrane can be well controlled, and the calcium ion influx - which induces fusion - is expected to change the conformation of the cubosome surface membrane from its planar bilayer conformation to the fusogenic saddle-saddle conformation. (It is known phase transitions of membrane lipids can occur when exposed to calcium, e.g. [40]). 

Even for polymerizable surfactants, curvature control is still very important, and Eastoe et al. describe mixtures of polymerizable surfactants that retain the same preferred curvature before and after cross-linking [44, 45]. Current approaches to the one-to-one replication of bicontinuous or other surfactant mesophases without the use of polymerizable surfactants involve the use of surfactants of high molecular weight [46] or highly viscous cubic phases featuring slower rearrangement dynamics. 

Investigator Type of correlation Phases involved Model associated Model equation Kunii and Smith [29] Effective thermal conductivity of packed bed Fluid-solid One-dimensional heat transfer model Spheres in cubic array = <°- W>(K K) (in - ) .21 ... 

A theoretical phase diagram for a lyotropic system is shown in Figure 17 and reveals, in addition, the Vj and V2 phases which are bicontinuous cubic phases (normal and reversed, respectively) whose structure can be described by models involving interpenetrating rods or periodic minimal surfaces. Note also that each pair of phases is separated, at least in principle, by a cubic phase (a, b, c, d in Figure 17), and with a biphasic interface (two phases coexisting). 

Phases built up of discrete aggregates include the normal and reversed micellar solutions, micellar-type microemulsions, and certain (micellar-type) normal and reversed cubic phases. However, discrete self-assemblies are also important in other contexts. Adsorbed surfactant layers at solid or liquid surfaces may involve micellar-type structures and the same applies to mixed polymer-surfactant solutions. 

Although liquid crystal (LC) theory predicts the existence of as many as 18 distinct structures for a given molecular composition and structure. Nature appears to have been kind in that only four of those possibilities have been identified in simple, two-component surfactant-water systems. The four LC phases usually associated with surfactants include the lamellar, hexagonal (normal and inverted), and cubic (Fig. 15.3). Of the four, the cubic phase is the most difficult to define and detect. It may have a wide variety of structural variations including a bicontinuous or interpenetrating structure that involve components of the other mesophases. The remaining types are more easily characterized and, as a result, better understood. 

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