Periodicity cubic phases

Luzzati V, Delacroix FI and Gulik A 1996 The micellar cubic phases of lipid-containing systems Analogies with foams, relations with the infinite periodic minimal surfaces, sharpness of the polar/apolar partition J. Physique. II 6 405-18... 

In the latter the surfactant monolayer (in oil and water mixture) or bilayer (in water only) forms a periodic surface. A periodic surface is one that repeats itself under a unit translation in one, two, or three coordinate directions similarly to the periodic arrangement of atoms in regular crystals. It is still not clear, however, whether the transition between the bicontinuous microemulsion and the ordered bicontinuous cubic phases occurs in nature. When the volume fractions of oil and water are equal, one finds the cubic phases in a narrow window of surfactant concentration around 0.5 weight fraction. However, it is not known whether these phases are bicontinuous. No experimental evidence has been published that there exist bicontinuous cubic phases with the ordered surfactant monolayer, rather than bilayer, forming the periodic surface. 

The inclusion of Somatostatin into a cubic phase markedly prolonged the apparent half-life. As can be seen in Figure 4b, the plasma level of Somatostatin-like immunoreactivity (SRIF-LI) after sc administration of cubic preparations of SRIF was nearly constant during the observation time of six hours, and no decline in the plasma level could be seen. During this period, the level of SRIF-LI in plasma thus seems to correlate with a zero-order release process of SRIF (cf. dDAVP). In Figure 4b is also shown the plasma SRIF-LI after sc administration of the peptide solubilized in cubic phases with varying ratios of MO/LE. It can be seen that increasing the amount of LE... 

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)... 

Depending on temperature, transitions between distinct types of LC phases can occur.3 All transitions between various liquid crystal phases with 0D, ID, or 2D periodicity (nematic, smectic, and columnar phases) and between these liquid crystal phases and the isotropic liquid state are reversible with nearly no hysteresis. However, due to the kinetic nature of crystallization, strong hysteresis can occur for the transition to solid crystalline phases (overcooling), which allows liquid crystal phases to be observed below the melting point, and these phases are termed monotropic (monotropic phases are shown in parenthesis). Some overcooling could also be found for mesophases with 3D order, namely cubic phases. The order-disorder transition from the liquid crystalline phases to the isotropic liquid state (assigned as clearing temperature) is used as a measure of the stability of the LC phase considered.4... 

Generally, lipids forming lamellar phase by themselves, form lamellar lipoplexes in most of these cases, lipids forming Hn phase by themselves tend to form Hn phase lipoplexes. Notable exceptions to this rule are the lipids forming cubic phase. Their lipoplexes do not retain the cubic symmetry and form either lamellar or inverted hexagonal phase [20, 24], The lamellar repeat period of the lipoplexes is typically 1.5 nm higher than that of the pure lipid phases, as a result of DNA intercalation between the lipid bilayers. In addition to the sharp lamellar reflections, a low-intensity diffuse peak is also present in the diffraction patterns (Fig. 23a) [81]. This peak has been ascribed to the in-plane positional correlation of the DNA strands arranged between the lipid lamellae [19, 63, 64, 82], Its position is dependent on the lipid-DNA ratio. The presence of DNA between the bilayers has been verified by the electron density profiles of the lipoplexes [16, 62-64] (Fig. 23b). 

For diblock copolymers, periodically arranged spheres (micelles), hexago-nally packed cylinders, and a lamellar phase have been observed [1]. A more complex bicontinuous cubic phase with QIasymmetry (gyroid structure) has also been identified. These supramolecular structures, with length scales on the order of 1 to 102 nm, may be controlled by changing the amount of solvent, the length of blocks, or the proportions of A and B monomeric units [128-131]. 

In accordance with obtained results one can to suppose that simple cubic phase of C32 is insulator with forbidden gap width about 1.5 eV and crystal lattice period a = 6.749 A. 

Fig. 30. Interlocking rod model for the Im3m (A) and Ia3d (B) cubic phases and the infinite periodic minimum surface model for Im3m (C).

The polymerization of one or more components of a lyotropic liquid crys in such a way as to preserve and fixate the microstructure has recently been successfully performed. This opens up new avenues for the study and technological application of these periodic microstructures. Of particular importance are the so-called bicontinuous cubic phases, having triply-periodic microstructures in which aqueous and hydrocarbon components are simultaneously continuous. It is shown that the polymerization of one of these components, followed by removal of the liquid components, leads to the first microporous polymeric material exhibiting a continuous, triply-periodic porespace with monodisperse, nanometer-sized pores. It is also shown that proteins can be immobilized inside of polymmzed cubic phases to create a reaction medium allowing continuous flow of reactants and products, and providing a natural lipid environment for the proteins. 

This chapter focuses on the fixation of lyotropic liquid crystalline phases by the polymerization of one (or more) component(s) following equilibration of the phase. The primary emphasis will be on the polymerization of bicontinuous cubic phases, a particular class of liquid crystals which exhibit simultaneous continuity of hydrophilic — usually aqueous — and hydrophobic — typically hydrocarbon — components, a property known as bicontinuity (1), together with cubic crystallographic symmetry (2). The potential technological impact of such a process lies in the fact that after polymerization of one component to form a continuous polymeric matrix, removal of the other component creates a microporous material with a highly-branched, monodisperse, triply-periodic porespace (3). 

Figure 1. A. Computer graphic portion of a periodic surface of constant mean curvature, having the same space group and topological type as the Schwarz D minimal surfhce. This surbce, together with an identical displaced copy, would represent the polar/apolar dividing surface in a cubic phase with space group 224 (Pn3m). The two graphs shown would thread the two aqueous subspaces. B. Computer graphic of a portion of the Schwarz D minimal sur ce (mean curvature identically zero). In the 224 cubic phase structure, this sur ce would bisect the surfactant bilayer.

This potential force occurs in microstructured fluids like microemulsions, in cubic phases, in vesicle suspensions and in lamellar phases, anywhere where an elastic or fluid boundary exists. Real spontaneous fluctuations in curvature exist, and in liposomes they can be visualised in video-enhtuiced microscopy [59]. Such membrane fluctuations have been invoked as a mechanism to account for the existence of oil- or water-swollen lamellar phases. Depending on the natural mean curvature of the monolayers boimding an oil region - set by a mixture of surfactant and alcohol at zero -these swollen periodic phases can have oil regions up to 5000A thick With large fluctuations the monolayers are supposed to be stabilised by steric hindrance. Such fluctuations and consequent steric hindrance play some role in these systems and in a complete theory of microemulsion formation. 

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