Diffusion cubic crystalline structure

The mechanism of diffusion varies greatly depending on the crystalline structure and the nature of the solute. For crystals with lattices of cubic symmetry, the dif-fusivity is isotropic, but not so for noncubic crystals. In interstitial mechanisms of diffusion, small diffusing solute atoms pass through from one interstitial site to the next. The matrix atoms of the crystal lattice move apart temporarily to provide the necessary space. When there are vacancies where lattice sites are unoccupied, an atom in an adjacent site may jump into such a vacancy. This is called the vacancy mechanism. 

The mechanisms of diffusion vary greatly depending upon the crystalline structure and the nature of the solute [16, 17]. For crystals with lattices of cubic... 

The mesogen structures may be formed not only by covalent bonds, but also by non-covalent interactions, such as hydrogen bonds, ionic interactions, and metal coordination [71]. A recent example [72] of this concept comprised the self-assembly of complex salts into stable hierarchical aggregates with a dense core and a diffuse shell. These materials were made from diblock copolymers poly(acrylic acid)-block-poly(acrylamide) and the cationic surfactant dodecyltrimethylammonium. Due to non-covalent interactions the surfactant/polymer aggregates exhibited a liquid crystalline structure of cubic symmetry. 

The possibility that IPMS can occur in lipid systems as a structure of microemulsions or liquid-crystalline phases was first pointed out by Scriven (1976). The concept of IPMS and the possibilities of cubic phases consisting of lipid bilayers curved as an IPMS has attractive features that merit consideration. The lipid bilayer is the dominating structure type in lipid systems. In most cases there is an L -phase on one side of the cubic phase in the phase diagram. The IPMS is intersection free, so that the main difference compared to the infinite bilayer structure of the L -phase is the curvature, which can allow for wedge-shaped molecules (see further discussions in Section 8.2.8). The hydrostatic pressure is the same everywhere in an IPMS structure. All molecules can in fact have an identical close-packing environment, with lateral diffusion freedom similar to that of the L -phase. 

Diffusivities of binary, ternary and multi-component liquid crystalline mixtures, e.g. of soap (potassium laurate (PL), water [25, 58], and lipid (dipalmitoylphosphatidylcho-line (DPPC) [25, 59] systems in lamellar, hexagonal, cubic, nematic and micellar mesophases [25,60,61] have been studied extensively by pulsed-field-gradient NMR [25] and optical techniques [62], partly because of their intimate relation to the structure and dynamical performance of biological membranes [18]. The main distinction from thermotropic phases is that for layered structures a noticeable diffusion occurs only within the layers (i.e. lateral, frequently written as Dl, but in our notation DjJ, whereas it is negligibly small and difficult to detect across the layers [60-62] (transverse migration, for bilayers denoted by flip-flop ) so the mobility is essentially two dimensional, and the anisotropy ratio is so great that it is seldom specified explicit-... 

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