Bicontinuity, description

Recently an alternative approach for the description of the structure in systems with self-assembling molecules has been proposed in Ref. 68. In this approach no particular assumption about the nature of the internal interfaces or their bicontinuity is necessary. Therefore, within the same formahsm, localized, well-defined thin films and diffuse interfaces can be described both in the ordered phases and in the microemulsion. This method is based on the vector field describing the orientational ordering of surfactant, u, or rather on its curlless part s defined in Eq. (55). 

In the first case, the BCD s droplets dispersed in the Diesel oil (continuous medium) form the emulsion. In the second case Diesel oil s droplets are dispersed in BCO (continuous medium). The third case s description is more complex in fact theoretically there are no droplets and Diesel oil and water phases are continuous and form a bicontinuous emulsion". 

From the results of self-diffusion, Lindman et al. (71) have proposed the structure of microemulsions as either the systems have a bicontinuous (e.g. both oil and water continuous) structure or the aggregates present have interfaces which are easily deformable and flexible and open up on a very short time scale. This group has become more inclined to believe that the latter proposed structure of microemulsion is more realistic and close to the correct description. However, no doubt much more experimental and theoretical investigations are needed to understand the dynamic structure of these systems. 

However, even without structural studies, Friberg et al. [32], Shinoda [33], and others noted that the broad existence range with respect to the water/oil ratio could not be consistent with a micellar-only picture. Also, the rich polymorphism in general in surfactant systems made such a simplified picture unreasonable. It was natural to try to visualize microemulsions as disordered versions of the ordered liquid crystalline phases occurring under similar conditions, and the rods of hexagonal phases, the layered structure of lamellar phases, and the minimal surface structure of bicontinuous cubic phases formed a starting point. We now know that the minimal surfaces of zero or low mean curvature, as introduced in the field by Scriven [34], offer an excellent description of balanced microemulsions, i.e., microemulsions containing similar volumes of oil and water. 

One of the major steps to enhancing the understanding of surfactant association structures is to investigate the phase equilibria of water-oil-surfactant mixtures. Since the pioneering contributions of P. Ekwall in Scandinavia and K. Shinoda in Japan, who analyzed ternary systems containing ionic and nonionic surfactants, respectively, extensive experimental work has been devoted to different kinds of microemulsion systems [7-20]. During recent decades, detailed descriptions of the phase behavior of many ternary (water-oil-surfactant), quaternary (water-oil-surfactant-alcohol), and even quinary (water-oil-surfactant-alcohol-salt) systems have been presented (for example, see Refs. 21-36). These studies have provided evidence for several new phases where the surfactant creates surfaces. Thus, in addition to bicontinuous microemulsions, one finds dilute lamellar phases (L ) [37-43] and liquid isotropic phases of randomly connected bilayers called... 

The frequent description of bicontinuous structures in terms of a percolative process is misleading. Bicontinuity describes a situation with a dynamic equilibrium structure and not a temporary opening of extended pathways between droplets [5]. 

It is worth noting that this description assumes implicitly that the = 1 case is associated with a zero-curvature C layer, which could be provided either by a lamellar liquid crystal structure with alternating O and W flat layers or a zero curvature surface of the Schwartz type or as a transient and fluctuating combination of Si and S2 structures. It is now well recognized that middle-phase microemulsions, which are in equilibrium with both oil and water excess phases, exhibit bicontinuous structures as shown in Fig. 7 [27] that are not far from the transient mixture of Si and S2 swollen micelles predicted by Winsor. 

IPMS has also been a useful tool in the description of the structure of bicontinuous reversed cubic phases of lipids (7). The symmetries of bicon-tinuous cubic phases are classified by their space group, which is determined by X-ray diffraction. Three different symmetries, of interest here, are known for bicontinuous cubic membrane lipids namely., laSd, Pn3m and ImSm. 

Figure 24.2 Nanostructure of bicontinuous nanocomposites. Top Pictorial description of interconnected organic and inorganic domains with gradient density interphase. Bottom TEM micrograph of an epoxy/silica bicontinuous nanocomposite.

Lyotropic liquid crystal phases has been observed when l-Alkyl-3-methylimidazolium bromide (CnmimBr) was mixed with p-xylene and water. SAXS, POM, NMR and rheology measurements were performed to investigate the lyotropic liquid crystal phases. A lyotropic bicontinuous cubic phase formed in imidazolium-type ionic liquid (IL) system was found for the first time. The strong %-% stacking of imidazolium based ILs and their 71-cation interactions with p-xylene molecules have unique effect on the structural parameters.Description of NMR of quadrupolar systems using the Holstein-Primakoff (HP) formalism and its analogy with a Bose-Einstein condensate (BEC) system has been presented. Two nuclear spin... 

In the presence of water, surfactants and lipids give rise to a variety of phases referred to as lyotropic phases or mesophases.i The most important of these phases are the lamellar, hexagonal, cubic micellar, and cubic bicontinuous phases denoted by L, H and V, and Q, respectively (see Figure 1.11 in Chapter 1). The subscripts 1 or 2 attached to these phase symbols indicate that the phase is direct (water continuous) or inverse (discontinuous water domains). Many other lyotropic phases have been identified that differ from the main ones by the state of the alkyl chain (crystalline or disordered) and of the head group arrangement (ordered or disordered). In the particular case of the lamellar phase, additional variations come from the possible different orientations adopted by the alkyl chains with respect to the plane of the lamellae (angle of tilt of the chain) and also from the state of the surface of the lamellae that can be planar or rippled. Numerous detailed descriptions have been given for the equilibrium state of the various phases that surfactants and lipids can form in the presence of water. 

Bicontimous network of ionic clusters Elliott and co-workers demonstrated a unified morphological description of PFSAs based on both statistical (MaxEnt) and thermodynamic (DPD) descriptions, which broadly favours a bicontinuous network of ionic clusters embedded in a matrix of fluorocarbon chains. Elliott, 201 The existence of a continuous network of water-filled channels explains the high water diffusion coefficient of water in Nafion. 

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