Bicontinuous structure

Figure 9.20 Typical pore network topologies found in ordered mesoporous silica materials. From left to right 2-D hexagonal p6mm pore structure, bicontinuous 3-D cubic la 3 d) pore structure, 3-D interconnected body-centered cubic cage-bke structure Im 3 tri), and 3-D interconnected/ace-centererf cubic cage-like structure Fm 3 m).

Fig, XIV-12. Freeze-fracture transmission electron micrographs of a bicontinuous microemulsion consisting of 37.2% n-octane, 55.8% water, and the surfactant pentaethy-lene glycol dodecyl ether. In both cases 1 cm 2000 A (for purposes of microscopy, a system producing relatively coarse structures has been chosen), [(a) Courtesy of P. K. Vinson, W. G. Miller, L. E. Scriven, and H. T. Davis—see Ref. 110 (b) courtesy of R. Strey—see Ref. 111.]... 

Amphiphilic molecules (surfactants) are composed of two different parts hydrophobic tail and hydrophilic head [1 ]. Due to their chemical structure they self-assemble into internal surfaces in water solutions or in mixtures of oil and water, where the tails are separated from the water solvent. These surfaces can form closed spherical or cylindrical micelles or bicontinuous phases [3,5]. In the latter case a single surface extends over the volume of the system and divides it into separated and mutually interwoven subvolumes. 

When comparable amounts of oil and water are mixed with surfactant a bicontinuous, isotropic phase is formed [6]. This bicontinuous phase, called a microemulsion, can coexist with oil- and water-rich phases [7,1]. The range of order in microemulsions is comparable to the typical length of the structure (domain size). When the strength of the surfactant (a length of the hydrocarbon chain, or a size of the polar head) and/or its concentration are large enough, the microemulsion undergoes a transition to ordered phases. One of them is the lamellar phase with a periodic stack of internal surfaces parallel to each other. In binary water-surfactant mixtures, or in... 

The period of the lamellar structures or the size of the cubic cell can be as large as 1000 A and much larger than the molecular size of the surfactant (25 A). Therefore mesoscopic models like a Landau-Ginzburg model are suitable for their study. In particular, one can address the question whether the bicontinuous microemulsion can undergo a transition to ordered bicontinuous phases. 

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). 

A. Ciach, J. S. Hoye, G. Stell. Microscopic model for microemulsion. II. Behavior at low temperatures and critical point. J Chem Phys 90 1222-1228, 1989. A. Ciach. Phase diagram and structure of the bicontinuous phase in a three dimensional lattice model for oil-water-surfactant mixtures. J Chem Phys 95 1399-1408, 1992. 

It is well known that block copolymers and graft copolymers composed of incompatible sequences form the self-assemblies (the microphase separations). These morphologies of the microphase separation are governed by Molau s law [1] in the solid state. Nowadays, not only the three basic morphologies but also novel morphologies, such as ordered bicontinuous double diamond structure, are reported [2-6]. The applications of the microphase separation are also investigated [7-12]. As one of the applications of the microphase separation of AB diblock copolymers, it is possible to synthesize coreshell type polymer microspheres upon crosslinking the spherical microdomains [13-16]. 

On a microscopic scale, a microemulsion is a heterogeneous system and, depending on the relative amounts of the constituents, three main types of structures can be distinguished [69] oil in water (OAV, direct micellar structure), water in oil (W/O, reverse micellar structure) and a bicontinuous structure (B) (Figure 6.1). By adding oil in water, OAV dispersion evolves smoothly to a W/O dispersion via bicontinuous phases. 

The mechanism of formation of morphology structures in iPP-E-plastomers blends via shear-dependent mixing and demixing was investigated by optical microscopy and electron microscopy. A single-phase stmcture is formed under high shear condition in injection machine after injection, namely under zero-shear environments, spinodal decomposition proceeds and leads to the formation of a bicontinuous phase stmcture. The velocity of spinodal decomposition and the phase separation depend on the molecular stmcture of iPP and E-plastomer components. 

Solubilization of biomolecules could induce change in the microemulsion structure. For example, in the presence of the human serum albumin and at low R value, the ternary microemulsion AOT/water/isoctane shows a transition to a bicontinuous microstructure [172],... 

Two system-dependent interpretative pictures have been proposed to rationalize this percolative behavior. One attributes percolation to the formation of a bicontinuous structure [270,271], and the other it to the formation of very large, transient aggregates of reversed micelles [249,263,272], In both cases, percolation leads to the formation of a network (static or dynamic) extending over all the system and able to enhance mass, momentum, and charge transport through the system. This network could arise from an increase in the intermicellar interactions or for topological reasons. Then all the variations of external parameters, such as temperature and micellar concentration leading to an extensive intermicellar connectivity, are expected to induce percolation [273]. 

FIG. 2 Example media (a) Surfactant-water phase diagram. (Reprinted from Ref. 206, Copyright 1991, with permission from Elsevier Science.) (b) Ordered periodic and bicontinuous structures. (Reprinted from Ref. 178 with permission from Academic Press, Ltd.) (c) Nonordered membrane structures from ternary microemulsions. (Reprinted with permission from Ref. 177, Copyright 1989, American Chemical Society.)... 

Several unifying conclusions may be based upon the order parameter results illustrated here for microstructural transitions driven by three different field variables, (1) disperse phase volume fraction, (2) temperature, and (3) chemical potential. It appears that the onset of percolating cluster formation may be experimentally and quantitatively distinguished from the onset of irregular bicontinuous structure formation. It also appears that... 

In the Hn phase and in the inverted micellar cubic phase, the water associated with the polar headgroups is trapped inside a ring structure and is not in rapid exchange with bulk water [18]. In a bicontinuous cubic phase, however, there is a continuous network of aqueous channels. 

This research has given insight to a very unique bicontinuous blend system. It has also shown that the pore structure and release rates from EVAc matrices are not only dependent on particle size and loading but also on the blending technique. It becomes apparent that it is possible to tailor these systems not only for release rates but also for initial time of release of insoluble biologically active agents. 

Finally, it should be emphasized that the spinodal-type of crystallization produces a bicontinuous structure consisting of regions with higher and lower degrees of crystallinity, which provides industrially important high-performance materials with an ideal homogeneous microstructure. 

The G phase is a complex phase possessing a bicontinuous structure which is located in or close to the compositional range of the PL phase. The minority component forms two interpenetrating threefold coordinated networks [10]. 

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

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