Lamellar phases phase prisms

Figure B3.6.5. Phase diagram of a ternary polymer blend consisting of two homopolymers, A and B, and a synnnetric AB diblock copolymer as calculated by self-consistent field theory. All species have the same chain length A and the figure displays a cut tlirough the phase prism at%N= 11 (which corresponds to weak segregation). The phase diagram contains two homopolymer-rich phases A and B, a synnnetric lamellar phase L and asynnnetric lamellar phases, which are rich in the A component or rich in the B component ig, respectively. From Janert and Schick [68].

Figure 1.4 T(7)-sections through the phase prism of the systems H20-n-octane-C6E2, C8E3, Q0E4 and C12E5 at an oil/(water + oil) volume fraction of = 0.5. In order to determine the respective X-point the phase boundaries are measured only for surfactant mass fractions 7 > 7. An increase of both the hydrophobic chain length / and the size of the hydrophilic head group j shifts the X-point to lower values of 7, i.e. the efficiency increases. Simultaneously the stability range of the bicontinuous one phase microemulsion shrinks dramatically due to the increased extension of the lamellar mesophase (La). (From Ref. [26], reprinted with permission of Elsevier.)...

To determine complete ternary phase diagrams, in particular at a number of different temperatures, is a lengthy process, and has been carried out for only for a few systems. Rather, one often reduce the number of composition degrees of freedom by one and studies a planar section through the phase prism. The section defined by 0vv = 0o ( fish-cut ) is shown schematically in Figure 17.3. In this section, one can determine 7] and Tu and the minimum amount of surfactant necessary to solubilize equal amounts of water and oil, which we here denote as 0. The lower 0, then the more efficient is the surfactant. We see also that the microemulsion at higher surfactant concentrations is in equilibrium with a lamellar phase (L ), a typical feature of long-chain surfactants. 

A section through the phase prism at constant surfactant concentration ( Shinoda-cut ) is particularly illustrative. This shows the interrelation between the temperature-dependence and the dependence on the water-to-oil ratio. By choosing the surfactant concentration to be slightly above 0, one obtains a phase behaviour that is illustrated schematically in Figure 17.4. This section contains a rich variety of microstructures, e.g. the microemulsion phase which has a surfactant monolayer structure and the lamellar phase and the sponge phase which both have a bilayer... 

Figure 17.4. (a) Illustration of a section at constant surfactant concentration through the phase prism, (b) A schematic phase diagram, plotted as temperature versus the volume fraction of oil, 0, at constant surfactant concentration. Illustrated are also various microstructures found in different regions of the isotropic liquid phase, L. At higher temperatures, the liquid phase is in equilibrium with excess water (L + W), and at lower temperatures with excess oil (L -f O). At intermediate temperatures, a lamellar phase is stable at higher water contents and at higher oil contents, respectively... 

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