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 3.28 Illustrative section from the phase prism of a mixture of oil, water, and surfactant. This section is for constant surfactant concentration (T is temperature). The section shows a middle-phase microemulsion phase existing together with oil (upper) and water (lower) phases. The surfactant is partitioned among all of the phases. The cross-hatching shows how the microemulsion can be O/W (to the left), or W/O (to the right), or bicontinuous (centre). From Schwuger et al. [226]. Copyright 1995, American Chemical Society.

Figure 4. Generic phase prism of a nonionic surfactant, water, and oil system. Reprinted with permission from Kahlweit et at. [11],...

Figure 1.1 Schematic view of the phase behaviour of the three binary systems water (A) oiI (B), oil (B)-non-ionic surfactant (C), water (A)-non-ionic surfactant (C) presented as an unfolded phase prism [6]. The most important features are the upper critical point cpc, of the B-C miscibility gap and the lower critical point cpp of the binary A-C diagram. Thus, at low temperatures water is a good solvent for the non-ionic surfactant, whereas at high temperatures the surfactant becomes increasingly soluble in the oil. The thick lines represent the phase boundaries, while the thin lines represent the tie lines.

Figure 1.3 (a) Schematic phase prism of the system water-oil-non-ionic surfactant showing the... 

Stacking the isothermal Gibbs triangles on top of each other results in a phase prism (see Fig. 1.3(a)), which represents the temperature-dependent phase behaviour of ternary water-oil-non-ionic surfactant systems. As discussed above, non-ionic surfactants mainly dissolve in the aqueous phase at low temperatures (2). Increasing the temperature one observes that this surfactant-rich water phase splits into two phases (a) and (c) at the temperature T of the lower critical endpoint cepp, i.e. the three-phase body appears. Subsequently, the lower water-rich phase (a) moves towards the water corner, while the surfactant-rich middle phase (c) moves towards the oil corner of the phase prism. At the temperature Tu of the upper critical endpoint cepa a surfactant-rich oil phase is formed by the combination of the two phases (c) and (b) and the three-phase body disappears. Each point in such a phase prism is unambiguously defined by the temperature T and two composition variables. It has proved useful [6] to choose the mass fraction of the oil in the... 

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.)...

The phase behaviour of water-rich and oil-rich micro emulsions can be studied most conveniently by considering vertical sections through the phase prism at a constant surfactant/(water + surfactant) mass fraction... 

Figure 1.7 Vertical sections T(wb) and 7 (wA) through the phase prism which start at the binary water-surfactant (wb = 0) and the binary oil-surfactant (wA = 0) corner, respectively. These sections have been proven useful to study the phase behaviour of water- and oil-rich microemulsions, (a) Schematic view of the sections T wg) and T(wA) performed at a constant surfactant/fwater + surfactant) mass fraction ya and at a constant surfactant/(oil + surfactant) mass fraction 7b, respectively, (b) T(wb) section through the phase prism of the system FhO-n-octane-CioEs at ya = 0.10. Starting from the binary system with increasing mass fraction of oil wg, the oil emulsification boundary (2- 1) ascends, while the near-critical phase boundary (1 - 2) descends, (c) T(wA) section through the phase prism of the system EbO-n-octane-QoEs at 7b = 0.10. The inverse temperature behaviour is found on the oil-rich side With increasing fraction of water wA the water emulsification boundary (1 - 2) descends, whereas the near-critical phase boundary (2 —> 1) ascends.

The X-point for the system under consideration lies at 8 = 0.276 and y = 0.161, which shows that the surfactant/co-surfactant mixture (3-C8Gi/C8E0 solubilises water and n-octane with a medium efficiency. Comparing the wD(wc)-section performed through the phase tetrahedron with the T(y)-section through the phase prism (see, e.g. Fig. 1.3) one... 

Considering the phase behaviour of the system H20/NaCl (A)-n-decane (B)-AOT (D) as an example, the temperature-dependent phase behaviour of the system can be represented as a first approximation in an upright Gibbs phase prism, if the mixture of H20 and NaCl (often referred to as brine) is treated as a pseudo-component. It holds for the mass fraction of NaCl in the H20/NaCl mixture... 

Figure 1.14 Schematic phase prism (a) and interfacial tensions (b) as function of temperature for the system water-oil-non-ionic surfactant. The minimum of the water/oil interfacial tension crab at T is a consequence of the phase behaviour. Increasing the temperature the aqueous phases separates into the phases (a) and (c) at the critical endpoints cepp whereas the phases (b) and (c) merge into a single oil-rich phase at cepa. Thus, the interfacial tensions

Figure 3.3 Two types of bidimensional cuts through multidimensional phase prisms, (a) Cut through a phase prism at a 1 1 water-to-oil ratio as a function of the temperature (7) and the surfactant concentration (y), the so-called fish diagram, (b) Cut through a phase prism at constant 7 and y as a function of the ethoxylation degree EON) and the water-to-oil ratio (WOR), the so-called x diagram. ...

Figure 4.1 Sections through a phase prism at equal volumes of water and n-decane. The well-known fish is shown for water-n-decane-C- oE4 as hollow circles. The effect of increasing surfactant head group size (C10E5) and tail size (C12E4) is demonstrated. Note the associated temperature shifts. Adding traces of polymer PEP5-PE05 leads to an enormous efficiency increase (full circles) at constant temperature. (From Ref. [2], reprinted with permission of the American Chemical Society.)...

Figure 5.13 Section of the phase prism at constant surfactant concentration. Different structures within the one-phase region are indicated by hatching. In the water-rich region, swollen micelles solubilise oil. In the oil-rich region, reverse micelles of nanometre size exist. Bicontinuous structures are found in the intermediate range. (From Ref. [45], reprinted with permission of Elsevier.)...

Figure 5.15 Section of phase prism and separation times of water, oil, non-ionic surfactant system as function of temperature.

Figure 9 A schematic phase diagram of a cut at constant surfactant concentration through the temperature-composition phase prism of a ternary system with nonionic surfactant showing the characteristic X-like extension of the isotropic liquid phase L. (O is the volume fraction of oil in the solvent mixture.) Schematic drawings of the various microstructures are also shown. (Courtesy of Ulf Olsson.)...

Figure 1 A vertical slice through the phase prism for equal oil and water concentrations. The three-phase region exists in the temperature interval Tl to Tv. (From Ref. 75.)...

Figure 4 Illustration of the section through the phase prism denned by a constant surlactant-to-oil ratio and a partial phase diagram of the 12 5 /D20/decane system at constant ratioOg/tD = 0.815. (Figure redrawn fi om Ref. 9.)...

Figure 3.1 Phase prism with different cuts, (a) Shinoda cut, (b) Kahlweit cut, and (c) Lund cut. The phase triangle, consisting of surfactant (S), oil (O), and water (W), becomes a phase prism with the dependence of temperature (T) that these systems have.

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