Isotropic solutions phase equilibria

This section is concerned with the semidilute and concentrated regimes in which the virial expansion is no longer valid. Our discussion is confined to 11 or SII/Sc of isotropic solutions phase equilibria including lyotropic liquid crystal formation of rigid-polymer solutions are out of the scope. 

Fig. 2.22. Phase diagram of the system H20-Ci2H2s0(CH2CH20)8H according to Shinoda98. A denotes a two phase area with two isotropic solutions in equilibrium, B a one phase area of an isotropic solution and LC liquid crystalline phases. (From Ref.1))...

The presence of mixed surfactant adsorption seems to be a factor in obtaining films with very viscous surfaces [411]. For example, in some cases the addition of a small amount of non-ionic surfactant to a solution of anionic surfactant can enhance foam stability due to the formation of a viscous surface layer, which is possibly a liquid crystalline surface phase in equilibrium with a bulk isotropic solution phase [25,110], In general, some very stable foams can be formed from systems in which a liquid crystal phase is present at lamella surfaces and in equilibrium with an isotropic interior liquid. If only the liquid crystal phase is present, stable foams are not produced. In this connection foam phase diagrams may be used to delineate compositions that will produce stable foams [25,110],... 

L. Homogeneous, isotropic solutions in water L2. Homogeneous, isotropic solutions in decanol Li + L2. Two-phase region consisting of L and L2 Liquid crystal area comprises all regions where mesomorphous matter exists. Areas denoted by -f contain mesomorphous matter and homogeneous isotropic solutions in equilibrium... 

Sato T, Shimizu T, Kasabo F, Teramoto A (2003) Isotropic-cholesteric phase equilibrium in solutions of cellulose tris(phenyl carbamate). Macromolecules 36 2939... 

Precipitation of the polymer on addition of a nonsolvent or with any changes in the thermodynamic parameters in solutions whose conc tration is below the critical point of the transition to the liquid-crystalline state is the most typical case of the intermediate phase equilibrium in rigid-chain polymer-solvent systems. Instead of the anticipated establishment of isotropic-anisotrqric phase equilibrium, equilibrium of two amorphous (isotropic) phases initially arises if the parameter x attains values greater than +0.5. 

An ordered solid phase is formed, at equilibrium with a very dilute isotropic solution, when the isotropic solution of PBT is slowly coagulated by gradual absorption of atmospheric moisture. The... 

Figure 6 shows the phase diagrams plotting temperature T vs c for PHIC-toluene systems with different Mw or N [64], indicating c( and cA to be insensitive to T, as is generally the case with lyotropic polymer liquid crystal systems. This feature reflects that the phase equilibrium behavior in such systems is mainly governed by the hard-core repulsion of the polymers. The weak temperature dependence in Fig. 6 may be associated with the temperature variation of chain stiffness [64]. We assume in the following theoretical treatment that liquid crystalline polymer chains in solution interact only by hardcore repulsion. The isotropic-liquid crystal phase equilibrium in such a solution is then the balance between S and Sor, as explained in the last part of Sect. 2.2. 

When analyzing the deviations of phase equilibrium for real polymeric systems forming a mesophase from the theoretically calculated phase diagram, we must pay attention to one more circumstance, namely, polydisperse nature of real polymers. In all the cases the transition from an isotropic solution to anisotropic one is a result of superposition of equilibria typical of individual fractions of a polymer, which differ in molecular mass. As was shown by Flory this must result in a broadening... 

According to the principle of mutual independence of individual types of phase equilibrium it should be expected that upon a change of thermodynamic conditions in the initial monophase solution, first the equilibrium with the separation into amorphous phases is established, this equilibrium being unstable with respect to other types of phase equilibrium, and only after that the transition to the stable equilibrium takes place. As an example, we can consider the case of a gradual transition from the unstable liquid crystalhne equilibrium to the stable equilibrium with the formation of a crystallosolvate for a PBA-sulphuric acid system, which we discussed earlier In the lower left part on Fig. 15 there are the particles of liquid crystalline phase which transforms, via the isotropic phase (dark background) into a crystallosolvate (spherulites in the upper part of the figure). The process is completed by a total disappearance of the liquid crystalline phase and by the establishment of the equilibrium between the isotropic solution and the crystallosolvate, which corresponds to the region I + CS on Fig. 12. 

Below temperature TB (cloud point for low polymer concentrations) and at a polymer weight fraction lower than wB, isotropic solutions are stable. Above the weight fraction wA and at a temperature below the line AD (clouds points for concentrated polymer concentrations) pure cholesteric phase separates. All other compositions are biphasic, the liquid crystals being in equilibrium with a dilute isotropic solution. At low temperature this domain exists in the small concentration range delimited by wA and wB. Note that TA may be below body or even room temperature. 

These are of two kinds related to each other by the difference in association structure as illustrated by the temperature variation of surfactant solubility and association. Figure 6 provides a schematic description of the interdependence. At low temperatures the solubility limit of the xmimers (s, solid line. Fig. 6) is lower than the limit for amphiphilic association (cmc, dashed line. Fig. 6), and, hence, the latter is not reached and a two-phase equilibrium, aqueous solution of monomers—hydrated surfactant, is established. At temperatures in excess of the Krafft point, Tj (Fig. 6), the association concentration (cmc, solid line, Fig. 6), is now beneath the solubility limit (s, dashed line. Fig. 6). Association takes place and the total solubility (ts. Fig. 6) is drastically increased. Hence, the water—siufactant phase diagram shows a large solubility range for the isotropic liquid solution (unimers plus micelles. Fig. 6) because the association structure, the micelle, is soluble in water. This behavior is characteristic of smfactants with Ninham R values less than 0.5. 

Sato T, Kakihara T, Teramoto A. Isotropic-liquid crystal phase equilibrium in semiflexible polymer solutions xanthan, a rigid polyelectrolyte. Polymer 1990 31 824-827. 

The phase equilibrium in systems containing rigid-chain polymers is characterized by the formation of a liquid-crystalline state, which fact can be illustrated by the diagram due to Flory reproduced in Figure 3. At x values below 0,the polymer-solvent system forms either an isotropic (one-phase) solution mixture of... 

Change in phase in bulk liquid, such as formation of iiquid crystais in equilibrium with an isotropic liquid phase. A homogeneous solution may foam at a critical concentration and temperature where a transition into two separate liquid phases is imminent... 

We also find the three-phase equilibrium (triple point) where two isotropic phases and a nematic phase can simultaneously coexist. At high temperature, the solution is homogeneous since the entropy of mixing is dominant. As temperature decreases, the isotropic-isotropic phase separation takes place where the interaction parameter x between solute and solvent molecules becomes dominant. Further decrease in temperature, the attractive interaction Xa between liquid crystals dominates and so the... 

In type II experiments (path 3 —> 4 in Figure 5.7a, which brings the system from the lower isotropic channel to the higher one), a transition is induced between two isotropic solutions separated by a liquid crystalline phase. If the temperature was raised at a sufficiently slow rate that the equilibrium was established all the time, we could see, using adequate methods, the formation of a liquid crystal. When a fast temperature-jump is applied so that the final temperature corresponds to point 4 shown in the phase diagram, we may have three different situations (1) the transition requires... 

One of the first experimental phase equilibrium diagrams was obtained by Miller et al. [14] for solutions of PEG in dimethylformamide (DMF). This diagram is shown in Fig. 2.7, which indicates that the transition from the narrow concentration corridor to the broad two-phase region, where the concentration of polymer in the isotropic phase is very low and the concentration of the anisotropic phase is within the limits of 0.70-0.85 vol. fractions of polymer, takes place at a temperature below 15°C. With an increase in the temperature (correspondingly, with a decrease in %) beyond 15 C, the coexisting isotropic and anisotropic phases differ relatively little with respect to the concentration of polymer, i.e., V2 /v2 is close to 1.5, as Flory theoretically calculated. It has not... 

This course of the curves of the thermal transition between the isotropic and anisotropic phases not only derives from the specific features of polymers in comparison to low-molecular-weight substances, but also from the fact that the firee volume in the system increases with an increase in the temperature, and this results in an increase in the probability of independent arrangement of the macromolecules in solution. However, this also simultaneously means broadening of the concentration regions of the isotropic-anisotropic phase transition. The inflection of the phase equilibrium curves discussed in the studies cited above thus not only follows from the formal topological analysis but also from the thermodynamic concepts of the structure of liquids. 

W/O gel emulsions separate into two isotropic liquid phases at equilibrium one phase is a submicellar surfactant solution in water and the other phase is a swollen reverse micellar solution (or W/O microemulsion). This phase equilibrium is represented in Figure 11.11 by the ternary diagrams at and T . Similarly, O/W gel emulsions separate into two isotropic liquid phases at equilibrium an oil phase and an aqueous micellar solution or O/W microemulsion. The phase equilibrium is represented by the ternary diagrams at Ti and T2 of Figure 11.11. Gel emulsions exist only in limited regions of the miscibility gap (the two-phase region). The boundaries of the gel emulsion regions depend on the system and also on the method of preparation. 

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