Liquid Crystal Phases at High Concentrations

The Gibbs phase rule is useful to relate the number of phases, P, that can exist in amphiphile solutions with two (solvent plus amphiphile) or more components, C, to the number of degrees of freedom, F, of the system. The degrees of freedom are the independent intensive variables that describe the thermodynamic state of the system, i.e. for surfactant solutions these are temperature, pressure and composition. The phase rule states that 

For a binary surfactant/solvent mixture, we must have F - - F = 4. Thus, a one-phase region of the phase diagram is specified by three degrees of 

At high concentrations, amphiphiles tend to self-assemble into ordered structures called lyotropic liquid crystal phases. The prefix lyo- (from the Greek for solvent) indicates that concentration is a controlling variable in the phase behaviour, as well as temperature. Temperature alone controls the self-assembly of thermotropic liquid crystals, which is the subject of the next chapter. Lyotropic liquid crystal phases can be formed in non-aqueous solvents. However, here we shall consider lyotropic liquid crystal phases formed in water, since these are by far the most important and widely studied. 

The nature of the lyotropic liquid crystal phase formed by amphiphiles in solution is described at a molecular level by the surfactant packing parameter model, introduced in Section 4.9. Consider the situation where the head group has a larger effective cross-sectional area than the chain. This is the usual situation, and the resulting structures are termed normal structures. If there is a large difference in cross-sectional area between the head group and chain (Ns ), spherical micelles are formed (Fig. 4.24a). For molecules with less of a mismatch between the effective head and tail cross-sectional areas, rod-like micelles provide a more 

The sequence of phases observed on increasing mean curvature is shown in the idealized phase diagram shown in Fig. 4.26. Here the 

---

Typically, micelles tend to be approximately spherical over a fairly wide range of concentration above the c.m.c., but often there are marked transitions to larger, non-spherical liquid-crystal structures at high concentrations. Systems containing spherical micelles tend to have low viscosities, whereas liquid-crystal phases tend to have high viscosities. The free energies of transition between micellar phases tend to be small and, consequently, the phase diagrams for these systems tend to be quite complicated and sensitive to additives. 

Use of liquid crystalline phases Surfactants produce liquid crystalline phases at high concentrations. Three main types of Hquid crystals can be identified hexagonal phase (sometimes referred to as middle phase) cubic phase and lamellar (neat phase). All of these structures are highly viscous and also show elastic responses. If produced in the continuous phase of suspensions, they can eliminate sedimentation of the particles. These Hquid crystalline phase are particularly useful for application in liquid detergents which contain high surfactant concentrations. Their presence reduces sedimentation of the coarse builder particles (phosphates and silicates). 

The hydrocarbon chain melting transition is facilitated by factors that reduce the polar headgroup network cohesion. The addition of water to cetyltrimethylam-monium tosylate produces a peak at 23°C, which is related to the melting of CTAT crystals (embedded in saturated aqueous solution below 23 C) to produce a liquid crystalline phase (in highly concentrated CTAT systems) or micellar solutions (in dilute systems). The peak is broad, probably due to the existence of a biphase transition zone. No melting peak related to the polar network was detected, probably because of the relatively weak cohesive forces in this particular polar network. The second peak detected in concentrated water-surfactant samples was due to the hexagonal mesophase-isotropic liquid transition [53]. 

Ternary phase diagrams were obtained for partial and complete miscibility between the solvent and the silica or organosilica precursor at the reduced temperature r =8.0. In some cases, a liquid crystal phase with high surfactant concentration is at equilibrium with a solvent-rich phase containing a small fi action of free monomers or micelles. Hexagonal phases are obtained for surfactant volume fractions between 50% and 70%, whereas lamellar... 

Nucleosome-nucleosome interaction potentials can be calibrated by comparison with the characteristics of liquid crystals of mononucleosomes at high concentrations. Under suitable conditions, nucleosome core particles form a hexagonal-columnar phase with a distance of 11.55 1 nm between the columns and a mean distance of 7.16 0.65 nm between the particles in one column [44,46]. These distances may be assumed to correspond to the positions of the minima of an attractive internucleosomal potential. The depth of the interaction potential (i.e., the binding energy per nucleosome) was estimated in the stretching experiments of Cui and Bustamante [66] to 2.6-3.4 kT. A slightly lower potential minimum of 1.25 kT is obtained by a comparison of the stability of the nucleosome liquid crystal phase with simulations [50]. 

A liquid crystal is a general term used to describe a variety of anisotropic structures formed by amphiphilic molecules, typically but not exclusively at high concentrations. Hexagonal, lamellar, and cubic phases are all examples of liquid crystalline phases. These phases have been examined as drug delivery systems because of their stability, broad solubilization potential, ability to delay the release of encapsulated drug, and, in the case of lamellar phases, their ability to form closed, spherical bilayer structures known as vesicles, which can entrap both hydrophobic and hydrophilic drug. This section will review SANS studies performed on all liquid crystalline phases, except vesicles, which will be considered separately. Vesicles will be considered separately because, with a few exceptions, generally mixed systems, vesicles (unlike the other liquid crystalline phases mentioned) do not form spontaneously upon dispersal of the surfactant in water and because there have been many more SANS studies performed on these systems. 

In Fig. 2, a variety of micelle structures are shown. Typical shapes of micelles are spherical, rod-like, and worm-like. At high concentrations of surfactant or at high concentrations of counterions, liquid crystals are usually formed. Hexagonal, cubic, and lamellar are common liquid crystal phases that occupy much of a... 

The effect of temperature increase is typical for surfactants whose solubility increases with temperature increase, converting all liquid crystal phases to micellar solutions when the temperature is high enough. At high surfactant concentration and low temperature, solid surfactant may precipitate. 

Even if all blocks of a block polymer are solvated in solution, that is, by using a nonselective solvent, phase segregation of the solvated blocks may occur at high concentration. The result is a supermolecular ordering in solution comparable to that in liquid crystals. In certain cases the aggregates are sufficiently large to diffract visible light, and, as has been mentioned earlier, block polymer solutions that are irridescent above a critical concentration have been observed (81). 

Since the liquid crystal forms the continuous phase of the binary mixture, we are only interested in a small part of the total phase diagram. Weight fractions of the liquid crystal in the range 0.9 to 1 were used to determine the partial phase diagram of the mixture which is shown in Fig. 2. The system forms an isotropic (I) phase at high temperature, and a diphasic equilibrium between an isotropic and a nematic phase (N-i-I) at low temperature. A nematic domain (N) is found at intermediate temperatures and low silicone oil concentrations. As pointed out in the experimental section, the existence of this nematic domain has some importance prior to quenching the system to the diphasic region. The present mixture exhibits classical features usually observed in other mixtures of nematic liquid crystals and polymers or isotropic fluids [29,30]. 

If more surfactant is added above the cmc, the concentration of micelles increases (rather than the concentration of free surfactant) until the micelle concentration becomes so high that they themselves organize to form ordered arrays of lyotropic liquid-crystal phase. There are several well-characterized lyotropic liquid-crystal phases and a host of so-called intermediate phases whose characterization is not unequivocal. While cmc values are typically found in the range lO -lO moldm, formation of lyotropic mesophases typically starts at around 20wt.% of the surfactant in water. 

Very recently, Schmidt et al. synthesized novel polyamides 51 by using arylsubstituted terephthalic acids moieties such as para- or ortfto-terphenyI-2,5-dicarboxylic acids in combination with substituted and non-coplanar diamines [70]. Those polyamides 51 from substituted diacids, diamines or non-coplanar diamines showed high solubility in DMAc, and in most cases without addition of inorganic salts (LiCl). In DMAc (LiCl), polyamide 51ca (rjinh = 1-63 dl/g) forms a lyotropic liquid crystalline phase at > 8 wt % at room temperature, and at > 5 wt % at 110 °C for polyamide 51ae (T)i h = 3.58 dl/g). On the other hand, with the copolyamides 52 the critical concentrations of liquid crystal formation are around 40-45% at room temperature. For these copolyamides, concentrated solutions in DMAc/LiCl with polymer concentration up to 50wt% could be prepared for polymers with x > 0.6. 

The process can be described by reference to the phase diagram (Figure 5.18). At low concentrations of protein and salt (or other precipitant) the protein is below the solubility limit and remains in solution. At high concentrations, however, the solution becomes thermodynamically unstable (supersaturated) and, once nucleation takes place, the protein will precipitate out of solution until the concentration in the liquid phase falls back to the solubility limit. If this happens too quickly, then the precipitate tends to be amorphous or just composed of very tiny crystals. 

The most frequently discussed topic in washing is the role of solubilisation processes. Many investigators [76] attract attention to the fact that the surfactant concentration in a washing solution is much lower than CMC, and in this connection, solubilisation of oils is principally excluded due to absence of surfactant micelles. At the same time, the review of recent works [85, 86] show that solubilisation can play a dominant role both in washing fabrics and in the removal of soils from solid surfaces. These views are based on the following mechanisms. Surfactants adsorb at w/o interfaces under formation of densely packed adsorption layers which leads to a high local surfactant concentration as compared with the rather low concentration in the washing solution. After that, noticeable penetration of water into the oily soil is possible, under formation of liquid-crystal phases. Then, mesomorphic phases are swelled and destroyed under the formation of emulsion droplets. 

Fig. 1. The fatty acid soap-water phase diagram of McBain (58) modified (1) to show the molecular arrangement in relation to aqueous concentration (abscissa) and temperature (ordinate). Ideal solution, i.e., true molecular solution, is to the left of the vertical dashed line, indicating the critical micellar concentration (CMC), which varies little with temperature. At concentrations above the CMC, provided that the temperature is above the critical micellar temperature (CMT), a micellar phase is present. At high concentrations, the soap exists in a liquid crystalline arrangement, provided that the solution is above the transition temperature of the system, i.e., the temperature at which a crystalline phase becomes liquid crystalline. The Krafft point is best defined (D. M. Small, personal communication) as the triple point, i.e., the concentration and temperature at which the three phases (true solution, micelles, and solid crystals) coexist, but in the past the Krafft point has been equated with the CMT. The diagram emphasizes the requirement for micelle formation (a) a concentration above the CMC, (b) temperature above the CMT, and (c) a concentration below that at which the transition from micelles to liquid crystals occurs. Modified from Hofmann and Small (1).

---