Reentrant phases

FIGURE 1.14. The phase diagram for MBBA (A)-EBBA (B) mixture [34]. Two eutectic points Eui and Eu2 are seen. 

For a composition fixed close to the apex of the parabola (e.g., x = 0.4, where x is the weight ratio of 60CB/80CB) with decreasing temperature we meet the nematic, the smectic A, and again the nematic phase. The parabolic shape of the phase diagram is accounted for in terms of modern phase transition theory with a competition of the orientational and translational orders taken into account [32]. A microscopic explanation is based on the frustration phenomenon taking into account the competition between the steric and dipole-dipole interactions [38-40]. 

Apart from the N-SmA-Nre sequence the reentrant nematic phase was observed on cooling the SmC phase. The other reentrant phases, e.g., the smectic Cre, were also discovered [41]. 

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In order to finally address the question whether our system has a reentrant phase transition, as predicted by the mean-field study the low temperature region was analyzed by the cumulant intersection finite-size scahng method described in Sec. IV A. For the rotational constant 0 = 0.6109 an... 

Some of these phases occur in reentrant phase diagrams showing single [30] and sometimes multiple reentrant behaviour, described by the phase sequence I-N-Aa-N-Aa-N-Ai-C-A2-C2 on cooling [46, 57],... 

There is a large body of experimental work on ternary systems of the type salt + water + organic cosolvent. In many cases the binary water + organic solvent subsystems show reentrant phase transitions, which means that there is more than one critical point. Well-known examples are closed miscibility loops that possess both a LCST and a UCST. Addition of salts may lead to an expansion or shrinking of these loops, or may even generate a loop in a completely miscible binary mixture. By judicious choice of the salt concentration, one can then achieve very special critical states, where two or even more critical points coincide [90, 160,161]. This leads to very peculiar critical behavior—for example, a doubling of the critical exponent y. We shall not discuss these aspects here in detail, but refer to a comprehensive review of reentrant phase transitions [90], We note, however, that for reentrant phase transitions one has to redefine the reduced temperature T, because near a given critical point the system s behavior is also affected by the existence of the second critical point. An improper treatment of these issues will obscure results on criticality. 

T. Amiya, Y. Hirokawa, Y. Hirose, Y. Li, and T. Tanaka, Reentrant phase-transition of N-isopropylacrylamide gels in mixed-solvents, J. Chem. Phys. 86(4), 2375-2379 (1987). 

Keywords reentrant phase transitions, Brillouin light scattering, sound velocity, sound absorption, critical phenomena. 

For the systems without erystal field, the two features identified in the previous seetion in the ease of the planar rotors, namely the stronger ordering tendeney in the X=1 ease, and the reentrant phase transition in the X=2 case are present in the case of linear rotors as well. 

Raman scattering, electrical conductivity, Reentrant phase transition... 

Katayama S, Hirokawa Y, Tanaka T (1984) Reentrant phase transition in acrylamide-derivative copolymer gels. Macromolecules 17 2641-2643... 

A scaling representation of DLS and SANS correlation radii. In a review of reentrant LL phase transitions, Narayanan and Kumar comment, ...the most compelling issue concerning experimental investigations of reentrant phase transitions (RPT s) is how to recover universal exponents for the RPT. In other words which field variable should be used in place of and elsewhere, In other words, it is difficult to obtain the correct... 

There are several related phenomena that will not be treated in this chapter. They include the well documented transformation of nematic phases into cholesteric (twisted nematic) phases by adding small amounts of optically active molecules to a nematogen [171], creation of smectic phases from mixtures of molecules which alone form only nematic phases [172,173], and the presence of reentrant phases [174] due to molecular reorganizations based upon the relative importances of various short- and long-range intermolecular interactions in different temperature regimes (as mediated by the interplay of entropy and enthalpy terms) [175 -177]. Each has been exploited to create interesting and novel systems and devices based upon mesomorphism. 

On the other hand, Hirschfelder et al. [6] pointed out that the lower critical solution temperature appears as a result of heteromolecular association in solutions of water or alcohol with ammonia derivatives. The problem posed by them has been smdied in relation to reentrant phase separation in liquid mixtures. 

It should be noted that the theory predicts the possibility of reentrant phase transitions of both swelling-collapse-swelling (described above) and collapse-swelling-collapse types in mixed solvents. The latter situation takes place if a network is swollen in a mixture of two solvents, each of them being thermodynamically poor for the polymer. Then the network is in a collapsed state in each solvent taken separately, while being capable of swelling in their mixture. 

Under certain conditions, one can observe a double reentrant transition. For example, a weakly charged gel based on NIPA-sodium acrylate copolymer swollen in a water-methanol mixture undergoes reentrant phase transition two times when the methanol concentration is gradually increased. This behavior can be connected with leveling off the solvent compositions inside and outside the gel at equal volume fractions of both the solvent components in the system, which is caused by a gain in the entropy of mixing. 

Of special interest are the CB and PCH series, for which dielectric results under high pressure will be presented below. In the nOCB series 80CB has attracted much attention because it exhibits the reentrant phase behavior. This means the following unusual sequence of phase transitions on cooling under pressure ... 

Daoudi et al. [83] applied the thermodynamic approach equal Gibbs energy analysis to the pressure-composition phase diagrams of binary mixtures exhibiting reentrant phase behavior. Three different solution models are tested. The experimental data for the 4-n-hexyloxy- and 4-n-octyl-oxy-4 -cyanobiphenyl system are successfully described by the regular solution hypothesis. 

L. J. Yu, A. Saupe, Phys. Rev. Lett. 1980, 45, 1000. The system is mixtures of potassium lau-rate, 1-decanol and D2O. This system also exhibits a reentrant nematic transition (cf. the Chapter in this Handbook on Reentrant Phase Transitions). The higher temperature nematic is rod-like while the lower temperature nematic is disc-like. In addition, the isotropic liquid is also re-entrant in this system. 

There are several notable phenomena in the phase transition of gels in mixed solvents. One of them is the reentrant phase transition phenomenon. This is the phenomenon in which a successive change, swelling-shrinking-swelling, occurs as a function of solvent composition. Although... 

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