Re-entrance

A spin-gas microscopic theory has been pursued by Berker et al. [32] to explain the multiplicity of smectic ordering and the re-entrance phenomenon in strongly polar mesogens. They have used a model Hamiltonian of the form... 

Kloosterman, F., Haeften, T. V., Witter, M. and Lopes da Silva, F. H. Electrophysiological characterization of interlaminar entorhinal connections an essential link for re-entrance in the hippocampal-entorhinal system. Eur. J. Neurosci. 18 3037-3052,2003. 

Following the thermodynamical laws, the order within the individual mesophases increase normally during cooling. In some very special cases (e.g. for polar molecules) sometimes an inverse phase sequence occurs, where cooling gives rise to a less ordered phase like a nematic phase at low temperature. This phenomenon, so-called re-entrance, has been well investigated and different models have been proposed to explain the behaviour18,19. 

As seen from Ref 9, data for the rotational diffusion coefficient also shows a far milder dependence wit temperature than its translational counterpart. However the observed decoupling from the SE and SED behaviors is there seen to follow a far less drastic behaviour than that here found. On such a basis we deem that the presence of a strong directional interaction cannot account for the higher mobility observed by experiment if compared to the Brownian dynamics estimates of SE and SED. Finally it is worth to emphasize that the observed breakdown of both SE and SED approximations only appear for the miscible phase below Tl but not after the re-entrance above Tu into the high temperature, miscible phase. Such fact is thus suggestive of the existence of phenomena additional to those responsible of the re-entrant behavior being... 

Mayol, X. and Grana, X., The pi 30 pocket protein keeping order at cell cycle exit/re-entrance transitions,FrontBiosci., 3,Dll, 1998. 

Single re-entrance may occur in mean field the coupling of two order parameters may generate a curved N-SmA phase boundary and thus produce a re-entrant phenomenon if the physical temperature axis is a suitable combination of the two Landau control parameters. 

Beside these phenomenological approaches that say nothing about the microscopic origin of re-entrance, molecular theories have been proposed. The frustrated spin glass model of Indekeu and Berker [70, 71] has been particularly successful. 

Re-entrance may also occur as closed nematic domains (or nematic bubbles ) deep in the smectic region. Such bubbles seem to be closely related to the existence of a SmA2-SmAd or SmAj-SmAj critical point [105, 109],... 

The pressure-induced re-entrant phase behavior is not restricted to one re-entrant N phase and not only to N phases. Raja et al. [38] studied the effect of high pressure on the phase transitions in the seventh to tenth homologs of 4-alkoxyphenyl-4 -nitroben-zoyloxybenzoates. The decyloxy member, and only this one, exhibits a conspicuous phase diagram besides two pressure-induced SmA phases and a bounded SmC phase a quadruple re-entrance is observed SmA-N-SmAd-N-SmAj-N. 

Goodby and coworkers [24] elegantly showed that re-entrance in cyano compounds resulted from a sensitive balance between dipolar and steric factors. They synthesized two benzene ring materials with an ester link that either reinforced (resulting in exclusively re-entrant nematic behavior) or opposed (resulting in the appearance of a SmC phase below the SmA) the cya-nophenyl mesomeric relay [24], The conclusion is that, when dipolar forces domi-... 

While the phase was also found in ni-tro compounds with two benzene rings [28], re-entrant phenomena in liquid crystals made a giant leapforward in 1979, when the stable Nj-e-SmA transition [29] and multiple re-entrance [30] was discovered at 1 atm... 

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