The Re-entrant Phenomenon

When the layer thickness d is less than the length I of the molecule in a smectic A phase, the molecules are either assumed to be symmetric units or their molecular asymmetry is nullified at least at a local level. When molecules possess a terminal parorCN or -NO2 group, the dipole moment can now distinguish a head and a tail in the molecule. For such asymmetric molecules, antiparallel dipole correlation causes pairing of molecules to form a variety of A phases with a layer thickness / < d < 2Z [1.18]. The dipole-dipole interaction has a profound effect on many physical properties [1.19]. This has been used to account for the re-entrant phenomenon in liquid crystals. Two types of smectic A phases may be visualized when polarized... 

Although not specific of liquid crystals, the re-entrant phenomenon (i.e. re-appearance of the phase of higher symmetry upon cooling) is often observed in frustrated smectics [80,106]. Theoretical analyses suggest that there is no universal explanation for re-en-trance in the N-SmA problem. 

Figure 10. An example of the re-entrant phenomenon in complex superconductors [33] having a phase-diagram topology similar to that in Figure 9. At low fields the normal metal state is not re-entrant, as predicted from theory [34]. However, at extremely low temperatures and with increasing applied field, the superconducting state (S) is first restored and then destroyed again above 20 T.

The re-entrant phenomenon was discovered on strong polar compounds [139]. Therefore, it was assumed that an equilibrium between monomers and associates is responsible for the return of the nematic phase below a smectic [140]. Without any doubt in strong polar compounds, a reduction of the effective dipole moment jj. to an apparent /lapp can be observed by dilution of the sample in an unpolar solvent. Experimental data, measured on 4- -pentyl-4 -cy-... 

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. 

In matrix-impurity systems in which the matrix is a superconductor and Tg is sufficiently low compared to the critical temperature of the pure host, the temperature dependent scattering of conduction electrons by impurity spins may even lead to the striking phenomenon of re-entrant superconductivity (where alloys within a certain impurity concentration range exhibit a transition to the superconducting state at a critical temperature Tg, which is followed by a return to the normal state at a second lower critical temperature as well as pronounced deviations of the specific heat jump from the BCS law of corresponding states. 

This phenomenon can also lead to an effect known as re-entrant behavior. Thus, there is an accepted thermodynamic ordering of liquid crystal phases, which is shown in 1 for the phases considered so far ... 

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