Re-entrant behavior

The superconducting properties induced in the normal metal manifest themselves in many different ways, including energy-dependent transport properties and a modification of the local density of states. For instance, the conductance of a normal conductor connected to a superconducting electrode shows a striking re-entrant behavior [4]. At non-zero temperature and/or bias, the conductance of the normal metal is enhanced as compared to the normal-state. At zero temperature and zero bias, the expected conductance coincides with the normal-state value. The conductance has therefore a non-monotonous behavior. 

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... 

In addition to the remarkable re-entrant behavior of the TjTe vs n curve, the depression of the specific heat jump AC at as a function of Tc (Armbriister et al., 1974 Luengo et al., 1972 Bader et al., 1975) also displays some interesting features which are shown in fig. 11.10. Here, it can be seen that the curve of reduced specific heat jump AClACo vs reduced transition temperature shows a pronounced downward deviation from both the BCS law of corresponding states and, as well, the AG theory. It is worth noting that recent specific heat measurements (Bader et al., 1975) on a re-entrant (LaCejAh specimen (0.64 at.% Ce) to temperatures lower than indicate that the tran-... 

Of course not aU of these mesophase have to appear in a single liquid crystalline system. For very few liquid crystals, exceptions from this sequence rule are known to exist. In these liquid crystals a mesophase with a higher symmetry reappears on cooling, even though a less symmetric mesophase has already formed at higher temperatures. Such phases are called re-entrant and are indicated with a subscript RE . Re-entrant behavior was first observed for a N-SmA-NRE-Cr phase sequence [39], but it was also found for other types of mesophases [40, 41]. It is not completely clarified when and why re-entrant phases appear. Different approaches to explain the re-entrant behavior were made, e.g. on the basis of frustration, geometric complexity or competing fluctuations [42, 43]. 

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 ... 

The orthogonal arrangement of the disc-like molecules in the columns of and D id phases makes these phases uniaxial, while the tilted phases (Drd and Doh.d and Dt) are optically biaxial. There are two additional columnar phases labeled as and that have not yet been classified. The columnar phases were discovered before the observation of a nematic phase for disc-like molecules. Both chiral nematic phases and the re-entrant behavior have now been observed in discotics. The phase diagram and molecular structure of a typical discotic liquid crystal are shown in Fig. 1.11. Finally, it is noted that another classification scheme for the discotic mesophases has been used [1.26], which is based on the notation used for the conventional smectics. 

Note The re-entrant behavior for the fee phase of La published in this paper affeets only La, and none of the heavier lanthanides, sinee the eorresponding eritieal radius ratio of r ial.9 implies low symmetry f-bonded struetures already for all the other lanthanides (see fig. 5). 

The mean field analysis of the Frost s model of frustrated smectics describes most of the reported experimental observations on polar smectics. Situations where fluctuations are important are however not correctly described the understanding of multiply re-entrant behavior, the appearance of nematic bubbles and the scaling properties of the SmA2-SmAcritical point for instance require more elaborate analysis. Some of these points will be discussed in the following sections. 

This is confirmed of a pressure-induced nematic phase in the case of the tri- and tetra-decyloxy members. The pressure behavior of the particular smectic ranges (C, G, H, I) is very complex. Some smectic phases vanish at higher pressures. Two compounds investigated additionally 4-n-octyloxy-4 -cyanobiphenyl and 4-cyanobenzylidene-4 -n-octyloxy aniline and their mixtures show pressure-induced nematic re-entrant behavior. 

Shashidhar and Rao [74] performed high pressure X-ray studies on liquid crystals with re-entrant behavior with an opposed diamond anvil cell. They found that the layer spacing of the SmA phase of 4-n-octyloxy-4 -cyanobiphenyl first decreases more or less linearly with increasing pressure up to 140 MPa, then increases at still higher pressures. Since this compound shows re-entrant nematic behavior at high pressures, this result confirms the prediction of Cladis et al. that the occurrence of a re-entrant nematic phase is associated with an expansion of the SmA phase layer spacing. 

Following the Bordeaux discovery by Hardouin et al. [29], many three-ring cyano compounds were discovered, particularly by the Halle group [37], that showed stable Nre phases in cyano compounds with three benzene rings. An overview of the chemical structure and re-entrant behavior of three benzene ring compounds has been given by Weissflog et al. [38]. 

A phenomenon which is closely related to smectic polymorphism is that of re-entrant behavior, where unusual phase sequences. 

Ye, et al. note an odd viscosity dependence associated with re-entrant behavior (22). At the lower concentrations at which stj/sqtjq has not yet reached its maximum, 5 tracks the single-chain viscosity t] = + [r/]c), [r/] being the... 

From limited results, s(c) of sedimenting probes in a polymer matrix generally follows a stretched exponential in c. With a small matrix polymer, s(c) of a probe chain simply tracks the solution viscosity. In solutions of large matrix polymers, s and rj do not show the same concentration dependence. With probe spheres, 5(c) may track the solution viscosity or may show re-entrant behavior. The agreement of 5(c) with a stretched-exponential form is less outstanding when re-entrance is observed. The literature describes too few probe polymer pairs to be able to say if re-entrant behavior is common or rare. 

Ullmann, et al.O ) extended Ullmann and Philhes(31) to study probe diffusion of carboxylate-modified polystyrene spheres in aqueous polyethylene oxide Triton X-100. The Dp for most sphere matrix combinations follows a stretched exponential in c, as seen in Figure 9.18. However, Dp of the 655 nm diameter spheres shows re-entrant behavior, both in the 18.5 kDa polymer and to a lesser extent... 

A few systems show re-entrant behavior in which a relaxation rate increases with increasing c, and then perhaps decreases again at an even larger c, as reported by Bremmell, et a/.(35,36), Dunstan and Stokes(37), and Ullmann, et al.OT). In a very few systems, an apparent small-c plateau is observed Dp or r p is nearly independent of c for c up to some small concentration, and then declines at larger c, as described by Yang and Jamieson(57) and by Papagiannopolis, et a/. (89). 

In a few systems, Dp c) shows re-entrant behavior, in which the probe diffusion coefficient increases with increasing c, and then perhaps falls at still larger c. Re-entrance is prominent in systems having multimodal spectra there is a need for more systematic smdy. The Dp (c) also sometimes has a plateau at very low concentrations. The interpretations of re-entrance and plateau behavior are uncertain. 

Where does one not find stretched-exponential behavior In dilute solution, very modest deviations - concentration dependences weaker than expected - are sometimes seen. A few cases of re-entrant behavior, in which Ds c)t] c) 7 D (0) y(0) over some limited concentration range, have been noted. For melts, extensive reviews of the literature(2,3) generally find scaling behavior for tj and D, at least for adequately large polymers. It is then reasonable to expect that as the melt is approached there should be a transition to power-law behavior. Experiments of Tao, et al. are consistent with this expectation(4). 

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