Disorder line

For strongly structured microemulsions, g is negative, and the structure functions show a peak at nonzero wavevector q. As long as g < 2 /ca, inverse Fourier transform of S q) still reveals that the water-water correlation functions oscillate rather than decay monotonically. The lines in phase space where this oscillating behavior sets in are usually referred to as disorder lines, and those where the maximum of S q) moves away from zero as Lifshitz lines. ... 

The second difference is related to the structure of the lamellar phase. The Euler characteristic has been assumed zero in the whole lamellar phase by Gompper and Kraus [47], whereas we show that it fluctuates strongly in the lamellar phase between the transition line and the topological disorder fine. The notion of the topological disorder line has not appeared in their paper. We think that the topological disorder line is much closer to the transition... 

R. Holyst, W. Gozdz. Fluctuating Euler characteristics, topological disorder line, and passages in lamellar phases. J Chem Phys 706 4773- 780, 1997. 

Except for a few special cases (most notably, /inear rules (see below) and the P2 = I line for the isotropic peripheral PCA discussed above, which happens to be an endpoint of a disorder line of an exactly solved 2-dim Ising model on a triangular lattice and can be solved exactly [kinzel85b]), phase-diagrams for PCA... 

Figure 7. Topological fluctuations of the lamellar phase at different points of the phase diagram, (a) Single fusion between the lamellae by a passage (this configuration is close to the topological disorder line), (b) Configuration close to the transition to the disordered microemulsion phase the Euler characteristic is large and negative.

In the model of the previous section, we have encountered the situation that outside the regime bounded by the disorder line the correlation function, Eq. (53), is characterized by an angle which is incommensurate with the lattice. Now it is well known that in d 2 dimensions, incommensurate long-range order (which would be described by <5,5 )x = cos[ r -Tjl(/ -F A< ] instead of Eq. (53)) is unstabie against thermal fluctuations (this is a two-component ordering - amplitude tj/, phase A0 - similar to the XY model). Nevertheless, it is possible to have a phase transition where in Eq. (53) diverges, but for T [Pg.126]

It is not clear whether in the centered rectangular lattice gas of section 3.2 such a Kosterlitz-Thouless transition occurs, or whether the disordered phase extends, though being incommensurate, down to the commensurate (3x1) phase (then this transition is believed to belong to a new chiral universality class ), or whether there is another disorder line for (3 x 1) correlations. However, Kosterlitz-Thouless type transitions have been found for various two-dimensional models the XY ferromagnet , the Coulomb gas . ... 

Fig. 6.43 Phase diagram for a ternary mixture of equal concentrations of A and B homopolymers and symmetric AB diblock (all with equal degrees of polymerization) computed by Holyst and Schick (1992). The Lifshitz tricritical point is shown at L, the line CL is that of continuous transitions from the disordered phase to coexisting A-rich and B-rich phases, and LG is the line of continuous transitions from the disordered to the lamellar phase. LD is the disorder line.

How do we redeem ourselves he asked the empty botde and the disorderly line of glasses in front of him. 

Figure 2 DFT formation energies as a function of temperature for the Tc interstitial (triangles), Tu interstitial (circles), Be interstitial (diamonds), and vacancy (squares), averaged over different replicas. Error bars denote the magnitude of the fluctuations due to proton disorder. Lines represent polynomial fits to the average results.

Fig. 30. Phase diagram of the two-dimensional ANNN1 model. The broken curve in the paramagnetic phase is the disorder line below this line, the correlation function has a simple ferromagnetic exponential decay (uniform in sign), while above this line an oscillatory decay of the type of eq, (119) is found. From Beale ei al. (1985).

Schubert, K.V. and Strey, R. (1991) Small-angle neutron-scattering from microemulsions near the disorder line in water formamide octane QEj systems. /. Chem. Phys., 95, 8532-8545. 

LL),. tfo = 0, where the peak of the scattering intensity at nonzero wave vector q first appears the second is the disorder line (DOL), go = where the correlation function... 

Thus, the correlation function changes its behavior at the disorder line from oscillatory to monotonic (exponential decay) [65]. More positive values of fa correspond to tricritical points (where three coexisting liquid phases become simultaneously identical) [83]. 

Figure 12. ESR spectra of irradiated chlorodifluoroacetamide crystals with the magnetic field parallel to the ESR a axis when (a.) T = 90°K and no previous warming, (b.) crystal warmed to T = 170°K and (c.) crystal cooled toT =-90°K. Lines A and R indicate the high and low field lines of two magnetically nonequivalent sites of CF CONHs caused by rotational disorder. Lines C are caused by a partially decayed precursor radical.

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