Chirality phase transitions

The 2D chiral systems of NN and PVBA do not need a change in local adsorbate geometry in order to show a chiral phase transition [83,86]. Homochiral structures have been observed for PVBA (Fig. 7a) and SDA on Cu(100) [95]. A CW-rotated structure contains exclusively A.-PVBA, while the CCW-rotated structure contains only 5-PVBA (Fig. 29) [86]. Increasing the PVBA coverage above 0.05 molecules per copper atom induces a phase transition into a single achiral structure that possesses two mirror planes (Fig. 29c). Highly resolved STM shows that this structure is now comprised of a <5-/k-PVBA racemate and that the unit cell contains equal numbers of CCW-and CW-rotated units. 

The introduction of a second chiral atom in the system leads to a reduction in the mesogenic properties and only a monotropic chiral nematic transition is observed for compound 23. However, when this compound is cooled down from the isotropic liquid state at a cooling rate of 0.5 °Cmin , very unusual blue phases BP-III, BL-II and BP-I are observed in the range 103-88 °C. Blue phases usually require pitch values below 500 nm. Hence the pitch value of the cholesteric phase for 23 must be very short, suggesting that the packing of two chiral carbons forces a faster helical shift for successive molecules packed along the perpendicular to the director. 

At lower temperatures, the standard 3D helical order with all chains having not only the same chirality but also the same phase can be established. The two magnetic phase transitions present very different features. In fact, the transition to the... 

Then, there are model Hamiltonians. Effectively a model Hamiltonian includes only some effects, in order to focus on those effects. It is generally simpler than the true full Coulomb Hamiltonian, but is made that way to focus on a particular aspect, be it magnetization, Coulomb interaction, diffusion, phase transitions, etc. A good example is the set of model Hamiltonians used to describe the IETS experiment and (more generally) vibronic and vibrational effects in transport junctions. Special models are also used to deal with chirality in molecular transport junctions [42, 43], as well as optical excitation, Raman excitation [44], spin dynamics, and other aspects that go well beyond the simple transport phenomena associated with these systems. 

They developed a continuum elastic-free energy model that suggests these observations can be explained as a first-order mechanical phase transition. In other recent work on steroids, Terech and co-workers reported the formation of nanotubes in single-component solutions of the elementary bile steroid derivative lithocholic acid, at alkaline pH,164 although these tubules do not show any chiral markings indicating helical aggregation. 

In reality, we are more interested in the intermediate density region, where the color superconducting phase may exist in the interior of neutron stars or may be created in heavy ion collisions. Unfortunately, we have little knowledge about this region we are not sure how the deconfinement and the chiral restoration phase transitions happen, how the QCD coupling constant evolves and how the strange quark behaves in dense matter, etc. Primarily, our current... 

One expects the diquark condensate to dominate the physics at densities beyond the deconfinement/chiral restoration transition and below the critical temperature. Various phases are possible. E.g., the so called 2-color superconductivity (2SC) phase allows for unpaired quarks of one color. There may also exist a color-flavor locked (CFL) phase [7] for not too large value of the strange quark mass ms, for 2A > m2s/fiq, cf. [8], where the color superconductivity... 

We compare results in the chiral limit (mo = 0) with those for finite current quark mass mo = 2.41 MeV and observe that the diquark gap is not sensitive to the presence of the current quark mass, which holds for all form-factors However, the choice of the form-factor influences the critical values of the phase transition as displayed in the quark matter phase diagram (/j,q — T plane) of Fig. 2, see also Fig. 1. A softer form-factor in momentum space gives lower critical values for Tc and at the borders of chiral symmetry restoration and diquark condensation. 

At nonzero temperatures the mass gap decreases as a function of the chemical potential already in the phase with broken chiral symmetry. Hence the model here gives unphysical low-density excitations of quasi-free quarks. A systematic improvement of this situation should be obtained by including the phase transition construction to hadronic matter. However, in the present work we circumvent the confinement problem by considering the quark matter phase only for densities above the nuclear saturation density no, i.e. ub > 0.5 no. 

We have investigated the influence of diquark condensation on the thermodynamics of quark matter under the conditions of /5-equilibrium and charge neutrality relevant for the discussion of compact stars. The EoS has been derived for a nonlocal chiral quark model in the mean field approximation, and the influence of different form-factors of the nonlocal, separable interaction (Gaussian, Lorentzian, NJL) has been studied. The model parameters are chosen such that the same set of hadronic vacuum observable is described. We have shown that the critical temperatures and chemical potentials for the onset of the chiral and the superconducting phase transition are the lower the smoother the momentum dependence of the interaction form-factor is. 

We have demonstrated that a chiral vesicle composed of di-palmitoyl-L- a-phosphatidylcholine(l-DPPC) doped with the azobenzene containing amphiphiles shown in Scheme 2 is a subject to photochemically triggered phase transition and exhibits a non-linear photoresponse in terms of ICD appearing at the absorption band of azobenzene. 

The phase transitions of cholesteryl nonanoate have been studied with a new apparatus for thermal analytical microscopy. The enantiomer ratio of some chiral sulphoxides can be changed from racemic to a modest preference for one enantiomeric form by dissolution in a cholesteryl ester in its liquid-crystalline ( cholesteric ) state. 5,6-Epoxycholestan-3-yl p-nitrobenzoates exhibit liquid-crystal properties, but 5,6-diols and dibromides are inactive. ... 

There are only a few reports on chiral phase transfer mediated alkylations". This approach, which seems to offer excellent opportunities for simple asymmetric procedures, has been demonstrated in the catalytic, enantioselective alkylation of racemic 6,7-dichloro-5-methoxy-2-phenyl-l-indanone (1) to form ( + )-indacrinone (4)100. /V-[4-(tnfluoromethyl)phenylmethyl]cinchoninium bromide (2) is one of the most effective catalysts for this reaction. The choice of reaction variables is very important and reaction conditions have been selected which afford very high asymmetric induction (92% cc). A transition state model 3 based on ion pairing between the indanone anion and the benzylcinchoninium cation has been proposed 10°. 

The epoxidation of enones using chiral phase transfer catalysis (PTC) is an emerging technology that does not use transition metal catalysts. Lygo and To described the use of anthracenylmethyl derivatives of a cinchona alkaloid that are capable of catalyzing the epoxidation of enones with remarkable levels of asymmetric control and a one pot method for oxidation of the aUyl alcohol directly into... 

The complexes bearing one chiral substituent display a smectic A mesophase when the non-chiral chain is long, or an enantiotropic cholesteric and a monotropic SmA phase for shorter alkoxy chains. A TGBA phase is observed for the derivative which contains the chiral isocyanide combined with the diethyloxy, when the SmA to cholesteric transition is studied. The compound with two chiral ligands shows a monotropic chiral nematic transition. When this compound is cooled very slowly from the isotropic liquid it exhibits blue phases BP-III, BP-II, and BP-I. 

CB) [9]. The enhancement occurs in both chiral domains, although the dopant is nonchiral. The phase diagram with chemical structures of the two components are shown in Fig. 17. The B2 and B3 phases readily disappear by the introduction of a small amount of 5CB, and the B4 phase is stabilized. In the mixtures with more than 50 wt% 5CB, we observe a new phase transition at an almost constant temperature of 32 °C, corresponding to the Iso-N transition of 5CB. This transition point can be detectable by DSC [58] and texture observation, but not by X-ray analysis [59]. Based on the experimental fact of no layer structure changes, we can infer that P8-O-PIMB and 5CB molecules are nanosegregated. Namely helical nanofilaments are in the isotropic and nematic sea of 5CB in the B4 and lower phases, respectively. Hereafter we call these phases B4/Iso and B4/N phases, respectively. 

Finally, dispersions of MWCNT in chiral nematic liquid crystals were studied as well. These experiments suggested no change in the helical twisting characteristics of the chiral nematic phase. However, the MWCNTs were thought to disrupt the translational order in the SmA phase (decrease of the SmA-N phase transition) yet follow the twist of the nematic director in the chiral nematic phase [498]. 

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