Phase diagrams of cholesteric liquid crystals obtained with a generalized Landau-de Gennes theory

Phase diagrams of chiral nematic liquid crystals are studied within the framework of a generalized Landau-Ginzburg-de Gennes theory. Using the parametrization of Grebel, Hornreich, and Shtrikman for the tensor order parameter Q, all relevant elastic terms are included for the helicoidal phase and the blue phases of chiral nematic liquid crystals up to fourth order in Q and its gradient ∂Q. The influence of the additional elastic terms on the phase diagrams of the chiral nematic phases is then investigated. The theory correctly describes the variation of the pitch with temperature and the induced biaxiality of the cholesteric phase. The results resolve the discrepancies encountered by Hornreich and Shtrikman in the comparison of experiment and theory. New features in the topology of the phase diagrams of blue phases, like re-entrant phase transitions, are predicted.     

The limit diffusion mechanism of relaxation for spin systems

The diffusion limit theorem for stochastic differential equations is applied to analyse the dynamical evolutions of spin systems. Bloch equations are derived and the stability of asymptotic evolutions is proved. The theory is applied to nuclear magnetic relaxation of two spins.     

Biaxial nematic phase in model bent-core systems

We determine the bifurcation phase diagrams with isotropic (I), uniaxial (N(U)) and biaxial (N(B)) nematic phases for model bent-core mesogens using Onsager-type theory. The molecules comprise two or three Gay-Berne interacting ellipsoids of uniaxial and biaxial shape and a transverse central dipole. The Landau point is found to turn into an I-N(B) line for the three-center model with a large dipole moment. For the biaxial ellipsoids, a line of Landau points is observed even in the absence of the dipoles.     

UV-spectroscopic study of the influence of traces of water on the protolytic equilibria of substituted pyridine N-oxides in aprotic solvents

Using a UV-spectrophotometric method, an attempt has been made to estimate quantitatively the influence of traces of water in aprotic solvents on the acidic-basic equilibria involving heterocyclic N-oxides. The N-oxides under study were pyridine N-oxide (PyO), 4-methoxy-pyridine N-oxide (4-MeOPyO), and 2-, 3-, and 4-picoline N-oxide (2-, 3-, and 4-PicO). For particular N-oxide the UV-spectra of acetonitrile solutions containing the free base and/or its simple or semiperchlorate have been recorded. To carry out the calculations various equilibrium models which include the protolytic equilibrium with water and basic species present in the solvent have been tested using the program STOICHIO which is based on non-linear regression analysis. It turned out that apart from the acidic-basic dissociation of a protonated N-oxide and cationic homoconjugation (the equilibria which are usually considered in such systems) it is absolutely necessary to take into account the protolytic equilibrium between the cationic acid and water present as impurity. Implications concerning investigations of other equilibrium systems in aprotic solvents and, in particular, the quality of the acidity constants for the calibration agents used in potentiometry are discussed.     

Modeling of the hysteresis phenomena in finite-sized slitlike nanopores. Revision of the recent results by rigorous numerical analysis

The systematic investigation of the hysteresis phenomena in finite-sized slitlike nanopores via the Aranovich-Donohue (AD) lattice density functional theory (LDFT) is presented. The new reliable quantitative modeling of the adsorption and desorption branch of the hysteresis loop, through the formation and movement of the curved meniscus, is formulated. As a result, we find that our proposal, which closely mimics the experimental findings, can reproduce a rounded shape of the desorption branch of the hysteresis loop. On the basis of the exhausted commutations, we proved that the hysteresis loop obtained in the considered finite-sized slitlike geometry is of the H1 type of the IUPAC classification. This fundamental result and the other most important results do not confirm the results of the recent studies of Sangwichien et al., whereas they fully agree with the recent lattice studies due to Monson et al. We recognize that the nature of the hysteresis loops (i.e. position, width, shape, and the multiple steps) mainly depends on the value of the energy of both the adsorbate-adsorbate and adsorbate-adsorbent interactions; however, the first one is critical for the appearance of hysteresis. Thus, for relatively small adsorbate-adsorbate interactions, the adsorption-desorption process is fully reversible in the whole region of the bulk density. We show that the strong adsorbate-adsorbent interactions produce (also observed experimentally) multiple steps within hysteresis loops. Contrary to the other studies of the hysteresis phenomena in confined geometry via the LDFT formalism, we constructed both ascending and descending scanning curves, which are known from the experimental observations. Additionally, we consider the problem of the stability of both the obtained adsorption and desorption branches of the computed hysteresis loop in finite-sized slitlike nanopores.     

15N-NMR study of activated enamines. Structural dependence of δ (15N) and nJ(N,H) in primary,secondary and tertiary enamino-ketones,esters and amides

The pulse sequence INEPT was used to obtain proton-coupled ¹⁵N-NMR spectra in natural isotope abundance for enamines substituted in 2-position with electron-with-drawing groups. The chemical shifts and coupling constants are discussed in terms of their relationship to structural features such as multiple N-alkyl substitution, double-bond configuration, H-bonding, N-lone-pair delocalization within the conjugated system, and steric effects. It is concluded that ¹⁵N chemical shifts are a sensitive probe for local structural modifications at the N-atom and conformational changes in a remote part of a conjugated molecule, while one-bond N,H-coupling essentially reflects N-hybridization and subtle local geometric distortions. Stereospecific three-bond N,H spin coupling to olefinic protons (4.0 ± 0.2 Hz) has been found a characteristic feature of (Z)-isomers in all investigated compounds, whereas two-bond coupling to olefinic protons (²J(N,H) = 0.5 to 5 Hz) is observed in (E)-isomers. The sensitivity to solvents and steric properties of remote substituents renders geminal coupling a useful probe for studying electronic effects in the C? N bond.     

On the James constant and B-convexity of Cesàro and Cesàro-Orlicz sequence spaces

The classical James constant and the nth James constants, which are measure of B-convexity for the Cesàro sequence spaces cesp and the Cesàro-Orlicz sequence spaces cesM, are calculated. These investigations show that cesp,cesM are not uniformly non-square and even they are not B-convex. Therefore the classical Cesàro sequence spaces cesp are natural examples of reflexive spaces which are not B-convex. Moreover, the James constant for the two-dimensional Cesàro space is calculated.     

On the interpolation constant for Orlicz spaces

In this paper we deal with the interpolation from Lebesgue spaces and , into an Orlicz space , where and for some concave function , with special attention to the interpolation constant . For a bounded linear operator in and , we prove modular inequalities, which allow us to get the estimate for both the Orlicz norm and the Luxemburg norm,

where the interpolation constant depends only on and . We give estimates for , which imply . Moreover, if either or , then . If , then , and, in particular, for the case this gives the classical Orlicz interpolation theorem with the constant .

     

Weakly compact operators and interpolation

The class of weakly compact operators is, as well as the class of compact operators, a fundamental operator ideal. They were investigated strongly in the last twenty years. In this survey, we have collected and ordered some of this (partly very new) knowledge. We have also included some comments, remarks and examples.