Synthesis and thermal behavior of Janus dendrimers,part 1

Eight Janus-type dendrimers up to the second generation were synthesized, and their thermal properties were evaluated. Compounds consist of the dendritic bisMPA based polyester moieties, and either 3,4-dihexyloxybenzoic acid or 3,4-dihexadecyloxybenzoic acid moieties, attached to opposite sides of the pentaerythritol core. The structures of the molecules were verified with ¹H NMR, ¹³C NMR, ESI TOF mass spectrometry and elemental analysis. The thermal stability was evaluated by thermogravimetric analysis, displaying onset decomposition temperatures (T_d) ranging from 241 to 308 °C. Phase transitions were studied by differential scanning calorimetry. Based on the performed studies it was confirmed that OH terminated dendrimers 2, 4, 6 and 8 exhibited liquid crystalline phases. Also, the X-ray powder diffraction measurements were accomplished for the dendrimers having terminal hydroxyl groups.     

Influence of diffusion on pore size distributions determined by xenon porometry

Xenon porometry is a new method for characterization of porous materials. In this method, the material is immersed in a medium, and its properties are studied by means of 129Xe NMR spectra of xenon dissolved in the sample. The method is particularly suitable for the determination of pore size distribution of the material, since the spectra display two signals whose chemical shift is dependent on the pore size. A prerequisite for an accurate determination is the fact that the diffusion of xenon between different pores is slow enough. The diffusion is studied in this work using two-dimensional exchange spectroscopy (2-D EXSY). The spectra measured as a function of the mixing time imply that the exchange is really slow as compared with the NMR time scale, and therefore the distribution of the resonance frequencies indeed represents the pore size distribution.     

Phase equilibria on four binary systems containing 3-methylthiophene

Isothermal vapor–liquid equilibrium (VLE) for 3-methylthiophene + 2,2,4-trimethylpentane at 368.15 K, 3-methylthiophene + 2,4,4-trimethyl-1-pentene at 368.15 K, 3-methylthiophene  + cyclohexane at 348.15 K, and 3-methylthiophene + 1-hexene at 333.15 K were measured with a recirculation still. All systems exhibit positive deviation from ideality. No azeotropic behavior was found in all systems. The experimental results were correlated with the Wilson model and also compared with the original UNIFAC and UNIFAC-Dortmund predictive models. Analyses of liquid and vapor-phase composition were determined with gas chromatography (GC). All VLE measurements passed the used thermodynamic consistency tests (integral, infinite dilution and point test). The activity coefficients at infinite dilution are also presented.     

Remarks on ideals in join-semilattices

A set of results analogous to the corresponding results in lattices is derived for neutral ideals in join-semilattices, for congruence relations generated by neutral ideals in join-semilattices, and for permutable congruence relations generated by ideals in modular join-semilattices.     

Fuzzy mappings and algebraic structures

Kauffman's fuzzy morphisms are considered. The concept of structure preserving fuzzy morphisms is defined and their properties are described by means of compatible tolerance relations and related mappings.     

Analysis of a bilinear finite element for shallow shells. II: Consistency error

We consider a bilinear reduced-strain finite element of the MITC family for a shallow Reissner-Naghdi type shell. We estimate the consistency error of the element in both membrane- and bending-dominated states of deformation. We prove that in the membrane-dominated case, under severe assumptions on the domain, the finite element mesh and the regularity of the solution, an error bound can be obtained if the contribution of transverse shear is neglected. Here is the thickness of the shell, the mesh spacing, and a smoothness parameter. In the bending-dominated case, the uniformly optimal bound is achievable but requires that membrane and transverse shear strains are of order as . In this case we also show that under sufficient regularity assumptions the asymptotic consistency error has the bound .

     

The anisotropic forces acting on the bonds of benzene in liquid crystals

The HH and CH dipolar couplings of benzene measured in five different liquid crystal solvents are subjected to an analysis which allows for the correlation between the molecular reorientational and vibrational motions. The number of adjustable parameters is reduced by treating the CH bonds or both the CH and CC bonds as effectively cylindrically symmetric entities. In this way detailed information on the anisotropic forces acting on the bonds of benzene dissolved in liquid crystals is obtained. The behaviour of the CC bonds, but not that of the CH bonds, may be explained by anisotropic dispersion forces. There is an approximately linear relation between the torques acting on the CH bonds of benzene and methane in the same liquid crystal environment. This suggests that these forces stem from a common interaction mechanism, possibly the van der Waals interaction between the atoms of the solute molecule and the liquid crystal surroundings or the interaction between the molecular quadrupole moment and the electric field gradient due to the surrounding medium. A bond additivity model for the molecular quadrupole moment tensor is developed and discussed.     

Electrostatics of the ferroelectric phases of BaTiO3

Extensive theoretical calculations are reported here on the electrostatics of the three ferroelectric phases of BaTiO₃ using the static polarizable point-ion model. For each structure the following quantities have been calculated: monopole and dipole fields at ionic sites, field gradients, spontaneous polarization, high frequency dielectric constant and the Coulomb energy terms. The parameters of the model have been fitted on the basis of the experimental information on the tetragonal structure and then treated as constants for all the studied structures. The use of the experimental positional parameters of the orthorhombic structure gives such exceptional behaviour for all the calculated quantities that a redetermination of the structural parameters for this phase is suggested. Numerical study of the changes in the Coulomb energy as a function of the macroscopic depolarization potential demonstrated that the most stable state is achieved with the value zero for the potential.     

A note on intersections of free submonoids of a free monoid

According to a theorem of Tilson [6] any intersection of free submonoids of a free monoid is free. Here we consider intersections of the form {x, y}^* ∩ {u, v}^*, where x, y, u and v are words in a finitely generated free monoid Σ^*, and show that if both the monoids {x, y}^* and {u, v}^* are of the rank two, then the intersection is a free monoid generated either by (at most) two words or by a regular language of the form β₀ + β((γ(1+ δ + ... δ^t))^*ε for some words β⁰, β, γ, δ and ε, and some integer t≥0. An example is given showing that the latter possibility may occur for each t≥0 with nonempty values of the words.