From monomeric to polymeric ferroelectric liquid crystals A comparative study of ferroelectric properties

Two new ferroelectric oligosiloxanes, a cyclic tetramer and a twin, have been synthesized. By a comparative study with their corresponding monomer and side chain polysiloxanes, the influence of oligo- and polymerization on the liquid crystalline and ferroelectric properties have been investigated. Polymerization leads to a stabilization of LC phases through increase of the clearing temperatures and suppression of crystallization. Oligomerization also leads to mesophase broadening, but, due to the low degree of polymerization, the effect is inferior to the linear polysiloxanes. The low viscosity of the oligosiloxanes ensures response times in the microsecond region, thus being comparable with their monomer and conventional LMWFLCs. It is found that polymerization increases the spontaneous polarization P_s. This is attributed to the density increase after polymerization, enhancing the inter-mesogenic interactions. The collective and local dynamics of the OFLCs are influenced differently with respect to their molecular structures. Each oligomer is already a good model for its corresponding polymer concerning the soft mode dynamics. For the local β-relaxation a similar temperature dependence of the relaxation times τ for the cyclic tetramer and for the side chain polysiloxanes is observed. The long axial rotation of the twin, having a very efficient decoupling, is significantly faster, thus resembling the monomer.     

Classification of the space spanned by theta series and applications

We determine a class of functions spanned by theta series of higher degree. We give two applications: A simple proof of the inversion formula of such theta series and a classification of skew-holomorphic Jacobi forms.

     

Zeros of functions with finite Dirichlet integral

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

     

Synthesis and applications of chiral bis-THF in asymmetric synthesis

The synthesis of enantiopure bis-THF is described, starting from d-mannitol. Bis-THF is used as chiral ligand for organolithium reagents in four different reactions. The enantioselectivity provided by this ligand is moderate, and the asymmetric induction is in line with the expected model.     

Partitioning Balls into Topologically Equivalent Pieces

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Partitioning Balls into Topologically Equivalent Pieces

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HPLC with amperometric detection for the determination of pesticides of high polarity

A relatively simple procedure is described for the selective and highly sensitive determination of amitrole (3-amino-1,2,4-triazole) by ionpair HPLC with amperometric detection. The separation was achieved on a polar CN-column using hexane, propanol, water (62:36:2) with LiClO₄ (2.5 g·l^–1) and trichloroacetic acid (2 g·l^–1) as electrolytes. The determination range lies between 500 pg and 500 ng and the limit of detection was found to be 200 pg (s.d.: 11%; N=9). The minimum detectability for the alternative UV-monitoring was 2.5 ng. The developed method may be helpful in production and quality control and for the selective determination of amitrole in commercial formulations.