Effects of the H-bond donor structure on the properties of supramolecular side chain liquid crystalline polymers based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane)s and stilbazoles

Supramolecular side chain liquid crystalline polymers (SCLCPs) based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane) (PSIX, X=100, 76, 60, 41 or 23, denoting the mole percentage of 3-carboxypropylmethylsiloxane unit in the polymer) and stilbazole derivatives have been obtained through intermolecular hydrogen bonding (H-bonding) interactions between the carboxylic acid and the pyridyl moieties. The formation of H-bonding and self-assembly results in the formation of new mesogenic units, in which H-bonds function as molecular connectors. FTIR shows the existence of H-bonding in the complexes. The polymeric complexes behave as single component liquid crystalline polymers and exhibit stable and enantiotropic mesophases. The liquid crystalline properties of the supramolecular SCLCPs were studied using differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction, and were found to exhibit smectic A phases with focal-conic textures. The thermal stability of the SCLCP increases on increasing the carboxylic acid content in the polysiloxane and the concentration of the stilbazole derivative in the complex. However, the thermal stability decreases on increasing the chain length of the stilbazole derivative. The crystal phase was not formed even on cooling to the glass transition temperature of the polymeric complex.     

Metal-dielectric-metal plasmonic waveguide devices for manipulating light at the nanoscale Invited Paper

We review some of the recent advances in the development of subwavelength plasmonic devices for ma- nipulating light at the nanoscale, drawing examples from our own work in metal-dielectric-metal (MDM) plasmonic waveguide devices. We introduce bends, splitters, and mode converters for MDM waveguides with no additional loss. We also demonstrate that optical gain provides a mechanism for on/off switch- ing in MDM plasmonie waveguides. Highly efficient compact couplers between dielectric waveguides and MDM waveguides are also introduced.     

Thin-film polymerization and characterization of Sumitomo's Sumikasuper®-type liquid crystalline polymers

Using the thin film polymerization approach, we have studied the texture evolution when synthesizing a novel liquid crystalline polymer (LCP) system based on Sumikasuper^® LCPs. The main monomers used were p-acetoxybenzoic acid (ABA), 4,4′-biphenol (BP), isophthalic acid (IA), phthalic acid (PA) and terephthalic acid (TA). Polarizing optical microscopy (POM), FTIR, X-ray diffraction (XRD) and atomic force microscopy (AFM) were employed to study the thin film polymerization process and characterize the products. The generation and evolution of liquid crystal phases were monitored; the results revealed that there exists a composition range for the monomers to react and form liquid crystal materials. The critical temperature for LC formation in ABA/BP/IA system decreased with increasing ABA content. FTIR results confirmed the formation of polymers. AFM investigation suggested a similar process of morphological change to that observed using POM. An increasing surface roughness of the thin films with the progress of polymerization was also obtained from AFM analysis. A nematic LC texture of the polymer system was suggested by XRD examination. Results obtained by replacing BP with acetylated BP, and by conducting polymerization using two-monomer systems, suggest that BP units are included in polymers obtained by the thin film polymerization method.     

Effect of electron donor-acceptor interaction on the thermal stability of supramolecular side chain liquid crystalline polymers based on poly(3-carboxypropylmethylsiloxane)

Supramolecular side chain liquid crystalline polymers were prepared from poly(3-carboxypropylmethylsiloxane) (PSI100) and azobenzene-based derivatives through intermolecular hydrogen bonding between the carboxylic acid groups of PSI100 and the imidazole rings in the azobenzene-based derivatives. The presence of H-bonding was confirmed using FTIR spectroscopy. The polymeric complexes behave as liquid crystalline polymers and exhibit nematic mesophases identified on the basis of the observation of Schlieren textures. The mesogenic behaviour of these complexes was studied by polarizing optical microscopy and X-ray diffraction. The thermal behaviour of the complexes was investigated by differential scanning calorimetry. On increasing the spacer length, the transition temperatures initially increase. A further increase in spacer length, however, leads to a decrease in the transition temperatures. The electron donor-acceptor interaction between unlike mesogenic units in supramolecular copolymeric complexes helps to stabilize the mesophase.     

Statistics and characterization of matrices by determinant and trace

The Ramanujan Journal - Answering a question of Erdös, Komlós proved in 1968 that almost all $$ntimes n$$ Bernoulli matrices are nonsingular as $$nrightarrow infty $$ . In this paper,...     

The preparation of primary mathematics teachers in Singapore: programs and outcomes from the TEDS-M study

This paper describes five aspects of primary mathematics teacher education in Singapore: (a) the teaching profession in Singapore, (b) the structure of pre-service teacher education programs offered by the National Institute of Education, (c) self-reports of Singapore future primary mathematics teachers about the opportunities to learn mathematics-related contents offered by these programs, based on the Teacher Education and Development Study in Mathematics (TEDS-M) survey, (d) the performance of these future teachers in mathematics content knowledge and mathematics pedagogical content knowledge assessed by the TEDS-M study, and (e) the relationships of opportunities to learn with this performance. The paper concludes with some suggestions about how to improve the quality of initial teacher preparation in the areas of recruitment and training.     

Spectral analysis of eigenparameter dependent boundary value transmission problems

In this paper, the singular second order differential operators are considered defined on the multi-interval. Some boundary and transmission conditions are imposed on the maximal domain functions with the spectral parameter. After constructing the differential operators associated with the boundary value transmission problems on the suitable Hilbert spaces, it is proved that these operators are the maximal dissipative operators. Finally constructing the model operators which are established with the help of the scattering functions, it is proved that all root vectors of the maximal dissipative operators are complete in the Hilbert spaces.     

Polyamide-imide/polyetherimide dual-layer hollow fiber membranes for pervaporation dehydration of C1–C4 alcohols

To circumvent the common swelling and deteriorated performance of integral asymmetric hollow fiber membranes for pervaporation dehydration, we have developed novel polyamide-imide (PAI)/polyetherimide (PEI) hollow fiber membranes with synergized performance with the aid of dual-layer spinning technology. Dehydration of C1–C4 alcohols has been conducted and the orders of their fluxes and permeances have been analyzed. The hollow fibers spun at 2 cm air gap and annealed at 75 °C exhibit the highest pervaporation performance: separation factors for t-butanol/water and iso-butanol/water binary systems are greater than 50,000 with flux more than 700 g/m² h. A comparison with literature data shows that the newly developed membranes outperform most other polymeric membranes for the dehydration of IPA and butanols. The dual-layer hollow fiber membranes also exhibit good long-term stability up to 200 h. The superior performance can be attributed to (1) the balanced properties of PAI as the selective layer for dehydration pervaporation; (2) the low water uptake and less swelling characteristic of the PEI supporting layer; and (3) the desirable membrane morphology consisting of a fully porous inner layer, a porous interface, and an ultrathin dense-selective outer skin.