Providing a traceable assigned value in a proficiency testing programme on the determination of benzoic acid in orange juice

A proficiency testing (PT) programme on the determination of benzoic acid in orange juice was organised by the Chemical Metrology Laboratory, Health Sciences Authority, Singapore, for the local food testing laboratories. The PT programme used a metrologically traceable assigned value determined by isotope dilution mass spectrometry to assess the performance of the participating laboratories. This paper discusses the reasons and approach to applying metrological principles to determine the assigned value of a PT programme. The procedure undertaken by the Laboratory to prepare a batch of PT sample, conduct homogeneity and stability testings, as well as value assignment, is presented. The discussions also include the estimation of the measurement uncertainties arising from the characterisation, testing for homogeneity and testing for stability of the PT sample. The Coordinator of the PT programme used the assigned value and its associated measurement uncertainty, together with those of the participating laboratories to assess their performances. Statistical tools applied in the performance evaluations are also presented.     

Optimal direct coupling from single-mode fibers to Ti:LiNbO3, channel waveguides

We investigate the optimal direct coupling from single-mode fibers to Ti:LihbO₃, channel waveguides using a very general formula and a heuristic optimization technique in this article. The coupling efficiency of the optical power depends on both the fiber positions and the modal sizes of the incident fields. From our numerical simulation, it is found that the optimal positions of the fiber axes are not in alignment with the peaks of the waveguiding modal fields and that the coupling efficiency can be improved by microlenses.     

Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots

In this article we study the impact of the spin-orbit interaction on the electron quantum confinement for narrow gap semiconductor quantum dots. The model formulation includes: (1) the effective one-band Hamiltonian approximation; (2) the position- and energy-dependent quasi-particle effective mass approximation; (3) the finite hard wall confinement potential; and (4) the spin-dependent Ben Daniel-Duke boundary conditions. The Hartree-Fock approximation is also utilized for evaluating the characteristics of a two-electron quantum dot system. In our calculation, we describe the spin-orbit interaction which comes from both the spin-dependent boundary conditions and the Rashba term (for two-electron quantum dot system). It can significantly modify the electron energy spectrum for InAs semiconductor quantum dots built in the GaAs matrix. The energy state spin-splitting is strongly dependent on the dot size and reaches an experimentally measurable magnitude for relatively small dots. In addition, we have found the Coulomb interaction and the spin-splitting are suppressed in quantum dots with small height. Received 15 May 2001 / Received in final form 14 May 2002 Published online 13 August 2002     

Kinetic stages of single-component colloidal crystallization

To harness the full potential of colloidal self-assembly, the dynamics of the transition between colloids in suspension to a colloidal crystalline film should be better understood. In this report, the structural changes during the self-assembly process in a vertical configuration for colloids in the size range 200-400 nm are monitored in situ, using the transmission spectrum of the colloidal assembly treated as an emergent photonic crystal. It is found that there are several sequential stages of colloidal ordering: in suspension, with a larger lattice parameter than the solid state, in a close-packed wet state with solvent in the interstices, and, finally, in a close-packed dry state with air in the interstices. Assuming that these stages lead continuously from one to another, we can interpret colloidal crystallization as being initiated by interparticle forces in suspension first, followed by capillary forces. This result has implications for identifying the optimum conditions to obtain high-quality nanostructures of submicrometer-sized colloidal particles.     

Self-assembly of perfunctionalized beta-cyclodextrins on a quartz crystal microbalance for real-time chiral recognition

This study reports the development of novel chiral sensors based on the self-assembly of perfunctionalized beta-cyclodextrins (beta-CD) on a quartz crystal microbalance transducer for real time chiral recognition. Ten chiral sensors immobilized with mercaptyl perfunctionalized beta-cyclodextrins were found to exhibit promising enantioselectivity in the gas phase. Well-defined sizes of molecular cavities of the modified beta-CDs associated with cooperative weak interactions with the host molecules afforded enhanced chiral discrimination. This study contributes to the realization of novel chiral sensors applicable for real-time recognition and analysis of enantiomeric alcohols and lactates.     

Layer-by-layer growth of attractive binary colloidal particles

We investigate the two-dimensional (2D) colloidal structures formed by oppositely charged polystyrene monolayers grown layer-by-layer, where the electrostatic forces are recruited to assist in the packing of the layers. Our results show a transition through several 2D-superlattices to more close-packed structures with increasing ionic strength. The observed geometrical packing constraints of the 2D-superlattice structures agree well with the estimated Debye screening length of the electric double layer. By tuning interaction forces between charged colloids, electrostatic interactions could enhance the template-directed self-assembly process to achieve more complex and diverse structures.     

Supramolecule-regulated photophysics of oligo(p-phenyleneethynylene)-based rod-coil block copolymers: effect of molecular architecture

Three new topology-varied rod-coil block copolymers, comprising the same oligo(p-phenyleneethynylene) (OPE) rod components and the same coil components, were synthesized by atom-transfer radical polymerization. Their photophysical properties were systematically studied and compared in consideration of their solid-state structures and self-assembly abilities. These copolymers have similar intrinsic photophysical properties to the OPE rods, as reflected in dilute solution. However, their photophysical properties in the solid state are manipulated to be dissimilar by supramolecular organization. Wide-angle X-ray diffraction (WAXD) and atomic force microscopy (AFM) data demonstrate that these copolymers possess different self-assembly abilities due to the molecular-architecture-dependent pi-pi interactions of the rods. Hence, the aggregates in the solid state are formed with a different mechanism for these copolymers, bringing about the discrepancy in the solid-state luminescent properties.     

Regular matrices and their strong preservers over semirings

An m×n matrix A over a semiring is called regular if there is an n×m matrix G over such that AGA=A. We study the problem of characterizing those linear operators T on the matrices over a semiring such that T(X) is regular if and only if X is. Complete characterizations are obtained for many semirings including the Boolean algebra, the nonnegative reals, the nonnegative integers and the fuzzy scalars.     

A note on the perturbation of positive matrices by normal and unitary matrices

In a recent paper, Neumann and Sze considered for an n × n nonnegative matrix A, the minimization and maximization of ρ(A + S), the spectral radius of (A + S), as S ranges over all the doubly stochastic matrices. They showed that both extremal values are always attained at an n × n permutation matrix. As a permutation matrix is a particular case of a normal matrix whose spectral radius is 1, we consider here, for positive matrices A such that (A + N) is a nonnegative matrix, for all normal matrices N whose spectral radius is 1, the minimization and maximization problems of ρ(A + N) as N ranges over all such matrices. We show that the extremal values always occur at an n × n real unitary matrix. We compare our results with a less recent work of Han, Neumann, and Tastsomeros in which the maximum value of ρ(A + X) over all n × n real matrices X of Frobenius norm was sought.