The Uptake and Assembly of Alkanes within a Porous Nanocapsule in Water: New Information about Hydrophobic Confinement

In Nature, enzymes provide hydrophobic cavities and channels for sequestering small alkanes or long‐chain alkyl groups from water. Similarly, the porous metal oxide capsule [{Mo^VI₆O₂₁(H₂O)₆}₁₂{(Mo^V₂O₄)₃₀(L)₂₉(H₂O)₂}]^41? (L=propionate ligand) features distinct domains for sequestering differently sized alkanes (as in Nature) as well as internal dimensions suitable for multi‐alkane clustering. The ethyl tails of the 29 endohedrally coordinated ligands, L, form a spherical, hydrophobic “shell”, while their methyl end groups generate a hydrophobic cavity with a diameter of 11 Å at the center of the capsule. As such, C₇ to C₃ straight‐chain alkanes are tightly intercalated between the ethyl tails, giving assemblies containing 90 to 110 methyl and methylene units, whereas two or three ethane molecules reside in the central cavity of the capsule, where they are free to rotate rapidly, a phenomenon never before observed for the uptake of alkanes from water by molecular cages or containers.     

On the Construction of Composite Wannier Functions

We give a constructive proof for the existence of a Bloch basis of rank \({N}\) which is both smooth (real analytic) and periodic with respect to its \({d}\)-dimensional quasi-momenta, when \({1\leq d\leq 2}\) and \({N\geq 1}\). The constructed Bloch basis is conjugation symmetric when the underlying projection has this symmetry, hence the corresponding exponentially localized composite Wannier functions are real. In the second part of the paper, we show that by adding a weak, globally bounded but not necessarily constant magnetic field, the existence of a localized basis is preserved.     

Use of a kinetic energy orifice as a probe of metastable dissociation in Fourier transform ion cyclotron resonance mass spectrometry

Although Fourier transform ion cyclotron resonance mass spectrometry is a powerful tool in the qualitative observation of gas phase reactions, ion detection is on the millisecond time scale, orders of magnitude longer than typically found when using a sector instrument. Observations of short-lived species such as chemically activated adduct ions can be accomplished using selective ion excitation as a probe of intermediate lifetime. Whereas ion elimination has been shown to be effective in monitoring ion lifetimes on the microsecond time scale, problems associated with detecting ions produced with high kinetic energies limits the technique. Use of a kinetic energy orifice as an ion skimmer effectively eliminates ions near the center of the ion cell at relatively low kinetic energies. By modifying a single section cell to include a kinetic energy orifice, the lifetimes of chemically activated adduct ions have been investigated.     

Invariant Manifolds,Nonclassical Normal Modes,and Proper Orthogonal Modes in the Dynamics of the Flexible Spherical Pendulum

It is shown that the flexible spherical pendulum undergoes purely slow motions with master and slaved components. The family of slow motions is realized as a three-dimensional invariant manifold in phase space. This manifold is computed analytically by applying the method of geometric singular perturbations. This manifold is nonlinear and for all energy and angular momentum levels is characterized precisely by three PO (proper orthogonal) modes. Its submanifold of zero angular momentum is a two-dimensional invariant manifold; it is the geometric realization of a nonclassical nonlinear normal mode. This normal mode is characterized precisely by two PO modes. The slaved slow dynamics are characterized precisely by a single PO mode. The stability of the slow invariant manifold as well as interactions between fast and slow dynamics are considered.     

Realizing Holonomic Constraints in Classical and Quantum Mechanics

We consider the problem of constraining a particle to a smooth compact submanifold Σ of configuration space using a sequence of increasing potentials. We compare the classical and quantum versions of this procedure. This leads to new results in both cases: an unbounded energy theorem in the classical case, and a quantum averaging theorem. Our two step approach, consisting of an expansion in a dilation parameter, followed by averaging in normal directions, emphasizes the role of the normal bundle of Σ, and shows when the limiting phase space will be larger (or different) than expected. Received: 16 November 2000 / Accepted: 2 February 2001     

Electroanalytical voltammetry in flowing solutions

A review is given of the principles, key developments and representative applications of small electrodes in flow-through electrochemical (ec) detectors having very low effective dead volume (<10 μl) for voltammetric and amperometric detection in flowing solutions. Emphasis is placed on factors contributing to high sensitivity, reliability and selectivity of ec detection as an integral part of larger analytical systems utilizing continuously flowing, unsegmented streams, e.g., flow-injection and liquid chromatographic analyses. Solid and mercury electrodes are considered under potentiostatic and potentiodynamic control. A review is given also of auxiliary chemical and photolytic derivatizations coupled to ec detection. The majority of the literature on the subject relates to liquid chromatography with electrochemical detection (l.c./ec); however, applications to these concepts to specific examples in flow-injection systems, as well as for on-line process control, should be obvious. Details of chromatographic separations and design of total analytical systems are not reviewed.     

Perturbation of embedded eigenvalues in the generalizedN-body problem

We discuss the perturbation of continuum eigenvalues without analyticity assumptions. Among our results, we show that generally a small perturbation removes these eigenvalues in accordance with Fermi's Golden Rule. Thus, generically (in a Baire category sense), the Schrödinger operator has no embedded non-threshold eigenvalues.Supported in part by NSF Grant DMS 8602826     

The use of a highly sulfated cyclodextrin for the simultaneous chiral separation of amphetamine-type stimulants by capillary electrophoresis

We investigated the simultaneous chiral separation of nine amphetamine type stimulants (dl-norephedrine, dl-norpseudoephedrine, dl-ephedrine, dl-pseudoephedrine, dl-amphetamine, dl-methamphetamine, dl-methylenedioxyamphetamine (MDA), dl-methylenedioxymethamphetamine (MDMA), and dl-methylenedioxyethylamphetamine (MDEA)) by capillary electrophoresis using highly sulfated gamma-cyclodextrin (SU(XIII)-gamma-CD) as a chiral selector. Three different approaches using SU(XIII)-gamma-CD with 50 mM phosphate background electrolyte were designed; (I) high CD concentration (10 mM SU(XIII)-gamma-CD) at neutral pH (pH 7.0) in the normal polarity mode, (II) low CD concentration (1.0 mM) at low pH (pH 2.6) in the normal polarity mode and (III) high CD concentration at low pH (pH 2.6) in the reversed-polarity mode. In mode (II), the effects of adding three neutral CDs (beta-CD, dimethyl-beta-CD and hydroxypropyl-beta-CD) were also investigated. The best separation was obtained after optimizing mode (III) as follows: run buffer of 10 mM SU(XIII)-gamma-CD with 50 mM phosphate background electrolyte at pH 2.6, applied voltage of -12 kV and capillary temperature of 15 degrees C.