Encapsulation of Arenes within a Porous Molybdenum Oxide {Mo132} Nanocapsule

The use of confined space to modulate chemical reactivity and to sequester organic compounds spans significant disciplines in chemistry and biology. Here, the inclusion and assembly of arenes into a water‐soluble porous metal oxide nanocapsule [{(Mo^VI)Mo^V₅O₂₁(H₂O)₆}₁₂{Mo^V₂O₄(CH₃COO)}₃₀]^42? (Mo₁₃₂) is reported. The uptake of benzene, halobenzenes, alkylbenzenes, phenols, and other derivatives was studied by NMR, where it was possible to follow the encapsulation process from the outside of the capsule through its pores and then into the interior. The importance of size or shape of the arenes, and various intermolecular bond interactions contributed by the benzene substituent on the encapsulation process was studied, showing the importance of π–π stacking and CH–π interactions. Furthermore, by using NOESY, ROESY, and HOESY NMR techniques it was possible to understand the interaction of the encapsulated arenes and the acetate linkers or ligands that line the interior of the Mo₁₃₂ capsule.     

Identification of binding sites for acetaldehyde adsorption on titania nanorod surfaces using CIMS

The interaction of acetaldehyde with TiO(2) nanorods has been studied under low pressures (acetaldehyde partial pressure range 10(-4)-10(-8) Torr) using chemical ionization mass spectrometry (CIMS). We quantitatively separate irreversible adsorption, reversible adsorption, and an uptake of acetaldehyde assigned to a thermally activated surface reaction. We find that, at room temperature and 1.2 Torr total pressure, 2.1 ± 0.4 molecules/nm(2) adsorb irreversibly, but this value exhibits a sharp decrease as the analyte partial pressure is lowered below 4 × 10(-4) Torr, regardless of exposure time. The number of reversible binding sites at saturation amounts to 0.09 ± 0.02 molecules/nm(2) with a free energy of adsorption of 43.8 ± 0.2 kJ/mol. We complement our measurements with FTIR spectroscopy and identify the thermal dark reaction as a combination of an aldol condensation and an oxidative adsorption that converts acetaldehyde to acetate or formate and CO, at a measured combined initial rate of 7 ± 1 × 10(-4) molecules/nm(2) s. By characterizing binding to different types of sites under dark conditions in the absence of oxygen and gas phase water, we set the stage to analyze site-specific photoefficiencies involved in the light-assisted mineralization of acetaldehyde to CO(2).     

Acceleration of convergence of general linear sequences by the Shanks transformation

The Shanks transformation is a powerful nonlinear extrapolation method that is used to accelerate the convergence of slowly converging, and even diverging, sequences {A _n }. It generates a two-dimensional array of approximations \({A^{(j)}_n}\) to the limit or anti-limit of {A _n } defined as solutions of the linear systems

$A_l=A^{(j)}_n +\sum^{n}_{k=1}\bar{\beta}_k(\Delta A_{l+k-1}),\ \ j\leq l\leq j+n,$

where \({\bar{\beta}_{k}}\) are additional unknowns. In this work, we study the convergence and stability properties of \({A^{(j)}_n}\) , as j → ∞ with n fixed, derived from general linear sequences {A _n }, where \({{A_n \sim A+\sum^{m}_{k=1}\zeta_k^n\sum^\infty_{i=0} \beta_{ki}n^{\gamma_k-i}}}\) as n → ∞, where ζ _k  ≠ 1 are distinct and |ζ ₁| = ... = |ζ _m | = θ, and γ _k  ≠ 0, 1, 2, . . .. Here A is the limit or the anti-limit of {A _n }. Such sequences arise, for example, as partial sums of Fourier series of functions that have finite jump discontinuities and/or algebraic branch singularities. We show that definitive results are obtained with those values of n for which the integer programming problems

$\begin{array}{ll}{\quad\quad\quad\quad\max\limits_{s_1,\ldots,s_m}\sum\limits_{k=1}^{m}\left[(\Re\gamma_k)s_k-s_k(s_k-1)\right],}\\ {{\rm subject\,to}\,\, s_1\geq0,\ldots,s_m\geq0\quad{\rm and}\quad \sum\limits_{k=1}^{m} s_k = n,}\end{array}$

have unique (integer) solutions for s ₁, . . . , s _m . A special case of our convergence result concerns the situation in which \({{\Re\gamma_1=\cdots=\Re\gamma_m=\alpha}}\) and n = mν with ν = 1, 2, . . . , for which the integer programming problems above have unique solutions, and it reads \({A^{(j)}_n-A=O(\theta^j\,j^{\alpha-2\nu})}\) as j → ∞. When compared with A _j ? A = O(θ ^j j ^α ) as j → ∞, this result shows that the Shanks transformation is a true convergence acceleration method for the sequences considered. In addition, we show that it is stable for the case being studied, and we also quantify its stability properties. The results of this work are the first ones pertaining to the Shanks transformation on general linear sequences with m > 1.

     

Lorentz effect imaging of ionic currents in solution

Current functional MRI techniques relying on hemodynamic modulations are inherently limited in their ability to accurately localize neural activity in space and time. To address these limitations, we previously proposed a novel technique based on the Lorentz effect and demonstrated its ability to directly image minute electrical activity with a millisecond temporal resolution in gel phantoms containing conductive wires as well as in the human median nerve in vivo. To better characterize its contrast mechanism and ultimately further improve its sensitivity for in vivo applications, we now apply this technique to image ionic currents in solution, which serve as a better model for neural conduction in biological systems than the electronic currents in conductive wires used in previous phantom studies. Our results demonstrate that ionic currents with durations and current densities on the same order of magnitude as those induced by neuroelectric activity in nerve fibers and in the brain can be detected.     

Series Expansions for the First Passage Distribution of Wong–Pearson Jump-Diffusions

Abstract

We explore the Erlang series approach for the first-time passage problem for a particular class of jump-diffusions with polynomial state-dependent coefficients. This approach may be viewed as a discrete analog of the Laplace transform, which replaces the differential equations with polynomial coefficients satisfied by this function by algebraic recurrences. We identify cases in which the expansion is finite and in which the recurrence is of second order, and thus more easily solved.