Synthesis and electrochemical properties of a novel calix[4]arene derivative for facilitated transfer of alkali metal ions across water/1,2-dichloroethane micro-interface

The alkali metal ion transfers facilitated by a novel calix[4]arene derivative (OPEC) across the water/1,2-dichloroethane (1,2-DCE) micro-interface supported at the tip of a micropipette were presented. The well-defined voltammetric behaviours except Cs⁺ was obtained by cyclic voltammetry and differential pulse voltammetry. The bulk concentration of metal ions was much higher than that of OPEC in the performed measurements. The diffusion coefficient of OPEC in the 1,2-DCE phase was calculated as 5.18 ± 0.70 × 10^? 6 cm² s^? 1. On the basis of the changes of the half-wave transfer potentials, the logarithms of the association constants having 1:1 ionophore–ion complex stoichiometry for Li⁺, Na⁺, K⁺ and Rb⁺ in 1,2-DCE were determined as 4.80, 4.62, 4.98 and 5.32, respectively. The facilitated ion transfers were also evaluated by the Randles equivalent circuit used for ac-impedance data analysis.     

Three‐Dimensional Architectures Incorporating Stereoregular Donor–Acceptor Stacks

We report the synthesis of two [2]catenane‐containing struts that are composed of a tetracationic cyclophane (TC⁴⁺) encircling a 1,5‐dioxynaphthalene (DNP)‐based crown ether, which bears two terphenylene arms. The TC⁴⁺ rings comprise either 1) two bipyridinium (BIPY²⁺) units or 2) a BIPY²⁺ and a diazapyrenium (DAP²⁺) unit. These degenerate and nondegenerate catenanes were reacted in the presence of Cu(NO₃)₂?2.5 H₂O to yield Cu‐paddlewheel‐based MOF‐1050 and MOF‐1051. The solid‐state structures of these MOFs reveal that the metal clusters serve to join the heptaphenylene struts into grid‐like 2D networks. These 2D sheets are then held together by infinite donor–acceptor stacks involving the [2]catenanes to produce interpenetrated 3D architectures. As a consequence of the planar chirality associated with both the DNP and hydroquinone (HQ) units present in the crown ether, each catenane can exist as four stereoisomers. In the case of the nondegenerate (bistable) catenane, the situation is further complicated by the presence of translational isomers. Upon crystallization, however, only two of the four possible stereoisomers—namely, the enantiomeric RR and SS forms—are observed in the crystals. An additional element of co‐conformational selectivity is present in MOF‐1051 as a consequence of the substitution of one of the BIPY²⁺ units by a DAP²⁺ unit: only the translational isomer in which the DAP²⁺ unit is encircled by the crown ether is observed. The overall topologies of MOF‐1050 and MOF‐1051, and the selective formation of stereoisomers and translational isomers during the kinetically driven crystallization, provide evidence that weak noncovalent bonding interactions play a significant role in the assembly of these extended (super)structures.     

Facilitated Proton Transfer by a Novel 2-Aminothiazole Derivative Across the Water/1,2-Dichloroethane Interface

The behavior of proton transfer facilitated by a novel thiazole derivative, N-methyl-4-(4-phenoxyphenyl)thiazol-2-amine (MPPT), across the water/1,2-dichloroethane (1,2-DCE) interface was investigated electrochemically. The ionic partition diagram for MPPT was obtained from interpretation of the cyclic voltammograms. The apparent partition coefficient of MPPT was evaluated by the shaking-flask method under experimental conditions, while that for the protonated form of MPPT was calculated from its transfer potential obtained from the ionic partition diagram. It was suggested that the mechanism for transfer of MPPT across the water/1,2-DCE) interface depends on the pH of the aqueous phase. The parameters of the facilitated proton transfer across the water/1,2-DCE interface were evaluated as a quantitative measure of its lipophilicity.     

Experimental and modeling assessment of sulfur release from coal under low and high heating rates

Coal combustion releases elevated amounts of pollutants to the atmosphere including SO_X. During the pyrolysis step, sulfur present in the coal is released to the gas phase as many different chemical species such as H₂S, COS, SO₂, CS₂, thiols and larger tars, also called SO_X precursors, as they form SO_X during combustion. Understanding the sulfur release process is crucial to the development of reliable kinetic models, which support the design of improved reactors for cleaner coal conversion processes. Sulfur release from two bituminous coals, Colombian hard coal (K1) and American high sulfur coal (U2), were studied in the present work. Low heating rate (LHR) experiments were performed in a thermogravimetric analyzer coupled with mass spectrometry (TG-MS), allowing to track the mass loss and the evolution of many volatile species (CO, CO₂, CH₄, SO₂, H₂S, COS, HCl and H₂O). High heating rate (HHR) experiments were performed in an entrained flow reactor (drop-tube reactor – DTR), coupled with MS and nondispersive infrared sensor (NDIR). HHR experiments were complemented with CFD simulation of the multidimentional reacting flow field. A kinetic model of coal pyrolysis is employed to reproduce the experiments allowing a comprehensive assessment of the process. The suitability of this model is confirmed for LHR. The combination of HHR experiments with CFD simulations and kinetic modeling revealed the complexity of sulfur chemistry in coal combustion and allowed to better understand of the individual phenomena resulting in the formation of the different SO_X precursors. LHR and HHR operating conditions lead to different distribution of sulfur species released, highly-dependent on the gas-phase temperature and residence time. Higher retention of total sulfur in char is observed at LHR (63%) when compared to HHR (37–44%), at 1273 K. These data support the development of reliable models with improved predictability.     

Principal functions of non-selfadjoint matrix Sturm-Liouville equations

In this paper we investigate the principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem

     

Restriction varieties and geometric branching rules

This paper develops a new method for studying the cohomology of orthogonal flag varieties. Restriction varieties are subvarieties of orthogonal flag varieties defined by rank conditions with respect to (not necessarily isotropic) flags. They interpolate between Schubert varieties in orthogonal flag varieties and the restrictions of general Schubert varieties in ordinary flag varieties. We give a positive, geometric rule for calculating their cohomology classes, obtaining a branching rule for Schubert calculus for the inclusion of the orthogonal flag varieties in Type A flag varieties. Our rule, in addition to being an essential step in finding a Littlewood–Richardson rule, has applications to computing the moment polytopes of the inclusion of SO(n) in SU(n), the asymptotic of the restrictions of representations of SL(n) to SO(n) and the classes of the moduli spaces of rank two vector bundles with fixed odd determinant on hyperelliptic curves. Furthermore, for odd orthogonal flag varieties, we obtain an algorithm for expressing a Schubert cycle in terms of restrictions of Schubert cycles of Type A flag varieties, thereby giving a geometric (though not positive) algorithm for multiplying any two Schubert cycles.     

A multilateral Bailey lemma and multiple Andrews–Gordon identities

A multilateral Bailey lemma is proved, and multiple analogues of the Rogers–Ramanujan identities and Euler’s pentagonal theorem are constructed as applications. The extreme cases of the Andrews–Gordon identities are also generalized using the multilateral Bailey lemma where their final form are written in terms of determinants of theta functions.