A characterization of some q-orthogonal polynomials

We show that the only orthogonal polynomials satisfying a q-difference equation of the form π(x)D _q P _n (x) = (α _n x + β _n )P _n (x) + γ _n P _n−1(x) where π(x) is a polynomial of degree 2, are the Al-Salam Carlitz 1, little and big q-Laguerre, the little and big q-Jacobi, and the q-Bessel polynomials. This is a q-analog of the work carried out in [1]. 2000 Mathematics Subject Classification Primary—33C45, 33D45     

Process-Structure-Formulation Interactions for Enhanced Sodium Ion Battery Development: A Review

Before the viability of a cell formulation can be assessed for implementation in commercial sodium ion batteries, processes applied in cell production should be validated and optimized. This review summarizes the steps performed in constructing sodium ion (Na-ion) cells at research scale, highlighting parameters and techniques that are likely to impact measured cycling performance. Consistent process-structure-performance links have been established for typical lithium-ion (Li-ion) cells, which can guide hypotheses to test in Na-ion cells. Liquid electrolyte viscosity, sequence of mixing electrode slurries, rate of drying electrodes and cycling characteristics of formation were found critical to the reported capacity of laboratory cells. Based on the observed importance of processing to battery performance outcomes, the current focus on novel materials in Na-ion research should be balanced with deeper investigation into mechanistic changes of cell components during and after production, to better inform future designs of these promising batteries.     

One-pot synthesis of MWW zeolite nanosheets using a rationally designed organic structure-directing agent

A new material MIT-1 comprised of delaminated MWW zeolite nanosheets is made in a one-pot synthesis using a rationally designed organic structure-directing agent (OSDA). The OSDA consists of a hydrophilic head segment that resembles the OSDA used to synthesize the zeolite precursor MCM-22(P), a hydrophobic tail segment that resembles the swelling agent used to swell MCM-22(P), and a di-quaternary ammonium linker that connects both segments. MIT-1 features high crystallinity and surface areas exceeding 500 m² g^–1, and can be synthesized over a wide synthesis window that includes Si/Al ratios ranging from 13 to 67. Characterization data reveal high mesoporosity and acid strength with no detectable amorphous silica phases. Compared to MCM-22 and MCM-56, MIT-1 shows a three-fold increase in catalytic activity for the Friedel–Crafts alkylation of benzene with benzyl alcohol.     

Heteronuclear chemical shift correlation and J-resolved MAS NMR spectroscopy of lipid membranes

Direct observation of J-couplings remains a challenge in high-resolution solid-state NMR. In some cases, it is possible to use Lee-Goldburg (LG) homonuclear decoupling during rare spin observation in MAS NMR correlation spectroscopy of lipid membranes to obtain J-resolved spectra in the direct dimension. In one simple implementation, a wide line separation-type (13)C-(1)H HETCOR can provide high-resolution (1)H/(13)C spectra, which are J-resolved in both dimensions. Coupling constants, (1)J(HC), obtained from (1)H doublets, can be compared with scaled (1)J(θ)(CH)-values obtained from the (13)C multiplets to assess the LG efficiency and scaling factor. The use of homonuclear decoupling during proton evolution, LG-HETCOR-LG, can provide J-values, at least in the rare spin dimension, and allows measurements in less mobile membrane environments. The LG-decoupled spectroscopic approach is demonstrated on pure dioleoylphosphatidylcholine (DOPC) membranes and used to investigate lipid mixtures of DOPC/cholesterol and DOPC/cholesterol/sphingomyelin.     

Effects of mutation on the amyloidogenic propensity of apolipoprotein C-II(60-70) peptide

Using experimental and computational methods we identified the effects of mutation on the structure and dynamics of the amyloidogenic peptide apoC-II(60-70), in monomeric and oligomeric states. Methionine (Met60) substitutions to hydrophilic Gln, hydrophobic Val, and methionine sulfoxide residues were investigated and the results compared with observations of fibril formation by the wild-type, Met60Gln, Met60Val, and oxidised Met60 (oxi-Met) apoC-II(60-70) peptides. ThT fluorescence measurements showed fibril formation by all peptides, however with different kinetics. The wild-type and Met60Val peptides formed fibrils fastest, while oxi-Met and Met60Gln peptides exhibited significantly longer lag phases. Molecular dynamics simulations showed that the mutated monomers exhibited structural features consistent with fibril-forming propensity, such as β-hairpin conformation and a hydrophobic core. However, important differences to the wild-type were also noted, such as increased structural flexibility (oxi-Met and Met60Gln systems) and a broader distribution of the aromatic angle orientation, which could contribute to the different fibrillation kinetics observed in these peptides. Our results also showed that the critical nucleus size for fibril formation by apoC-II(60-70) may not be very large, since tetrameric oligomers in anti-parallel configuration were very stable within the 100 ns of simulations. The single-point mutations Met60Val and Met60Gln had no significant effect on the structural stability of the tetramer. The rate of fibril formation by apoC-II(60-70) peptides was generally much faster compared to longer apoC-II(56-76) peptides. Also, the effects of amino acid modifications on the kinetics of peptide fibril formation differ from the effects observed for apoC-II(56-76) and full-length apoC-II, suggesting that additional mechanisms are involved in fibril formation by mature apoC-II.     

Photoinduced electron transfer and solvation in iodide-doped acetonitrile clusters

We have used ultrafast time-resolved photoelectron imaging to measure charge transfer dynamics in iodide-doped acetonitrile clusters I(-)(CH(3)CN)(n) with n = 5-10. Strong modulations of vertical detachment energies were observed following charge transfer from the halide, allowing interpretation of the ongoing dynamics. We observe a sharp drop in the vertical detachment energy (VDE) within 300-400 fs, followed by a biexponential increase that is complete by approximately 10 ps. Comparison to theory suggests that the iodide is internally solvated and that photodetachment results in formation of a diffuse electron cloud in a confined cavity. We interpret the initial drop in VDE as a combination of expansion of the cavity and localization of the excess electron on one or two solvent molecules. The subsequent increase in VDE is attributed to a combination of the I atom leaving the cavity and rearrangement of the acetonitrile molecules to solvate the electron. The n = 5-8 clusters then show a drop in VDE of around 50 meV on a much longer time scale. The long-time VDEs are consistent with those of (CH(3)CN)(n)(-) clusters with internally solvated electrons. Although the excited-state created by the pump pulse decays by emission of a slow electron, no such decay is seen by 200 ps.     

In situ temperature-jump dynamic nuclear polarization: enhanced sensitivity in two dimensional 13C-13C correlation spectroscopy in solution

Dynamic nuclear polarization is combined with temperature-jump methods to develop a new 2D 13C-13C NMR experiment that yields a factor of 100-170 increase in sensitivity. The polaization step is performed at 100 K, and the sample is subsequently melted with a 10.6 microm laser pulse to yield a sample with highly polarized 13C spins. 13C detected 2D 13C-13C spectroscopy is performed in the usual manner.