Natural factors of the Medvedev lattice capturing IPC

Skvortsova showed that there is a factor of the Medvedev lattice which captures intuitionistic propositional logic (IPC). However, her factor is unnatural in the sense that it is constructed in an ad hoc manner. We present a more natural example of such a factor. We also show that the theory of every non-trivial factor of the Medvedev lattice is contained in Jankov’s logic, the deductive closure of IPC plus the weak law of the excluded middle \({\neg p \vee \neg \neg p}\) . This answers a question by Sorbi and Terwijn.     

Template-aluminosilicate structures at the early stages of zeolite ZSM-5 formation. A combined preparative, solid-state NMR, and computational study

Species at three stages in the self-assembly of zeolite ZSM-5 have been studied with one- and two-dimensional magic-angle-spinning 13C, 27Al, 29Si, and 1H NMR spectroscopy and compared with the earlier proposed structures: (1) precursor species containing 33-36 T sites around a tetrapropylammonium (TPA) cation, (2) nanoslabs consisting of a flat 4 x 3 array of such precursors, and (3) the final TPA-ZSM-5 zeolite. Synthesis was carried out in D2O to suppress the water and silanol protons. Under such conditions, the effective Si-H and Al-H distances measured with 29Si-{1H} and 27Al-{1H} rotational echo double resonance (REDOR) reflect the interactions between TPA cations and the surrounding aluminosilica. The 29Si-{1H} REDOR curves for Q4-type silicon atoms at the three mentioned stages are closely similar, as well as the observed 27Al-1H REDOR curve for the precursor species compared to that for the TPA-ZSM-5. This indicates that in addition to externally attached TPA, there is also internal TPA already incorporated at an early stage into the aluminosilicate in a similar way as in the final zeolite, in accordance with the earlier proposed MFI self-assembly pathway (Kirschhock et al. Angew. Chem. Int. Ed. 2001, 40, 2637). However, the effective distances extracted from the initial REDOR curvatures are significantly (10-15%) larger than those computed for the model. Since there is no temperature effect, we tentatively assign this difference to a reduction of the 29Si-1H and 27Al-1H interactions by multispin decoherence effects or self-decoupling caused by proton spin diffusion. By assuming the computed model distances and fitting Anderson-Weiss curves to the observed REDOR data, we obtain similar "decoherence times" in the order of 0.1 ms. The observed 29Si-{1H} REDOR dephasing for the Q3 sites in the precursors is significantly faster than that for the Q4 sites. This is tentatively ascribed to a partial deuteron-proton back exchange at the silanol positions.     

Developing a new class of axial chiral phosphorus ligands: preparation and characterization of enantiopure atropisomeric phosphinines

Both enantiomers of the first atropisomeric phosphinine (1) have been isolated by using analytical HPLC on a chiral stationary phase. The enrichment of one enantiomer and a subsequent investigation into its racemization kinetics revealed a barrier for internal rotation of DeltaG(298)(double dagger) = (109.5+/-0.5) kJ mol(-1), which is in excellent agreement with the theoretically predicted value of DeltaG(298)(double dagger) =116 kJ mol(-1). Further analysis with UV and circular dichroism spectroscopies and density functional theory calculations led to the determination and assignment of the absolute configurations of both enantiomers. These results are the basis for future investigations into this new class of axially chiral phosphinine-based ligands and their possible applications in asymmetric homogeneous catalysis.     

Location of Mg cations in mordenite zeolite studied by IR spectroscopy and density functional theory simulations with a CO adsorption probe

The location of Mg cations in the channel of mordenite zeolite was studied using a combination of DFT simulations and IR spectroscopy of adsorbed CO. The calculated adsorption energies and frequencies of CO on Mg cations are in good agreement with the results from the IR spectra of adsorbed CO. It is found that the Mg cations can occupy the sites A, C, D and E in mordenite and the distribution of the Mg cations in these sites follows the priority order, site C > site A > site D and site E.     

Sub-micromolar affinity of Escherichia coli NikR for Ni(II)

The dissociation constant of Ni(II) for Escherichia coli NikR was determined using three independent techniques, including binding kinetics, and shown to be in the sub-micromolar range.     

Atropisomeric phosphinines: design and synthesis

The first atropisomeric phosphinine was designed and prepared by introducing substituents into specific positions of the heterocyclic framework; the presence of axial chirality was predicted by means of DFT calculations and experimentally verified by chiral HPLC analysis, derivatization experiments as well as temperature dependent 31P{1H} NMR spectroscopy.     

Kinetic Monte Carlo modeling of silicate oligomerization and early gelation†

We present a lattice-gas kinetic Monte Carlo model to investigate the formation of silicate oligomers, their aggregation and the subsequent gelation process. In the early oligomerization stage, the 3-rings are metastable, 5-rings and 6-rings are formed in very small quantities, 4-rings are abundant species, linear and branched species are transformed into more compact structures. Results reveal that the gelation proceeds from 4-ring containing species. A significant amount of 5-rings and 6-rings, sharing Si with 4-ring, form in the aging stage. These reveal the formation mechanism of silicate rings and clusters during zeolite synthesis.     

Sources and sinks: a stochastic model of evolution in heterogeneous environments

We study evolution driven by spatial heterogeneity in a stochastic model of source-sink ecologies. A sink is a habitat where mortality exceeds reproduction so that a local population persists only due to immigration from a source. Immigrants can, however, adapt to conditions in the sink by mutation. To characterize the adaptation rate, we derive expressions for the first arrival time of adapted mutants. The joint effects of migration, mutation, birth, and death result in two distinct parameter regimes. These results may pertain to the rapid evolution of drug-resistant pathogens and insects.