A simple proof of Hardy-Lieb-Thirring inequalities

We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schroedinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).Comment: 12 page

Catechin or quercetin guests in an intrinsically microporous polyamine (PIM-EA-TB) host: accumulation, reactivity, and release

Microporous polymer materials based on molecularly "stiff"structures provide intrinsic microporosity, typical micropore sizes of 0.5 nm to 1.5 nm, and the ability to bind guest species. The polyamine PIM-EA-TB contains abundant tertiary amine sites to interact via hydrogen bonding to guest species in micropores. Here, quercetin and catechin are demonstrated to bind and accumulate into PIM-EA-TB. Voltammetric data suggest apparent Langmuirian binding constants for catechin of 550 (±50) × 103 M-1 in acidic solution at pH 2 (PIM-EA-TB is protonated) and 130 (±13) × 103 M-1 in neutral solution at pH 6 (PIM-EA-TB is not protonated). The binding capacity is typically 1 : 1 (guest : host polymer repeat unit), but higher loadings are readily achieved by host/guest co-deposition from tetrahydrofuran solution. In the rigid polymer environment, bound ortho-quinol guest species exhibit 2-electron 2-proton redox transformation to the corresponding quinones, but only in a thin mono-layer film close to the electrode surface. Release of guest molecules occurs depending on the level of loading and on the type of guest either spontaneously or with electrochemical stimuli

Fuel cell anode catalyst performance can be stabilized with a molecularly rigid film of polymers of intrinsic microporosity (PIM)

There remains a major materials challenge in maintaining the performance of platinum (Pt) anode catalysts in fuel cells due to corrosion and blocking of active sites.</p

One-step preparation of microporous Pd@cPIM composite catalyst film for triphasic electrocatalysis

Triphasic microporous materials (containing solid, liquid, and gas) are of interest in electrocatalysis. In this exploratory study, a polymer of intrinsic microporosity (PIM-EA-TB) is impregnated with PdCl42− metal precursor and vacuum‑carbonised to give an electrically conductive microporous heterocarbon with embedded Pd nanoparticles of typically 10–30nm diameter. This microporous composite catalyst is formed (via spin-coating) as “flakes” of typically 100nm thickness and 1 to 20μm diameter that are readily re-deposited onto glassy carbon electrode substrates. Due to the triphasic conditions, Pd@cPIM electrocatalytic reactivity is high but only for gases (H2 oxidation or O2 reduction). This selectivity is observed even in the presence of excess formic acid fuel in the aqueous/liquid phase. The potential for application in membrane-less micro-fuel cells is discussed. Keywords: Gas binding, Triple phase reaction zone, Fuel cell, CO2 reduction, Microporosit

Hydrogen Peroxide Versus Hydrogen Generation at Bipolar Pd/Au Nano-catalysts Grown into an Intrinsically Microporous Polyamine (PIM-EA-TB)

Binding of PdCl42− into the polymer of intrinsic microporosity PIM-EA-TB (on a Nylon mesh substrate) followed by borohydride reduction leads to uncapped Pd(0) nano-catalysts with typically 3.2 ± 0.2 nm diameter embedded within the microporous polymer host structure. Spontaneous reaction of Pd(0) with formic acid and oxygen is shown to result in the competing formation of (i) hydrogen peroxide (at low formic acid concentration in air; with optimum H2O2 yield at 2 mM HCOOH), (ii) water, or (iii) hydrogen (at higher formic acid concentration or under argon). Next, a spontaneous electroless gold deposition process is employed to attach gold (typically 10- to 35-nm diameter) to the nano-palladium in PIM-EA-TB to give an order of magnitude enhanced production of H2O2 with high yields even at higher HCOOH concentration (suppressing hydrogen evolution). Pd and Au work hand-in-hand as bipolar electrocatalysts. A Clark probe method is developed to assess the catalyst efficiency (based on competing oxygen removal and hydrogen production) and a mass spectrometry method is developed to monitor/optimise the rate of production of hydrogen peroxide. Heterogenised Pd/Au@PIM-EA-TB catalysts are effective and allow easy catalyst recovery and reuse for hydrogen peroxide production

Effective electroosmotic transport of water in an intrinsically microporous polyamine (PIM-EA-TB)

Tertiary-amine-based Polymers of Intrinsic Microporosity (PIMs) provide a class of highly porous molecularly rigid materials for the electrochemical transport of both ionic and neutral species. Here, the transport of water molecules together with chloride anions (i.e. the electroosmotic drag coefficient) is studied for the intrinsically microporous polyamine PIM-EA-TB immersed in aqueous 0.01 M NaCl (i) when protonated for pH  4. Preliminary data suggest that in both cases a high electroosmotic drag coefficient is observed based on direct H2O transport into a D2O-filled compartment (quantified by 1H-NMR). For PIM-EA-TB there is a strong pH dependence with a higher electroosmotic drag coefficient in less acidic solutions (going from approx. 400 H2O per anion at pH 3 to approx. 4000 H2O per anion at pH 7), although the underlying absolute rate of water transport at a fixed voltage of −1 V appears to be essentially pH independent. Water transport through the PIM-EA-TB microchannels is rationalised based on the relative populations of chloride anions and of water in the micropores (essentially a ‘piston’ mechanism)