On Rado's Boundedness Conjecture

We prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Studien zur Kombinatorik is true if it is true for homogeneous equations. We then prove the first nontrivial case of Rado's Boundedness Conjecture: if a₁,a₂, and a₃ are integers, and if for every 24-coloring of the positive integers (or even the nonzero rational numbers) there is a monochromatic solution to the equation a₁x₁+a₂x₂+a₃x₃=0, then for every finite coloring of the positive integers there is a monochromatic solution to a₁x₁+a₂x₂+a₃x₃=0.     

Comparative Study of Natural Terpenoid Precursors in Reactive Plasmas for Thin Film Deposition

If plasma polymer thin films are to be synthesised from sustainable and natural precursors of chemically heterogeneous composition, it is important to understand the extent to which this composition influences the mechanism of polymerisation. To this end, a well-studied monoterpene alcohol, terpinen-4-ol, has been targeted for a comparative study with the naturally occurring mix of terpenes (viz. Melaleuca alternifolia oil) from which it is commonly distilled. Positive ion mode mass spectra of both terpinen-4-ol and M. alternifolia oil showed a decrease in disparities between the type and abundance of cationic species formed in their respective plasma environments as applied plasma power was increased. Supplementary biological assay revealed the antibacterial action of both terpinen-4-ol and M. alternifolia derived coatings with respect to S. aureus bacteria, whilst cytocompatibility was demonstrated by comparable eukaryotic cell adhesion to both coatings. Elucidating the processes occurring within the reactive plasmas can enhance the economics of plasma polymer deposition by permitting use of the minimum power, time and precursor pre-processing required to control the extent of monomer fragmentation and fabricate a film of the desired thickness and functionality.     

Use of Lanthanide‐Containing Polyoxometalates to Sensitise the Emission of Fluorescent Labelled Serum Albumin

Monitoring the interaction of biomolecules is important, and the use of energy transfer is a principal technique in elucidating nanoscale interactions. Lanthanide compounds are promising luminescent probes for biological samples as their emission is longer‐lived than any native autofluorescence. Polyoxometalates (POMs) are interesting structural motifs to incorporate lanthanides, offering low toxicity and a size pertinent for biological applications. Here, we employ iso‐structured POMs containing either terbium or europium and assess their interaction with serum albumin by sensitisation of a fluorescent tag on the protein via LRET (luminescence resonance energy transfer) by exciting the lanthanide. Time‐resolved measurements showed energy transfer with an efficiency of over 90 % for the POM–protein systems. The Tb–POM results were relatively straightforward, while those with the iso‐structured Eu–POM were complicated by the effect of protein shielding from the aqueous environment.     

Electrochemical origin of voltage-controlled molecular conductance switching

We have studied electron transport in bipyridyl-dinitro oligophenylene-ethynelene dithiol (BPDN) molecules both in an inert environment and in aqueous electrolyte under potential control, using scanning tunneling microscopy. Current-voltage (IV) data obtained in an inert environment were similar to previously reported results showing conductance switching near 1.6 V. Similar measurements taken in electrolyte under potential control showed a linear dependence of the bias for switching on the electrochemical potential. Extrapolation of the potentials to zero switching bias coincided with the potentials of redox processes on these molecules. Thus switching is caused by a change in the oxidation state of the molecules.     

Study on structural properties and solution dynamics of zinc complexes with the (N,N-dimethylaminomethyl)ferrocenyl ligand

The reaction of {C,N-[Fe(η⁵-C₅H₅)(η⁵-C₅H₃(CH₂NMe₂)-2)]}Li, (FcN)Li, with zinc chloride affords the diorganozinc complex (FcN)₂Zn (1). In solution, 1 appears as a mixture of rac and meso diastereomers, whereas in the solid state it crystallizes solely as a rac diastereomer. The ratio of rac/meso diastereomers in solution is solvent-, temperature- and concentration-dependent, consistent with an intermolecular exchange between diastereomers. An intramolecular dynamic phenomenon involving dissociation and recoordination of Zn---N bonds was also observed. The reaction of 1 with zinc chloride yields the monoorganozinc compound (FcN)ZnCl (2) as a slightly soluble yellow microcrystalline powder.     

Experimental studies on the applicability of the Kelvin equation to highly curved concave menisci

The thermodynamic properties of liquids trapped in microscopic pores are described in theory by the Kelvin equation, which relates the equilibrium meniscus curvature to the relative vapor pressure. We report here two series of experiments designed to test the validity of the Kelvin equation by direct measurement of the mean radius of curvature of the surface of cyclohexane condensed between crossed mica cylinders. In one series of experiments, the relative vapor pressure of the volatile cyclohexane was controlled by mixing it with a relatively involatile solute (n-dodecane or n-hexadecane). We found that the mean radius of curvature rapidly reached that predicted by the Kelvin equation at each relative vapor pressure of the volatile liquid, but that there was also a slow, but continuous, accumulation of the “involatile” solute at the point of condensation as the system approached true equilibrium. Such accumulation of very low vapor pressure materials may be one factor responsible for the discordant results reported by earlier workers. We find that the process of impurity buildup is complex, and suggest that studies of real porous systems may be affected by accumulation of “involatile” impurities through the vapor phase and by surface diffusion. The other series of experiments was designed to eliminate the impurity problem by maintaining the vapor pressure by temperature control of the pure liquid. The results from this series of experiments were not time dependent, and no evidence of contamination was found. The measured radii were within ±6% of those predicted by the Kelvin equation, for radii in the range 4–20 nm. We conclude that the thermodynamic basis of the Kelvin equation is valid in principle for menisci with radii as low as 4 nm.     

Bond dissociation energies and radical stabilization energies associated with model peptide-backbone radicals

Bond dissociation energies (BDEs) and radical stabilization energies (RSEs) have been calculated for a series of models that represent a glycine-containing peptide-backbone. High-level methods that have been used include W1, CBS-QB3, U-CBS-QB3, and G3X(MP2)-RAD. Simpler methods used include MP2, B3-LYP, BMK, and MPWB1K in association with the 6-311+G(3df,2p) basis set. We find that the high-level methods produce BDEs and RSEs that are in good agreement with one another. Of the simpler methods, RBMK and RMPWB1K achieve good accuracy for BDEs and RSEs for all the species that were examined. For monosubstituted carbon-centered radicals, we find that the stabilizing effect (as measured by RSEs) of carbonyl substituents (CX=O) ranges from 24.7 to 36.9 kJ mol(-1), with the largest stabilization occurring for the CH=O group. Amino groups (NHY) also stabilize a monosubstituted alpha-carbon radical, with the calculated RSEs ranging from 44.5 to 49.5 kJ mol(-1), the largest stabilization occurring for the NH2 group. In combination, NHY and CX=O substituents on a disubstituted carbon-centered radical produce a large stabilizing effect ranging from 82.0 to 125.8 kJ mol(-1). This translates to a captodative (synergistic) stabilization of 12.8 to 39.4 kJ mol(-1). For monosubstituted nitrogen-centered radicals, we find that the stabilizing effect of methyl and related (CH2Z) substituents ranges from 25.9 to 31.7 kJ mol(-1), the largest stabilization occurring for the CH3 group. Carbonyl substituents (CX=O) destabilize a nitrogen-centered radical relative to the corresponding closed-shell molecule, with the calculated RSEs ranging from -30.8 to -22.3 kJ mol(-1), the largest destabilization occurring for the CH=O group. In combination, CH2Z and CX=O substituents at a nitrogen radical center produce a destabilizing effect ranging from -19.0 to -0.2 kJ mol(-1). This translates to an additional destabilization associated with disubstitution of -18.6 to -7.8 kJ mol(-1).     

Mechanism of hierarchical porosity development in MFI zeolites by desilication: the role of aluminium as a pore-directing agent

The role of the concentration and the nature of aluminium in the creation of hierarchical porosity in both commercial and synthesized MFI zeolites have been investigated through controlled mesoporosity development by desilication in alkaline medium. Framework aluminium controls the process of framework silicon extraction and makes desilication selective towards intracrystalline mesopore formation. An optimal molar Si/Al ratio in the range 25-50 has been identified; this leads to an optimal mesoporosity centred around 10 nm and mesopore surface areas of up to 235 m(2) g(-1) while preserving the intrinsic crystalline and acidic properties. At lower framework Si/Al ratios the relatively high Al content inhibits Si extraction and hardly any mesopores are created, while in highly siliceous ZSM-5 unselective extraction of framework Si induces formation of large pores. The existence of framework Al sites in different T positions that are more or less susceptible to the alkaline treatment, and the occurrence of re-alumination, are tentative explanations for the remarkable behaviour of Al in the desilication process. The presence of substantial extra framework Al, obtained by steam treatment, inhibits Si extraction and related mesopore formation; this is attributed to re-alumination of the extraframework Al species during the alkaline treatment. Removal of extraframework Al species by mild oxalic acid treatment restores susceptibility to desilication, which is accompanied by formation of larger mesopores due to the enhanced Si/Al ratio in the acid-treated zeolite.