An approximate solution for planar solidification with Newton cooling at the surface

Summary The classical moving boundary problem for the planar freezing of a semi-infinite saturated liquid with Newton cooling at the wall is well known not to admit an exact solution. Existing perturbation solutions are valid only when the Stefan number is large. Further, since the implementation of the Newton cooling condition involves the step size, numerical solutions are only accurate if extremely small sizes are taken which involves large computing times. Here two new approximate analytic solutions are obtained, the first is an initial or starting solution while the second is valid for subsequent times. In the limit of large Stefan number the pseudo-steady state and first order corrected motions arise from both approximations. Further, in the limit of no Newton cooling at the wall the large time solution gives rise to precisely the well known Stefan or Neumann solution. The validity of the approximations is illustrated numerically with reference to previous work and known upper and lower bounds.

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Zusammenfassung Das klassische Problem der Bestimmung der variablen Grenze beim Gefrieren eines halbunendlich gesättigten Fluids mit Newton-Kühlung an der Wand besitzt bekanntlich keine geschlossene Lösung. Näherungslösungen sind nur für große Stefan-Zahlen bekannt. Bei Newton Kühlung erfordern die gängigen numerischen Methoden eine Schrittweite, die so klein ist, daß genaue Resultate große Rechenzeiten erfordern. Hier werden zwei Näherungslösungen konstruiert, die eine für kleine und die andere für große Zeiten. Im Fall einer großen Stefan-Zahl erhalten wir mit beiden Lösungen einen pseudostationären Zustand mit Korrekturen erster Ordnung. Der Grenzfall der verschwindenden Newton-Kühlung ergibt genau die bekannte Stefan-oder Neumann-Lösung. Im allgemeinen Fall wird die Gültigkeit der Näherung durch Vergleich mit Resultaten früherer Arbeiten sowie mit bekannten oberen und unteren Schranken verifiziert.

     

Investigation of drift gas selectivity in high resolution ion mobility spectrometry with mass spectrometry detection

Recent studies in electrospray ionization (ESI)/ion mobility spectrometry (IMS) have focussed on employing different drift gases to alter separation efficiency for some molecules. This study investigates four structurally similar classes of molecules (cocaine and metabolites, amphetamines, benzodiazepines, and small peptides) to determine the effect of structure on relative mobility changes in four drift gases (helium, nitrogen, argon, carbon dioxide). Collision cross sections were plotted against drift gas polarizability and a linear relationship was found for the nineteen compounds evaluated in the study. Based on the reduced mobility database, all nineteen compounds could be separated in one of the four drift gases, however, the drift gas that provided optimal separation was specific for the two compounds.     

Determination of residues of pirimicarb and its desmethyl and desmethylformamido metabolites in fruits and vegetables by liquid chromatography-electrospray/mass spectrometry

A method was developed for the simultaneous determination of residues of pirimicarb (I) and its desmethylformamido (II) and desmethyl (III) metabolites in plums, peas, green beans, broad beans, carrots, and swedes. The compounds were extracted with ethyl acetate and determined, without cleanup, by reversed-phase liquid chromatography and electrospray mass spectrometry (MS). MS and MS/MS were used concurrently to monitor the protonated molecules and their common collision-induced dissociation product. The limit of detection (signal-to-noise ratio of >3) was 1 ng/mL, corresponding to crop concentrations of <0.0015 mg/kg. All 3 compounds were determined in plums, broad beans, and green beans by MS without interference. Interferences which affected the determination of desmethylformamido-pirimicarb in peas, and to a lesser extent in carrots and swedes, were eliminated by MS/ MS. Recoveries for all 3 compounds, at 0.05 mg/kg for plums and 0.005 mg/kg for other commodities, were in the range 83-124%. No interconversion of I, II and III, occurred during extraction, and the compounds were stable in extracts for > or = 7 days under appropriate conditions.     

(Fe(III)(OH(2))(2))(3)(A-alpha-PW(9)O(34))(2)](9-) on cationic silica nanoparticles,a new type of material and efficient heterogeneous catalyst for aerobic oxidations

Polyoxometalates (POMs) electrostatically bind to silica nanoparticles coated with cationic aluminum oxide "(Si/AlO2)n+" to form a new type of material (the anionic POMs replace Cl- counterions associated with the cationic surface sites). Association of a new approximately D3h POM of formula [(FeIII(OH2)2)3(A-alpha-PW9O34)2]9- (1) with the cationic nanoparticles (to form "K81/(Si/AlO2)") was studied in detail. Elemental analysis, particle sizes from both laser light scattering and TEM before and after association of 1, the size of 1 from X-ray crystallography, and other methods provide mutually consistent data that indicate about 58 K8[(FeIII(OH2)2)3(A-alpha-PW9O34)2]- monoanions associate with the average nanoparticle (diameter of the K81/(Si/AlO2) product = approximately 17 nm). While heterogeneity of the cationic sites and roughness of the (Si/AlO2)n+ surfaces make the associated POMs structurally nonuniform, the equivalent of approximately 1 monolayer of 1 is present in K81/(Si/AlO2). Remarkably, while 1, the precursor (Si/AlO2)n+, and the components of 1, each alone, are inactive as catalysts for O2/air-based oxidation of sulfides or aldehydes in solution, K81/(Si/AlO2) is an active catalyst for both reactions (facile reaction with air at low temperature).     

Cupric decamolybdodivanadophosphate. A coordination polymer heterogeneous catalyst for rapid, high conversion, high selectivity sulfoxidation using the ambient environment

A new type of coordination network polymer involving the redox-active polyanion, PV(2)Mo(10)O(40)(5)(-), and bridging -Cu(II)(OH(2))(4)- units, [[(Cu(II)(OH(2))(4))(3)(OH)]PV(2)Mo(10)O(40)](n)() (1), has been characterized by X-ray crystallography and several other methods. It is the first efficient heterogeneous (insoluble) catalyst for selective and rapid sulfoxidation using only the ambient environment (air at room temperature). Catalytic activity is enhanced by soluble nitrate in nontoxic perfluoropolyether (PFPE) media.     

Thermal and mechanical properties of radiation crosslinked poly(tetrafluoroethylene-co-perfluoromethyl vinyl ether)

The effect of irradiation temperature on the polymer properties was investigated for the fluoroelastomer poly(tetrafluoroethylene-co-perfluoromethylvinyl ether) (TFE/PMVE). TFE/PMVE samples were γ-irradiated to 150 kGy at temperatures ranging from 77 K to 373 K. Analysis of the sol/gel behaviour, tensile properties, and glass transition temperatures indicated that crosslinking commenced in the temperature range 195 to 263 K, for a dose of 150 kGy. The latter temperature was 13 K below the glass transition temperature. Crosslinking remained relatively constant to higher temperatures. Chain scission reactions were found to occur well below the glass transition temperature and increased at higher temperatures. The optimum temperature for the radiation crosslinking of TFE/PMVE, for the temperatures investigated, was 263 K.     

Microfabrication of three-dimensional bioelectronic architectures

The functionality and structural diversity of biological macromolecules has motivated efforts to exploit proteins and DNA as templates for synthesis of electronic architectures. Although such materials offer promise for numerous applications in the fabrication of cellular interfaces, biosensors, and nanoelectronics, identification of techniques for positioning and ordering bioelectronic components into useful patterns capable of sophisticated function has presented a major challenge. Here, we describe the fabrication of electronic materials using biomolecular scaffolds that can be constructed with precisely defined topographies. In this approach, a tightly focused pulsed laser beam capable of promoting protein photo-cross-linking in specified femtoliter volume elements is scanned within a protein solution, creating biomolecular matrices that either remain in integral contact with a support surface or extend as free-standing structures through solution, tethered at their ends. Once fabricated, specific protein scaffolds can be selectively metallized via targeted deposition and growth of metal nanoparticles, yielding high-conductivity bioelectronic materials. This aqueous fabrication strategy opens new opportunities for creating electronic materials in chemically sensitive environments and may offer a general approach for creating microscopically defined inorganic landscapes.     

Rhodium carbene complexes as hydrosilylation catalysts

The catalytic activity of various rhodium carbene complexes has been investigated. These complexes are active for the hydrosilylation of a wide variety of unsaturated organic molecules such as olefins, acetylenes and dienes. Their activity is comparable to other rhodium(I) complexes previously used as hydrosilylation catalysts. The yield of products is found to vary with catalyst, silane and organic substrate.     

Hairdressing shish-kebabs; comprehensive survey and theoretical discussion of overgrowth crystallization

The platelet component of shish-kebabs crystallizes after the core, during cooling or storage below the formation temperature of the core. Three basic platelet morphologies were previously identified which were mutually interconvertible, a process we have termed “hairdressing”. In this paper we show that these three categories are special cases of a continuous range of overgrowth spacings. Crystallization at high temperatures gives widely spaced overgrowths and, as the crystallization temperature is reduced, so the overgrowth spacing decreases gradually. In the extreme case (only obtainable by quenching) the overgrowths become so close as to overlap and appear continuous. We also report a variety of further effects which were caused by exposing the shish-kebabs, while in solvent, to temperatures above their initial formation temperature. A new theoretical approach is described which considers the depletion of material available to form new overgrowths during crystallization. Two versions of this theory are presented (one a computer simulation and one analytic); interpreting our results on the basis of this theory we show that shish-kebabs crystallize at high temperatures even when quenched (90°C and above except in a few exceptional circumstances) and we are able to explain all the features of shish-kebab crystallization that we have observed.