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.

     

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.     

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.     

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.     

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.     

Reactions of trivacant Wells-Dawson heteropolytungstates. Ionic strength and Jahn-Teller effects on formation in multi-iron complexes

Reaction of alpha-P(2)W(15)O(56)(12-) and Fe(III) in a saturated NaCl solution produces a trisubstituted Wells-Dawson structure with three low-valent metals, alpha-(Fe(III)Cl)(2)(Fe(III)OH(2))P(2)W(15)O(59)(11-) (1). Dissolution of this species into 1 M NaBr (Br(-) is non-coordinating) gives the triaquated species alpha-(Fe(III)OH(2))(3)P(2)W(15)O(59)(9-) (2). Ionic strength values of 1 M or greater are necessary to avoid decomposition of 1 or 2 to the conventional sandwich-type complex, alpha beta beta alpha-(Fe(III)OH(2))(2)Fe(III)(2)(P(2)W(15)O(56))(2)(12-) (3). If the pH is greater than 5, a new triferric sandwich, alpha alpha beta alpha-(NaOH(2))(Fe(III)OH(2))Fe(III)(2)(P(2)W(15)O(56))(2)(14-) (4), forms rather than 3. Like the previously reported Wells-Dawson-derived sandwich-type structures with three metals in the central unit ([TM(II)Fe(III)(2)(P(2)W(15)O(56))(P(2)TM(II)(2)W(13)O(52))],(16-) TM = Cu, Co), this complex has a central alpha-junction and a central beta-junction. Thermal studies suggest that 4 is more stable than 3 over a wide range of temperatures and pH values. The intrinsic Jahn-Teller distortion of d-electron-containing metal ions incorporated into the external sites of the central multi-metal unit impacts the stoichiometry of their incorporation (with a consequent change in the inter-POM-unit connectivity, where POM = polyoxometalate). Reaction of non-distorting Ni(II) with the diferric lacunary sandwich-type POM alpha alpha alpha alpha-(NaOH(2))(2)Fe(III)(2)(P(2)W(15)O(56))(2)(16-) (5) produces alpha beta beta alpha-(Ni(II)OH(2))(2)Fe(III)(2)(P(2)W(15)O(56))(2)(14-) (6), a Wells-Dawson sandwich-type structure with two Ni(II) and two Fe(III) in the central unit. All structures are characterized by (31)P NMR, IR, UV-vis, magnetic susceptibility, and X-ray crystallography. Complexes 4 and 6 are highly selective and effective catalysts for the H(2)O(2)-based epoxidation of alkenes.     

Free‐volume variation in polyethylenes of different crystallinities: Positron lifetime,density, and X‐ray studies

High‐quality positron lifetime measurements (70 million total counts) are reported for polyethylenes (PEs) of different crystallinities (X_c = 3–82%). The specific volumes of the crystalline and amorphous phases (V_c and V_a, respectively) were estimated from density and wide‐angle X‐ray scattering (WAXS) experiments. Some samples (those with low values of X_c) were branched PEs, and those with high values of X_c were linear PEs for which X_c was varied with changes in the crystallization temperature. Both V_c and V_a increase with decreasing X_c in the range 0% ≤ X_c ≤ 56% (the branched PEs) but are constant for X_c ≥ 56% (the linear PEs). The lifetime spectra were analyzed with the MELT and LIFSPECFIT routines. Artifacts that can appear in the spectrum analysis were checked via an analysis of computer‐generated spectra. Four lifetime components appeared in all of the PEs; the two long‐lived ones are attributed to pick‐off annihilation of ortho‐positronium (o‐Ps) in crystalline regions (τ₃) and in holes of the amorphous phase (τ₄). With increasing X_c, τ₃ decreases from about 1.2 to 1 ns, τ₄ decreases from 3.0 to 2.5 ns, and the intensity I₄ decreases from 29 to 0%. An increase in I₃ from 6 to 12% was observed. A comparison with simulations shows that the true I₃ value approaches 0 for X_c → 0%. The decrease in I₄ is weaker than the increase in X_c; this leads to the conclusion that the apparent specific o‐Ps yield in the amorphous phase I₄^Xc increases with X_c. Possible reasons for this surprising results are discussed. The fractional free hole volume [h = (V_a ? V_occ)/V_a, where V_occ is the crystalline occupied volume] was estimated from density and WAXS results. Between X_c = 0 and 56%, h decreases from 0.151 to 0.090, but it does not change further above X_c = 56%. The mean size (v) of the local free volumes (holes) estimated from τ₄ decreases from 200 to 150 ų. The number density of holes (N_h) calculated from these values (N_h = h/v) also decreases from 0.8 to 0.6 nm^?3 in the range 0% ≤ X_c ≤ 56%. The values of V_a, V_c, h, and N_h increase with an increasing degree of branching but do not vary for linear PEs. The possible influence of a crystalline–amorphous interfacial phase (three‐phase model) on the observed lifetime parameters is also discussed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 65–81, 2002     

{(Mo)Mo5O21(H2O)3(SO4)}12(VO)30(H2O)20]36-: a molecular quantum spin icosidodecahedron

Self-assembly of aqueous solutions of molybdate and vanadate under reducing, mildly acidic conditions results in a polyoxomolybdate-based {Mo72V30} cluster compound Na8K16(VO)(H2O)5[K10 subset{(Mo)Mo5O21(H2O)3(SO4)}12(VO)30(H2O)20].150H2O, 1, a quantum spin-based Keplerate structure.     

Arsenic(III) halide complexes with acyclic and macrocyclic thio- and selenoether coligands: synthesis and structural properties

The preparations of the new complexes [AsBr(3)[MeS(CH(2))(2)SMe]], [AsX(3)([9]aneS(3))] (X = Cl, Br or I; [9]aneS(3) = 1,4,7-trithiacyclononane), [AsCl(3)([14]aneS(4))] ([14]aneS(4) = 1,4,8,11-tetrathiacyclotetradecane), [AsX(3)([8]aneSe(2))] ([8]aneSe(2) = 1,5-diselenacyclooctane), [(AsX(3))(2)([16]aneSe(4))] ([16]aneSe(4) = 1,5,9,13-tetraselenacyclohexadecane), and [(AsBr(3))(2)([24]aneSe(6))] ([24]aneSe(6) = 1,5,9,13,17,21-hexaselenacyclotetracosane) are described. These are obtained from direct reaction of the appropriate AsX(3) and 1 mol equiv of the thio- or selenoether ligand in anhydrous CH(2)Cl(2) (or thf for X = I) solution. The products have been characterized by microanalysis and IR and (1)H NMR spectroscopy. In solution they are extensively dissociated, reflecting the weak Lewis acidity of AsX(3). Reaction of AsX(3) with MeSe(CH(2))(2)SeMe or MeC(CH(2)EMe)(3) (E = S or Se) gave only oils. Treatment of PCl(3) or PBr(3) with Me(2)S, MeE(CH(2))(2)EMe, or [9]aneS(3) failed to give solid complexes, and there was no evidence from NMR spectroscopy for any adduct formation in solution. The crystal structures of the first series of thioether and selenoether complexes of As(III) are described: [AsBr(3)[MeS(CH(2))(2)SMe]], C(4)H(10)AsBr(3)S(2), a = 10.2818(6) A, b = 7.8014(5) A, c = 14.503(1) A, beta = 102.9330(2) degrees, monoclinic, P2(1)/c, Z = 4; [AsI(3)[MeS(CH(2))(2)SMe]], C(4)H(10)AsI(3)S(2), a = 9.1528(1) A, b = 11.5622(2) A, c = 12.0939(2) A, beta = 93.863(1) degrees, monoclinic, P2(1)()/n, Z = 4; [AsCl(3)([9]aneS(3))], C(6)H(12)AsCl(3)S(3), a = 17.520(4) A, b = 17.520(4) A, c = 16.790(7) A, tetragonal, I4(1)cd, Z = 16; [AsCl(3)([14]aneS(4))], C(10)H(20)AsCl(3)S(4), a = 13.5942(2) A, b = 7.7007(1) A, c = 18.1270(3) A, beta = 111.1662(5) degrees, monoclinic, P2(1)()/n, Z = 4; [(AsCl(3))(2)([16]aneSe(4))], C(12)H(24)As(2)Cl(6)Se(4), a = 9.764(3) A, b = 13.164(1) A, c = 10.627(2) A, beta = 114.90(1) degrees, monoclinic, P2(1)()/n, Z = 2; [(AsBr(3))(2)([16]aneSe(4))], C(12)H(24)As(2)Br(6)Se(4), a = 10.1220(1) A, b = 13.4494(2) A, c = 10.5125(2) A, beta = 113.49(2) degrees, monoclinic, P2(1)()/n, Z = 2. [AsBr(3)[MeS(CH(2))(2)SMe]] and [AsI(3)[MeS(CH(2))(2)SMe]] reveal discrete mu(2)-halo As(2)X(6) dimeric structures involving distorted octahedral As(III), with the dithioether ligand chelating. [AsCl(3)([9]aneS(3))] adopts a discrete molecular distorted octahedral geometry with the thioether behaving as a weakly coordinated fac-capping ligand. [AsCl(3)([14]aneS(4))] forms an infinite sheet involving two mu(2)-chloro ligands on each As but bridging to two distinct As centers. Each macrocycle coordinates to two adjacent As centers via one S atom, giving a cis-octahedral Cl(4)S(2) donor set at As(III). The structures of [(AsCl(3))(2)([16]aneSe(4))] and [(AsBr(3))(2)([16]aneSe(4))] adopt 2-dimensional sheet structures with mu(2)-dihalo As(2)X(6) dimers cross-linked by mu(4)-tetraselenoether macrocycles, giving a disorted cis-X(4)Se(2) donor set at each As center. These species are compared with their antimony(III) and bismuth(III) analogues where appropriate.