Very large, soluble endohedral fullerenes in the series La2C90 to La2C138: isolation and crystallographic characterization of La2@D5(450)-C100

An extensive series of soluble dilanthanum endohedral fullerenes that extends from La(2)C(90) to La(2)C(138) has been discovered. The most abundant of these, the nanotubular La(2)@D(5)(450)-C(100), has been isolated in pure form and characterized by single-crystal X-ray diffraction.     

Synthesis and structures of a pentanuclear Al(iii) phosphonate cage, an In(iii) phosphonate polymer, and coordination compounds of the corresponding phosphonate ester with GaI(3) and InCl(3)

A cationic, pentanuclear aluminium phosphonate cage, [L(4)Al(5)Cl(6)(THF)(6)]Cl, 1, supported by (phthalimidomethyl) phosphonate, (L), has been synthesized and characterized. This polynuclear cage features the phosphonate ligand in an unusual coordination mode, supporting five aluminium atoms in two different environments. In comparison, the aqueous reaction of LH(2) with In(ClO(4))(3) afforded [{(LH)In(H(2)O)}(H(2)O)(2)(ClO(4))](n), 2, an indium(iii) phosphonate coordination polymer, that has been crystallographically characterized. Reactions of the corresponding phosphonate ester, diethyl (phthalimidomethyl) phosphonate, (L'), with GaI(3) and InCl(3) afforded the simple coordination complexes, [L'·GaI(3)], 3, and [L'·InCl(3)(THF)], 4.     

Is the isolated pentagon rule merely a suggestion for endohedral fullerenes? The structure of a second egg-shaped endohedral fullerene--Gd3N@C(s)(39663)-C82

The structure of Gd3N@Cs(39663)-C82 has been determined through single crystal X-ray diffraction on Gd3N@Cs(39663)-C82.NiII(OEP).2(C6H6) The carbon cage has a distinct egg shape because of the presence of a single pair of fused pentagons at one apex of the molecule. Although 9 IPR structures are available to the C82 cage, one of the 39709 isomeric structures that do not conform to the IPR was found in Gd3N@Cs(39663)-C82. The egg-shaped structure of Gd3N@Cs(39663)-C82 is similar to that observed previously for M3N@Cs(51365)-C84 (M = Gd, Tm, Tb). As noted for other non-IPR endohedral fullerenes, one Gd atom in Gd3N@Cs(39663)-C82 is nestled within the fold of the fused pentagons.     

M2@C79N (M = Y, Tb): isolation and characterization of stable endohedral metallofullerenes exhibiting M-M bonding interactions inside aza[80]fullerene cages

Y2@C79N and Tb2@C79N have been prepared by conducting the Kratschmer-Huffman electric-arc process under 20 Torr of N2 and 280 Torr of He with metal oxide-doped graphite rods. These new heterofullerenes were separated from the resulting mixture of empty cage fullerenes and endohedral fullerenes by chemical separation and a two-stage chromatographic process. Crystallographic data for Tb2@C79N x Ni(OEP) x 2 C6H6 demonstrate the presence of an 80-atom cage with idealized I(h) symmetry and two, widely separated Tb atoms inside with a Tb-Tb separation of 3.9020(10) A for the major terbium sites. The EPR spectrum of the odd-electron Y2@C79N indicates that the spin density largely resides on the two equivalent yttrium ions. Computational studies on Y2@C79N suggest that the nitrogen atom resides at a 665 ring junction in the equator on the fullerene cage and that the unpaired electron is localized in a bonding orbital between the two yttrium ions of this stable radical. Thus, the Tb-Tb bond length of the single-electron bond is an exceedingly long metal-metal bond.     

Free surface problems in rheological fluid mechanics

Summary In this paper we review our work on the theory of domain perturbations of the rest state of a viscoelastic fluid and its applications to the science of rheometry. To explain the principle behind the domain perturbation analysis we begin the paper with a discussion of a model problem, free of rheological complications, in which the principles involved may be clearly demonstrated. In Chapter two we formulate the analysis for rheological problems and we present some new, previously unpublished, simplifications of the theory. The canonical forms for stress tensors which perturb the state of rest are given in Chapter three. Chapter four is devoted to the problem of steady rod climbing. There we discuss the main physical features of the motion, the phenomenon of the critical radius, the effects of surface tension and temperature, secondary motions, the applicability of theory and experiment for rheological measurements, and an interesting new normal stress anplifier. Unsteady problems of rod climbing are considered in Chapter five. We review recent results on the free surface induced by torsional oscillations of a rod, and we show how to use these results to find the form of the material functions in the canonical forms of the stress. The breathing instability of steady axisymmetric rod climbing (aHopf bifurcation) and the flower instability of time-periodic climb induced by the oscillating rod (a symmetry-breakingPoincaré bifurcation) are also described in Chapter five. In Chapter six we consider other free surface problems: the free surface on a fluid between oscillating planes, die swell and edge effects in rheometers.

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Zusammenfassung Es wird ein Überblick über die Untersuchungen der Verfasser zum Thema Gebietsstörungen des Ruhezustandes (domain perturbations of the rest state) einer viskoelastischen Flüssigkeit und ihre Anwendung auf die Rheometrie gegeben. Zur Erläuterung der Grundlagen der Gebietsstörungs-Analyse wird in Kap. 1 die Diskussion eines Modellproblems vorangestellt, das keinerlei rheologische Komplikationen enthält, so daß die betreffenden Prinzipien in einfacher Weise erläutert werden können. In Kap. 2 wird die Analyse auf rheologische Probleme angewendet, und es werden einige bisher unveröffentlichte Vereinfachungen der Theorie vorgestellt. In Kap. 3 werden die kanonischen Formen der die Störung des Ruhezustandes hervorrufenden Spannungstensoren angegeben. In Kap. 4 wird das Problem des Hochkletterns einer Flüssigkeit am stationär rotierenden Zylinder behandelt. Dabei werden die Hauptmerkmale der Bewegung, das Phänomen des kritischen Radius, die Wirkung von Oberflächenspannung und Temperatur, Sekundärbewegungen, die Anwendbarkeit von Theorie und Experiment auf rheologische Messungen, sowie ein interessanter neuer Normalspannungs-Verstärker diskutiert. In Kap. 5 wird das Problem des Hochkletterns bei instationärer Bewegung des Zylinders betrachtet. Es werden neuere Ergebnisse über die durch eine Torsionsschwingung erzeugte freie Oberfläche referiert, und es wird gezeigt, wie diese Ergebnisse zur Bestimmung der Stoff-Funktionen in der kanonischen Darstellung der Spannungen verwendet werden können. Die atmende Instabilität beim stationären Hochklettern (eine Verzweigungslösung vomHopfschen Typ) und die blütenförmige Instabilität beim zeitlich-periodischen Hochklettern infolge der Zylinder-Oszillation (eine die Symmetrie brechende Verzweigungslösung vomPoincaréschen Typ) werden hier ebenfalls beschrieben. In Kap. 6 schließlich werden weitere an freien Oberflächen auftretende Probleme behandelt: nämlich die freie Oberfläche einer Flüssigkeit zwischen oszillierenden Platten, die Strahlaufweitung und die Randeffekte in Rheometern.

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With 13 figures