Laboratory photo-chemistry of covalently bonded fluorene clusters: observation of an interesting PAH bowl-forming mechanism

The fullerene C$_{60}$, one of the largest molecules identified in the interstellar medium (ISM), has been proposed to form top-down through the photo-chemical processing of large (more than 60 C-atoms) polycyclic aromatic hydrocarbon (PAH) molecules. In this article, we focus on the opposite process, investigating the possibility that fullerenes form from small PAHs, in which bowl-forming plays a central role. We combine laboratory experiments and quantum chemical calculations to study the formation of larger PAHs from charged fluorene clusters. The experiments show that with visible laser irradiation, the fluorene dimer cation - [C$_{13}$H$_{9}$$-$C$_{13}$H$_{9}$]$^+$ - and the fluorene trimer cation - [C$_{13}$H$_{9}$$-$C$_{13}$H$_{8}$$-$C$_{13}$H$_{9}$]$^+$ - undergo photo-dehydrogenation and photo-isomerization resulting in bowl structured aromatic cluster-ions, C$_{26}$H$_{12}$$^+$ and C$_{39}$H$_{20}$$^+$, respectively. To study the details of this chemical process, we employ quantum chemistry that allows us to determine the structures of the newly formed cluster-ions, to calculate the hydrogen loss dissociation energies, and to derive the underlying reaction pathways. These results demonstrate that smaller PAH clusters (with less than 60 C-atoms) can convert to larger bowled geometries that might act as building blocks for fullerenes, as the bowl-forming mechanism greatly facilitates the conversion from dehydrogenated PAHs to cages. Moreover, the bowl-forming induces a permanent dipole moment that - in principle - allows to search for such species using radio astronomy.Comment: 8 pages, 7 figures, accepte

A New Curve Algebraically but not Rationally Uniformized by Radicals

We give a new example of a curve C algebraically, but not rationally, uniformized by radicals. This means that C has no map onto the projective line P^1 with solvable Galois group, while there exists a curve C' that maps onto C and has a finite morphism to P^1 with solvable Galois group. We construct such a curve C of genus 9 in the second symmetric product of a general curve of genus 2. It is also an example of a genus 9 curve that does not satisfy condition S(4,2,9) of Abramovich and Harris.Comment: 12 page

Conductivity of Mono- and Divalent Cations in the Microporous Zincosilicate VPI-9

Impedance spectroscopy is used to investigate the long-range ionic conductivity of the microporous, zincosilicate VPI-9 (Si/Zn = 4.0) (International Zeolite Association framework type VNI) containing the alkali cations Li^+, Na^+, K^+, Rb^+, and Cs^+, and the alkaline earth cations Mg^(2+), Ca^(2+), and Sr^(2+). Monovalent cation-exchanged samples Li- and Na-VPI-9 lose X-ray crystallinity upon vacuum dehydration at 450 °C, whereas K-, Rb-, and Cs-VPI-9 remain crystalline and exhibit conductivities of 1.7 × 10^(−4), 3.5 × 10^(−4), and 4.9 × 10^(−4) S/cm, respectively, at 450 °C and activation energies of 0.72, 0.64, and 0.69 eV, respectively, in the temperature range 150−450 °C. Divalent cation-exchanged sample Mg-VPI-9 also loses X-ray crystallinity, but Ca- and Sr-VPI-9 remain crystalline and exhibit conductivities of 2.3 × 10^(−6) S/cm and 7.7 × 10^(−7) S/cm, respectively, at 450 °C, and activation energies of 0.88 and 0.91 eV, respectively, over the temperature range 150−450 °C. When compared to aluminosilicate zeolite X (Si/Al = 1.25) exchanged with the same cations, all crystalline M-VPI-9 materials have greater conductivities than M-X, with the exception of K-X (1.6 × 10^(−3) S/cm at 450 °C), with the greatest differences arising between the divalent exchanged materials. Dense, crystalline zincosilicate samples with the compositions K_2ZnSi_xO_(2(x+1)) (x = 2−5), Rb_2ZnSi_5O_(12), and Cs_2ZnSi_5O_(12) are also prepared and characterized for comparison with the microporous materials and exhibit much lower conductivities than their microporous counterparts at the same composition

Equivariant Corks

For suitable finite groups G, we construct contractible 4-manifolds C with an effective G-action on $\partial C$ whose associated pairs (C,g) for all $g \in G$ are distinct smoothings of the pair $(C,\partial C)$. Indeed C embeds in a 4-manifold so that cutting out C and regluing using distinct elements of G yield distinct smooth 4-manifolds.Comment: 9 pages, 3 figure

Groupoid algebras as Cuntz-Pimsner algebras

We show that if $G$ is a second countable locally compact Hausdorff \'etale groupoid carrying a suitable cocycle $c:G\to\mathbb{Z}$, then the reduced $C^*$-algebra of $G$ can be realised naturally as the Cuntz-Pimsner algebra of a correspondence over the reduced $C^*$-algebra of the kernel $G_0$ of $c$. If the full and reduced $C^*$-algebras of $G_0$ coincide, we deduce that the full and reduced $C^*$-algebras of $G$ coincide. We obtain a six-term exact sequence describing the $K$-theory of $C^*_r(G)$ in terms of that of $C^*_r(G_0)$.Comment: 5 pages. V2: James Fletcher discovered an error Lemma 9. No other results are affected. In this version, statements (2) and (3), and the proof, of Lemma 9 have been corrected. Remark 10 has been added to give details of the error. An erratum will appear in Math Scand, referring to this version of the arXiv posting for detail