Particle shape optimization by changing from an isotropic to an anisotropic nanostructure: preparation of highly active and stable supported Pt catalysts in microemulsions

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.We recently introduced a new method to synthesize an active and stable Pt catalyst, namely thermo-destabilization of microemulsions (see R. Y. Parapat, V. Parwoto, M. Schwarze, B. Zhang, D. S. Su and R. Schomäcker, J. Mater. Chem., 2012, 22 (23), 11605–11614). We are able to produce Pt nanocrystals with a small size (2.5 nm) of an isotropic structure i.e. truncated octahedral and deposit them well on support materials. Although we have obtained good results, the performance of the catalyst still needed to be improved and optimized. We followed the strategy to retain the small size but change the shape to an anisotropic structure of Pt nanocrystals which produces more active sites by means of a weaker reducing agent. We found that our catalysts are more active than those we reported before and even show the potential to be applied in a challenging reaction such as hydrogenation of levulinic acid.DFG, EXC 314, Unifying Concepts in Catalysi

Particle shape optimization by changing from an isotropic to an anisotropic nanostructure: preparation of highly active and stable supported Pt catalysts in microemulsions

We recently introduced a new method to synthesize an active and stable Pt catalyst, namely thermo-destabilization of microemulsions (see R. Y. Parapat, V. Parwoto, M. Schwarze, B. Zhang, D. S. Su and R. Schomäcker, J. Mater. Chem., 2012, 22 (23), 11605–11614). We are able to produce Pt nanocrystals with a small size (2.5 nm) of an isotropic structure i.e. truncated octahedral and deposit them well on support materials. Although we have obtained good results, the performance of the catalyst still needed to be improved and optimized. We followed the strategy to retain the small size but change the shape to an anisotropic structure of Pt nanocrystals which produces more active sites by means of a weaker reducing agent. We found that our catalysts are more active than those we reported before and even show the potential to be applied in a challenging reaction such as hydrogenation of levulinic acid

Posets arising as 1-skeleta of simple polytopes, the nonrevisiting path conjecture, and poset topology

Given any polytope $P$ and any generic linear functional ${\bf c}$, one obtains a directed graph $G(P,{\bf c})$ by taking the 1-skeleton of $P$ and orienting each edge $e(u,v)$ from $u$ to $v$ for ${\bf c} (u) < {\bf c} ( v)$. This paper raises the question of finding sufficient conditions on a polytope $P$ and generic cost vector ${\bf c}$ so that the graph $G(P, {\bf c} )$ will not have any directed paths which revisit any face of $P$ after departing from that face. This is in a sense equivalent to the question of finding conditions on $P$ and ${\bf c}$ under which the simplex method for linear programming will be efficient under all choices of pivot rules. Conditions on $P$ and ${\bf c}$ are given which provably yield a corollary of the desired face nonrevisiting property and which are conjectured to give the desired property itself. This conjecture is proven for 3-polytopes and for spindles having the two distinguished vertices as source and sink; this shows that known counterexamples to the Hirsch Conjecture will not provide counterexamples to this conjecture. A part of the proposed set of conditions is that $G(P, {\bf c} )$ be the Hasse diagram of a partially ordered set, which is equivalent to requiring non revisiting of 1-dimensional faces. This opens the door to the usage of poset-theoretic techniques. This work also leads to a result for simple polytopes in which $G(P, {\bf c})$ is the Hasse diagram of a lattice L that the order complex of each open interval in L is homotopy equivalent to a ball or a sphere of some dimension. Applications are given to the weak Bruhat order, the Tamari lattice, and more generally to the Cambrian lattices, using realizations of the Hasse diagrams of these posets as 1-skeleta of permutahedra, associahedra, and generalized associahedra.Comment: new results for 3-polytopes and spindles added; exposition substantially improved throughou

Elections with Three Candidates Four Candidates and Beyond: Counting Ties in the Borda Count with Permutahedra and Ehrhart Quasi-Polynomials

In voting theory, the Borda count’s tendency to produce a tie in an election varies as a function of n, the number of voters, and m, the number of candidates. To better understand this tendency, we embed all possible rankings of candidates in a hyperplane sitting in m-dimensional space, to form an (m - 1)-dimensional polytope: the m-permutahedron. The number of possible ties may then be determined computationally using a special class of polynomials with modular coefficients. However, due to the growing complexity of the system, this method has not yet been extended past the case of m = 3. We examine the properties of certain voting situations for m ≥ 4 to better understand an election’s tendency to produce a Borda tie between all candidates