Ion binding to polyelectrolytes: Monte Carlo simulations versus classical mean field theories

The influence of ion size and surface charge model in titrations of ionizable polyelectrolytes is studied by means of the Semi Grand Canonical Monte Carlo simulation method in the context of the primitive model. Three models describing a discrete distribution of charged functional groups on the polyelectrolyte and different values for the radius of the background electrolyte spanning from ionic to hydrated radii values were analyzed. The polyelectrolyte titrations were simulated by calculating the degree of ionization versus pH curves at two ionic strengths. The results allow us to quantify the impact of the sizes of the background salt ions and surface functional groups of the polyelectrolyte on the dissociation degree. This influence is explained in terms of the effectiveness of the screening of the charged surface sites. Finally, by comparison with the Non-Linear Poisson–Boltzmann model, the influence of ionic correlations and finite size of the solution ions is assessed.     

Is there a unique consistent theory of quantum gravity?

Superstrings have been proposed as a quantum-theoretical framework for unifying all the fundamental forces, including gravity. We consider the question of whether there might be more general supersymmetric possibilities, based on higher extended objects such as membranes, jellies, etc. We argue that all the possible extended objects in all possible spacetime dimensions are quantummechanically inconsistent except for the 10-dimensional superstring and the 11-dimensional supermembrane. These are also the only two such theories that contain massless gravitons and, thus, that can describe gravity at low energies. It is remarkable that the range of possibilities can be narrowed down to this extent. Whether these can be further narrowed down to just one consistent theory remains open to further research.This essay received the first award from the Gravity Research Foundation for the year 1988.-Ed.     

Dimensionality switching through a thermally induced reversible single-crystal-to-single-crystal phase transition in a cyanide complex

The heterometallic hexanuclear cyanide-bridged complex {[Mn(bpym)(H(2)O)](2)[Fe(HB(pz)(3))(CN)(3)](4)} (1), its C(15)N and D(2)O enriched forms {[Mn(bpym)(H(2)O)](2)[Fe(HB(pz)(3))(C(15)N)(3)](4)} (2) and {[Mn(bpym)(D(2)O)](2)[Fe(HB(pz)(3))(CN)(3)](4)} (3), and the hexanuclear derivative complex {[Mn(bpym)(H(2)O)](2)[Fe(B(pz)(4))(CN)(3)](4)}·4H(2)O (4) [bpym = 2,2'-bipyrimidine, HB(pz)(3)(-) = hydrotris(1-pyrazolyl)borate, B(pz)(4)(-) = tetra(1-pyrazolyl)borate] have been synthesized. Their structures have been determined through single-crystal X-ray crystallography at different temperatures. Whereas 3 and 4 maintain a discrete hexanuclear motif during the entire temperature range investigated (down to 95 K), 1 and 2 exhibit a thermally induced reversible single-crystal to single-crystal phase transition driven by a remarkable concerted rearrangement of hydrogen and cyanide coordination bonds. While hexanuclear complexes are observed in the high temperature phases (noted 1a and 2a) above 200 K, the low temperature phases are composed of one-dimensional coordination polymers noted 1b and 2b. The magnetic properties of the four compounds have been investigated in the 2-300 K range, and they reveal the occurrence of an overall antiferromagnetic behavior. The thermal dependence of the optical reflectivity and the FT-IR absorbance have been studied for 1 in the range 10-300 K and 130-300 K, respectively. A comparative analysis of the structural and electronic properties for 1-4 clearly underlines the major role of the intermolecular interactions in the topological and dimensional rearrangement observed during the structural phase transition. This result opens new perspectives in the design of cyanide-based switchable magnetic materials using coordination bonds rearrangements.     

Reversibly Switchable Fluorescent Molecular Systems Based on Metallacarborane–Perylenediimide Conjugates

Icosahedral metallacarboranes are θ-shaped anionic molecules in which two icosahedra share one vertex that is a metal center. The most remarkable of these compounds is the anionic cobalt-based metallacarborane [Co(C₂B₉H₁₁)₂]⁻, whose oxidation-reduction processes occur via an outer sphere electron process. This, along with its low density negative charge, makes [Co(C₂B₉H₁₁)₂]⁻ very appealing to participate in electron-transfer processes. In this work, [Co(C₂B₉H₁₁)₂]⁻ is tethered to a perylenediimide dye to produce the first examples of switchable luminescent molecules and materials based on metallacarboranes. In particular, the electronic communication of [Co(C₂B₉H₁₁)₂]⁻ with the appended chromophore unit in these compounds can be regulated upon application of redox stimuli, which allows the reversible modulation of the emitted fluorescence. As such, they behave as electrochemically-controlled fluorescent molecular switches in solution, which surpass the performance of previous systems based on conjugates of perylendiimides with ferrocene. Remarkably, they can form gels by treatment with appropriate mixtures of organic solvents, which result from the self-assembly of the cobaltabisdicarbollide-perylendiimide conjugates into 1D nanostructures. The interplay between dye π-stacking and metallacarborane electronic and steric interactions ultimately governs the supramolecular arrangement in these materials, which for one of the compounds prepared allows preserving the luminescent behavior in the gel state.     

Sur l’annulation du deuxième foncteur de (co)homologie d’André-Quillen

For a given idealI of a commutative ringA, B=A/I, the vanishing of the second André-Quillen (co)homology functorH ₂ (A, B, δ) is characterized in terms of the canonical homomorphism α:S(I)→R(I) from the symmetric algebra of the idealI onto its Rees algebra. This is done by introducing a Koszul complex that characterizes commutative graded algebras which are symmetric algebras.

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This article was processed by the author using the LAT_EX style filecljour1 from Springer-Verlag.     

Automorphisms and weighted values

The notion of automorphism is an essential tool to capture the meaning of any mathematical structure. We apply this idea to cooperative games and obtain two interesting characterizations of the automorphisms of such a game: the one, in the complete case, as the permutations of players which preserve the (classical) Shapley value; the other, for the general case, as the permutations preservingall weighted Shapley values.Carreras' research supported by project UPV 036321-HA186/92 of the Basque Country University. Owen's research supported by the National Science Foundation, Grant DMS-9116416. This collaboration was made possible by the Polytechnic University of Catalonia, which sponsored Owen's visit to Terrassa.