Dynamics of a triphenylene discotic molecule,HAT6, in the columnar and isotropic liquid phases

Discotic molecules have planar, disklike polyaromatic cores that can self-assemble into "molecular wires". Highly anisotropic charge transfer along the wires arises when there is sufficient intermolecular overlap of the pi-orbitals of the molecular cores. Discotic materials can be applied in molecular electronics, field-effect transistors, and-recently with record quantum efficiencies-photovoltaics (Schmidt-Mende, L.; Fechtenk?tter, A.; Müllen, K.; Moons, E.; Frien, R. H.; MacKenzie, J. D. Science 2001, 293, 1119). A combination of quasielastic neutron scattering (QENS) measurements with molecular dynamics simulations on the discotic molecule hexakis(n-hexyloxy)triphenylene (HAT6) shows that the dynamics of the cores and tails of discotic molecules are strongly correlated. Core and tail dynamics are not separated, the system being characterized by overall in-plane motion, on a time scale of 0.2 ps, and softer out-of-plane motions at 7 ps. Because charge transfer between the molecules is on similar time scales, these motions are relevant for the conducting properties of the materials. Both types of motion are dominated by van der Waals interactions. Small-amplitude in-plane motions in which the disks move over each other are almost entirely determined by tail/tail interactions, these also playing an important role in the out-of-plane motion. The QENS measurements reveal that these motions are little changed by passing from the columnar phase to the isotropic liquid phase, just above the clearing temperature. The model of four HAT6 molecules in a column reproduces the measured QENS spectrum of the liquid phase, suggesting that correlations persist within the liquid phase over about this number of disks.     

Independence of inadmissible strategies and best reply stability: a direct proof

Hillas (1990) introduced a definition of strategic stability based on perturbations of the best reply correspondence that satisfies all of the requirements given by Kohlberg and Mertens (1986). Hillas et al. (2001) point out though that the proofs of the iterated dominance and forward induction properties were not correct. They also provide a proof of the IIS property, a stronger version of both iterated dominance and forward induction, using the results of that paper. In this note we provide a direct proof of the IIS property.Received February 2002     

A family of quantum projective spaces and related -hypergeometric orthogonal polynomials

A one-parameter family of two-sided coideals in is defined and the corresponding algebras of infinitesimally right invariant functions on the quantum unitary group are studied. The Plancherel decomposition of these algebras with respect to the natural transitive -action is shown to be the same as in the case of a complex projective space. By computing the radial part of a suitable Casimir operator, we identify the zonal spherical functions (i.e. infinitesimally bi-invariant matrix coefficients of finite-dimensional irreducible representations) as Askey-Wilson polynomials containing two continuous and one discrete parameter. In certain limit cases, the zonal spherical functions are expressed as big and little -Jacobi polynomials depending on one discrete parameter.

     

Player splitting in extensive form games

By a player splitting we mean a mechanism that distributes the information sets of a player among so-called agents. A player splitting is called independent if each path in the game tree contains at most one agent of every player. Following Mertens (1989), a solution is said to have the player splitting property if, roughly speaking, the solution of an extensive form game does not change by applying independent player splittings. We show that Nash equilibria, perfect equilibria, Kohlberg-Mertens stable sets and Mertens stable sets have the player splitting property. An example is given to show that the proper equilibrium concept does not satisfy the player splitting property. Next, we give a definition of invariance under (general) player splittings which is an extension of the player splitting property to the situation where we also allow for dependent player splittings. We come to the conclusion that, for any given dependent player splitting, each of the above solutions is not invariant under this player splitting. The results are used to give several characterizations of the class of independent player splittings and the class of single appearance structures by means of invariance of solution concepts under player splittings. Received: December 1996/Revised Version: January 2000     

Tunable biohybrid hydrogels from coacervation of hyaluronic acid and PEO-based block copolymers

Accurately tuning the macroscopic properties of biopolymer-based hydrogels remains challenging due to the ill-defined molecular architecture of the natural building blocks. Here, we report a biohybrid coacervate hydrogel, combining the biocompatibility and biodegradability of naturally occurring hyaluronic acid (HA) with the tunability of a synthetic polyethylene oxide (PEO) -based ABA-triblock copolymer. Coacervation of the cationic ammonium or guanidinium-functionalized copolymer A-blocks with the anionic HA leads to hydrogel formation. Both mechanical properties and water content of the self-healing hydrogels can be controlled independently by altering the copolymer structure. By controlling the strength of the interaction between the polymer network and small-molecule cargo, both release rate and maximum release are controlled. Finally, we show that coacervation of HA and the triblock copolymer leads to increased biostability upon exposure to hyaluronidase. We envision that noncovalent crosslinking of HA hydrogels through coacervation is an attractive strategy for the facile synthesis of tunable hydrogels for biomedical applications.     

Linear alkylbenzene sulfonates (LAS) in sewage sludges, soils and sediments: analytical determination and environmental safety considerations

Linear Alkylbenzenesulphonates (LAS), a major anionic surfactant used in laundry products, can be measured specifically in the environment by instrumental analysis. In addition to a desulphonation-gas chromatography approach, a method based on high performance liquid chromatography has been developed. The main features of the methods are outlined, and LAS concentrations measured in sewage sludge, sediments and sludge amended soils are reported. Knowledge of usage volumes, sewage treatment practices and environmental transport and transformation mechanisms has been used to predict concentrations of LAS. These calculated concentrations were found to agree well with those actually measured in the environment. Both measured and calculated ambient concentrations of LAS are below those which could produce potentially adverse effects in representative surface water, benthic and terrestrial organisms.     

On the set of proper equilibria of a bimatrix game

In this paper it is proved that the set of proper equilibria of a bimatrix game is the finite union of polytopes. To that purpose we split up the strategy space of each player into a finite number of equivalence classes and consider for a given >0 the set of all -proper pairs within the cartesian product of two equivalence classes. If this set is non-empty, its closure is a polytope. By considering this polytope as goes to zero, we obtain a (Myerson) set of proper equilibria. A Myerson set appears to be a polytope.     

Helical bias in supramolecular polymers accounts for different stabilities of kinetically trapped states

The idea to synthesize and self-assemble nano-graphenes with structural precision into supramolecular polymers is just one of Klaus Müllen's many pioneering contributions to the chemical sciences. To honor his impact in the field of polymer science, we here describe a study that combines experimental and computational methods in studying the stability of kinetically trapped states of supramolecular polymers. We show that the introduction of stereocenters in the sidechains allow helical supramolecular polymers based on chiral triphenylene-2,6,10-tricarboxamide monomers to escape a kinetic trap more efficiently than polymers based on their achiral analogs. Partial depolymerization of the kinetically trapped state by increasing the temperature followed by polymerization by lowering the temperature shows that monomers either polymerize on existing stacks or self-nucleate to form the thermodynamically more stable state. Chiral monomers prefer the latter more than achiral monomers.     

Development of a fast liquid chromatography/mass spectrometry screening method for angiotensin‐converting enzyme (ACE) inhibitors in complex natural mixtures like snake venom

A new robust high‐performance liquid chromatography/electrospray ionization mass spectrometry (HPLC/ESI‐MS)‐based screening method for angiotensin‐converting enzyme (ACE)‐inhibiting substances in crude samples is described. The ACE assay is carried out in a typical offline setup by incubation of the samples with ACE and angiotensin I (AI), followed by stopping the reaction with acetonitrile containing val⁵‐AI serving as internal standard (I.S.). AI and the product angiotensin II (AII) are extracted from the incubation mixture by turbulent‐flow chromatography (TFC) applied in backflush mode as online solid‐phase extraction and are directly quantified by ESI(+)‐MS. The presence of ACE inhibitors (ACEi) is detected by an increase in AI signal intensity and a corresponding decrease of AII signal, as compared to the blank assay. The overall time of analysis of the TFC/ESI‐MS method was 5 min, thus making the described setup suitable for a rapid screening method. The assay was validated using a known ACE inhibitor and the IC₅₀ values found were in good accordance with a common HPLC/UV method and literature data. The method was successfully applied for the screening of size‐exclusion chromatography fractions of the venom of the pitviper Bothrops moojeni. Three of 18 analyzed fractions inhibited ACE, due to peptides present as components of this snake venom. These compounds were extracted from the two most‐active fractions by means of TFC and isolated by means of HPLC. Three peptides with ACE inhibitory activity were characterized and their structures were elucidated with ESI‐MS/MS‐based de novo sequencing to be ZKWPPGKVPP, ZKWPRPGPEIPP and ZNWPRPGPEIPP, respectively (Z = pyroglutamic acid). Copyright © 2010 John Wiley & Sons, Ltd.