The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics

We discuss a new class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting non-conserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high an low density phases, two and three phase coexistence regions and a boundary independent ``Meissner'' phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert $W$-functions. It allows to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.Comment: 22 pages, 23 figures. Accepted for publication on Phys. Rev.

The Electronic Influence of Ring Substituents and Ansa Bridges in Zirconocene Complexes as Probed by Infrared Spectroscopic, Electrochemical, and Computational Studies

The electronic influence of unbridged and ansa-bridged ring substituents on a zirconocene center has been studied by means of IR spectroscopic, electrochemical, and computational methods. With respect to IR spectroscopy, the average of the symmetric and asymmetric stretches (ν_(CO(av))) of a large series of dicarbonyl complexes (Cp^R)_2Zr(CO)_2 has been used as a probe of the electronic influence of a cyclopentadienyl ring substituent. For unbridged substituents (Me, Et, Pri, But, SiMe_3), ν_(CO(av)) on a per substituent basis correlates well with Hammett σ_(meta) parameters, thereby indicating that the influence of these substituents is via a simple inductive effect. In contrast, the reduction potentials (E°) of the corresponding dichloride complexes (Cp^R)_2ZrCl_2 do not correlate well with Hammett σ_(meta) parameters, thereby suggesting that factors other than the substituent inductive effect also influence E°. Ansa bridges with single-atom linkers, for example [Me_2C] and [Me_2Si], exert a net electron-withdrawing effect, but the effect is diminished upon increasing the length of the bridge. Indeed, with a linker comprising a three-carbon chain, the [CH_2CH_2CH_2] ansa bridge becomes electron-donating. In contrast to the electron-withdrawing effect observed for a single [Me_2Si] ansa bridge, a pair of vicinal [Me_2Si] ansa bridges exerts an electron-donating effect relative to that from the single bridge. DFT calculations demonstrate that the electron-withdrawing effect of the [Me_2C] and [Me_2Si] ansa-bridges is due to stabilization of the cyclopentadienyl ligand acceptor orbital, which subsequently enhances back-donation from the metal. The calculations also indicate that the electron-donating effect of two vicinal [Me_2Si] ansa bridges, relative to that of a single bridge, is a result of it enforcing a ligand conformation that reduces back-donation from the metal

Versatile Coordination of Cyclopentadienyl-Arene Ligands and Its Role in Titanium-Catalyzed Ethylene Trimerization

Cationic titanium(IV) complexes with ansa-(η5-cyclopentadienyl,η6-arene) ligands were synthesized and characterized by X-ray crystallography. The strength of the metal-arene interaction in these systems was studied by variable-temperature NMR spectroscopy. Complexes with a C1 bridge between the cyclopentadienyl and arene moieties feature hemilabile coordination behavior of the ligand and consequently are active ethylene trimerization catalysts. Reaction of the titanium(IV) dimethyl cations with CO results in conversion to the analogous cationic titanium(II) dicarbonyl species. Metal-to-ligand backdonation in these formally low-valent complexes gives rise to a strongly bonded, partially reduced arene moiety. In contrast to the η6-arene coordination mode observed for titanium, the more electron-rich vanadium(V) cations [cyclopentadienyl-arene]V(NiPr2)(NC6H4-4-Me)+ feature η1-arene binding, as determined by a crystallographic study. The three different metal-arene coordination modes that we experimentally observed model intermediates in the cycle for titanium-catalyzed ethylene trimerization. The nature of the metal-arene interaction in these systems was studied by DFT calculations.