Free Energy as a Geometric Invariant

The free energy plays a fundamental role in statistical and condensed matter physics. A related notion of free energy plays an important role in the study of hyperbolic dynamical systems. In this paper we introduce and study a natural notion of free energy for surfaces with variable negative curvature. This geometric free energy encodes a new type of marked length spectrum of closed geodesics, which lies between the well-known marked length spectrum (marked by the corresponding element of the fundamental group) and the unmarked length spectrum. We prove that the free energy parametrizes the boundary of the domain of convergence of a Poincaré series which also encodes this spectrum. We also show that this new length spectrum, or equivalently the geometric free energy, is not an isometry invariant. In the final section we use tools from multifractal analysis to effect a fine asymptotic comparison of word length and geodesic length of closed geodesics. We hope that our geometric understanding of free energy will provide new insight into this fundamental physical and dynamical quantity. The work of the second author was partially supported by a National Science Foundation grant DMS-0355180. This work was completed during a visit by the first author to Penn State as a Shapiro Fellow.     

High-throughput approaches for the discovery and optimization of new olefin polymerization catalysts

The discovery of new olefin polymerization catalysts is currently a time-intensive trial-and-error process with no guarantee of success. A fully integrated high-throughput screening workflow for the discovery of new catalysts for polyolefin production has been implemented at Symyx Technologies. The workflow includes the design of the metal-ligand libraries using custom-made computer software, automated delivery of metal precursors and ligands into the reactors using a liquid-handling robot, and a rapid primary screen that serves to assess the potential of each metalligand-activator combination as an olefin polymerization catalyst. "Hits" from the primary screen are subjected to secondary screens using a 48-cell parallel polymerization reactor. Individual polymerization reactions are monitored in real time under conditions that provide meaningful information about the performance capabilities of each catalyst. Rapid polymer characterization techniques support the primary and secondary screens. We have discovered many new and interesting catalyst classes using this technology.     

Synthesis of seven-membered ring diazepin-2-ones via palladium-catalyzed highly regioselective cyclization of 2-vinylpyrrolidines with aryl isocyanates

The first palladium-catalyzed ring-expansion reaction of 2-vinylpyrrolidines with aryl isocyanates to form seven-membered ring heterocycles is described. This regioselective reaction requires 5 mol % of Pd(2)(dba)(3).CHCl(3) and 10 mol % of dppp at 40-60 degrees C in THF and results in the formation of 1,3-diazepin-2-ones in good isolated yields. When Pd(OAc)(2) and PPh(3) were utilized in the reaction, an intramolecular hydrogen migration occurs resulting in the formation of conjugated diene derivatives of urea.     

Organic chemistry of dinitrogen and related ligands. Part 2. Non-radical acylation of ligating dinitrogen

Summary Ligating dinitrogen, in the complexes,trans-M(N₂)₂(Ph₂PCH₂CH₂PPh₂)₂ (where M=Mo or W) may be acylated by trifluoroacetic anhydride, to give trifluoroacetyldiazenido complexes in high yield. Unlike corresponding reactions with acyl halides, trifluoroacetylation proceeds under nonradical conditions, and a mechanism analogous to that of protonation is suggested.Dinitrogen-derived ligands may also be acylated by (CF₃CO)₂O, so that the methyldiazenido ligand is converted into a methyl (trifluoroacetyl) hydrazido (2-) ligand, and the acetyldiazenido ligand undergoes transacylation to give a trifluoroacetyl diazenido derivative.New complexes were characterised by i.r.,¹⁹F and¹H n.m.r. spectra, and by elemental analysis.Part 1 is ref. 10     

Prediction of cathodic E1/21 and E1/22 values for viologen-containing conjugated unimers and dimers from calculated pKb values of the aromatic substituents

A library of 18 conjugated, rod-like compounds with either one or two viologen residues were synthesized and characterized electrochemically. Containing up to 8 aromatic/heterocyclic rings in conjugation, the members of the library differ in the substitution pattern of electron-withdrawing or -donating groups on the aromatic substituents of the viologen units. The first and second half-wave potentials of each member were found to be linearly correlated with the calculated pK_b values of the aromatic end-groups. This relationship will enable the half-wave potentials of related, novel, substituted viologen species to be predicted using a simple, empirical formula.     

An LX-10 kinetic model calibrated using simulations of multiple small-scale thermal safety tests

A new chemical kinetic model for the beta-delta transition and decomposition of LX-10 (95% octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine, 5% Viton A binder) is presented here. This model implements aspects of previous kinetic models but calibrates the model parameters to data sets of three experiments: differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and one-dimensional time to explosion (ODTX). The calibration procedure contains three stages: one stage uses open-pan DSC and TGA to develop a base reaction for formation of heavy gases, a second stage features closed-pan DSC to ascertain the autocatalytic behavior of reactant gases attacking the solid explosive, and a final stage adjusts the rate for the breakdown of heavy reactant gases using ODTX experimental data. The resultant model presents a large improvement in the agreement between simulated DSC and TGA results and their respective experiments while maintaining the same level of agreement with ODTX, scaled thermal explosion, and laser heating explosion times when compared to previous models.     

Influence of solvent polarity upon salt solubilities,II: Solubilities of two potassium carboxylates at 85°C in aqueous 1,4-dioxane

The solubilities of potassium acetate and benzoate in aqueous 1,4-dioxane at a temperature of 85°C are reported together with a quasi-thermodynamic general treatment of the experimental results.This brief contribution is a second report upon the results of systematic solubility measurements, commenced with Ref.¹, which have been performed by Dr.John A. McNaney during his abruptly truncated lifetime.