Metastable decay rates,asymptotic expansions,and analytic continuation of thermodynamic functions

The grand potentialP(z)/kT of the cluster model at fugacityz, neglecting interactions between clusters, is defined by a power series _n Q _n z ⁿ , whereQ _n , which depends on the temperatureT, is the partition function of a cluster of sizen. At low temperatures this series has a finite radius of convergencez _s . Some theorems are proved showing that ifQ _n , considered as a function ofn, is the Laplace transform of a function with suitable properties, thenP(z) can be analytically continued into the complexz plane cut along the real axis fromz _s to + and that (a) the imaginary part ofP(z) on the cut is (apart from a relatively unimportant prefactor) equal to the rate of nucleation of the corresponding metastable state, as given by Becker-Döring theory, and (b) the real part ofP(z) on the cut is approximately equal to the metastable grand potential as calculated by truncating the divergent power series at its smallest term.     

Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems

We consider quantum unbounded spin systems (lattice boson systems) in -dimensional lattice space Z. Under appropriate conditions on the interactions we prove that in a region of high temperatures the Gibbs state is unique, is translationally invariant, and has clustering properties. The main methods we use are the Wiener integral representation, the cluster expansions for zero boundary conditions and for general Gibbs state, and explicitly -dependent probability estimates. For one-dimensional systems we show the uniqueness of Gibbs states for any value of temperature by using the method of perturbed states. We also consider classical unbounded spin systems. We derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case.     

Virial expansion for a polymer with a realistic pair-potential interaction

No modern theory of polymer excluded volume adequately describes the crossover from poor solvent to good solvent conditions; a fundamental difficulty is a singularity in the binary cluster integral. Mayer expansion techniques are applied to a model with a pair interaction between monomers to clarify the distinction between geometric and solvent contributions to excluded volume. Detailed calculations are undertaken for a hard-core potential and a mimic Lennard-Jones potential. The significance of the singularity in the binary cluster integral for calculations in the crossover regime is discussed.     

Polarized emission from a rhenium metal-ligand complex

We report the first observation of polarized emission from a rhenium-phenanthroline complex, Re(CO)₃(phen)Cl. Highly luminescent rhenium complexes are known, with quantum yields near 0.5 and lifetimes in excess of 10 s. The detection of polarized emission suggests the use of rhenium complexes as probes of the hydrodynamics of large macromolecular complexes and for use in fluorescence polarization immunoassays with gated detection.     

The covariance matrix of the Potts model: A random cluster analysis

We consider the covariance matrix,G ^mm =q ²<(_x,m);(_y,m)>, of thed-dimensionalq-states Potts model, rewriting it in the random cluster representation of Fortuin and Kasteleyn. In any of theq ordered phases, we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances, thereby attributing algebraic significance to these stochastic geometric quantities. We also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers. For dimensiond=2, we show that this correlation length and the correlation length of the two-point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two. For systems with first-order transitions, this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self-dual point _o. For systems with second order transitions, this relation implies the equality of the correlation length exponents from above and below threshold, as well as an amplitude ratio of two. In the course of proving the above results, we establish several properties of independent interest, including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions, and left continuity of the two-dimensional free boundary condition percolation probability at _o. We also introduce DLR equations for the random cluster model and use them to establish ergodicity of the free measure. In order to prove these results, we introduce a new class of events which we call decoupling events and two inequalities for these events. The first is similar to the FKG inequality, but holds for events which are neither increasing nor decreasing; the second is similar to the van den Berg-Kesten inequality in standard percolation. Both inequalities hold for an arbitrary FKG measure.     

Metastable fluid flow described via a discrete-velocity coagulation-fragmentation model

A discrete-velocity Boltzmann model is introduced. It is based on two principles: (i) clusters of particles move in ³ with seven fixed momenta; (ii) clusters may gain or lose particles according to the rules of Becker-Döring cluster equations. The model provides a kinetic representation of evaporation and condensation. The model is used to obtain macroscopic fluid equations which are valid into the metastable fluid regime, , where is any positive number, is the inelastic Knudsen number, and _s is the saturation density.     

Synthesis and structural characterization of novel bridged platinum(II) biscarbene complexes

Novel bridged platinum(II) biscarbene complexes are reported: 1,1′-dimethyl-3,3′-methylene-4-diimidazolin-2,2′-diylidene platinum(II) (3) and 1,1′-dimethyl-3,3′-ethylene-4-diimidazolin-2,2′-diylidene platinum(II) complexes 4 are directly accessible in high yields starting from platinum halides. The one-pot synthesis obviates the need for multi-step reactions via metal precursors or free carbenes. An X-ray crystal structure of 1,1′-dimethyl-3,3′-methylene-4-diimidazolin-2,2′-diylidene platinum(II) dibromide (3b) confirmed the structural similarity to the known corresponding palladium complexes. Since free 1,1′-di-R-3,3′-methylene-4-diimidazolin-2,2′-diylidenes are only available in low yields this synthetic route provides an easy access to the corresponding carbene complexes.     

Chemistry of λ-2H-azaphosphirene metal complexes

In this review, important aspects of λ³-2H-azaphosphirene metal complexes are discussed in relation to synthesis, physical properties and synthetic applications; ab-initio calculations on relative energies of CH₂NP isomers and of λ³-2H-azaphosphirene metal complexes (Cr, Mo, W) are also presented. Currently, there are three routes to this unsaturated three-membered ring system, which are discussed in detail: two of them use a rearrangement of metal carbene complexes, whereas the other relies on [2+1] cycloaddition reactions of electrophilic terminal phosphanediyl complexes and carbonitriles. The structural data show characteristics of a very strained heterocyclic ring system, which partially helps to understand the reactivity of this heterocycle complex in solution. The synthetic potential of λ³-2H-azaphosphirene metal complexes is illustrated by selected examples, which demonstrate their ability to serve, under very mild conditions as precursor for various new building blocks, i.e. nitrilium phosphanylide complexes, electrophilic terminal phosphanediyl complexes and phosphavinyl-nitrene complexes.     

Triphenylphosphan-Nickel(0)-Komplexe mit Isocyanid-Liganden — [(RNC)nNi(PPh3)4–n] (n = 1–3)

Triphenylphosphane Nickel(0) Complexes with Isocyanide Ligands — [(RNC)_nNi(PPh₃)_4–n] (n = 1–3) Synthesis and properties of the isocyanide triphenylphosphane nickel(0) complexes [(RNC)Ni(PPh₃)₃], [(RNC)₂Ni(PPh₃)₂] and [(RNC)₃Ni(PPh₃)] (R = ^tBu, Cy, PhCH₂, p-TosCH₂) are described. I.r. and ³¹P n.m.r. spectra were recorded and the X-ray crystal structure of [(PhCH₂NC)₂Ni(PPh₃)₂] was determined.     

Surface tension measurements in the study of molecular complexes

Surface tension measurements can be used to investigate molecular complex formation in liquid solutions for strong and weak complexes. The association constant and epthalpy for triethylamine-iodine, hexamethylbenzene-tetracyanoethylene and ethanol-iodine in cyclohexane are 4·55×10³, 218 and 0.93M⁻¹ at 25° C and 12·5, 7·7 and 5·1 kcal/mol respectively. These values compare well with those reported in the literature by other methods.