Multicomponent dynamical nucleation theory and sensitivity analysis

Vapor to liquid multicomponent nucleation is a dynamical process governed by a delicate interplay between condensation and evaporation. Since the population of the vapor phase is dominated by monomers at reasonable supersaturations, the formation of clusters is governed by monomer association and dissociation reactions. Although there is no intrinsic barrier in the interaction potential along the minimum energy path for the association process, the formation of a cluster is impeded by a free energy barrier. Dynamical nucleation theory provides a framework in which equilibrium evaporation rate constants can be calculated and the corresponding condensation rate constants determined from detailed balance. The nucleation rate can then be obtained by solving the kinetic equations. The rate constants governing the multistep kinetics of multicomponent nucleation including sensitivity analysis and the potential influence of contaminants will be presented and discussed.     

Complex homogeneous spaces of real groups with top homology in codimension two

SupposeX=G/H is a connected homogeneous complex manifold, whereG is a Lie group andH is a closed subgroup. Assume (X) and letG/H G/I be the holomorphic reduction ofX. If the top nonvanishing homology group ofX with coefficients in ₂ is in codimension two, then either a complex Lie group acts tansitively onG/I (see [3]) orG/I is biholomorphic to the unit disk.Partially supported by NSERC Grant A3494 and by the Deutsche Forschungsgemeinschaft     

The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log _n , where _n is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional ₍₂₎ ² -distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio _n are possible and the asymptotic distribution of 2 log _n is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the ²-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log _n are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2)100 percentiles of ₍₁₎ ² . In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log _n is pivotal. Selected (1–) 100 percentiles are presented and shown to differ between the two models.     

Structural and Spectroscopic Characterization of Iron(III) Dioxoporphodimethene Complexes and Their Autoreduction to an Iron(II) Complex in Pyridine

Three iron complexes of the meso-dioxo derivative of octaethylporphryin (trans-H(2)OEPO(2)) were characterized by X-ray diffraction. Green ClFe(III)(trans-OEPO(2)).1.5C(6)H(6) crystallizes in the monoclinic space group P2(1)/c with a = 13.766(3) ?, b = 19.075(3) ?, c = 15.217(3) ?, beta = 99.87(2) degrees at 123 K with Z = 4. Refinement of 2712 reflections with F > 6.0sigma(F) and 223 parameters yielded R = 0.0624, R(w) = 0.0596. The iron complex contains a domed dioxoporphodimethene macrocyclic ligand. The observation of a five-coordinate iron(III) ion with an axial Fe-Cl distance of 2.232(2) ? and in-plane Fe-N distances averaging 2.082 ? is consistent with its high-spin (S = (5)/(2)) character. This monomer is readily converted to the green {Fe(III)(trans-OEPO(2))}(2)O using aqueous hydroxide. {Fe(III)(trans-OEPO(2))}(2)O crystallizes in the monoclinic space group C2/c with a = 23.541(8) ?, b = 15.392(5) ?, c = 18.686(8) ?, and beta = 90.09(3) degrees at 294 K with Z = 8. Refinement of 3472 reflections with F > 6.0sigma(F) and 393 parameters yielded R = 0.0484, R(w) = 0.0527. The complex possesses a crystallographically imposed 2-fold symmetry axis that passes through the oxo ligand. The dioxoporphodimethene ligands within the molecule are roof-shaped and fold away from each other. The axial Fe-O distance is 1.749(1) ? with longer in-plane Fe-N distances (average 2.077 ?). The Fe-O-Fe angle of 165.4(2) degrees deviates significantly from linearity and is more acute than related porphyrin complexes. Pyridine solutions of either the iron(III) monomer or &mgr;-oxo dimer autoreduce over a period of days to give (py)(2)Fe(II)(trans-OEPO(2)). This red compound crystallizes in the space group P2(1) with a = 19.177(4) ?, b = 20.039(4) ?, c = 10.547(2) ?, and beta = 100.36(3) degrees at 130 K with Z = 2. Refinement of 5090 reflections with one restraint and 984 parameters yielded R1 = 0.0684, wR2 = 0.1763. The complex crystallizes with two distinct molecules in the asymmetric unit; each molecule contains a different degree of disorder with respect to the trans meso oxygen atoms (50/50, 71/29). Each independent molecule exhibits severe ruffling of the macrocycle. The six coordinate iron(II) center is diamagnetic. The axial Fe-N(pyridine) distances average 1.98 ?, and the in-plane Fe-N(pyrrole) distances average 1.95 ?. A common trend observed for the dioxoporphodimethene macrocycle in all of these structures is an elongation toward the trans oxidized meso carbons. These complexes were originally prepared as cis and trans isomeric mixtures that can be enriched in the trans isomer by fractional crystallization. This is evident in their distinctive (1)H NMR spectra. In addition, these compounds are characterized by electron impact mass spectrometry and UV-visible, ESR, and infrared spectroscopies.     

Proton-ionizable crown compounds. 4. New macrocyclic polyether ligands containing a triazole subcyclic unit

A series of macrocyclic polyether (crown) ligands containing the proton-ionizable s-triazole subcyclic unit were prepared by reacting the 1-THP blocked 3,5-bis(chloromethyl)-1H-1,2,4-triazole with various oligoethylene glycols. The starting bis(chloromethyl)triazole is a vessicant and must be used with caution. Triazolo-18-crown-6 ( 5 ) formed stable complexes with barium, strontium, copper and benzylammonium cations but not with potassium or lithium. The crystal structure of 5 showed the triazole proton to be on nitrogen 3 which is outside the macroring cavity.     

Structure of the phonon sidebands in the t1 → s0 transition of naphthalene in p-dibromobenzene, α-phase p-dichlorobenzene,and γ-phase p-dichlorobenzene host crystals

The theory used for predicting the intensity distributions in phonon sidebands in the electronic spectra of molecular crystals is briefly reviewed with particular emphasis on chemically mixed crystals. Criteria are suggested for the identification of pseudolocalized features in phonon sidebands. The phonon sidebands associated with the phosphorescence of naphthalene in p-dibromobenzene and α-phase p-dichlorobenzene seem to exhibit some degree of localization, while the phonon sideband of the phosphorescence of naphthalene in γ-phase p-dichlorobenzene appears to be entirely delocalized. The results are compared with those of other workers and a correlation is established between the degree of localization and the strength of the exciton-phonon coupling as measured by the optical Debye-Waller factor. It is further shown that the strength of coupling of the phonons to the electronic transition is independent of the gas-to-crystal shift of the impurity.     

A ruler for determining the position of proteins in membranes

Both the oxygen diffusion rate and the oxygen solubility vary with depth into the interior of biological membranes. The product of these two gradients generates a single gradient, a permeability gradient, which is a smooth continuous function of the distance from the center of the membrane. Using electron paramagnetic resonance and the spin-probe method, the relaxation gradient of oxygen, which is directly proportional to the permeability gradient, is the quantity that can be directly measured in membranes under physiological conditions. The gradient obtained provides a calibrated ruler for determining the membrane depth of residues either from loop regions of membrane-binding proteins or from the membrane-exposed residues of transmembrane proteins. We have determined the relaxation gradient of oxygen in zwitterionic and anionic phospholipid membranes by attaching a single nitroxide probe to a transmembrane alpha-helical polypeptide at specific residues. The peptide ruler was used to determine the depth of penetration of the calcium-binding loops of the C2 domain of cytosolic phospholipase A(2). The positions of selected residues of this membrane-binding protein that penetrate into the membrane, determined using this ruler, compared favorably with previous determinations using more complex methods. The relaxation gradient constrains the possible values of the membrane-dependent oxygen concentration and the oxygen diffusion gradients. The average oxygen diffusion coefficient is estimated to be at least 2-fold smaller in the membrane than that in water.