Fluctuation phenomena in electrochemistry part II. Modelling the noise sources

A discussion of the modelling of the primary and secondary noise sources introduced in the formalism of fluctuation phenomena in a previous report is presented. It is illustrated that the generalisation of the modelling of noise sources in mass transport as given by Tyagai is limited in its applicability. A general procedure for the same is discussed in detail.

Interfacial area measurement in a gas - liquid ejector for a sodium chloride - air system

Interfacial area measurement has been carried out experimentally by measuring the bubble size and holdup for air-sodium chloride solution system. The size of the bubble is predominantly established by the air hold up. High speed photography technique for bubble size measurement and gamma ray attenuation method for holdup measurements are followed. The measured values are compared with the theoretically predicted values. Interracial area as a function of the liquid flow rate and also its distance from the nozzle of the ejector has been reported in this paper. The results obtained for this non-reactive system are also compared with those of air-water system.

Effect of Structural Modification on the Quantum-Size Effect in II-VI Semiconducting Nanocrystals

The electronic structure of group II-VI semiconductors in the stable wurtzite form is analyzed using state-of-the-art ab initio approaches to extract a simple and chemically transparent tight-binding model. This model can be used to understand the variation in the bandgap with size, for nanoclusters of these compounds. Results complement similar information already available for same systems in the zinc blende structure. A comparison with all available experimental data on quantum size effects in group II-VI semiconductor nanoclusters establishes a remarkable agreement between theory and experiment in both structure types, thereby verifying the predictive ability of our approach. The significant dependence of the quantum size effect on the structure type suggests that the experimental bandgap change at a given size compared to the bulk bandgap, may be used to indicate the structural form of the nanoclusters, particularly in the small size limit, where broadening of diffraction features often make it difficult to unambiguously determine the structure.

A Theoretical Investigation of the Ni(II)-Catalyzed Hydrovinylation of Styrene

We report a detailed and full computational investigation on the hydrovinylation reaction of styrene with the Ni(II)-phospholane catalytic system, which was originally presumed to proceed through a cationic mechanism involving a nickel hydride intermediate. The following general features emerge from this study on a specific catalyst complex that was found to give quantitative yield and moderate selectivity: (a) the activation barrier for the initiation (18.8 kcal/mol) is higher than that for the reaction due to a low-lying square-planar pentenyl chelate intermediate originating from a Ni(II)-allyl catalyst precursor. Consequently there is an induction period for the catalysis; (b) the exit of product from the catalyst is via a β-H-transfer step instead of the usual β-H elimination pathway, which has a very high activation energy due to a trans effect of the phospholane ligand; (c) the turnover-limiting and enantio- determining transition state is also the β-H-transfer; (d) because of the absence of a hydride intermediate, the unwanted isomerization of the product is prevented; (e) since the enantio-discrimination is decided at the H-transfer stage itself, the configuration of the product in a catalytic cycle influences the enantioselectivity in the subsequent cycle; (f) the trans effect of the sole strong ligand in the d8 square-planar Ni(II), the stability of the η3-benzyl intermediate, and the availability of three coordination sites enable regioselective hydrovinylation over the possible oligomerization/polymerization of the olefin substrates and linear hydrovinylation. This work has also confirmed the previously recognized role of the hemilabile group at various stages in the mechanism.

Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Type II beta-turn conformation of pivaloyl-L-prolyl-alpha-aminoisobutyryl-N-methylamide: Theoretical, spectroscopic, and X-ray studies

Pivaloyl-L-Pro-Aib-N-methylamide has been shown to possess one intramolecular hydrogen bond in (CD3)2SO solution, by 1H-nmr methods, suggesting the existence of beta -turns, with Pro-Aib as the corner residues. Theoretical conformational analysis suggests that Type II beta-turn conformations are about 2 kcal mol-1 more stable than Type III structures. A crystallographic study has established the Type II beta-turn in the solid state. The molecule crystallizes in the space group P21 with a = 5.865 Å, b = 11.421 Å, c = 12.966 Å, beta = 97.55°, and Z = 2. The structure has been refined to a final R value of 0.061. The Type II -turn conformation is stabilized by an intramolecular 4 1 hydrogen bond between the methylamide NH and the pivaloyl CO group. The conformational angles are Pro = -57.8°, Pro = 139.3°, Aib = 61.4°, and Aib = 25.1°. The Type II beta-turn conformation for Pro-Aib in this peptide is compared with the Type III structures observed for the same segment in larger peptides.

Pressure effect on the phase transition of trissarcosine calcium chloride

The dielectric measurement of ferroelectric trissarcosine calcium chloride (TSCC) was made under various pressures up to 6 kbar. A striking decrease in the peak value of the permittivity, epsilon r, at the transition temperature, Tc, was observed with increasing pressure. The value of Tc increases linearly with a pressure coefficient dTc/dp=11.1K kbar-1 at low pressures. This increase in Tc supports the suggestion that the ferroelectric transition is of the pure order-disorder type. It is suggested on the basis of the behaviour of epsilon r with pressure that the order of the ferroelectric transition changes from second to first order on application of pressure.

Metal chelates in vinyl polymerization: Kinetics and mechanism of acrylonitrile polymerization initiated by Cu(II) imine complexes

The free radical polymerization of acrylonitrile (AN) initiated by Cu(II) 4-anilino 2-one [Cu(II) ANIPO] Cu(II), 4-p-toluedeno 3-pentene 2-one [Cu(II) TPO], and Cu(II) 4-p-nitroanilino 3-pentene 2-one [Cu(II) NAPO] was studied in benzene at 50 and 60°C and in carbon tetrachloride (CCl4), dimethyl sulfoxide (DMSO), and methanol (MeOH) at 60°C. Although the polymerization proceeded in a heterogeneous phase, it followed the kinetics of a homogeneous process. The monomer exponents were 2 at two different temperatures and in different solvents. The square-root dependence of Rp on initiator concentration and higher monomer exponents accounted for a 1:2 complex formation between the chelate and monomer. The complex formation was shown by ultraviolet (UV) study. The activation energies, kinetics, and chain transfer constants were also evaluated.

Electrochemical phase formation (ECPF) and macrogrowth Part II. Two-rate models

A general theory is evolved for a class of macrogrowth models which possess two independent growth-rates. Relations connecting growth-rates to growth geometry are established and some new growth forms are shown to result for models with passivation or diffusion-controlled rates. The corresponding potentiostatic responses, their small and large time behaviours and peak characteristics are obtained. Numerical transients are also presented. An empirical equation is derived as a special case and an earlier equation is corrected. An interesting stochastic result pertaining to nucleation events in the successive layers is proved.

Coalescence of rigid droplets in a stirred dispersion-II. Band-limited force fluctuations

The coalescence of nearly rigid liquid droplets in a turbulent flow field is viewed as the drainage of a thin film of liquid under the action of a stochastic force representing the effect of turbulence. The force squeezing the drop pair is modelled as a correlated random function of time. The drops are assumed to coalesce once the film thickness becomes smaller than a critical thickness while they are regarded as separated if their distance of separation is larger than a prescribed distance. A semi-analytical solution is derived to determine the coalescence efficiency. The veracity of the solution procedure is established via a Monte-Carlo solution scheme. The model predicts a reversing trend of the dependence of the coalescence efficiency on the drop radii, the film liquid viscosity and the turbulence energy dissipation per unit mass, as the relative fluctuation increases. However, the dependence on physical parameters is weak (especially at high relative fluctuation) so that for the smallest droplets (which are nearly rigid) the coalescence efficiency may be treated as an empirical constant. The predictions of this model are compared with those of a white-noise force model. The results of this paper and those in Muralidhar and Ramkrishna (1986, Ind. Engng Chem. Fundam. 25, 554-56) suggest that dynamic drop deformation is the key factor that influences the coalescence efficiency.

X-Ray Structure Of A Ternary Metal-Complex - Copper(Ii) Inosine 5'-Monophosphate Imidazole - Metal-Binding To The N(7) Atom Of The Nucleotide In A Mixed-Ligand System Containing An Aromatic Amine

A ternary metal-nucleotide complex, Na2[Cu(5’-IMP)2(im)o,8(H20)l,2(H20)2h]as~ 1be2e.n4 pHr2ep0a,r ed and its structure analyzed by X-ray diffraction (5’-IMP = inosine 5’-monophos hate; im = imidazole). The complex crystallizes in space group C222, with a = 8.733 (4) A, b = 23.213 (5) A, c = 21.489 (6) 1, and Z = 4. The structure was solved by the heavy-atom method and refined by full-matrix least-squares technique on the basis of 2008 observed reflections to a final R value of 0.087. Symmetry-related 5’-IMP anions coordinate in cis geometry through the N(7) atoms of the bases. The other cis positions of the coordination plane are statistically occupied by nitrogen atoms of disordered im groups and water oxygens with occupancies 0.4 and 0.6, respectively. Water oxygens in axial positions complete the octahedral coordination of Cu(I1). The complex is isostructural with C~S-[P~(S’-IMP),(NH~)~a] m”,o del proposed for Pt(I1) binding to DNA. The base binding observed in the present case is different from the typical ”phosphate only” binding shown from earlier studies on metal-nucleotide complexes containing various other ?r-aromatic amines.

Synthesis and physico-chemical properties of diruthenium(III, II) tetra-aryl carboxylato compounds

Monochloro-tetra-μ-aryl-carboxylatodiruthenium(III, II) compounds Ru2Cl (O2CAr)4 (Ar = -C6H5; -C6H4-p-OCH3), are prepared and characterized. The compounds have magnetic moments that correspond to three unpaired spins per dimer. The Rusingle bondRu bond order is 2.5 and the ground electronic configuration is σ2π4δ2(δ*π*)3. The visible spectral band is observed at ca 450 nm along with a shoulder near 580 nm in DMF solution. The compounds undergo a one-electron Ru(III)Ru(II) → Ru(II)Ru(II) quasi-reversible reduction in DMF near 0.0 V vs sce.

Theoretical studies of lithium bonding in lithium chloride/aliphatic amine complexes

In the systematic study of amine … LiCl [amines = NH3, CH3NH2, (CH3)2NH] complexes the possibility of an ion-pair structure and the effect of methylation on the stabilization energy is investigated. ΔEis evaluated by the SCF/4-31G method and augmented by the approximate dispersion energy calculated perturbationally. The interaction energy decreases with the increasing number of methyl groups in the amine. The dispersion energy plays a negligible role in the stabilization of complexes. None of the systems studied are ion pairs; their Li bonds are of a so-called molecular type. Due to the divergence of the multipole expansion, the attempt to correct the 4-31G stabilization energies via the electrostatic energy fails. The relative order of the ΔE in the series of complexes is verified instead in the extended basis set calculation. The lithium bonds are compared with their H-bonded analogues.

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.