Simulation of dielectric relaxation in periodic binary systems of complex geometry

Dielectric relaxation in binary mixtures containing particles or lamellae with complex geometry has been simulated within the quasielectrostatic approximation by a three-dimensional finite-difference method. The method was tested using simple models corresponding to water-in-oil (W/O) and oil-in-water (O/W) emulsions with volume fraction P up to 0.5. The dielectric spectra calculated by the finite difference method agreed with those expected from Wagner's equation at P < or =0.3 and approached those from Hanai's equation at P>0.4. This method was applied to more complicated binary mixtures of oil and water: a bicontinuous cubic structure, a suspension of particles with projections, and a planar bilayer with a rippled or interdigitated interface. The bicontinuous phase that is supposed to appear near the transition between W/O and O/W emulsions showed dielectric properties similar to those of the O/W emulsion. The undulation of the particle surface and the interface of the planar bilayer affected all parameters of dielectric relaxation, especially the relaxation intensity.     

Toward mimicking viral geometry with metal-organic systems

Icosahedral and cuboctahedral arrangements of calixarenes, a nanometer-scale, spheroidal assembly of 12 calixarene molecules, can be manipulated in a highly controlled fashion. Previously, such assemblies were observed to favor placement of the calixarenes at the vertexes of an icosahedron. A supramolecular constraint is employed in order to enforce molecular alignment and produce a cuboctahedral arrangement. The internal volume of the cuboctahedron is approximately 30% greater than that of the icosahedron. Furthermore, in stark contrast to that of the icosahedral Platonic solid, the shell of the cuboctahedral Archimedean solid is porous.     

Differential geometry of chemically reacting systems

This paper is a detailed differential geometrical study of chemically reacting systems. In particular the following coordinate-free properties of chemically reacting systems are obtained: 1) the general solution of the intrinsic reaction coordinate (IRC) (henceforth referred to as meta-IRC), 2) extended definitions of the Hessian matrix and normal vibrations at any non-equilibrium point on the surface, and 3) clarification of the close connection between the geometry of meta-IRC and the geography of the surface at a transition point. The theory is elucidated using a model potential surface.     

Measurement of residual stresses in film insert molded parts with complex geometry

Residual stress distribution of injection molded and film insert injection molded products were measured by using the hole drilling method after ejection and annealing, respectively. Non-isothermal three dimensional flow analysis was carried out for filling, packing and cooling stages. The flow analysis results were transported to a finite element stress analysis program and three dimensional stress analysis was performed for prediction of residual stresses in the parts. For comparison, residual stress distribution was measured by the layer removal method and calculated by the three dimensional numerical simulation in order to evaluate accuracy of the hole drilling method. Residual stress distributions obtained by both experiments and numerical methods accorded well with each other. Therefore, the hole drilling method is a reliable and useful method for measurement of residual stresses in injection molded parts, especially, products with complex geometry.     

Polarization functions and geometry optimization inab initio calculations of the rotational barrier in hydrogen peroxide

Ab initio calculations have been carried out for the hydrogen peroxide molecule with different size Gaussian basis sets in an attempt to determine the relative importance of carefully refined geometry and improvement of the wave function for calculation of the trans rotational barrier,d-type polarization functions on the oxygen atoms are found to be essential for calculation of a trans rotational barrier. Using the (O/7,3,1)(H/4,1) basis set, a trans rotational barrier of 0.63 kcal/mole is calculated (exp. value, 1.1 kcal/mole). Except for refined calculations approaching the Hartree-Fock limit, careful geometry optimization is found to be of secondary importance to the inclusion ofd-type functions on the oxygen atoms and may be carried out satisfactorily using a smaller basis set than is used for the energy calculations. The (O/7,3) (H/4,1) basis set which includesp-type polarization functions on the hydrogen atoms yields geometrical parameters in good agreement with experiment as well as good charge distribution between the hydrogen and oxygen atoms.

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Zusammenfassung Ab-initio Rechnungen für das Wasserstoffperoxidmolekül wurden mit Basissätzen verschiedener Größe durchgeführt um den Einfluß einer genauen Geometrie und einer Verbesserung der Wellen-funktion auf die Berechnung dertrans-Rotationsbarriere zu untersuchen. Es zeigte sich, daßd-Polarisationsfunktionen für solche Rechnungen äußerst wichtig sind. Mit dem Basissatz (O/7,3,1) (H/4,1) wurde die Rotationsbarriere mit 0,63 kcal/Mol berechnet (exp.: 1.1 kcal/Mol). Außer bei Rechnungen nahe am Hartree-Fock-Limit zeigte sich, daß die Geometrieoptimisierung gegenüber der Mitnahme vond-Funktionen von sekundärer Bedeutung ist und daher mit einem kleineren Basissatz durchgeführt werden kann, als die Energieberechnung. Der (O/7,3) (H/4,1) Basissatz, derp-Funktionen am Wasserstoffatom einschließt gibt die Geometrie und die Ladungsverteilung zwischen Wasserstoff- und Sauerstoffatom in guter Übereinstimmung mit dem Experiment.

     

Counterpoise技术和He-H2O配合物的平衡几何

在得到MP4, SCF的关于总能量及结合能的四个势能面的基础上,着重分析了电子相关作用, 消除基函数超位误差的Counterpoise(CP)技术对van der Waals配合物He-H2O的平衡几何的影响并得到了更精确的平衡几何预测。     

Intermediate nematic phases in binary systems with complex formation

The phase diagrams of some binary systems of smectogenic compounds are presented in which intermediate nematic phases occur over a large concentration range. An attempt has been made to interpret this behaviour in terms of structural differences between the smectic A phases of the components.     

Polymerization of styrene with nickel complex/methylaluminoxane catalytic systems

Polymerization of styrene using catalytic systems based on nickel derivatives and methylaluminoxane (MAO) was studied. Among tested catalysts, nickel bis(acetylacetonate) and nickel dichloride show the maximum activity. Bis(phosphine)nickel dichlorides exhibit lower activity, depending on the nature of the phosphine ligand. Polymer yields decrease by lowering the catalyst concentration, by increasing the reaction temperature, or by carrying out the polymerization in a polar donor solvent. Weight average molecular weight of most of the prepared polystyrenes ranges from 9000 to 25,000, with polydispersity indexes of 1.6–3.8. However, polystyrene prepared in dioxane solvent exhibits a small fraction of very high molecular weight (about 140,000). From NMR analysis, the products seem generally to be constituted of two polymers with different steric microstructure: atactic polystyrene and partially isotactic polystyrene (ca. 75–85% meso diads). Catalytic site specificity is correlated with the type of nickel ligand, while the effect of reaction temperature is less defined. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2119–2126, 1998     

Determination of binding geometry of DNA-adduct systems through induced circular dichroism

Many molecules (adducts) bound to DNA are postulated to intercalate between successive DNA base pairs. Linear dichroism (LD) has been used to yield information about the angular orientation of the adduct relative to the helix axis, but cannot probe the orientation within the plane perpendicular to this axis. A model is presented in this paper which predicts that the degree of alignment relative to a DNA fixed axis in this plane may be directly probed through the sign of the circular dichroism (CD) induced in an adduct transition of known polarization. Comparison with experimental data suggests that the method can complement LD studies in giving detailed information about the binding geometry.     

Numerical simulation of cyclic voltammetry for reversible systems with complex stoichiometry

Reversible waves of voltammetry with complex non-unity stoichiometry are studied here based on theory. Numerical simulations were performed for various stoichiometric systems in which coefficients m and q were independently varied from 1 to 4 in a general reaction scheme, mO + ne⁻ ai qR. The calculation results indicate that the peak current function at complex stoichiometry differs from that at simple unity stoichiometry. The relation between the half-wave potential and the formal potential has been partially corrected from that previously reported in the literature. Parameters in the relation between the peak potential and the half-wave potential are unique for each stoichiometric system. The parameter in the relation between the peak potential and the half-peak potential is also presented here.     

Meaningful activation energies for complex systems

It is known that the application of an inappropriate kinetic method to the thermal analysis of complex systems can lead to misleading results. To avoid this problem, the new parameter instantaneous mean activation energy is introduced and the Ozawa-Flynn-Wall method is assessed as a means of obtaining it. It is concluded that good results can generally be obtained by this method, provided that the various reactions occurring in the complex system are of the same type. The pyrolysis of coal is considered as a possible application of the method.

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Zusammenfassung Es ist bekannt, da\ die Anwendung einer ungeeigneten kinetischen Methode bei der thermischen Analyse komplexer Systeme zu falschen Ergebnissen führen kann. Um dieses Problem zu vermeiden, wird der neue Parameter momentane mittlere Aktivierungsenergie eingeführt. Die Ozawa-Flynn-Wall-Methode wird als zur Bestimmung dieses Parameters geeignet angesehen. Es wird der Schlu\ gezogen, da\ mit dieser Methode im allgemeinen gute Ergebnisse zu erhalten sein sollten, vorausgesetzt, da\ die in komplexen Systemen verlaufenden verschiedenen Reaktionen vom gleichen Typ sind. Die Pyrolyse von Kohle wird als mögliche Anwendung dieser Methode angesehen.

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The author wishes to thank the British Gas Corporation for permission to publish this work.     

Reaction rate analysis of complex kinetic systems

Using the elementary sensitivity densities, a reaction rate sensitivity gradient is obtained which is the derivative of the rate of species concentration change with respect to the rate coefficient. The dimensionless (log-normalized) form of the reaction rate sensitivity gradient is the ratio of the rate of concentration change of species i due to elementary reaction j and the net rate of concentration change of species i. This result provides a mathematical basis for the use of various forms of reaction rate analyses in the study of complex reaction mechanisms. The kinetic information inherent in the relative reaction rate matrix is extracted by principal component analysis. The method is used to analyze the mechanism of high-temperature formaldehyde oxidation and high-temperature propane pyrolysis. Ranking of the elementary reactions allowed us to reduce significantly the original mechanisms and a detailed study of the results revealed the reaction structures and the major reaction paths of the species.     

Meaningful activation energies for complex systems II

The validity of the Friedman method is assessed for systems of overlapping reactions. By means of mathematical analysis and numerical examples it is shown that, in the case of competitive reactions, the method gives the true value of the instantaneous mean activation energy. However, some error may be incurred if this method is applied to systems of independent reactions. The relative accuracy of the Friedman and Ozawa-Flynn-Wall methods is discussed in respect of complex systems of reactions.

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Zusammenfassung Die Gültigkeit der Friedman-Methode wird für Systeme von überlappenden Reaktionen einer Betrachtung unterzogen. Durch mathematische Analyse und numerische Beispiele wird gezeigt, daß im Falle kompetitiver Reaktionen die Methode den richtigen Wert der jeweiligen mittleren Aktivierungsenergie ergibt. Fehler können jedoch auftreten, wenn diese Methode auf Systeme voneinander unabhängiger Reaktionen angewandt wird. Die relative Genauigkeit der Methoden von Friedman und Ozawa-Flynn-Wall wird mit Hinsicht auf komplexe Reaktionssysteme diskutiert.

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The author wishes to thank the British Gas Corporation for permission to publish this work.     

Computing the density of paths in complex systems

Trajectories of duration tau joining two points q(0) and q(1) in the configuration space of a classical system satisfy Hamilton's principle: they are stationary points of the classical action. The second variation (fluctuations) of the action around the stationary point signals whether the latter is or not a minimum and delivers the density in trajectory space around the points q(0) and q(1). This concept of density of paths is of great importance in semiclassical quantum theory, where it weights the contribution to the propagator from the single classical trajectories. In this paper, two algorithms based on the concepts of molecular dynamics simulation are introduced for computing the density of paths, also called van Vleck [Proc. Natl. Acad. Sci. U.S.A. 14, 178 (1928)] determinant. Examples for realistic systems are presented, together with a suggestion about possible applications in the field of rare events in physics and chemistry.     

Fabrication of complex three-dimensional microchannel systems in PDMS

This paper describes a method for fabricating three-dimensional (3D) microfluidic channel systems in poly(dimethylsiloxane) (PDMS) with complex topologies and geometries that include a knot, a spiral channel, a "basketweave" of channels, a chaotic advective mixer, a system with "braided" channels, and a 3D grid of channels. Pseudo-3D channels, which are topologically equivalent to planar channels, are generated by bending corresponding planar channels in PDMS out of the plane into 3D shapes. True 3D channel systems are formed on the basis of the strategy of decomposing these complex networks into substructures that are planar or pseudo-3D. A methodology is developed that connects these planar and/or pseudo-3D structures to generate PDMS channel systems with the original 3D geometry. This technique of joining separate channel structures can also be used to create channel systems in PDMS over large areas by connecting features on different substrates. The channels can be used as templates to form 3D structures in other materials.