The role of molecular interactions and interfaces in diffusion: permeation through single-crystal and polycrystalline microporous membranes

In this second paper of a two part series, we investigate the implications of the interfacial phenomenon, caused by adsorbate-adsorbate interactions coupled with the difference in adsorbate density between the zeolite and the gas phase, upon benzene permeation through single-crystal and polycrystalline microporous NaX membranes. The high flux predicted for thin single-crystal membranes reveals that substantially enhanced flux should be expected in submicron films. Simulations also indicate that the standard local equilibrium assumption made for larger scale membranes is inapplicable at the submicron scale associated with nanometer size grains of thin and/or polycrystalline membranes. Apparent activation energies predicted for benzene permeation through NaX membranes via kinetic Monte Carlo (KMC) simulations are in good agreement with laboratory experiments. The simulations also uncover temperature-dependent flux pathways leading to non-Arrhenius behavior observed experimentally. The failure of the Darken approximation, especially in the presence of the interfacial phenomenon, leads to a substantial overprediction of the flux. Simulations of polycrystalline membranes suggest that this same interfacial phenomenon leads to resistance that can reduce flux by an order of a magnitude with only moderate polycrystallinity.     

Molecular dynamics studies on the role of tetramethylammonium cations in the stability of the silica octamers Si8O20(8-) in solution

The stability of silica octamers, Si(8) observed in tetramethylammonium (TMA) solutions by Kinrade et al. is investigated in connection with the TMA concentration by performing equilibrium molecular dynamics simulations of Si(8)-TMA-water mixture at two concentrations. At the experimental concentration at which the silica octamers have been observed spectroscopically, we find that, on the average, six TMA molecules surround the silica octamer, coordinated so that each cation occupies a face of the cubic octamer. We also find that upon TMA adsorption, water molecules associated with the siloxane oxygens leave the silica surface, whereas the hydrogen-bond network of the silanol oxygens with water molecules remains intact. No TMA adsorption is observed at the concentration at which the octamers have not been observed.     

Hypersurfaces and Codazzi tensors

In this paper we deal with the following problem. Let (M ⁿ ,〈,〉) be an n-dimensional Riemannian manifold and an isometric immersion. Find all Riemannian metrics on M ⁿ that can be realized isometrically as immersed hypersurfaces in the Euclidean space . More precisely, given another Riemannian metric on M ⁿ , find necessary and sufficient conditions such that the Riemannian manifold admits an isometric immersion into the Euclidean space . If such an isometric immersion exists, how can one describe in terms of f? Author’s address: Thomas Hasanis and Theodoros Vlachos, Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece     

Insights into the early stages of metal nanoparticle formation via first-principle calculations: the roles of citrate and water

The early stages of silver nanoparticle formation in the presence of citrate and water have been investigated via first-principle theoretical calculations. Our study revealed that the charge density of the clusters is a key factor determining the selectivity among various growth pathways. An optimal charge density appears to control the selection between neutral and charged species in cluster growth; partially positively charged clusters are thermodynamically preferred and can serve as seeds for further growth. They interact favorably with both the solvent, leading to their solubility, and the citrate. The solvent (water) plays an important role in cluster growth both on the energetics of reactions including highly charged clusters and on the geometry of the resulting silver structures by preventing the formation of asymmetric ones (a structure directing action). Contrary to the common belief we found, from an energetic viewpoint, that growth of small clusters is not blocked by the citrate. Citrate, by acting as a reducing agent, opens up new channels for cluster growth involving highly charged species. By regulating the cluster charge, cluster-cluster associations may be promoted by the citrate, providing a new mechanistic interpretation for the effect of citrate concentration on nanoparticle size substantially different from the classic nucleation theory. From the citrate-silver and water-silver cluster interactions, linear free energy relationships have been retrieved that provide insights into metal nanoparticle growth mechanisms.     

A method for automatic estimation of instantaneous local uncertainty in particle image velocimetry measurements

The uncertainty of any measurement is the interval in which one believes the actual error lies. Particle image velocimetry (PIV) measurement error depends on the PIV algorithm used, a wide range of user inputs, flow characteristics, and the experimental setup. Since these factors vary in time and space, they lead to nonuniform error throughout the flow field. As such, a universal PIV uncertainty estimate is not adequate and can be misleading. This is of particular interest when PIV data are used for comparison with computational or experimental data. A method to estimate the uncertainty from sources detectable in the raw images and due to the PIV calculation of each individual velocity measurement is presented. The relationship between four error sources and their contribution to PIV error is first determined. The sources, or parameters, considered are particle image diameter, particle density, particle displacement, and velocity gradient, although this choice in parameters is arbitrary and may not be complete. This information provides a four-dimensional “uncertainty surface” specific to the PIV algorithm used. After PIV processing, our code “measures" the value of each of these parameters and estimates the velocity uncertainty due to the PIV algorithm for each vector in the flow field. The reliability of our methodology is validated using known flow fields so the actual error can be determined. Our analysis shows that, for most flows, the uncertainty distribution obtained using this method fits the confidence interval. An experiment is used to show that systematic uncertainties are accurately computed for a jet flow. The method is general and can be adapted to any PIV analysis, provided that the relevant error sources can be identified for a given experiment and the appropriate parameters can be quantified from the images obtained.     

A characterization of the Clifford torus

We provide a characterization of the Clifford torus via a Ricci type condition among minimal surfaces in S⁴. More precisely, we prove that a compact minimal surface in S⁴, with induced metric ds² and Gaussian curvature K, for which the metric is flat away from points where K = 1, is the Clifford torus, provided that m is an integer with m > 2.Received: 8 September 2004     

Complete Minimal Hypersurfaces in a Sphere

In this paper we investigate complete minimal hypersurfaces with at most two principal curvatures. We prove that if the squared norm S of the second fundamental form satisfies S ≥ n, then S = n and f(Mⁿ) is a minimal Clifford torus.     

Binomial distribution based tau-leap accelerated stochastic simulation

Recently, Gillespie introduced the tau-leap approximate, accelerated stochastic Monte Carlo method for well-mixed reacting systems [J. Chem. Phys. 115, 1716 (2001)]. In each time increment of that method, one executes a number of reaction events, selected randomly from a Poisson distribution, to enable simulation of long times. Here we introduce a binomial distribution tau-leap algorithm (abbreviated as BD-tau method). This method combines the bounded nature of the binomial distribution variable with the limiting reactant and constrained firing concepts to avoid negative populations encountered in the original tau-leap method of Gillespie for large time increments, and thus conserve mass. Simulations using prototype reaction networks show that the BD-tau method is more accurate than the original method for comparable coarse-graining in time.     

Lead growth on Si(111) surfaces reconstructed by indium

We study the Pb growth on both √3 × √3-In and 4 × 1-In reconstructed Si(111) surfaces at room and low temperature (160 K). The study takes place with complementary techniques, to investigate the role of the substrate reconstruction and temperature in determining the growth mode of Pb. Specifically, we focus on the correlation between the growth morphology and the electronic structure of the Pb films. The information is obtained by using Auger electron spectroscopy, low energy electron diffraction, soft x-ray photoelectron spectroscopy, scanning tunneling microscopy and spot profile analysis-low energy electron diffraction. The results show that, at low temperature and coverage ≤12 ML on the Si(111)√3 × √3-In surface, Pb does not alter the initial semiconducting character of the substrate and three-dimensional Pb islands with poor crystallinity are grown on a wetting layer. On the other hand, for the same coverage range, Pb growth on the Si(111)4 × 1-In surface results in metallic Pb(111) crystalline islands after the completion of a double incomplete wetting layer. In addition, the bond arrangement of the adatoms is studied, confirming that In adatoms interact more strongly with the silicon substrate than the Pb ones. This promotes a stronger Pb-Pb interaction and enhances metallization. The onset of the metallization is correlated with the amount of pre-deposited In on the Si(111) surface. The decoupling of the Pb film from the 4 × 1-In interface can also explain the unusual thermal stability of the uniform height islands observed on this interface. The formation of these Pb islands is driven by quantum size effects. Finally, the different results of Pb growth on the two reconstructed surfaces confirm the importance of the interface, and also that the growth morphology, as well as the electronic structure of the Pb film can be tuned with the initial substrate reconstruction.