Precipitation In Small Systems--II. Mean Field Equations More Effective Than Population Balance

Part I (Manjunath et al., 1994, Chem. Engng Sci. 49, 1451-1463) of this paper showed that the random particle numbers and size distributions in precipitation processes in very small drops obtained by stochastic simulation techniques deviate substantially from the predictions of conventional population balance. The foregoing problem is considered in this paper in terms of a mean field approximation obtained by applying a first-order closure to an unclosed set of mean field equations presented in Part I. The mean field approximation consists of two mutually coupled partial differential equations featuring (i) the probability distribution for residual supersaturation and (ii) the mean number density of particles for each size and supersaturation from which all average properties and fluctuations can be calculated. The mean field equations have been solved by finite difference methods for (i) crystallization and (ii) precipitation of a metal hydroxide both occurring in a single drop of specified initial supersaturation. The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance. This comparison shows that the mean field predictions are substantially superior to those of population balance as judged by the close proximity of results from the former to those from stochastic simulations. The agreement is excellent for broad initial supersaturations at short times but deteriorates progressively at larger times. For steep initial supersaturation distributions, predictions of the mean field theory are not satisfactory thus calling for higher-order approximations. The merit of the mean field approximation over stochastic simulation lies in its potential to reduce expensive computation times involved in simulation. More effective computational techniques could not only enhance this advantage of the mean field approximation but also make it possible to use higher-order approximations eliminating the constraints under which the stochastic dynamics of the process can be predicted accurately.

Fracture Behavior of Ferrocement Beams

An attempt is made to study the fracture behavior of ferrocement beams using J-integral and critical crack opening displacement approaches. Ferrocement beams with three different relative notch depths and different percentages of mesh reinforcement were tested in four-point bending (third-point loading). The experimental results were used to evaluate the apparent J-integral and CODc values. Results show that the apparent J-integral does not seem to follow any particular trend in variation with notch depth, but is sensitive to the increase of mesh reinforcement. Hence, the apparent J-integral appears to be a useful fracture criterion for ferrocement. The computed values of CODt are found to be dependent on the depth of notch and, thus, cannot possibly be considered as a suitable fracture criterion for ferrocement.

Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates

This paper presents a unified exact analysis for the statics and dynamics of a class of thick laminates. A three-dimensional, linear, small deformation theory of elasticity solution is developed for the bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. All the nine elastic constants of orthotropy are taken into account. The solution is formally exact and leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems. For free vibration of plates, the present analysis yields a triply infinite spectrum of frequencies instead of only one doubly infinite spectrum by thin plate theory or three doubly infinite spectra by Reissner-Mindlin type analyses. Some numerical results are presented for plates and laminates. Comparison of results from thin plate, Reissner and Mindlin analyses with these yield some important conclusions regarding the validity and effects of the assumptions made in the approximate theories.

Substituent effects on the addition of alcohols and anilines to organic isothiocyanates

The addition reactions of alcohols, ROH (R = CH3, C2H5 n-C3H7, i-C3H7 and t-C4H9), to p-bromophenylisothiocyanate show that the rates decrease in the order, CH3OH> C2H5OH> n-C3H7OH> i-C3H7OH> t-C4H9OH, although the basicities of the alcohols vary in the reverse order. The results indicate the greater importance of steric factors as compared with polar factors. Evidence is also presented for the formation of a complex between the isothiocyanate and the alcohol in the first stage of the addition reaction. In the addition of aniline to substituted phenylisothiocyanates the rate data give a satisfactory linear correlation with Hammett σ constants and the results clearly show that electron-withdrawing groups favour the addition reaction. The addition of aniline to alkyl isothiocyanates have been studied in order to find out the nature of alkyl group interaction in these derivatives. Kinetic studies on the addition of substituted anilines to phenylisothiocyanate show that the rate of reaction increases with the electron-donating ability of the substituents on the aniline as also the basicity of the aniline.

Electron-hole recombination in cobalt-doped p-type germanium

The recombination properties of cobalt centers in p-type germanium containing cobalt in the concentration range 1014 to 1016 atoms/cm3 have been investigated. The measurement of lifetime has been carried out by steady-state photoconductivity and photo-magneto-electric methods in the temperature range 145 to 300°K. The cross-sections Sno (electron capture cross-section at neutral centers). Sn- (electron capture cross-section at singly negatively charged centers) and their temperature variations have been estimated by the analysis of the lifetime data on the basis of Sah-Shockley's multi-level formula. The value of Sno is (15±5).10-16 cm2 and is temperature independent. The value of Sn- is ≈4·10-16 cm2 around 225°K and it increases with increase of temperature. The possible mechanisms for capture at neutral and repulsive centers are discussed and a summary of the capture cross-sections for cobalt centers is given. A comparison of the cross-section values of cobalt and their temperature variations with those of the related impurities-manganese, iron and nickel-in germanium has been made.

Construction of energy-level diagram of oriented benzene using connectivity information obtained by modified z-cosy experiment

Experiments involving selective perturbation of a transition yield information about the directly connected transitions, which in turn yield information for deriving the parameters of the spin Hamiltonian of oriented molecules. Problems involved with selective perturbation are removed by the use of a two-dimensional experiment, namely, the modified Z-COSY-experiment, The use of this experiment is demonstrated for obtaining the connectivity information and for determining the parameters of the spin Hamiltonian of oriented benzene, a strongly coupled six-spin system

Precipitation in small systems-I. stochastic analysis

Precipitation in small droplets involving emulsions, microemulsions or vesicles is important for Producing multicomponent ceramics and nanoparticles. Because of the random nature of nucleation and the small number of particles in a droplet, the use of a deterministic population balance equation for predicting the number density of particles may lead to erroneous results even for evaluating the mean behavior of such systems. A comparison between the predictions made through stochastic simulation and deterministic population balance involving small droplets has been made for two simple systems, one involving crystallization and the other a single-component precipitation. The two approaches have been found to yield quite different results under a variety of conditions. Contrary to expectation, the smallness of the population alone does not cause these deviations. Thus, if fluctuation in supersaturation is negligible, the population balance and simulation predictions concur. However, for large fluctuations in supersaturation, the predictions differ significantly, indicating the need to take the stochastic nature of the phenomenon into account. This paper describes the stochastic treatment of populations, which involves a sequence of so-called product density equations and forms an appropriate framework for handling small systems.

Combustion synthesis and properties of the NASICON family of materials

The fine-particle NASICON family of materials, MZr2P3O12(where M = Na, K, ½Ca and ¼Zr) and NbZrP3O12, have been prepared by the combustion of aqueous heterogeneous mixtures of stoichiometric amounts of metal nitrate, zirconyl nitrate, niobium phosphate, diammonium hydrogen phosphate, ammonium perchlorate and carbohydrazide (CH) at 400 °C. The formation of NASICON materials was confirmed by powder X-ray diffraction (XRD), IR, solid-state (31P) NMR spectroscopy and thermal expansion coefficient measurements. The combustion-synthesized NASICON powders have an average agglomerate size of 9�13 µm with a specific surface area varying from 8 to 28 m2 g�1. The powders pelletized and sintered in the range 1100�1200 °C for 5 h achieved 95�97% theoretical density and showed fine-grain microstructure. The coefficient of thermal expansion of a sintered compact was measured up to 500 °C and ranged from �1.5 × 10�6°C�1 to 1.0 × 10�6°C�1 depending on the composition.

Demographic history of India and mtDNA-sequence diversity

The demographic history of India was examined by comparing mtDNA sequences obtained from members of three culturally divergent Indian subpopulations (endogamous caste groups). While an inferred tree revealed some clustering according to caste affiliation, there was no clear separation into three genetically distinct groups along caste lines. Comparison of pairwise nucleotide difference distributions, however, did indicate a difference in growth patterns between two of the castes. The Brahmin population appears to have undergone either a rapid expansion or steady growth. The low-ranking Mukri caste, however, may have either maintained a roughly constant population size or undergone multiple bottlenecks during that period. Comparison of the Indian sequences to those obtained from other populations, using a tree, revealed that the Indian sequences, along with ah other non-African samples, form a starlike cluster. This cluster may represent a major expansion, possibly originating in southern Asia, taking place at some point after modern humans initially left Africa.

Electrical and Optical Properties of Diketopyrrolopyrrole-Based Copolymer Interfaces in Thin Film Devices

Two donor acceptor diketopyrrolopyrrole (DPP)-based copolymers (PDPP-BBT and TDPP-BBT) have been synthesized for their application in organic devices such as metal-insulator semiconductor (MIS) diodes and field-effect transistors (FETs). The semiconductor-dielectric interface was characterized by capacitance-voltage and conductance-voltage methods. These measurements yield an interface trap density of 4.2 x 10(12) eV(-1) cm(-2) in TDPP-BBT and 3.5 x 10(12) eV(-1) cm(-2) in PDPP-BBT at the flat-band voltage. The FETs based on these spincoated DPP copolymers display p-channel behavior with hole mobilities of the order 10(-3) cm(2)/(V s). Light scattering studies from PDPP-BBT FETs show almost no change in the Raman spectrum after the devices are allowed to operate at a gate voltage, indicating that the FETs suffer minimal damage due to the metal-polymer contact or the application of an electric field. As a comparison Raman intensity profile from the channel-Au contact layer in pentacene FETs are presented, which show a distinct change before and after biasing.

Method for measurement of the angles of an equilateral (60-deg) prism

A simple technique is devised io measure the angles of equilateral (60-deg) prisms, without using the expensive spectrometers, autocollimators, and angle gauges. The method can be extended to unpolished and opaque prisms made out of materials other than glass. (C) 1997 Society of Photo-Optical Instrumentation Engineers.

Spectral asymptotics of the Helmholtz model in fluid-solid structures

A model representing the vibrations of a coupled fluid-solid structure is considered. This structure consists of a tube bundle immersed in a slightly compressible fluid. Assuming periodic distribution of tubes, this article describes the asymptotic nature of the vibration frequencies when the number of tubes is large. Our investigation shows that classical homogenization of the problem is not sufficient for this purpose. Indeed, our end result proves that the limit spectrum consists of three parts: the macro-part which comes from homogenization, the micro-part and the boundary layer part. The last two components are new. We describe in detail both macro- and micro-parts using the so-called Bloch wave homogenization method. Copyright (C) 1999 John Wiley & Sons, Ltd.

The thermodynamics and phase behaviour of Tb2Pd2O5 and Er2Pd2O5

Isothermal sections of the phase diagrams for the systems Ln-Pd-O (with Ln = Tb or Er) have been established by equilibration of samples at T = 1223 K, and phase identification after quenching by optical and scanning electron microscopy (OM, SEM), energy dispersive spectroscopy (EDS), and X-ray powder diffraction (XRPD). Two oxide phases were stable along the binary Tb-O: Tb2O3+x, a phase of variable composition, and Tb7O12 at T = 1223K. The oxide PdO was not stable at this temperature. Only one ternary oxide Tb2Pd2O5 was identified in the Tb-Pd-O system. No ternary compound was found in the system Er-Pd-O at T = 1223K. However, the compound Er2Pd2O5 could be synthesized at T = 1075 K by the hydrothermal route. In both systems, the alloys and inter-metallic compounds were all found to be in equilibrium with the lanthanide sesquioxide Ln(2)O(3) (where Ln is either Tb or Er). Two solid-state cells, each incorporating a buffer electrode, were designed to measure the Gibbs energy of formation of the ternary oxides, using yttria-stabilized zirconia as the solid electrolyte and pure oxygen gas as the reference electrode. Electromotive force measurements were conducted in the temperature range (900-1275) K for Th-Pd-O system, and at temperatures from (900-1075) K for the system Er-Pd-O. The standard Gibbs energy of formation Delta(f)G(m)degrees,, of the inter-oxide compounds from their component binary oxides Ln(2)O(3) and PdO are represented by equations linear in temperature. Isothermal chemical potential diagrams for the systems Ln-Pd-O (with Ln = Tb or Er) are developed based on the thermodynamic information. (C) 2002 Elsevier Science Ltd. All rights reserved.

Study of surface oxidation of rare-earth-metals by photoelectron-spectroscopy

Surface oxidation of La, Ce, Sm and Tb metals has been investigated by He(II) ultraviolet photoelectron spectroscopy (u.p.s.) and X-ray photoelectron spectroscopy (X.p.s.). Oxidation of La gives rise to La2O3 on the surface. While Ce2O3 appears to be the stable oxide on the surface, we find evidence for formation of CeO2 at high oxygen exposure. Valence band of Sm clearly shows the presence of both divalent and trivalent states due to interconfigurational fluctuation. Exposure of Sm to oxygen first depletes the divalent Sm at the surface. While Sm2O3 is the stable oxide on the surface of Sm, Tb2O3 is the stable oxide on the surface of Tb (and not any of the higher oxides).

Optical, electrochemical and morphological investigations of poly (3,4-propylenedioxythiophene)-sultone (PProDOT-S) thin films

In this paper, we have carried out thin film characterization of poly(3,4-propylenedioxythiophene)-sultone (PProDOT-S), a derivative of electrochromic poly(3,4-propylenedioxythiophene) (PProDOT). PProDOT-S was deposited onto transparent conducting oxide coated glass substrates by solution casting method. Single wavelength spectrophotometry is used to monitor the switching speed and contrast ratio at maximum wavelength (lambda (max)). The percentage transmittance at the lambda (max) of the neutral polymer is monitored as a function of time when the polymer film is repeatedly switched. This experiment gives a quantitative measure of the speed with which a film is able to switch between the two states i.e. the coloured and the bleached states. PProDOT-S films were switched at a voltage of 1 center dot 9 V with a switching speed of 2 s at lambda (max) of 565 nm and showed a contrast of similar to 37%. Cyclic voltammetry performed at different scan rates have shown the characteristic anodic and cathodic peaks. The structural investigations of PProDOT-S films by IR spectra were in good agreement with previously reported results. Raman spectra of PProDOT-S showed a strong Raman peak at 1509 cm (-aEuro parts per thousand 1) and a weak peak at 1410 cm (-aEuro parts per thousand 1) due to the C = C asymmetric and symmetric stretching vibrations of thiophene rings. The morphological investigations carried out by using scanning electron microscope (SEM) of polymer films have shown that these polymers are found to be arranged in dense packed clusters with non-uniform distribution having an average width and length of 95 nm and 160 nm, respectively.