Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

The influence of substrate kinetics on the microbial community structure in granular anaerobic biomass

The development of a strong, active granular sludge bed is necessary for optimal operation of upflow anaerobic sludge blanket reactors. The microbial and mechanical structure of the granules may have a strong influence on desirable properties such as growth rate, settling velocity and shear strength. Theories have been proposed for granule microbial structure based on the relative kinetics of substrate degradation, but contradict some observations from both modelling and microscopic studies. In this paper, the structures of four granule types were examined from full-scale UASB reactors, treating wastewater from a cannery, a slaughterhouse, and two breweries. Microbial structure was determined using fluorescence in situ hybridisation probing with 16S rRNA-directed oligonucleotide probes, and superficial structure and microbial density (volume occupied by cells and microbial debris) assessed using scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The granules were also modelled using a distributed parameter biofilm model, with a previously published biochemical model structure, biofilm modelling approach, and model parameters. The model results reflected the trophic structures observed, indicating that the structures were possibly determined by kinetics. Of particular interest were results from simulations of the protein grown granules, which were predicted to have slow growth rates, low microbial density, and no trophic layers, the last two of which were reflected by microscopic observations. The primary cause of this structure, as assessed by modelling, was the particulate nature of the wastewater, and the slow rate of particulate hydrolysis, rather than the presence of proteins in the wastewater. Because solids hydrolysis was rate limiting, soluble substrate concentrations were very low (below Monod half saturation concentration), which caused low growth rates. (C) 2003 Elsevier Ltd. All rights reserved.

Thermosetting Blends of Polybenzoxazine and Poly(ε-caprolactone): Phase Behavior and Intermolecular Specific Interactions

Polybenzoxazine (PBA-a)/poly(epsilon-caprolactone) (PCL) blends were prepared by an in situ curing reaction of benzoxazine (BA-a) in the presence of PCL. Before curing, the benzoxazine (BA-a)/PCL blends are miscible, which was evidenced by the behaviors of single and composition-dependant glass transition temperature and equilibrium melting point depression. However, the phase separation induced by polymerization was observed after curing at elevated temperature. It was expected that after curing, the PBA-a/PCL blends would be miscible since the phenolic hydroxyls in the PBA-a molecular backbone have the potential to form inter- molecular hydrogen-bonding interactions with the carbonyls of PCL and thus would fulfil the miscibility of the blends. The resulting morphology of the blends prompted an investigation of the status of association between PBA-a and PCL under the curing conditions. Although Fourier-transform infrared spectroscopy (FT-IR) showed that there were intermolecular hydrogen-bonding interactions between PBA-a and PCL at room temperature, especially for the PCL-rich blends, the results of variable temperature FT-IR spectroscopy by the model compound indicate that the phenolic hydroxyl groups could not form efficient intermolecular hydrogen-bonding interactions at elevated temperatures, i.e., the phenolic hydroxyl groups existed mainly in the non-associated form in the system during curing. The results are valuable to understand the effect of curing temperature on the resulting morphology of the thermosetting blends. SEM micrograph of the dichloromethane-etched fracture surface of a 90:10 PBA-a PCL blend showing a heterogeneous morphology.

Disposition kinetics of propranolol isomers in the perfused rat liver

The aim of this study was to define the determinants of the linear hepatic disposition kinetics of propranolol optical isomers using a perfused rat liver. Monensin was used to abolish the lysosomal proton gradient to allow an estimation of propranolol ion trapping by hepatic acidic vesicles. In vitro studies were used for independent estimates of microsomal binding and intrinsic clearance. Hepatic extraction and mean transit time were determined from outflow-concentration profiles using a nonparametric method. Kinetic parameters were derived from a physiologically based pharmacokinetic model. Modeling showed an approximate 34-fold decrease in ion trapping following monensin treatment. The observed model-derived ion trapping was similar to estimated theoretical values. No differences in ion-trapping values was found between R(+)- and S(-)- propranolol. Hepatic propranolol extraction was sensitive to changes in liver perfusate flow, permeability-surface area product, and intrinsic clearance. Ion trapping, microsomal and nonspecific binding, and distribution of unbound propranolol accounted for 47.4, 47.1, and 5.5% of the sequestration of propranolol in the liver, respectively. It is concluded that the physiologically more active S(-)- propranolol differs from the R(+)- isomer in higher permeability-surface area product, intrinsic clearance, and intracellular binding site values.

Kinetics of reduction of lead smelting slags with solid carbon

Research techniques and a methodology have been developed that enable the reduction kinetics of molten lead smelting slags with solid carbon to be studied. The rates of reduction of PbO-FeO-Fe2O3-CaO-SiO2 slags with carbon have been measured for a range of slag compositions for PbO concentrations between 3 and 100 weight percent, and temperatures between 1423 and 1573 K. The reduction rates were determined for both graphite and coke. Within the range of process conditions examined, it has been shown that the reaction rates are almost independent of carbon reactivity, SiO2/CaO and SiO2/Fe ratio in the range of compositions investigated and are not influenced by the presence of sulphur in the slag.The apparent first order rate constants for oxygen removal increase with increasing PbO concentration and oxygen activity in the slag. The data indicate that the rate limiting reaction step for the reduction of lead slags with solid carbon is the chemical reaction at the gas/slag interface.

Accessing chain length dependent termination rate coefficients of methyl methacrylate (MMA) via the reversible addition fragmentation chain transfer (RAFT) process

The RAFT-CLD-T methodology is demonstrated to be not only applicable to 1-substituted monomers such as styrene and acrylates, but also to 1,1-disubstituted monomers such as MMA. The chain length of the terminating macromolecules is controlled by CPDB in MMA bulk free radical polymerization at 80 degrees C. The evolution of the chain length dependent termination rate coefficient, k(t)(i,i), was constructed in a step-wise fashion, since the MMA/CPDB system displays hybrid behavior (between conventional and living free radical polymerization) resulting in initial high molecular weight polymers formed at low RAFT agent concentrations. The obtained CLD of k(t) in MMA polymerizations is compatible with the composite model for chain length dependent termination. For the initial chain-length regime, up to a degree of polymerization of 100, k(t) decreases with alpha (in the expression k(t)(i,i) = k(t)(0) . i(-alpha)) being close to 0.65 at 80 degrees C. At chain lengths exceeding 100, the decrease is less pronounced (affording an alpha of 0.15 at 80 degrees C). However, the data are best represented by a continuously decreasing nonlinear functionality implying a chain length dependent alpha.

Modeling the molecular weight distribution of block copolymer formation in a reversible addition-fragmentation chain transfer mediated living radical polymerization

Block copolymers have become an integral part of the preparation of complex architectures through self-assembly. The use of reversible addition-fragmentation chain transfer (RAFT) allows blocks ranging from functional to nonfunctional polymers to be made with predictable molecular weight distributions. This article models block formation by varying many of the kinetic parameters. The simulations provide insight into the overall polydispersities (PDIs) that will be obtained when the chain-transfer constants in the main equilibrium steps are varied from 100 to 0.5. When the first dormant block [polymer-S-C(Z)=S] has a PDI of 1 and the second propagating radical has a low reactivity to the RAFT moiety, the overall PDI will be greater than 1 and dependent on the weight fraction of each block. When the first block has a PDI of 2 and the second propagating radical has a low reactivity to the RAFT moiety, the PDI will decrease to around 1.5 because of random coupling of two broad distributions. It is also shown how we can in principle use only one RAFT agent to obtain block copolymers with any desired molecular weight distribution. We can accomplish this by maintaining the monomer concentration at a constant level in the reactor over the course of the reaction. (c) 2005 Wiley Periodicals, Inc.

Using different structure types of microemulsions for the preparation of poly(alkylcyanoacrylate) nanoparticles by interfacial polymerization

A phase diagram of the pseudoternary system ethyloleate, polyoxyethylene 20 sorbitan mono-oleate/sorbitan monolaurate and water with butanol as a cosurfactant was prepared. Areas containing optically isotropic, low viscosity one-phase systems were identified and systems therein designated as w/o droplet-, bicontinuous- or solution-type microemulsions using conductivity, viscosity, cryo-field emission scanning electron microscopy and self-diffusion NMR. Nanoparticles were prepared by interfacial polymerization of selected w/o droplet, bicontinuous- or solution-type microemulsions with ethyl-2-cyanoacrylate. Morphology of the particles and entrapment of the water-soluble model protein ovalbumin were investigated. Addition of monomer to the different types of microemulsions (w/o droplet, bicontinuous, solution) led to the formation of nanoparticles, which were similar in size (similar to 250 nm), polydispersity index (similar to 0.13), zeta-potential (similar to-17 mV) and morphology. The entrapment of the protein within these particles was up to 95%, depending on the amount of monomer used for polymerization and the type of microemulsion used as a polymerization template. The formation of particles with similar characteristics from templates having different microstructure is surprising, particularly considering that polymerization is expected to occur at the water-oil interface by base-catalysed polymerization. Dynamics within the template (stirring, viscosity) or indeed interfacial phenomena relating to the solid-liquid interface appear to be more important for the determination of nanoparticle morphology and characteristics than the microstructure of the template system. (c) 2005 Elsevier B.V. All rights reserved.

Design strategies for controlling the molecular weight and rate using reversible addition-fragmentation chain transfer mediated living radical polymerization

Living radical polymerization has allowed complex polymer architectures to be synthesized in bulk, solution, and water. The most versatile of these techniques is reversible addition-fragmentation chain transfer (RAFT), which allows a wide range of functional and nonfunctional polymers to be made with predictable molecular weight distributions (MWDs), ranging from very narrow to quite broad. The great complexity of the RAFT mechanism and how the kinetic parameters affect the rate of polymerization and MWD are not obvious. Therefore, the aim of this article is to provide useful insights into the important kinetic parameters that control the rate of polymerization and the evolution of the MWD with conversion. We discuss how a change in the chain-transfer constant can affect the evolution of the MWD. It is shown how we can, in principle, use only one RAFT agent to obtain a poly-mer with any MWD. Retardation and inhibition are discussed in terms of (1) the leaving R group reactivity and (2) the intermediate radical termination model versus the slow fragmentation model. (c) 2005 Wiley Periodicals, Inc.

Phosphate uptake and growth kinetics of Trichodesmium (Cyanobacteria) isolates from the North Atlantic Ocean and the Great Barrier Reef, Australia

We compared inorganic phosphate (P-i) uptake and growth kinetics of two cultures of the diazotrophic cyanobacterium Trichodesmium isolated from the North Atlantic Ocean (IMS101) and from the Great Barrier Reef, Australia (GBRTRLI101). Phosphate-limited cultures had up to six times higher maximum P-i uptake rates than P-replete cultures in both strains. For strain GBRTRLI101, cell-specific P-i uptake rates were nearly twice as high, due to larger cell size, but P-specific maximum uptake rates were similar for both isolates. Half saturation constants were 0.4 and 0.6 muM for P-i uptake and 0.1 and 0.2 muM for growth in IMS101 and GBRTRLI101, respectively. Phosphate uptake in both strains was correlated to growth rates rather than to light or temperature. The cellular phosphorus quota for both strains increased with increasing P-i up to 1.0 muM. The C:P ratios were 340-390 and N:P ratios were 40-45 for both strains under severely P-limited growth conditions, similar to reported values for natural populations from the tropical Atlantic and Pacific Oceans. The C:P and N:P ratios were near Redfield values in medium with >1.0 muM P-i. The North Atlantic strain IMS101 is better adapted to growing on P-i at low concentrations than is GBRTRLI101 from the more P-i-enriched Great Barrier Reef. However, neither strain can achieve appreciable growth at the very low (nanomolar) P-i concentrations found in most oligotrophic regimes. Phosphate could be an important source of phosphorus for Trichodesmium on the Great Barrier Reef, but populations growing in the oligotrophic open ocean must rely primarily on dissolved organic phosphorus sources.

Kinetics of reduction of FeO from slag by graphite and coal chars

The rates of reduction of FeO from iron-saturated FeO-CaO-Al2O3-SiO2 slags by graphite, coke, bituminous coal and anthracitic coal chars at temperatures in the range 1 673-1873 K have been measured using a sessile drop technique. The extents of reaction were determined using EPMA analysis of quenched samples, and on line gas analysis using a quadrupole mass spectrometer. The reaction rates have been shown to be dependent critically on carbon type. For the reaction geometry used in this investigation the reduction rates of graphite and coke are observed to be faster than with coal chars. This unexpected finding is shown to be associated with differences in the dominant chemical and mass transfer mechanisms occurring at the reaction interface. High reaction rates are observed to occur with the formation of liquid Fe-C alloy product and the associated gasification of carbon from the alloy. The rates of reduction by coal chars are determined principally by the chemical reaction at the carbon/gas interface and slag phase mass transfer.

Mg-based nanocomposites with high capacity and fast kinetics for hydrogen storage

Magnesium and its alloys have shown a great potential in effective hydrogen storage due to their advantages of high volumetric/ gravimetric hydrogen storage capacity and low cost. However, the use of these materials in fuel cells for automotive applications at the present time is limited by high hydrogenation temperature and sluggish sorption kinetics. This paper presents the recent results of design and development of magnesium-based nanocomposites demonstrating the catalytic effects of carbon nanotubes and transition metals on hydrogen adsorption in these materials. The results are promising for the application of magnesium materials for hydrogen storage, with significantly reduced absorption temperatures and enhanced ab/desorption kinetics. High level Density Functional Theory calculations support the analysis of the hydrogenation mechanisms by revealing the detailed atomic and molecular interactions that underpin the catalytic roles of incorporated carbon and titanium, providing clear guidance for further design and development of such materials with better hydrogen storage properties.

Preparation of poly (alkylcyanoacrylate) nanoparticles by polymerization of water-free microemulsions

Phase diagrams of the pseudoternary systems ethyloleate, polyoxyethylene 20 sorbitan mono-oleate/sorbitan monolaurate and propylene glycol with and without butanol as a co-surfactant were prepared. Areas containing optically isotropic, one-phase systems were identified and samples therein designated as droplet, bicontinuous or solution type microemulsions using conductivity, viscosity and self-diffusion NMR. Nanoparticles were prepared by polymerization of selected microemulsions with ethyl-2-cyanoacrylate and the morphology of the particles was investigated. Addition of monomer to all types of microemulsions led to the formation of nanoparticles, which had an average size of 244 +/- 25 nm, an average polydispersity index of 0.15 +/- 0.04 and a zeta-potential of -17 +/- 3 mV. The formation of particles from water-free microemulsions of different types is surprising, particularly considering that polymerization is expected to occur at a water-oil interface by base-catalysed polymerization. It would appear that propylene glycol is sufficiently nucleophilic to initiate the polymerization. The use of water-free microemulsions as templates for the preparation of poly (alkylcyanoacrylate) nanoparticles opens up interesting opportunities for the encapsulation of bioactives which do not have suitable properties for encapsulation on the basis of water-containing microemulsions.

Phase separation, porous structure, and cure kinetics in aliphatic epoxy resin containing hyperbranched polyester

Thermosetting blends of an aliphatic epoxy resin and a hydroxyl-functionalized hyperbranched polymer (HBP), aliphatic hyperbranched polyester Boltorn H40, were prepared using 4,4'-diaminodiphenylmethane (DDM) as the curing agent. The phase behavior and morphology of the DDM-cured epoxy/HBP blends with HBP content up to 40 wt% were investigated by differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and scanning electron microscopy (SEM). The cured epoxy/HBP blends are immiscible and exhibit two separate glass transitions, as revealed by DMA. The SEM observation showed that there exist two phases in the cured blends, which is an epoxy-rich phase and an HBP-rich phase, which is responsible for the two separate glass transitions. The phase morphology was observed to be dependent on the blend composition. For the blends with HBP content up to 10 wt%, discrete HBP domains are dispersed in the continuous cured epoxy matrix, whereas the cured blend with 40 wt% HBP exhibits a combined morphology of connected globules and bicominuous phase structure. Porous epoxy thermosets with continuous open structures on the order of 100-300 nm were formed after the HBP-rich phase was extracted with solvent from the cured blend with 40 wt% HBP. The DSC study showed that the curing rate is not obviously affected in the epoxy/HBP blends with HBP content up to 40 wt %. The activation energy values obtained are not remarkably changed in the blends; the addition of HBP to epoxy resin thus does not change the mechanism of cure reaction of epoxy resin with DDM. (c) 2006 Wiley Periodicals, Inc.