Reaction Time Scale Research Articles

Kinetic fractionation of Fe isotopes during transport through a porous quartz-sand column

Sorption and desorption processes are an important part of biological and geochemical metallic isotope cycles. Here, we address the dynamic aspects of metallic isotopic fractionation in a theoretical and experimental study of Fe sorption and desorption during the transport of aqueous Fe(III) through a quartz-sand matrix. Transport equations describing the behavior of sorbing isotopic species in a water saturated homogeneous porous medium are presented; isotopic fractionation of the system (Δ sorbed metal-soln) being defined in terms of two parameters: (i) an equilibrium fractionation factor, α e; and (ii) a kinetic sorption factor, α 1. These equations are applied in a numerical model that simulates the sorption-desorption of Fe isotopes during injection of a Fe(III) solution pulse into a quartz matrix at pH 0–2 and explores the effects of the kinetic and equilibrium parameters on the Fe-isotope evolution of porewater. The kinetic transport theory is applied to a series of experiments in which pulses of Na and Fe(III) chloride solutions were injected into a porous sand grain column. Fractionation factors of α e = 1.0003 ± 0.0001 and α 1 = 0.9997 ± 0.0004 yielded the best fit between the transport model and the Fe concentration and δ 56Fe data. The equilibrium fractionation (Δ 56Fe sorbed Fe-soln) of 0.3‰ is comparable with values deduced for adsorption of metallic cations on iron and manganese oxide surfaces and suggests that sandstone aquifers will fractionate metallic isotopes during sorption-desorption reactions. The ability of the equilibrium fractionation factor to describe a natural system, however, depends on the proximity to equilibrium, which is determined by the relative time scales of mass transfer and chemical reaction; low fluid transport rates should produce a system that is less dependent on kinetic effects. The results of this study are applicable to Fe-isotope fractionation in clastic sediments formed in highly acidic conditions; such conditions may have existed on Mars where acidic oxidizing ground and surface waters may have been responsible for clastic sedimentation and metallic element transport.

A computational study of a fast sampling valve designed to sample soot precursors inside a forming diesel spray plume

Accurate chemical reaction mechanisms are critically needed to fully optimize combustion strategies for modern internal-combustion engines. These mechanisms are needed to predict emission formation and the chemical heat release characteristics for traditional direct-injection diesel as well as recently-developed and proposed variant combustion strategies. Experimental data acquired under conditions representative of such combustion strategies are required to validate these reaction mechanisms. This paper explores the feasibility of developing a fast sampling valve which extracts reactants at known locations in the spray reaction structure to provide these data. CHEMKIN software is used to establish the reaction timescales which dictate the required fast sampling capabilities. The sampling process is analyzed using separate FLUENT and CHEMKIN calculations. The non-reacting FLUENT CFD calculations give a quantitative estimate of the sample quantity as well as the fluid mixing and thermal history. A CHEMKIN reactor network has been created that reflects these mixing and thermal time scales and allows a theoretical evaluation of the quenching process.

Dynamics of ligand substitution in labile cobalt complexes resolved by ultrafast T-jump

Ligand exchange of hydrated metal complexes is common in chemical and biological systems. Using the ultrafast T-jump, we examined this process, specifically the transformation of aqua cobalt (II) complexes to their fully halogenated species. The results reveal a stepwise mechanism with time scales varying from hundreds of picoseconds to nanoseconds. The dynamics are significantly faster when the structure is retained but becomes rate-limited when the octahedral-to-tetrahedral structural change bottlenecks the transformation. Evidence is presented, from bimolecular kinetics and energetics (enthalpic and entropic), for a reaction in which the ligand assists the displacement of water molecules, with the retention of the entering ligand in the activated state. The reaction time scale deviates by one to two orders of magnitude from that of ionic diffusion, suggesting the involvement of a collisional barrier between the ion and the much larger complex.

Inside Cover: Real‐Time Detection of Protein–Water Dynamics upon Protein Folding by Terahertz Absorption Spectroscopy (Angew. Chem. Int. Ed. 34/2008)

Kinetic terahertz absorption (KITA) uses a picosecond-duration terahertz pulse to monitor directly changes in solvent dynamics during molecular self-assembly on a reaction time scale of milliseconds to seconds. In their Communication on page 6486 ff., M. Gruebele and co-workers describe the application of this method to investigate the reorganization of solvent water during the folding of a protein (in this case ubiquitin).

Dynamics of the F2 reaction with the simplest π-bonding molecule

The reaction of F(2)+C(2)H(4) has been investigated with crossed molecular beam experiments and high level ab initio calculations. For a wide range of collision energies up to 11 kcal/mol, only one reaction channel could be observed in the gas phase. The primary products of this channel were identified as F+CH(2)CH(2)F. The experimental reaction threshold of collision energy was determined to be 5.5+/-0.5 kcal/mol. The product angular distribution was found to be strongly backward, indicating that the reaction time scale is substantially shorter than rotation. The calculated transition state structure suggests an early barrier; such dynamics is consistent with the small product kinetic energy release measured in the experiment. All experimental results consistently support a rebound reaction mechanism, which is suggested by the calculation of the intrinsic reaction coordinate. This work provides a clear and unambiguous description of the reaction dynamics, which may help to answer the question why the same reaction produces totally different products in the condensed phase.

Oscillatory and nonoscillatory behavior of a simple model for cool flames, Sal'nikov's reaction, P → A → B, occurring in a spherical batch reactor with varying intensities of natural convection

When cool flames, or indeed any exothermic chemical reaction, occur in a fluid inside an unstirred vessel, the heat from the reaction often induces temperature gradients and consequently motion, i.e., natural convection. The intensity of the resulting flow is governed by the Rayleigh number (Ra). This work simulates numerically the behavior of Sal'nikov's reaction, P → A → B, under the influence of natural convection in an unstirred spherical reactor. This reaction is the simplest to exhibit the thermokinetic oscillations characterizing cool flames. The behavior of this system can be represented on a three-dimensional regime diagram, whose axes are ratios of the characteristic timescales ( τ) for chemical reaction, diffusion (of both heat and mass), and natural convection. Previous work has identified a region of oscillations on this diagram in the purely diffusive limit, when Ra = 0. This work extends this analysis to the general 3D space, where diffusion and natural convection are both important. A region in which oscillations are observed has been found for fixed values of the first-order rate constants for Sal'nikov's reaction. There is a distinct change in the shape of the region of oscillations around the critical value of Ra ∼ 500, when natural convection becomes important. When diffusion dominates transport (Ra < 500), the boundaries between oscillatory and nonoscillatory solutions are largely independent of the ratio of timescales τ step 2 / τ convection and agree well with the values found previously in the purely diffusive limit. When natural convection is important (Ra > 500), the oscillations occur over a wider range of parameters than is the case for a diffusive system. The presence of natural convection also leads to various, more complex behaviors than are seen in the diffusive or well-mixed limits. A region in the regime diagram was found where the oscillations in temperature and the concentration of A have small amplitudes and a frequency that is quite different from those generated in a well-mixed system. It is possible that these oscillations are caused by natural convection, i.e., are not thermokinetic oscillations produced by the chemical reaction. It was also found that sometimes the oscillations in the temperature and the concentration of A are in phase; more generally they are in anti-phase. The evolution of nonoscillatory behavior with relatively small increases in temperature was found to be always fairly similar, regardless of the intensity of natural convection. The shape of the temperature profile along the vertical axis of the reactor did, however, change with the intensity of natural convection. Finally, the nonoscillatory solutions with a large rise in temperature in the presence of natural convection were found to be very much like those seen in the purely diffusive limit for small times, due to the relatively long induction time (∼3.5 s in a vessel with diameter 0.1 m) for the onset of natural convection.

Purification of chemical feedstocks by the removal of aerial carbonyl sulfide by hydrolysis using rare earth promoted alumina catalysts

The effect of rare earth doping of alumina catalysts is investigated for the carbonyl sulfide (COS) hydrolysis reaction (COS + H2O = CO2 + H2S). The effect of the catalyst preparation method is described and discussed, and three methods are compared, namely: impregnation by incipient wetness, coprecipitation and deposition precipitation. The most effective catalysts are prepared using the incipient wetness impregnation method. The addition of rare earth oxides, namely Y2O3, Gd2O3, Nd2O3, La2O3, increases the basicity of the material as shown by pulsed CO2 chemisorption and the basicity increases with the amount of rare earth oxide added. CO2 TPD shows that the La2O3-doped alumina has the strongest basic sites. The promoted catalysts are all effective for the COS hydrolysis reaction and the best results are obtained with Y2O3-doped materials, as these have the most pronounced promotion of activity over the reaction timescale we have examined. The combination of the results for COS conversion with the H2S selectivity data and the effects of H2S pre-treatment shows that a highly active catalyst also has a high H2S selectivity. The La2O3-doped materials deactivate rapidly and have poor H2S selectivities, and we propose that the higher basicity of this material leads to reaction with the acidic COS and H2S leading to the formation of the less basic lanthanum sulfide. This study has presented results for the first time showing that an alumina catalyst for COS hydrolysis can be promoted by the addition of rare earth oxides, and this is related to the enhanced basicity of the promoted catalyst.

Development of Time-Scale Interaction Combustion Model for Gasoline and Diesel Engines

The combustion processes of both gasoline and diesel engines are becoming similar, as a result of the application of direct fuel injection to the former and the reduction of the compression ratio of the latter. A novel time-scale interaction (TI) combustion model has been developed for simulating combustion phenomena with high accuracy, ranging from premixed charge combustion to diffusion combustion. This model is based on reasonable combustion modes, taking into account the characteristic time scales of the chemical reactions and turbulence eddy break-up. Comparisons of measured and calculated heat release rate patterns and cylinder pressure histories showed good agreement for various operating conditions. The diesel combustion mechanism was analyzed under several fuel injection timings and engine loads using the TI combustion model.

High-purity synthesis of scrolled mats of multi-walled carbon nanotubes using temperature modulation

Felt-like mats (6–7 μm thick) of multiwalled carbon nanotubes wrapped into scrolls have been synthesized by chemical vapor deposition from a toluene–ferrocene mixture using a temperature ramp from 680 °C to 550 °C in hydrogen–argon atmosphere. Thermogravimetric analysis reveals a very low catalyst content of ca. 1.25 wt% in the as-synthesized sample while, X-ray photo electron and Raman spectroscopies suggest the results matching with that of multiwalled carbon nanotubes. Considering, different time scales of various reactions and the diffusion of different reactants and products a tentative base growth mechanism has been proposed as per the available characterization data in conjunction with possible scrolling effects. Thermal expansion effects could explain a tentative mechanism for rolling action of sheets. Interestingly, electrical conductivity measurements as a function of temperature suggest a semiconducting behavior, despite being governed by different electron transport mechanisms with activation energies of 0.33 and 1.03 meV corresponding to two temperature ranges respectively. Cyclic voltammetry and electrochemical impedance analysis show a reversible redox behavior due to very low catalyst content and an irreversible etching of the Fe catalyst after acid treatment.

Analysis and Optimization of Nonequilibrium Capillary Electrophoresis of α-Fetoprotein Isoforms

The L3 isoform of alpha-fetoprotein (AFP) is a specific marker for hepatocellular carcinoma. The separation and quantitation of L3 isoform from the L1 isoform is facilitated by Lens culinaris agglutin (LCA) affinity of the L3 isoform. The affinity-based separation is characterized by nonequilibrium conditions since electrophoresis perturbs the species concentrations away from equilibrium. The design of such separations requires careful consideration of the interplay between the reaction, diffusion, and separation time scales. We performed experiments to investigate the effect of separation parameters such as LCA concentration and CE voltage on the L1-L3 separation dynamics. We also describe a comprehensive mathematical model to predict electropherograms for affinity-based separations. The model includes the effects of molecular diffusion, electromigration, nonequilibrium reaction, and detection process. Together, the results demonstrate a process by which to optimize the affinity-based separations of AFP isoforms. We also obtained the kinetic rate constants for LCA affinity (kon=1.6x10(3) mol(-1) s(-1) L, koff=1x10(-3) s(-1)) by comparing the model predictions with experimental data. This study provides insight into the physics of affinity-based separations and can be extended to describe and optimize other nonequilibrium CE systems.

Characterization of the Threshold Response of Initiation of Blood Clotting to Stimulus Patch Size

This article demonstrates that the threshold response of initiation of blood clotting to the size of a patch of stimulus is a robust phenomenon under a wide range of conditions and follows a simple scaling relationship based on the Damköhler number. Human blood and plasma were exposed to surfaces patterned with patches presenting clotting stimuli using microfluidics. Perturbations of the complex network of hemostasis, including temperature, variations in the concentration of stimulus (tissue factor), and the absence or inhibition of individual components of the network (factor IIa, factor V, factor VIII, and thrombomodulin), did not affect the existence of this response. A scaling relationship between the threshold patch size and the timescale of reaction for clotting was supported in numerical simulations, a simple chemical model system, and experiments with human blood plasma. These results may be useful for understanding the spatiotemporal dynamics of other autocatalytic systems and emphasize the relevance of clustering of proteins and lipids in the regulation of signaling processes.

Instabilities and soot formation in high-pressure, rich, iso-octane–air explosion flames: 1. Dynamical structure

Simultaneous OH planar laser-induced fluorescence (PLIF) and Rayleigh scattering measurements have been performed on 2-bar rich iso-octane–air explosion flames obtained in the optically accessible Leeds combustion bomb. Separate shadowgraph high-speed video images have been obtained from explosion flames under similar mixture conditions. Shadowgraph images, quantitative Rayleigh images, and normalized OH concentration images have been presented for a selection of these explosion flames. Normalized experimental equilibrium OH concentrations behind the flame fronts have been compared with normalized computed equilibrium OH concentrations as a function of equivalence ratio. The ratio of superequilibrium OH concentration in the flame front to equilibrium OH concentration behind the flame front reveals the response of the flame to the thermal–diffusive instability and the resistance of the flame front to rich quenching. Burned gas temperatures have been determined from the Rayleigh scattering images in the range 1.4 ⩽ ϕ ⩽ 1.9 and are found to be in good agreement with the corresponding predicted adiabatic flame temperatures. Soot formation was observed to occur behind deep cusps associated with large-wavelength cracks occurring in the flame front for equivalence ratio ϕ ⩾ 1.8 ( C/O ⩾ 0.576 ). The reaction time-scale for iso-octane pyrolysis to soot formation has been estimated to be approximately 7.5–10 ms.

A hybrid modeling approach to resolve pollutant concentrations in an urban area

A modeling tool that can resolve contributions from individual sources to the urban environment is critical for air-toxics exposure assessments. Air toxics are often chemically reactive and may have background concentrations originated from distant sources. Grid models are the best-suited tools to handle the regional features of these chemicals. However, these models are not designed to resolve pollutant concentrations on local scales. Moreover, for many species of interest, having reaction time scales that are longer than the travel time across an urban area, chemical reactions can be ignored in describing local dispersion from strong individual sources making Lagrangian and plume-dispersion models practical. In this study, we test the feasibility of developing an urban hybrid simulation system. In this combination, the Community Multi-scale Air Quality model (CMAQ) provides the regional background concentrations and urban-scale photochemistry, and local models such as Hybrid Single Particle Lagrangian Integrated Trajectory model (HYSPLIT) and AMS/EPA Regulatory Model (AERMOD) provide the more spatially resolved concentrations due to local emission sources. In the initial application, the HYSPLIT, AERMOD, and CMAQ models are used in combination to calculate high-resolution benzene concentrations in the Houston area. The study period is from 18 August to 4 September of 2000. The Mesoscale Model 5 (MM5) is used to create meteorological fields with a horizontal resolution of 1×1 km 2. In another variation to this approach, multiple HYSPLIT simulations are used to create a concentration ensemble to estimate the contribution to the concentration variability from point sources. HYSPLIT simulations are used to model two sources of concentration variability; one due to variability created by different particle trajectory pathways in the turbulent atmosphere and the other due to different flow regimes that might be introduced when using gridded data to represent meteorological data fields. The ensemble mean concentrations determined by HYSPLIT plus the concentrations estimated by AERMOD are added to the CMAQ calculated background to estimate the total mean benzene concentration. These estimated hourly mean concentrations are also compared with available field measurements.

Concentration blow up in a two-phase non-equilibrium model with source term

The scope of this brief note is to show that the solution (w, s) of (1)–(6) may blow up in finite time. We construct an example in order to illustrate this feature. The basic model assumptions that we are taking into account are standard: β > 0 and γ > 0 are Thiele-like moduli which compare the characteristic time scales of reaction and diffusion, η denotes the interface reaction kinetic which satisfies

Bayesian Modeling and Markov Chain Monte Carlo Simulations for a Kinetic Study of Homo‐ and Co‐ Polymerization Systems

AbstractA Bayesian modeling and Markov Chain Monte Carlo simulation was developed for a kinetic study of homopolymerization and copolymerization systems at the molecular scale. Two copolymerization models – the terminal unit model and the penultimate unit model – were considered. Prior estimates of the kinetic parameters were obtained by L1‐norm robust statistics. Using the structure of experimental data through a likelihood function, Bayesian modeling was employed to update the prior estimates. The joint posterior probability regions and shimmer bands were calculated for updated reactivity ratios. A method for assessing the power of experimental data in discrimination between copolymerization models is presented. This method was validated for free radical polymerization in binary systems. The evolution of species and radical populations during the course of polymerization were determined. The computational time was considerably decreased by calculating the propagation step from lifetime of the polymer chain and local monomer concentration. To avoid inaccuracies in the results caused by poor choice or false computation of the time step, the time step between successive Monte Carlo events was adapted to the time scale of the fastest reaction. The simulation algorithm is exact, in the sense that it takes full account of the fluctuations and correlations.magnified image

Analysis of Polymerization in Chaotic Mixers Using Time Scales of Mixing and Chemical Reactions

This study investigated the suitability of chaotic mixers as polymerization reactors by taking chain extension of thermoplastic polyurethanes as an example. The performance of chaotic mixers was an...

A comparison of measured temperatures with those calculated numerically and analytically for an exothermic chemical reaction inside a spherical batch reactor with natural convection

When any exothermic chemical reaction occurs inside e.g., an unstirred spherical vessel, the heating effect of the reaction often induces temperature gradients and consequently natural convection. This work sets out to compare previously measured temperatures at different positions inside such a batch reactor with values computed numerically and analytically. It is the first such study for a reaction with an order greater than zero, occurring in a spherical reactor. The main reaction considered is the thermal decomposition of the gas, azomethane, which has often been used in experimental studies of thermal explosion. Other experimental results for the reaction between nitric oxide and oxygen, as well as between hydrogen and chlorine are also considered here. The measured temperatures at the centre of the vessel are first compared with analytical scales, derived by inspecting the governing equations. It is found that the temperature rise when diffusion is the dominant transport mechanism (i.e., at small values of the Rayleigh number) is directly proportional to the ratio of the characteristic timescales for diffusion and for the reaction. Similarly, when natural convection is the dominant transport mechanism, the temperature rise is proportional to the ratio of the timescales for convection and reaction. A numerical scheme was developed to simulate the thermal decomposition of azomethane vapour under the influence of natural convection, as well as the diffusion of both matter and heat ( via thermal conduction). The results of these simulations are compared with the temperature profiles measured along the vertical axis of the reactor. There is excellent agreement between experimental and numerical results. This confirms the computational procedures. The simulations indicate that the hottest point in the reactor moves upwards above the centre of the vessel when Ra is increased. In fact, three distinct types of temperature profile occur, depending on the value of Ra. For low Ra, the temperature profile is approximately spherically symmetric, as expected. When Ra is increased, the symmetry in the temperature profile is disrupted by the flow produced by natural convection. In that case, the temperature profile becomes skewed, with the maximum occurring on the axis in the top half of the reactor. Thirdly, under some circumstances at high Ra, a large, sharp peak in the temperature profile near the top of the reactor is produced. This resembles a stabilised flame front, but could be an explosion. These three types of temperature distribution have also been observed experimentally. Finally, the ratio of the notional temperature rise in a purely diffusive system to that measured experimentally is compared over a wide range of Ra. The experimental results for the three reactions considered all follow the same trend; the numerical and analytical solutions are in excellent agreement with the experimental results, confirming that the onset of natural convection inside a spherical vessel occurs at Ra ∼ 500 . This result seems to be true, regardless of the order of the reaction, and only depends on the shape of the reactor.

Can N-body systems generate periodic gravitational waves?

None of N-body gravitating systems have been considered to emit periodic gravitational waves because of their chaotic orbits when N=3 (or more). We employ a figure-eight orbit as a specific model for a 3-body system in order to illustrate that some of triple stars are capable of generating periodic waves. This illustration would imply that a certain class of N-body gravitating systems may be relevant to the gravitational waves generation. We show also that the total angular momentum of this 3-body system is not carried away by gravitational waves. A waveform generated by this system is volcano-shaped and thus different from that of a binary system. Finally, by evaluating the radiation reaction time scale, we give an order-of-magnitude estimate of merging event rates. The estimate suggests that figure-eight sources, which require carefully prepared initial states, may be too rare to detect.

A Study of Cloud Mixing and Evolution Using PDF Methods. Part I: Cloud Front Propagation and Evaporation

AbstractThe evolution of mean relative humidity (RH) is studied in an isobaric system of clear and cloudy air mixed by an incompressible velocity field. A constant droplet radius assumption is employed that implies a simple dependence of the mixing time scale, τeddy, and the reaction (evaporation) time scale, τreact, on the specifics of the droplet size spectrum. A dilemma is found in the RH e-folding time, τefold, predicted by two common microphysical schemes: models that resolve supersaturation and ignore subgrid correlations, which gives τefold ∼ τreact, and PDF schemes that assume instantaneous evaporation and predict τefold ∼ τeddy. The resolution of this dilemma, Magnussen and Hjertager’s eddy dissipation concept (EDC) model τefold ∼ max(τeddy, τreact), is revealed in the results of 1D eddy diffusivity simulations and a new probability density function (PDF) approach to cloud mixing and evolution in which evaporation is explicitly resolved and the shape of the PDF is not specified a priori. The EDC model is shown to exactly solve the nonturbulent problem of spurious production of cloud-edge supersaturations described by Stevens et al. and produce good results in the more general turbulent case.

Similar Transition States Mediate the Q-cycle and Superoxide Production by the Cytochrome bc1 Complex

The cytochrome bc complexes found in mitochondria, chloroplasts and many bacteria play critical roles in their respective electron transport chains. The quinol oxidase (Q(o)) site in this complex oxidizes a hydroquinone (quinol), reducing two one-electron carriers, a low potential cytochrome b heme and the "Rieske" iron-sulfur cluster. The overall electron transfer reactions are coupled to transmembrane translocation of protons via a "Q-cycle" mechanism, which generates proton motive force for ATP synthesis. Since semiquinone intermediates of quinol oxidation are generally highly reactive, one of the key questions in this field is: how does the Q(o) site oxidize quinol without the production of deleterious side reactions including superoxide production? We attempt to test three possible general models to account for this behavior: 1) The Q(o) site semiquinone (or quinol-imidazolate complex) is unstable and thus occurs at a very low steady-state concentration, limiting O(2) reduction; 2) the Q(o) site semiquinone is highly stabilized making it unreactive toward oxygen; and 3) the Q(o) site catalyzes a quantum mechanically coupled two-electron/two-proton transfer without a semiquinone intermediate. Enthalpies of activation were found to be almost identical between the uninhibited Q-cycle and superoxide production in the presence of antimycin A in wild type. This behavior was also preserved in a series of mutants with altered driving forces for quinol oxidation. Overall, the data support models where the rate-limiting step for both Q-cycle and superoxide production is essentially identical, consistent with model 1 but requiring modifications to models 2 and 3.