Derived Rate Expressions Research Articles

Analysis and Optimization of Spectral and Energy Efficiency in Underlaid D2D Multi-Cell Massive MISO Over Rician Fading

This paper investigates the uplink spectral efficiency (SE) characterization and energy efficiency (EE) optimization of device-to-device (D2D) communications underlying a multi-cell massive multiple-input single-output (m-MISO) network, assuming that the channels are modeled with Rician fading. First, an analytical expression for the lower-bound of the ergodic capacity of a typical cellular user (CU) is derived with imperfect channel state information in the presence of D2D links’ interference. Then, a closed-form approximate achievable SE expression for a typical D2D pair is derived considering Rician fading between D2D pairs. The asymptotic SE behavior is analyzed in strong line-of-sight (LOS) conditions for CU and D2D pairs. Also, simplified expressions are obtained for the special case of Rayleigh fading. Next, to optimize the total EE, a transmit data power allocation based on the derived rate expressions is formulated. Since the optimization problem has a non-linear and non-convex objective function, it is intractable to be solved straightforwardly. Therefore, we resort to utilizing an iterative algorithm relying on fractional programming. The numerical results show that a stronger LOS component (i.e., larger Rician K-factor) between a typical CU and its serving BS leads to a significant improvement in the system performance, while it has less effect on the D2D network.

HȮ2 + HȮ2: High level theory and the role of singlet channels

At low temperatures and high pressures, the HȮ2 + HȮ2 reaction is an important reaction in combustion. There are significant unresolved discrepancies between prior theoretical and experimental studies of this reaction. It has generally been presumed to occur as an abstraction on the triplet surface to produce H2O2 + 3O2. We employ a combination of high-level electronic structure theory (the ANL0 composite method or multi-reference methods as appropriate), sophisticated transition state theory (vibrationally adiabatic torsions, variational, and variable reaction coordinate), and master equation analyses to predict the thermal kinetics on the H2O4 surface. Notably, this analysis suggests a significant branching to HȮ3 + ȮH near 1000 K via reaction on the singlet surface. This channel does not appear to have been considered in prior combustion models. HȮ3 itself is a metastable complex (bound by only 3 kcal mol–1) that rapidly dissociates to ȮH + 3O2. Thus, the net reaction for this channel, HȮ2 + HȮ2 → ȮH + ȮH + O2, converts two low reactivity HȮ2 radicals into two highly reactive ȮH radicals. The ramifications of these newly derived rate expressions are highlighted through kinetic modeling studies of H2, CH3OH, n-heptane, and isooctane oxidation; all at the high pressures of relevance to combustion devices.

A Chemical Kinetic Investigation on Butyl Formate Oxidation: Ab Initio Calculations and Experiments in a Jet-Stirred Reactor

Biofuels are expected to play a significant role in the quest for greener energy generation. In this perspective, esters produced from biomass are promising candidates. This work presents the first computational kinetic study on n-butyl formate (BF) oxidation under combustion conditions coupled to an experimental study in a jet-stirred reactor. Absolute rate constants for hydrogen abstraction reactions by the OH radical were calculated using the G3//MP2/aug-cc-pVDZ model chemistry, in conjunction with statistical rate theory (TST). Subsequently, the fate of the butyl formate radicals was also investigated by calculating absolute rate constants for combustion relevant decomposition channels such as β-scission and hydrogen transfer reactions. The derived rate expressions were used in the presently developed detailed kinetic mechanism, which was validated over experimental data obtained in a jet-stirred reactor at 10 atm and for three different mixtures (φ = 0.45, 0.9, and 1.8). Rate of production analyses w...

Kinetic studies on H+- and OH−-catalysed aquation of bis-aspartatochromium(III)

A potential synthetic biochromium source, bis-aspartatochromium(III) ion (where Asp is a tridentate N,O,O′-ligand, bonded via amine nitrogen and carboxylate oxygen atoms) has been obtained and characterized in aqueous solution. Kinetics of partial dechelation of the complex catalysed by H+ and OH− ions has been studied spectrophotometrically within 0.1–1.0 M HClO4 and 0.1–1.0 M NaOH ranges under first-order conditions. A linear dependence of the k obs,H on [H+] and independence of the k obs,OH on [OH−] were established. The derived rate expression and identification of components of the reaction mixture provide evidence for a reaction mechanism, where the key role in the overall process is the formation of an intermediate species with bidentate N,O-bonded Asp via both spontaneous and H+(OH−)-catalysed reaction paths. The intermediate is meta-stable and at pH 5–7 restores the substrate.

Single Pulse Shock Tube Study of Allyl Radical Recombination

The recombination and disproportionation of allyl radicals has been studied in a single pulse shock tube with gas chromatographic measurements at 1-10 bar, 650-1300 K, and 1.4-2 ms reaction times. 1,5-Hexadiene and allyl iodide were used as precursors. Simulation of the results using derived rate expressions from a complementary diaphragmless shock tube/laser schlieren densitometry study provided excellent agreement with precursor consumption and formation of all major stable intermediates. No significant pressure dependence was observed at the present conditions. It was found that under the conditions of these experiments, reactions of allyl radicals in the cooling wave had to be accounted for to accurately simulate the experimental results, and this unusual situation is discussed. In the allyl iodide experiments, higher amounts of allene, propene, and benzene were found at lower temperatures than expected. Possible mechanisms are discussed and suggest that iodine containing species are responsible for the low temperature formation of allene, propene, and benzene.

Influence of inert gas sparging on fatty acid lactylate esterification kinetics

I have proposed a novel reaction mechanism for the formation of acyl lactylate esters of fatty acids, and have determined the absolute esterification and reverse rate constants at several reaction temperatures, as well as having derived with rigor from basic physical chemistry precepts the gas-sparge dependent overall reaction rate expressions and rate constants of lactylate formation. Examples are given of acid values calculated from the derived rate expressions, compared to experimental values obtained as a function of time, during laboratory ester preparations. These fatty acid acyl lactylate esters and their salts have important commercial applications in both the food and non-food industries as emulsifiers, and their manufacture and sale is highly competitive. Therefore, an understanding of the cost versus benefit curve of sparge gas rates provided by this paper is highly desirable.

Microkinetic modeling of cis-cyclooctene oxidation on heterogeneous Mn–tmtacn complexes

Experiments and microkinetic modeling were used to investigate the reaction mechanism of cis-cyclooctene oxidation with H2O2 on heterogeneous manganese 1,4,7-trimethyl-1,4,7-triazacyclononane (Mn–tmtacn) catalysts. A mechanism based on literature reports and model discrimination was identified that captured experimental data well, including data at reaction conditions that were not used for parameter estimation. H2O2 activation on the heterogeneous catalytic complex was identified as the rate-determining step (RDS), and a simple analytical rate expression was derived using the RDS and the pseudo-steady-state approximation for all intermediates. Predicted reaction orders for cis-cyclooctene, water, H2O2, catalyst, and diol and epoxide products are also consistent with experimental observations and can be rationalized according to the derived rate expression. In addition, the ratio of productive to unproductive H2O2 use is analyzed, and catalyst deactivation is found to be an important step in the reaction mechanism that is highly sensitive to temperature.

Control of chemoselectivity in hydrogenations of substituted nitro- and cyano-aromatics by cluster-derived ruthenium nanocatalysts

Catalyst precursors 1 and 2, made by ion-pairing [H 3Ru 4(CO) 12] − with NR 4 + groups of functionalized MCM-41 and water-soluble poly(diallyldimethylammonium chloride), PDADMAC, respectively, have been evaluated for the chemoselective hydrogenation of nitro- and cyano-benzaldehydes. They are found to be inert toward –NO 2 and –CN groups, but active for the reduction of –CHO and >C=C< functionalities. Thus, 3, 4-nitrobenzaldehyde, nitrostyrene, and 3-cyanobenzaldehyde are hydrogenated with full selectivity to the corresponding nitrobenzylalcohols, 1-ethyl-3-nitrobenzene, and 3-cynaobenzylalcohol, respectively. No such chemoselectivity is observed either with PDADMAC-RuCl 4 ( 3) or with (5%)Ru-Al 2O 3, where both the functional groups are hydrogenated. Kinetic analyses have been carried out for the hydrogenation of 4-nitrobenzaldehyde with 2. Existence of an induction time and two competitive equilibriums followed by the product-forming rate-determining step are inferred from the empirically derived rate expression. The kinetic results, structural evidences, and previous work strongly suggest that the observed chemoselectivity is probably a result of the absence of multiple crystal planes, differing in Miller indices, in the cluster-derived catalysts.

A Unified Model for the Electrochemical Rate Constant That Incorporates Solvent Dynamics

A generalized Anderson−Newns Hamiltonian is employed to model electrochemical electron transfer kinetics via a potential energy surface approach. Important novel features of this treatment are inclusion of the electrode induced broadening of the reactant level and the effect of solvent dynamics on the pre-exponential factor, which is determined by a numerical integration of the Kramers’ diffusion controlled barrier crossing rate expression. An interpolation scheme is provided to treat nonadiabatic, transition state theory adiabatic, and solvent dynamical effects in the weak coupling (nonadiabatic) and strong coupling (adiabatic) limits in a unified manner. The derived rate expressions are valid for arbitrary values of the electrode−reactant coupling term V, solvent polarization mode frequency ωr, and longitudinal solvent dielectric relaxation time τL. A comparison of the results obtained here with the earlier treatments of electron transfer reactions is presented, and the relevance of the present formalis...

Multicomponent reactive transport modeling in variably saturated porous media using a generalized formulation for kinetically controlled reactions

A generalized formulation for kinetically controlled reactions has been developed and incorporated into a multicomponent reactive transport model to facilitate the investigation of a large variety of problems involving inorganic and organic chemicals in variably saturated media. The general kinetic formulation includes intra‐aqueous and dissolution‐precipitation reactions in addition to geochemical equilibrium expressions for hydrolysis, aqueous complexation, oxidation‐reduction, ion exchange, surface complexation, and gas dissolution‐exsolution reactions. The generalized approach allows consideration of fractional order terms with respect to any dissolved species in terms of species activities or in terms of total concentrations, which facilitates the incorporation of a variety of experimentally derived rate expressions. Monod and inhibition terms can be used to describe microbially mediated reactions or to limit the reaction progress of inorganic reactions. Dissolution‐precipitation reactions can be described as surface‐controlled or transport‐controlled reactions. The formulation also facilitates the consideration of any number of parallel reaction pathways, and reactions can be treated as irreversible or reversible processes. Two groundwater contamination scenarios, both set in variably saturated media but with significantly different geochemical reaction networks, are investigated and demonstrate the advantage of the generalized approach. The first problem focuses on a hypothetical case study of the natural attenuation of organic contaminants undergoing dissolution, volatilization, and biodegradation in an unconfined aquifer overlaid by unsaturated sediments. The second problem addresses the generation of acid mine drainage in the unsaturated zone of a tailings impoundment at the Nickel Rim Mine Site near Sudbury, Ontario, and subsequent reactive transport in the saturated portion of the tailings.

Methane combustion over La 2O 3-based catalysts and γ-Al 2O 3

The kinetics of methane combustion were examined over La 2O 3, Sr-promoted La 2O 3, 40% La 2O 3/γ-Al 2O 3 and γ-Al 2O 3 between 773 and 973 K, 0.4–5 Torr CH 4 and 3–23 Torr O 2. Rates (mol/(s g)) were highest for supported La 2O 3, but the rate on pure Al 2O 3 was one-third of this value; however, the specific activity (mol/(s m 2)) on La 2O 3 was 130-fold greater than that on γ-Al 2O 3. The apparent activation energies were 25±2 kcal/mol for the La 2O 3 catalysts and 20 kcal/mol for γ-Al 2O 3. Respective reaction orders on CH 4 and O 2 were 0.69–0.75 and 0.12–0.18 for the La 2O 3-based catalysts compared to respective orders near 0.6 and 0.3 for γ-Al 2O 3. A reaction mechanism invoking quasi-equilibrated adsorption of all reactants and products along with methyl radical formation as a slow step produced a derived rate expression, i.e. r CH 4 = kP CH 4 P O 2 1/2 (1+K CH 4 P CH 4 +K O 2 1/2P O 2 1/2) 2 that fit the data well and indicated that CO, CO 2 and H 2O have no significant effect on this reaction under the reaction conditions employed here. An analysis of the enthalpies and entropies of adsorption for CH 4 and O 2 showed that these parameters were thermodynamically consistent, with indicated heats of adsorption for methane of around 20 kcal/mol CH 4 on all four catalysts while for oxygen this value was around 30 kcal/mol O 2 on the La 2O 3-based catalysts and near 20 kcal/mol O 2 on γ-Al 2O 3. The activation energy calculated for the elementary step to form a methyl group on the surface was around 40 kcal/mol for all catalysts.

Ammonia Pyrolysis and Oxidation in the Claus Furnace

The modified Claus process is commonly used in oil refining and gas processing to recover sulfur and destroy contaminants formed in upstream processing. In oil refining, in addition to the typical modified Claus plant feed of H2S and CO2, NH3 is also often present. NH3 is a process contaminant and must be destroyed in the front-end furnace of the modified Claus plant, otherwise, it poses a risk of poisoning the catalyst beds and plugging off downstream equipment because of the formation of ammonium salts. In this paper, the pyrolysis and oxidation of NH3 was studied under Claus furnace temperatures and residence times. Experimental data was taken, and new reaction rate expressions were developed for NH3 pyrolysis and oxidation. The derived rate expressions are outlined as follows: the NH3 pyrolysis rate expression r = A exp(−Ea/RT)PNH31.25, where A is 0.00421 mol s-1 atm-1.25 cm-3 and Ea is 16.5 kcal mol-1, and the NH3 oxidation rate expression r = A exp(−Ea/RT)PNH3PO20.75, where A is 4430 mol s-1 atm-1....

Chromium Transformations in Natural Environments: The Role of Biological and Abiological Processes in Chromium(VI) Reduction

Chromium is a redox-dynamic element that has many industrial uses. As a consequence, it is often introduced at elevated levels into the surface environment through human activity. Additionally, ultramafic rocks such as serpentinite are commonly enriched in chromium, and thus can also lead to appreciable levels of this element within soils and waters. In the trivalent state, it poses little hazard to biological activity, but, unfortunately, in the hexavalent state it is very toxic to living matter. One must therefore assess the oxidation state of Cr in a given system and determine the potential for transformation between valence states. The objective of this paper to is review and provide new insight on reduction reactions of Cr(VI) within natural environments. A number of aerobic and anaerobic bacteria demonstrate the enzymatic ability to reduce Cr(VI) to Cr(III); two species can even grow using Cr(VI) as the terminal electron acceptor in respiration. The ability to reduce chromium in itself is not evidence that the process will take place at appreciable levels in natural environments, however. Reduced materials such as ferrous iron or hydrogen sulfide may compete with biological pathways in the reduction of Cr(VI). On the basis of measured reaction rates and derived rate expressions, we demonstrate that biological pathways are not likely to contribute to the reduction of chromate in anaerobic systems. Ferrous iron will dominate the reduction of chromate at pH values greater than ∼ 5.5, whereas hydrogen sulfide will dominate at pH values below this value. In contrast, bacteria may be the principal means by which Cr(VI) is converted to Cr(III) in aerobic environments. Thus, the process by which Cr(VI) is reduced will depend primarily on the aeration status of the system, and secondarily on pH and the concentrations of specific reduced phases.

Iron(II) oxidation by SO 2/O 2 in acidic media: : Part I. Kinetics and mechanism

The kinetics of iron(II) oxidation by SO 2/O 2 has been studied at 80°C as a means of generating Fe(III) and H 2SO 4 for subsequent leaching reactions. It is shown that both Fe(III) and S(IV) species are involved in the initial step of the oxidation. The rate of Fe(II) oxidation can be expressed by the following equation: r= k obs[Fe(III)][S(IV)]/ f obs([H +]) for 0–0.02 M Fe(III) at the optimum SO 2/O 2 ratio, where f obs([H +]) is a function of pH. At 80°C, the optimum gas composition of SO 2 is around 2% SO 2 and both Fe(II) and SO 2 were oxidised with the Fe(III)/H 2SO 4 ratio of about 2. At a SO 2/O 2 ratio above 9% SO 2 and pH 1, dithionate was detected, and the proportion of dithionate to sulphate increased with higher SO 2/O 2 ratio. A radical chain reaction mechanism is proposed, involving a slow rate of formation of the ferric sulphite complex FeSO 3 +and decomposition to produce the sulphite radical SO 3 ⋅−. This is followed by a fast reaction with O 2 to form the peroxo-monosulphate radical SO 5 ⋅−, which is responsible for the autoxidation of Fe(II). The form of the derived rate expression and the predicted ratio of Fe(III)/H 2SO 4 from the proposed mechanism essentially agree with the experimental results.

Kinetics and Mechanism of the Decomposition of S-Nitrosoglutathione by [formula omitted]-Ascorbic Acid and Copper Ions in Aqueous Solution to Produce Nitric Oxide

S-Nitrosothiols serve as a good source of nitric oxide (•NO) mainly due to the ease of cleavage of the S–N bond which consequently produces •NO. The reductive decomposition of S-nitrosoglutathione (GSNO) by l-ascorbic acid (vitamin C) yields •NO which was monitored both electrochemically (using NO-probe) and spectrophotometrically. The rate of reaction and •NO release was found to be pH dependent in a manner which drastically increases with pH demonstrating that the l-ascorbic acid dianion (A2−) is by far the most reactive species of l-ascorbic acid (H2A). The derived rate expression (measuring the disappearance of the absorption at ca. 336 nm due to GSNO) was established as rate = −d[GSNO]t/dt = ((ka[H+]2 + kb[H+]K1 + kcK1K2)/([H+]2 + K1[H+] + K1K2))[GSNO]t[H2A]t. ka, kb, and kc are second-order rate constants via the H2A, HA−, and A2− pathways, respectively, while K1 and K2 represent the first and second equilibrium dissociation constants of l-ascorbic acid. There is little or no reaction at low pH (below 5.5), where H2A is a predominant species, and as a result the rate constant (ka) via this route was found to be negligible. At 25°C, kb = 5.23 ± 1.47 × 10−3 dm3 mol−1 s−1 and kc = 1.22 ± 0.04 × 103 dm3 mol−1 s−1, activation parameters ΔH‡b = 54.4 ± 4.3 kJ mol−1, ΔS‡b = −106 ± 16 J K−1 mol−1, ΔH‡c = 80.5 ± 7.5 kJ mol−1, ΔS‡c = 84 ± 7 kJ mol−1. The experimental rate and activation parameters suggest that this redox process follows an outer-sphere electron transfer mechanism. GSNO is relatively stable in the dark, aqueous medium and even in the presence of trace quantities of Cu2+. Induced catalytic decomposition of GSNO only becomes significant above ca. 10 μM Cu2+, but after this it shows linear dependency. To nullify any catalysis by Cu2+ or any other transition metal ions, EDTA was added to all experimental reactions except those where catalysis by Cu2+ was studied.

Computational Studies on the Reactions of N2O with O(3P) and CO

Abstract We performed ab initio molecular orbital calculations to derive rate expressions for the reactions of N2O with O(3P) and CO. Major products of the O(3P) + N2O reactions are predicted to be NO + NO. Comparisons of calculated and experimental rate constants indicate good agreement exists with the most recent experimental values.

Catalytic and structural properties of ruthenium bimetallic catalysts: kinetics of hydrogenolysis of lower alkanes on variously pretreated [formula omitted] catalysts

The H 2 pressure dependence of rates of hydrogenolysis of ethane, propane and n-butane on Ru Al 2O 3 catalysts differing in dispersion and type of pretreatment has been measured at a number of temperatures, and the results interpreted in terms of a mechanism involving adsorbed partially dehydrogenated intermediates C n H x , and modelled by the derived rate expression. The rate-limiting step is taken as the reaction of C n H x with an adsorbed H atom. We thus obtain best-fit values of the rate constant k 1, the H 2 adsorption equilibrium constant K H, an equilibrium constant for the dehydrogenation of the alkane K A, and of x, for each set of results. The shapes of the kinetic curves, and the constants that describe them, change markedly with dispersion, and with pretreatment: oxidation and low-temperature reduction ( O LTR ), as well as causing some loss of dispersion, gives rise to other effects, ascribed to ‘morphological’ factors, not seen when catalysts are reduced at high temperature (753 K). What is most striking is that differences in activity seem to be determined much more by the constants K A and K H than by the rate constant k 1, which when expressed per Ru surface atom varies at most three-fold. In particular K H is much larger after the first high-temperature reduction (HTR1) than after O LTR . The true activation energy derived from the temperature-dependence of k 1 is about the same for each alkane (≈ 60 kJ mol −1), the enthalpy changes for H 2 chemisorption are small and for alkane dehydrogenation they lie between 50 and 130 kJ mol −1. The manner in which product selectivities vary with H 2 pressure also depends on dispersion and pretreatment, the dominant factor being the strength of H 2 chemisorption. Thus on a very highly dispersed catalyst for which K H is large, intermediate product selectivities are high because the high concentration of H atoms facilitates desorption of adsorbed species, and for this reason also selectivities scarcely respond to changes in H 2 pressure. With the same catalyst after O LTR , however, when K H is much decreased, selectivities respond sensitively to H 2 pressure because the adsorption is weaker. It is then deduced that approximately two more H atoms are required to effect desorption of intermediates as a product alkane than to cause further CC bond breaking. Our results strongly suggest that structure-sensitivity in alkane hydrogenolysis is more the result of variations in chemisorption energetics, and their consequential effects on surface coverage, than of kinetic effects; this concept also accounts for dispersion-dependent differences in the temperature-dependence of product selectivities previously reported.

Formation of H2S in the Bath Smelting Process.

With the direct utilization of coal to produce hot metal, impurities in the coal, such as sulfur, enter into the process. The amount of sulfur in each phase (metal, slag and gas) depends on the operating conditions. Trials at American Iron Steel Institute (AISI) Direct Steelmaking and Japan (DIOS) indicate that much of the sulfur enters the gas phase and the thermodynamics indicate that H2S will be the predominant specie. The sulfur can enter the gas phase by a reaction of the smelting gas with the slag or during the devolatilization and combustion of the coal. The rate of formation of H2S by the reaction of an Ar-H2-H2O gas with the slag was measured. It was found that the initial rate is dependent on PHO and the sulfur content of the slag. Under present experimental conditions the rate is controlled by liquid phase mass transport. The diffusion coefficient of the sulfur in liquid slag, assuming mass transfer control, is estimated to be 6.65×10-7 cm2/s at 1723 K which is in agreement with published values. The rate of H2O formation was also measured when gas was bubbled through the slag. A rate expression was derived for desulfurization with a foamy slag. The sulfur content of the slag as a function of time was calculated from the derived rate expressions for different circulation rates of slag from bulk to foam. The sulfur content of the bath smelting gas was estimated based on experimental results. Some coal samples were devolatilized and partially combusted with simulated bath smelting gas. The experimental results indicate that a large portion of the sulfur enters tha gas phase during devolatilization and combustion of the coal.

A model for mercuric ion reduction in recombinant Escherichia coli

Plasmid-encoded mercuric reduction involves transfer of Hg(2+) across the cellular envelope and reduction to Hg(0) by the cytoplasmic mercuric reductase using NADPH. A mathematical model was developed for the binding and transfer of Hg(2+) by transport proteins and the subsequent reduction of Hg(2+). The values of the model parameters were determined using experimental data. The derived rate expressions were similar to the previously experimentally determined ones. The model predicted that a differential amplification of the transport protein relative to mercuric reductase expression levels may enhance the Hg(2+) reduction rate in whole cells.

The hydrogenation of toluene and o-, m-, and p-xylene over palladium II. Reaction model

The similarity among activation energies and partial pressure dependencies for the hydrogenation of benzene, toluene, and the three xylene isomers allowed the use of our previous model for benzene hydrogenation, which could be simplified for the hydrogenation of toluene and the xylenes because there was no evidence of deactivation or significant coverages of hydrogen-deficient surface inhibitors. Thus a Langmuir-Hinshelwood model involving two sets of active sites, one on the Pd surface and the other composed of acid sites in the Pd-support interfacial region supplied by spilled-over hydrogen, readily describes the kinetics for these four aromatic hydrocarbons as well as benzene. The presence of these acid sites, presumed to be Brønsted sites, was confirmed by the parallel reaction of o-xylene isomerization to m-xylene, and rate enhancements in this reaction were nearly identical to those observed for the hydrogenation of o-xylene. The derived rate expression was computer fitted to the data and the obtained values of the equilibrium adsorption constants for H 2 and these aromatic compounds are consistent with assumptions in the model and provide trends in agreement with results from the literature.