Chain-branching Step Research Articles

A Comprehensive Modeling Study of n-Heptane Oxidation

A detailed chemical kinetic mechanism has been developed and used to study the oxidation of n-heptane in flow reactors, shock tubes, and rapid compression machines. Over the series of experiments numerically investigated, the initial pressure ranged from 1–42 atm, the temperature from 550–1700 K, the equivalence ratio from 0.3–1.5, and nitrogen-argon dilution from 70–99%. The combination of ignition delay time and species composition data provide for a stringent test of the chemical kinetic mechanism. The reactions are classed into various types, and the reaction rate constants are given together with an explanation of how the rate constants were obtained. Experimental results from the literature of ignition behind reflected shock waves and in a rapid compression machine were used to develop and validate the reaction mechanism at both low and high temperatures. Additionally, species composition data from a variable pressure flow reactor and a jet-stirred reactor were used to help complement and refine the low-temperature portions of the reaction mechanism. A sensitivity analysis was performed for each of the combustion environments. This analysis showed that the low-temperature chemistry is very sensitive to the formation of stable olefin species from hydroperoxy-alkyl radicals and to the chain-branching steps involving ketohydroperoxide molecules.

On the nonlinear stability and detonability limit of a detonation wave for a model three-step chain-branching reaction

The nonlinear stability of a pulsating detonation wave driven by a three-step chain-branching reaction is studied. The reaction model consists sequentially of a chain-initiation step and a chain-branching step, both governed by Arrhenius kinetics, followed by a temperature-independent chain-termination step. The model mimics the essential dynamics of a real chain-branching chemical system, but is sufficiently idealized that a theoretical analysis of the instability is possible. We introduce as a bifurcation parameter the chain-branching cross-over temperature (TB), which is the temperature at which the chain-branching and chain-termination rates are equal. In the steady detonation structure, this parameter controls the ratio of the chain-branching induction length to the length of the recombination zone. When TB is at the lower end of the range studied, the steady detonation structure, which is dominated by the temperature-independent recombination zone, is found to be stable. Increasing TB increases the length of the chain-branching induction region relative to the length of the recombination zone, and a critical value of TB is reached where the detonation becomes unstable, with the detonation shock pressure evolving as a single-mode low-frequency pulsating oscillation. This single-mode nonlinear oscillation becomes progressively less stable as TB is increased further, persisting as the long-term dynamical behaviour for a significant range of TB before eventually undergoing a period-doubling bifurcation to a two-mode oscillation. Further increases in TB lead to a chaotic behaviour, where the detonation shock pressure history consists of a sequence of substantive discontinuous jumps, followed by lower-amplitude continuous oscillations. Finally, for further increases in TB a detonability limit is reached, where during the early onset of the detonation instability, the detonation shock temperature drops below the chain-branching cross-over temperature causing the wave to quench.

Linear stability of a detonation wave with a model three-step chain-branching reaction

The linear stability of a planar detonation wave with a three-step chain-branching reaction is studied by a normal mode approach. The reaction model consists of a chain-initiation step and a chain-branching step governed by Arrhenius kinetics, with a chain-termination step which is independent of temperature. It mimics the essential reaction dynamics of a real chain-branching chemical system. The linear stability of the steady detonation wave to two-dimensional disturbances is studied with the chain-branching crossover temperature, i.e., the temperature at which chain-branching and chain-termination rates are equal, as a bifurcation parameter. This parameter determines the ratio of the length of the chain-branching induction zone to the chain-termination zone within the steady detonation wave. The effect of linear transverse disturbances is considered for two values of the chain-branching crossover temperature: in one the planar steady detonation wave is stable to one-dimensional disturbances, while in the other it is unstable to such disturbances.

Ignition of monomethyl amine

The ignition of monomethyl amine was studied in reflected shock waves over the temperature range from 1000 to 1300 K. In contrast to the behavior observed with hydrocarbons, monomethyl amine acts to accelerate rather than inhibit its own ignition. This behavior could be accounted for, based on extensive computer simulations of the ignition chemistry, as arising from the participation of hydrogen peroxide thermal decomposition as a chainbranching step in a manner that is not effective for the ignition of hydrocarbon fuels under similar conditions. The linear chain responsible for H 2O 2 formation in the induction zone is composed of the two reactions CH 3NH 2 + HO 2 → CH 2NH 2 + H 2O 2 and CH 2NH 2 + O 2 → CH 2NH + HO 2.

Promoted high-temperature reactions

An effect of promoting agents on ignition of various systems is analysed analytically, numerically and experimentally. For systems with straight chains analytical expressions are derived for the ignition delay as a function of the radical production rate in reactions involving promoter added and for the optimal rate constant of this radical production reaction. An eight-step scheme is suggested for high-temperature self-ignition of hydrocarbons that with the chosen magnitudes of the effective rate constants of the chain propagation and branching steps describes ignition of CH 4 -O 2 mixtures in a wide range of initial conditions. This scheme supplemented with reactions involving promoter molecules allowed quantitative estimation of the effect of promoters of different types as a function of temperature, promoter consumption rate, and additive concentration. Calculations agree fairly well with the experimental data. The approach proposed permits predicting promoter efficiency using known kinetic parameters and also selecting promoters with a required efficiency.

A cationic model of the chain-branching step in aflatoxin biosynthesis

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTA cationic model of the chain-branching step in aflatoxin biosynthesisCraig A. Townsend, Steven G. Davis, Masato Koreeda, and Bernard HulinCite this: J. Org. Chem. 1985, 50, 25, 5428–5430Publication Date (Print):December 1, 1985Publication History Published online1 May 2002Published inissue 1 December 1985https://doi.org/10.1021/jo00225a099RIGHTS & PERMISSIONSArticle Views115Altmetric-Citations20LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (387 KB) Get e-Alerts Get e-Alerts

The OH(v = 9) + O3 reaction pathway

AbstractThe oxygen‐hydrogen system, including the reactive species H, O, H2, O2, O3, OH, and HO2, is very complex, and contains numerous reactions whose kinetics and branches have been insufficiently explored. In the present study we use computer modeling to simulate observations made in a 300‐K ozone‐hydrogen mixture, in which a critical H2 pressure leads to rapid ozone decomposition, and generation of high concentrations of atomic oxygen. Initiation of the reaction chain involves heterogeneous O and/or H atom production, and the chain branching step is the reaction OH(v) + O3 → OH + O + O2, which is shown to be the predominant pathway for these reactants. The critical H2 pressure (ca. 3 torr) sets important constraints upon the system kinetics.

The ignition and combustion of propane/air mixtures in a fluidised bed

Mixtures of propane and air have been used to fluidise a bed of silica sand at atmospheric pressure. Both the ignition and combustion of these gas mixtures have been studied in this situation. It is noteworthy that high temperatures ( ca . 800°C) have to be reached before bubbles of propane and air ignite within the bed. The indications are that combustion occurs only in the bubble phase and not to any significant extent in the particulate phase. Moreover, it appears that a bubble of fuel and air has to reach a critical size (about 30 mm, depending on bed conditions) before it ignites. This is because ignition is controlled by a balance between near-isothermal chain branching and rapid removal of radicals from a bubble by gas circulating to the surrounding sand particles where radical recombination occurs. Analysis of the size of bubbles igniting at various temperatures indicates an activation energy for the chain branching step of around 254 kJ/mol. In addition, a correlation due to Darton appears preferable to an alternative one for predicting the sizes of gas bubbles in hot fluidised beds.

Branching in high molecular weight polyhydroxyethers based on bisphenol A

AbstractThe polyaddition reaction of bisphenol A with the diglycidyl ether of bisphenol A is treated statistically on the basis of cascade theory to describe the branching process. The chain lengthening step is based on the reaction of the epoxide functional group with the phenolic hydroxyl group and leads to the formation of a 1,3‐diphenoxy‐2‐propanol link. The peculiar feature of this polyaddition reaction is the possibility of further addition of an epoxide to a secondary hydroxyl group to form branched molecules. This branching reaction does not, however, lead to a loss of hydroxyl groups since a new secondary hydroxyl group is created when an epoxide functional group reacts with a secondary hydroxyl group. Closed analytic expressions are derived for the weight‐average (Mw) and number‐average (Mn) molecular weights in terms of the mole ratio R = mb/ma and the extents of reaction of the functional groups α(phenolic hydroxyl), β(epoxide), and p(branching), i.e. the probability p that an epoxide group has reacted with a secondary hydroxyl group, where mb and ma are the mole fractions of the diglycidyl ether of bisphenol A and of bisphenol A, respectively. Consideration of a simple kinetic mechanism shows that α,β and ρ are related to the ratio b = k2/k1, where k1 and k2 are the rate constants of the chain lengthening step and the chain branching step, respectively. The equations derived for Mw and Mn as a function of a α allow the determination of the branching probability p (or the kinetic rate constant ratio b). An equation for the gel point (Mw → ∞) is given which states a relationship between αc and pc where the subcript c refers to the critical point of gelation. Thus location of the gel point and measurement of αc, either directly or by extrapolation on samples taken prior to gelation, enables p to be measured.

The structure of laminar alkane-, alkene-, and acetylene flames

The detailed knowledge of combustion mechanisms is important for example for the control of (kinetically determined) pollutant formation (e.g., NO, hydrocarbons, soot), or for the extrapolation to technologically important but experimentally inaccessible conditions. By suitable separation and elimination of unimportant reactions, a mechanism is developed with the aid of the present kinetic data for the elementary reactions involved. This mechanism explains, without fitting, the currently available experimental results for laminar premixed flames of alkanes, alkenes, and acetylene (flame velocity and structure of free flames, concentration and temperature profiles in burner-stabilized flames). These experimental results are simulated by the solution of the corresponding conservation equations with suitable models describing diffusion and heat conduction in the multicomponent mixture considered. In lean and moderately rich flames the hydrocarbon is attacked by O, H, and OH, in the first step. These radicals are produced by the chain-branching steps of the oxyhydrogen reaction. The alkyl radicals formed in this way always decompose to smaller alkyl radicals by fast thermal elimination of alkenes. Only the relatively slow thermal decomposition of the smallest alkyl radicals (CH 3 and C 2 H 5 ) competes with recombination and with oxidation reactions by O atoms and O 2 . This part of the mechanism is rate-controlling in the combustion of alkanes and alkenes, and is therefore the reason for the similarity of all alkane and alkene flames.

Shock-tube studies on the ignition of ethylene-oxygen-argon mixtures

Ignition induction times were measured for 9 different ethylene-oxygen-argon mixtures with stoichiometric ratios between 0.125 and 2, with ethylene mole fractions ranging from 0.0025 to 0.02 and total pressures of 3 and 12 atm. The overall correlation equation is τ = 10 − 11.9 [ C 2 H 4 ] 0.3 [ O 2 ] − 1.1 [ A r ] 0.4 e 34.200 / R T where the time, τ, is in seconds and the concentrations are in moles per cc. Analytical data on quenched, partially reacted samples indicate that oxygen does not participate in the initiating steps of the reaction, but promotes chain-branching steps later on.

On the shock-induced ignition of explosive gases

The paper elucidates the distinction between two regimes of ignition, one strong and the other weak, that characterize the onset of combustion in homogeneous gaseous mixtures whose reaction mechanism is controlled by a chain-branching step, such as that associated with the H+O2 collision in the hydrogen-oxygen system. On the basis of experimental observations, made primarily by the use of a stroboscopic laser-schlieren system yielding a sequence of photographic records of the entire flow field behind a reflected shock near the closed end of the tube at a repetition rate of 2 microseconds between frames, it has been revealed that strong ignition is manifested by a practically instantaneous appearance of a relatively plane pressure front associated with the generation of a flow field across the whole cross section of the tube, while mild ignition starts in the form of distinct flame kernels whose growth is comparatively slow and essentially devoid of any gasdynamic effects. The demarcation line between the two regimes of ignition is then shown to be associated with a critical value of the gradient of the induction time with respect to temperature at constant initial pressure. Specifically, for a stoichiometric hydrogen-oxygen mixture, this turns out to be −2 microseconds/°K. Although basically controlled by the same elementary processes as those that establish the second explosion limit, this so-called strong ignition limit differs from the locus of states obtained by direct extrapolation of the second limit. Moreover, it does not intersect with any of the explosion limits, encompassing a region that is fully contained within the classical explosion regime.

Ignition kinetics of the carbon monoxide-oxygen reaction

An analytic solution for the ignition kinetics of the dry CO−O2 reaction is obtained by assuming an initiation reaction followed by the chain-branching steps C O + O → C O 2 * C O 2 * + O 2 → C O 2 + 2 O together with chain termination by quenching of CO2* and three-body recombination of CO and O. It is concluded that shock-tube induction times on reportedly dry CO−O2 mixtures cannot be explained by this mechanism. The shock-tube data can be explained by the following scheme, if a water vapor content of 20 ppm or less is assumed: C O + O 2 → k i C O 2 + O O + H 2 O → k 5 2 O H O H + C O → k 6 C O 2 + H H + O 2 → k 2 ' O H + O The rate constant for the initiation reaction was found to be k i = 2.5 × 10 9 exp ⁡ ( − 48 , 000 / R T ) l i t e r s m o l e − 1 sec ⁡ − 1 . The rate constant for the reaction between O and H2O at 1600°K was estimated by two different methods to be 8×108 and 1.5×109 liters mole−1 sec−1. Induction periods for mixtures with deliberate additions of hydrogen can be fit by adding the steps O + H 2 → k 3 ' O H + H O H + H 2 → k 1 ' H 2 O + H

High temperature preflame reactions of n-heptane

In the preflame reactions of dilute mixtures of n-heptane and oxygen in argon at temperatures just above 1 000°K, the predominant feature is cracking. The cracking sequence is not rapidly chain branching and is not markedly influenced by the oxygen present. The rate is proportional to the inert argon diluent. The ignition delays are lengthened by the addition of a number of hydrocarbons, including increased heptane concentration. Ethane and acetylene are exceptions and do not inhibit the ignition. Hydrogen promotes ignition. The reaction, H+ O 2→ OH+ O, is the likely important chain branching step among the reactions leading to ignition.

Effects of concentration and of vibrational relaxation on the induction period of the H 2−O 2 reaction

The possibility that slow vibrational relaxation of O 2 or H 2 might affect the induction period of the high-temperature H 2 −O 2 reaction is considered in terms of the data from three different kinds of shock-tube experiments. The data cover a wide range of initial composition and temperature and include observations in H 2 -air, H 2 −O 2 −Ar, and H 2 −O 2 mixtures. It is found that induction times in excellent agreement with experiment can be calculated by solving the differential rate equations based on the following simple kinetic scheme: an initiation reaction between molecular species, plus the three usual chain-branching reactions. It is not necessary to invoke vibrational effects to obtain this agreement, but it is necessary to solve the problem without incorporating steady-state assumptions or limitations on [H 2 ]/[O 2 ] ratios. Thus, it is concluded that existing data exhibit little or no effect of slow vibrational relaxation. In support of this conclusion, calculations are presented to show that the greatest possible effect of slow O 2 relaxation would, in fact, be a small one. The calculations were carried out by making the extreme assumption that all the activation energy of the slow chain-branching step must be supplied by vibrational energy of O 2 . Since the level of this energy varies during the induction period in a manner governed by the vibrational relaxation time, the reaction rate constant becomes time dependent. Unfortunately, the equivalent calculations for H 2 cannot be made, because the relaxation time of H 2 in the presence of O 2 is not known.