Theoretical investigation of the formic acid decomposition kinetics

Decomposition of formic acid (HCO₂H) proceeds via three unimolecular channels: dehydration, decarboxylation, and dissociation, the latter expected to be of minor contribution to the overall kinetics. In addition, despite the similar values reported for the individual activation energies for the dehydration and decarboxylation reactions, experimental works have shown that the former is dominant in the reaction mechanism. These reactions show pressure-dependent rate coefficients, and the high-pressure condition is not yet verified at atmospheric pressure. This work aims to investigate the influence of temperature and pressure on the rate coefficients. Hence, theoretical calculations at the CCSD(T)/CBS level have been performed to accurately describe the unimolecular reaction and Rice-Ramsperger-Kassel-Marcus (RRKM) rate coefficients have been calculated and integrated for the prediction of k(T,P) rate coefficients, adopting both strong and weak collision models, over the intervals 0.5-10 atm and 298-2200 K. Our results suggest that the isomerization path is important and explains the preference for the (CO + H₂O) channel. Rate coefficients for the (CO₂ + H₂) and (CO + H₂O) formations are given, in s⁻¹, as exp(−34404/T) and exp(−33785/T), respectively. The dissociation limit of 107.29 kcal mol^–1, with respect the Z-HCO₂H conformer, leading to OH + HCO, via a barrierless potential curve, with rate coefficients, in s⁻¹, expressed as k_HCO+OH(T) = 1.68 × 10¹⁷ exp(−56018/T). Temperature and pressure dependence for the HCO + OH → CO₂ + H₂ and HCO + OH → CO + H₂O reactions have also been estimated.     

Direct measurements of C3F7I dissociation rate constants using a shock tube ARAS technique

This work presents the first direct experimental study on the thermal unimolecular decomposition of n-C₃F₇I. Experiments were performed behind incident and reflected shock waves using the atomic resonance absorption spectroscopy (ARAS) technique on a resonant line of atomic iodine at 183.04 nm. The reaction C₃F₇I + Ar → C₃F₇ + I + Ar (1) was studied at specific temperature (800–1200 K) and pressure (0.6–8.3 bar) ranges. Under experimental conditions, the obtained values of the rate constant at temperatures below 950 K are close to the high-pressure limit; however, considering theoretical calculations, the influence of pressure on the rate constant at elevated temperatures remains noticeable. The resulting value of the experimental rate constant of reaction 1 is presented in the following Arrhenius form: Experimental data were found to correlate with the results of the Rice–Ramsperger–Kassel–Marcus –master equation analysis based on quantum-chemical calculations. The following low- and high-pressure limiting rate coefficients were obtained over the temperature range T = 300–3000 K: with the center broadening factor F_c = 0.119.     

Predicting polycyclic aromatic hydrocarbon formation with an automatically generated mechanism for acetylene pyrolysis

Using Reaction Mechanism Generator (RMG), we have automatically constructed a detailed mechanism for acetylene pyrolysis, which predicts formation of polycyclic aromatic hydrocarbons (PAHs) up to pyrene. To improve the data available for formation pathways from naphthalene to pyrene, new high‐pressure limit reaction rate coefficients and species thermochemistry were calculated using a combination of electronic structure data from the literature and new quantum calculations. Pressure‐dependent kinetics for the CH potential energy surface calculated by Zádor et al. were incorporated to ensure accurate pathways for acetylene initiation reactions. After adding these new data into the RMG database, a pressure‐dependent mechanism was generated in a single RMG simulation which captures chemistry from C to C. In general, the RMG‐generated model accurately predicts major species profiles in comparison to plug‐flow reactor data from the literature. The primary shortcoming of the model is that formation of anthracene, phenanthrene, and pyrene are underpredicted, and PAHs beyond pyrene are not captured. Reaction path analysis was performed for the RMG model to identify key pathways. Notable conclusions include the importance of accounting for the acetone impurity in acetylene in accurately predicting formation of odd‐carbon species, the remarkably low contribution of acetylene dimerization to vinylacetylene or diacetylene, and the dominance of the hydrogen abstraction CH addition (HACA) mechanism in the formation pathways to all PAH species in the model. This work demonstrates the improved ability of RMG to model PAH formation, while highlighting the need for more kinetics data for elementary reaction pathways to larger PAHs.     

Kinetics of two redox reactions in 2-butoxyethanol and water near its critical point of solution

The rate constants of two redox reactions and in the critical solution of 2-butoxyethanol and water have been measured by using the UV spectrophotometry at the initial reaction stage. It was found that the rate constants at various temperatures for two reactions were well described by the Arrhenius equation in the noncritical region. The critical slowing down effect was detected in the critical region. The critical slowing down exponents were determined to be 0.044 ± 0.004 and 0.046 ± 0.005 for reactions and , respectively. The values of the critical slowing down exponents showed that only dynamic critical slowing down effect, and no thermodynamic singularity could be observed for the two reactions.     

Oxidation of methylamine

A detailed chemical kinetic model for oxidation of methylamine has been developed, based on theoretical work and a critical evaluation of data from the literature. The rate coefficients for the reactions of CHNH + O CHNH / CHNH + HO, CHNH + H CH + NH, CHNH CHNH, and CHNH + O CHNH + HO were calculated from ab initio theory. The mechanism was validated against experimental results from batch reactors, flow reactors, shock tubes, and premixed flames. The model predicts satisfactorily explosion limits for CHNH and its oxidation in a flow reactor. However, oxidation in the presence of nitric oxide, which strongly promotes reaction at lower temperatures, is only described qualitatively. Furthermore, calculated flame speeds are higher than reported experimental values; the model does not capture the inhibiting effect of the NH group in CHNH compared to CH. More work is desirable to confirm the products of the CHNH + NO reaction and to look into possible pathways to NH in methylamine oxidation.     

Finding of remarkable synergistic effect on the aroxyl-radical-scavenging rates under the coexistence of α-tocopherol and catechins

Measurements of aroxyl radical (ArO^•)-scavenging rate constants () of antioxidants (AOHs) (α-tocopherol (α-TocH) and three catechins (CatHs) (ie, epicatechin (EC), epigallocatechin (EGC), and epigallocatechin gallate (EGCG)) were performed in ethanol solution, using stopped-flow spectrophotometry. values were measured not only for each AOH, but also for the mixtures of two AOHs (α-TocH and CatH). A notable synergistic effect that the value of α-TocH increases 1.29, 1.84, and 1.65 times under the coexistence of constant concentrations of EC, EGC, and EGCG, respectively, was observed for the solutions including α-TocH and CatH. Similarly, values of CatHs (EC, EGC, and EGCG) increased 1.72, 2.25, and 2.34 times under the coexistence of constant concentrations of α-TocH, respectively. UV-Vis absorption of α-tocopheroxyl radical (α-Toc^•) (λ_max = 428 nm), which had been produced by reaction of α-TocH with ArO^•, decreased remarkably under the coexistence of α-TocH and CatHs due to the fast α-TocH-regeneration reaction by CatHs. The result suggests that the prooxidant reaction due to α-Toc^• is suppressed by the coexistence of CatHs. By analyzing the formation and decay curves of α-Toc^•, it has been ascertained that one molecule of EGCG having three OH groups at B-ring may rapidly regenerate three molecules of α-Toc^• to α-TocH.     

Nonlinear Taft Polar Free Energy Relationship: Reactions of N‐Substituted Benzyl Amines with Benzyl Bromide in Methanol

The rates of reactions of N‐substituted benzyl amines with benzyl bromide were measured using a conductivity technique in methanol medium. The reaction followed a total second‐order path. The end product of the reaction is identified as dibenzyl alkyl amine (C₆H₅CH₂N(R)CH₂C₆H₅). The rates increased with a decrease in the electron‐donating capacity or with an increase in the Taft σ* value of electron‐donating alkyl substituents (R) such as t‐butyl (σ* = ?0.3), i‐propyl (σ* = ?0.19), n‐butyl (σ* = ?0.13), and ethyl (σ* = ?0.1) on nitrogen of the amine until the Taft σ* value becomes zero for the methyl group ( = 0.00), and then the rates decreased with an increase in the electron‐withdrawing capacity or with an increase in the Taft σ* value of electron‐withdrawing substituents (R) such H and C₆H₅ ( = 0.49 and = 0.6). The locus of the Taft polar free energy relationship has a maximum near the point for N‐methyl benzyl amine, showing that there is a sharp change in the rate‐determining step. A mechanism involving formation of an S_N2‐type transition state between the amine nucleophiles and the benzyl bromide and its subsequent decomposition is proposed. Activation parameters were calculated and are discussed.     

Thermal rate constant for the C(3P) + OH(X2Π) → CO(X1Σ) + H(2S) reaction using stochastic energy grained master equation method

In the present work, the kinetic mechanism of the reaction is studied. The rate constants were determined using the Master Equation Solver for Multi-Energy Well Reactions (MESMER). The master equation modeling was also employed to examine the pressure dependence for each pathway involved. The theoretical analysis shows that the overall rate coefficient is practically independent of pressure up to 100 Torr for the temperature range 125-500 K. The unusual dependence of the overall rate constant with temperature was fit with the d-Arrhenius expression , where cm³molecule⁻¹s⁻¹, , and  kJ·mol⁻¹, for 125⩽ T ⩽ 500 K. The thermal rate constant results are in relatively good agreement with other theoretical studies.     

An Experimental Study of the Kinetics of the Reactions of Isopropyl,sec‐Butyl,and tert‐Butyl Radicals with Molecular Chlorine at Low Pressures (0.5–7.0 Torr) in the Temperature Range 190–480 K

In this work, we have measured the rate coefficients of the reactions of isopropyl (propan‐2‐yl), sec‐butyl (butan‐2‐yl), and tert‐butyl (2‐methylpropan‐2‐yl) radicals with molecular chlorine as a function of temperature (190–480 K). The experiments were done in a tubular laminar flow reactor coupled to a photoionization quadrupole mass spectrometer employing a gas‐discharge lamp for ionization. The radicals were homogeneously produced in the reactor by photolyzing suitable precursor molecules with 193‐nm pulsed exciplex laser radiation. The bimolecular rate coefficients were obtained by monitoring the radical decay signals in real time under pseudo–first‐order conditions. The rate coefficients of all three reactions showed negative temperature dependence. The bath gas used in the experiments was helium, and the rate coefficients appeared to be independent of the helium concentrations employed ([2.4–14] × 10¹⁶ cm^?3) for all three reactions. The rate coefficients of the reactions can be approximated in the studied temperature range by the following parameterizations: We estimate that the overall uncertainties of the measured rate coefficients are ±20%. We were able to observe 2‐chloropropane (i‐C₃H₇Cl) product for the i‐C₃H₇^● + Cl₂ reaction. No products were observed for the other two reactions, and the reasons for this are briefly discussed in the text.     

Multiconformer transition state theory rate constants for the reaction between OH and -dimethoxyfluoropolyethers

In this work, we have calculated rate constants for the tropospheric reaction between the OH radical and -dimethoxyfluoropolyethers. The latter are a specific class of the hydrofluoropolyethers family with the general formula , from which we have selected three case studies: , , and . The calculations were performed by applying a cost-effective protocol developed for bimolecular hydrogen-abstraction reactions and based on multiconformer transition state theory relying on computationally accessible M08-HX/apcseg-2//M08-HX/pcseg-1 calculations. Within the protocol's uncertainties and approximations, the results show that (1) the calculated rate constants have the same order of magnitude and (2) if observed together with previous experimental and theoretical investigations, the chain length (that varies with q and p) is seen to have a small effect on the rate constant, which is consistent with the “no discernible effect” reported in the experimental work.     

Kinetics of wet air oxidation of sodium sulfide over heterogeneous iron catalyst

Wet air oxidation (WAO) is an established technique for reducing the chemical oxygen demand (COD) of refinery sulfidic spent caustic waste. In the present work, the heterogeneous form of the cheap and abundant catalyst ferrous sulfate (FeSO₄) was employed for WAO of sodium sulfide. The performance of this catalyst in the oxidative destruction of this model compound is thus far unfamiliar. Kinetic data for the non-catalytic and catalytic oxidation processes was collected in a batch reactor. For the catalytic process, temperature (T), oxygen partial pressure () and catalyst concentration (ω) were varied in the ranges 80-150°C, 0.69-2.06 MPa and 0.8-2.4 g/L respectively. Around 94% COD was destroyed within 1 h when feed containing 8 g/L of sulfide was oxidized at T = 100°C, = 0.69 MPa, and ω = 0.8 g/L. First, the data on disappearance of COD were fitted to a power law model and reaction rate constants were determined. The activation energy for the non-catalytic (91 kJ/mol) and catalytic (50 kJ/mol) oxidation process was found from the temperature dependence of the rate constants. Second, hyperbolic models based on Langmuir-Hinshelwood (L-H) and Eley-Rideal (E-L) kinetics were used for fitting kinetic data. It was found that the L-H model suggesting dissociative adsorption of oxygen provided the best fit. In this way, a deep insight into oxidation kinetics of sodium sulfide was provided.     

Twenty-species and 15-species chemical kinetic mechanisms for cyclohexane using the local self-similarity tabulation method

The 1081 species cyclohexane-oxidation elementary reaction mechanism of Silke et al. (DOI: 10.1021/jp067592d ) is reduced in the number of species by a factor using the local self-similarity tabulation (LS2T) method. Reduced-species mechanisms of both 20 (R20) and 15 (R15) species are created in the high-pressure combustion regime typical of diesel engines. To evaluate the performance of R20 and R15 against the elementary kinetics, simulations are performed for cyclohexane/air mixtures at initial temperatures of 1150, 900, 750, and 680 K and constant pressures of 20 and 40 bar for a variety of equivalence ratios (, 1.0, and 2 for 1150 and 900 K; for 750 K; for 680 K). Very good agreement between R20 and R15 with the elementary kinetics mechanism is demonstrated at 1150 and 900 K for which the self-similarity is very well obeyed; however, only fair agreement is obtained at 750 and 680 K, a fact which is traced to the less faithful adherence to the self-similarity due to the one order of magnitude increase in ignition time over the range 750-680 K. These results are found to be quasi-independent of the tabulation grid. Future work is proposed to improve the reduction in the cold-ignition, high-pressure regime.     

Experimental and theoretical investigation of the reaction of RO2 radicals with OH radicals: Dependence of the HO2 yield on the size of the alkyl group

The HO₂ yield in the reaction of peroxy radicals with OH radicals has been determined experimentally at 50 Torr helium by measuring simultaneously OH and HO₂ concentration time profiles, following the photolysis of XeF₂ in the presence of different hydrocarbons and O₂. The following yields have been obtained:  = (0.90 ± 0.1),  = (0.75 ± 0.15),  = (0.41 ± 0.08), and  = (0.15 ± 0.03). The clear decrease in HO₂ yield with increasing size of the alkyl moiety can be explained by an increased stabilization of the trioxide adduct, ROOOH. This has been confirmed by ab initio and Rice–Ramsperger–Kassel–Marcus master equation calculations. Extrapolation of the experimental results to atmospheric conditions shows that the stabilized adduct, ROOOH, is the nearly exclusive product of the reaction between OH radicals and peroxy radicals containing more than three C‐atoms. The fate and possible impact of these species is completely unexplored so far.     

A Shock Tube Study of H Atom Addition to Cyclopentene

We report shock tube studies of the kinetics of H atom addition to cyclopentene and modeling of the subsequent decomposition of cyclopentyl. Hydrogen atoms were generated with thermal precursors in dilute mixtures of cyclopentene and a reference compound in argon. Addition of H to the double bond leads to a cyclopentyl radical that rapidly ring opens and decomposes to ethene and allyl radical. The process was monitored by postshock gas chromatographic analysis of ethene and rate constants determined relative to H atom displacement of methyl from 1,3,5‐trimethylbenzene (135TMB). At 863–1167 K and 160–370 kPa, we find and, with , we obtain Using experimental values of about 3:1 for the ratio of C─C to C─H beta scission in cyclopentyl radicals and a corresponding transition‐state‐theory/Rice‐Ramsberger‐Kassel‐Marcus (TST/RRKM) model, the high‐pressure rate expression for addition of H to cyclopentene at 863–1167 K is derived as Combined with literature results from lower temperatures and a fitted TST model, the rate expression between 298 and 2000 K is determined as Results are compared with related systems. Near 1000 K, our data require a minimum value of 1.5 for branching between beta C─C and C─H scission in cyclopentyl radicals to maintain established trends in H addition rates. This conflicts with current computed values and those used in existing kinetics models of cyclopentane combustion. We additionally report and discuss minor observed channels in the decomposition of cyclopentene, including formation of 1,4‐pentadiene, (E/Z)‐1,3‐pentadiene, 1,3‐butadiene, and the direct elimination of H₂ from cyclopentene to give cyclopentadiene.     

Leaching kinetics of electric arc furnace dust in nitric acid solutions

Electric arc furnace dust contains mainly ZnO, ZnFe₂O₄, and iron oxides. In this study, chemical composition of ZnO, ZnFe₂O₄, and Fe₂O₃ and leaching kinetics of ZnO, ZnFe₂O₄, and Fe₂O₃ in HNO₃ solutions were investigated. It was seen that the dissolution of ZnO is very fast, therefore the leaching kinetics of ZnO cannot be determined. Kinetic parameters and model equations were derived for the leaching of ZnFe₂O₄ and Fe₂O_3. Leaching kinetics of ZnFe₂O₄ was explained by the pseudohomogeneous reaction model. Activation energy and order of HNO₃ concentration were found to be as 37.5 kJ mol⁻¹ and 0.37, respectively. The model equation was derived as . It was determined that experimental data for the leaching kinetics of Fe₂O₃ best fit with the shrinking core model (SCM). Activation energy and order of HNO₃ concentration were found to be as 51.5 kJ mol⁻¹ and 0.67, respectively The model equation was derived using SCM as _.     

Kinetic model for Ostwald's rule of stages with applications to Boc-diphenylalanine self-assembly

A kinetic model which describes Ostwald's rule of stages, during the process of crystal growth from solution, is reported here. Reaction equations for stages are given where the stages convert from one to another. The final stage reacts to release a portion of solute back into solution, while the remainder converts to the final equilibrium form. Additionally, a remnant of the solute that was not consumed by any of the transitional stages, ultimately is converted into the final product. This particular model was motivated by a recent report for Boc-diphenylalanine self-assembly where the dissolved peptide was observed to go through two polymorphic stages before reaching the equilibrium supramolecular assembly [A. Levin et al., Nat. Commun. 5, 5219, (2014)]. Kinetic data for the concentration of solute present during the process are listed in the above-mentioned report. We show here how the model, for , describes the time-dependent behavior of the solute decay during the growth process. After comparing the model to the experimental data, we are able to report values for all of the rate constants and propose a rule whereby the relative magnitudes of these constants can be used to predict whether a supersaturated substance will noticeably pass through transitional stages or simply convert from solute to the equilibrium solid form.     

A study of some kinetic aspects of the CCl4 interaction with oxide ions in KCl-SrCl2 melts with different content of SrCl2

A comparative investigation of a complex process of the interaction between CCl₄ vapor and oxide ions O^2– (carbochlorination) in K₂SrCl₄ and KSr₂Cl₅ melts at 973 K was performed by the potentiometric method using Pt(O₂)|ZrO₂(Y₂O₃) membrane oxygen electrode as reversible to oxide ion. The analysis of the limiting stages of this process was made on the basis of van't Hoff diagrams. The entire process can be divided into three stages with corresponding limiting processes: the rate of CCl₄ dissolution in the melts for stage 1, the chemical reaction in the melts for stage 2, and the rate of the contamination of the melts with oxygen-containing admixtures for the stage 3. The rate constants of the carbochlorination process in both melts at 973 K were calculated using the data corresponding to stage 2 as (4.4 ± 0.25) × 10⁵ kg mol⁻¹ min⁻¹ for K₂SrCl₄ and (1.83 ± 0.5) × 10⁵ kg mol⁻¹ min⁻¹ for KSr₂Cl₅. The final concentration of oxide ions after the treatment is higher ( = (1.6 ± 0.7) × 10⁻⁷ mol kg⁻¹ for KSr₂Cl₅ and  = (2.5 ± 1.3) × 10⁻⁸ mol kg⁻¹ for K₂SrCl₄ melt, respectively). This corresponds to the difference in the oxoacidic properties of the studied melts.     

Substitution Kinetics of [Fe(PDT/PPDT)n(phen)m]2+ (n ≠ m; n,m = 1,2) with 2,2′‐Bipyridine, 1,10‐Phenanthroline,and 2,2′,6,2″‐Terpyridine

The triazines 3‐(2‐pyridyl)‐5,6‐diphenyl‐1,2,4‐triazine (PDT), 3‐(4‐phenyl‐2‐pyridyl)‐5,6‐diphenyl‐1,2,4‐triazine (PPDT), and 1,10‐phenanthroline (phen) were coordinated to the Fe²⁺ ion to form (1) , (2) , , (3) and (4) . The complexes were synthesized and characterized by mass spectroscopy and elemental analysis. The rate of substitution of these complexes by 2,2′‐bipyridine (bpy), 1,10‐phenanthroline (phen), and 2,2′,6,2″‐terpyridine (terpy) was studied in a sodium acetate–acetic acid buffers over the range 3.6–5.6 at 25, 35, and 45°C under pseudo–first‐order conditions. The reactions are first order with respect to the concentration of the complexes. The reaction rates increase with increasing [bpy/phen/terpy] and pH, whereas ionic strength has no influence on the rate of reaction. Plots of k _obs versus [bpy/phen/terpy] and 1/[H⁺] are linear with positive slopes and significant y‐intercepts. This indicates that the reactions proceed by both dissociative as well as associative pathways for which the associative pathway predominates the substitution kinetics. Observed temperature‐depended rate constants at the three temperatures at which substitution reactions were studied together with the protonation constants of the substituting ligands (phen, bpy, terpy) were used to evaluate the specific rate constants (k ₁ and k ₂) and thermodynamic parameters (E_a , ΔH ^#, ΔS ^#, and ΔG ^#). The reactivity order of the four complexes depends on the phenyl groups present on the triazine (PDT/PPDT) molecule. The π‐electrons on phenyl rings stabilizes the charge on the metal center by inductive donation of electrons toward the metal center resulting in a decrease in reactivity of the complex, and the order is 1 < 2 < 3 < 4 . The rate of substitution is also influenced by the basicity of the incoming ligand (bpy/phen/terpy), and it decreased in the order: phen > terpy > bpy. Higher rate constants, low E_a values_, and more negative entropy of activation (−ΔS ^#) values were observed for the associative path, revealing that substitution reactions at the octahedral iron(II) complexes by bpy, phen, and terpy occur predominantly by the associative mechanism. Density functional theory calculations support the interpretations.     

Oxidative Cleavage of S–S Bond During the Reduction of Tris(pyridine‐2‐carboxylato)manganese(III) by Dithionite in Sodium Picolinate–Picolinic Acid Buffer Medium

The reduction of tris(pyridine‐2‐carboxylato)manganese(III) by dithionite has been investigated within the temperature window 288–303 K and at pH range 5.22–6.10 in sodium picolinate–picolinic acid buffer medium. The reaction obeys the following stoichiometry: The reaction is described in terms of a mechanism that involves an initial complex formation between S₂O₄^2? and [Mn^III(C₅H₄NCO₂)₃] followed by S–S bond cleavage to give 2HSO₃^? and [Mn^II(C₅H₄NCO₂)₂(H₂O)₂] as the products via the formation of SO₂^●? radical anion. Kinetics and spectrophotometric evidences are cited in favor of the suggested mechanism. Thermodynamic parameters associated with the equilibrium step and the activation parameters with the rate‐determining step have been computed.     

Shock Tube Study of Dimethylamine Oxidation

Dimethylamine (DMA) ignition delay times and OH time histories during the oxidation process were investigated behind reflected shock waves. The ignition delay time measurements cover the temperature range of 1181–1498 K, with pressures near 0.9, 1.5, and 2.8 atm, and equivalence ratios of 0.5, 1, and 2, in 4% oxygen/argon. The ignition delay time data feature low scatter and can be correlated to a single expression with ² ～ 0.99: τ_ign = 7.30 × 10^{?4 ?0.68} Φ^0.45 exp(18,265/), where τ_ign is in μs, in atm, and in K. OH time histories were measured using laser absorption of the R₁(5) line of the A‐X(0,0) transition near 306.7 nm, in stoichiometric mixtures of 500 ppm DMA/O₂/argon. The mechanism developed by Li et al. was used initially to simulate the measured DMA ignition delay times and the OH time histories. The Li et al. mechanism was then updated by adding the DMA unimolecular decomposition channel: DMA = CH₃NH + CH₃, with the reaction rate constant estimated by analogy to dimethyl ether decomposition, previously investigated by Cook et al. The reactions of DMA + OH were also updated based on recent work in our laboratory. The simulation results using the modified Li et al. mechanism are in good agreement with both the ignition delay times and OH time‐history data.