Rate constants for the gas‐phase reactions of chlorine atoms with 1,4‐cyclohexadiene and 1,5‐cyclooctadiene at 298 K

Rate constants for the reactions of Cl atoms with two cyclic dienes, 1,4‐cyclohexadiene and 1,5‐cyclooctadiene, have been determined, at 298 K and 800 Torr of N₂, using the relative rate method, with n‐hexane and 1‐butene as reference molecules. The concentrations of the organics are followed by gas chromatographic analysis. The ratios of the rate constants of reactions of Cl atoms with 1,4‐cyclohexadiene and 1,5‐cyclooctadiene to that with n‐hexane are measured to be 1.29 ± 0.06 and 2.19 ± 0.32, respectively. The corresponding ratios with respect to 1‐butene are 1.50 ± 0.16 and 2.36 ± 0.38. The absolute values of the rate constants of the reaction of Cl atom with n‐hexane and 1‐butene are considered as (3.15 ± 0.40) × 10^?10 and (3.21 ± 0.40) × 10^{? 10} cm³ molecule^?1s^?1, respectively. With these, the calculated values are k(Cl + 1,4‐cyclohexadiene) = (4.06 ± 0.55) × 10^?10 and k(Cl + 1,5‐cyclooctadiene) = (6.90 ± 1.33) × 10^?10 cm³ molecule^?1 s^?1 with respect to n‐hexane. The rate constants determined with respect to 1‐butene are marginally higher, k(Cl + 1,4‐cyclohexadiene) = (4.82 ± 0.80) × 10^{? 10} and k(Cl + 1,5‐cyclooctadiene) = (7.58 ± 1.55) × 10^{? 10} cm³ molecule^?1 s^?1. The experiments for each molecule were repeated three to five times, and the slopes and the rate constants given above are the average values of these measurements, with 2σ as the quoted error, including the error in the reference rate constant. The relative rate ratios of 1,4‐cyclohexadiene with both the reference molecules are found to be higher in the presence of oxygen, and a marginal increase is observed in the case of 1,5‐cyclooctadiene. Benzene is identified as one major product in the case of 1,4‐cyclohexadiene. Considering that the cyclohexadienyl radical, a product of the hydrogen abstraction reaction, is quantitatively converted to benzene in the presence of oxygen, the fraction of Cl atoms that reacts by abstraction is estimated to be 0.30 ± 0.04. The atmospheric implications of the results are discussed. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 431–440, 2011     

呋喃西林水溶液在光和热作用下的稳定性

The influence of both light and heat on the stability of nitrofurazone aqueous solution was studied. Results show that in either heating experiments or the exposure to light at high temperatures, the degradation rate obeyed zero-order kinetics. The total rate constant ktotal caused by both light and heat can be divided into two parts: ktotal =kdark klight, where kdark and klight are the degradation rate constants caused by heat and light, respectively. The klight can be expressed as klight=Alight*exp(-Ea,light/RT)*E, where E is the illuminance of light, and Alight and Ea,light both are experimental constants. The values of these kinetic parameters were determined based on the experiments in the dark and upon exposure to three different light sources. Results show that the values of Alight and Ea, light varied with the light source. To save time, labor, and drugs, exponential heating experiments were employed and compared with the isothermal experiments. Results indicated that kinetic parameters obtained by exponential heating experiments are comparable to those obtained by isothermal experiments either in the dark or upon exposure to light.     

A New Curing Kinetic Model and Its Application to BPSER/DDM Epoxy System

A new model has been deduced by assumed autocatalytic reactions. It includes two rate constants, k ₁ and k ₂, two reaction orders, m and n, and the initial concentration of [OH]. The model proposed has been applied to the curing reaction of a system of bisphenol-S epoxy resin (BPSER), with4,4'-diaminodiphenylmethane (DDM) as a curing agent. The curing reactions were studied by means of differential scanning calorimetry (DSC). Analysis of DSC data indicated that an autocatalytic behavior showed in the curing reaction. The new model was found to fit to the experimental data exactly. Rate constants, k ₁ and k ₂ were observed to be greater when curing temperature increased. The activation energies for k ₁ and k ₂ were 95.28 and 39.69 kJ mol^–1, respectively. Diffusion control was incorporated to describe the cure in the latter stages. This revised version was published online in July 2006 with corrections to the Cover Date.     

Kinetics and mechanism of osmium (VIII) and ruthenium(III) catalyzed oxidation of aliphatic amines by chloramine-T in alkaline and perchloric acid media

The kinetics of oxidation of aliphatic amines viz., ethylamine, n-butylamine, isopropylamine (primary amines), diethylamine (secondary amine), and triethylamine (tertiary amine) by chloramine-T have been studied in NaOH medium catalyzed by osmium (VIII) and in perchloric acid medium with ruthenium(III) as catalyst. The order of reaction in [Chloramine-T] is always found to be unity. A zero order dependence of rate with respect to each [OH^?] and [Amine] has been observed during the osmium(VIII) catalyzed oxidation of diethylamine and triethylamine while a retarding effect of [OH^?] or [Amine] on the rate of oxidation is observed in case of osmium(VIII) catalyzed oxidation of primary aliphatic amines. The ruthenium(III) catalyzed oxidation of amines follow almost similar kinetics. The order of reactions in [Amine] or [Acid] decreases from unity at higher amine or acid concentrations. The rate of oxidation is proportional to {k′ and k″ [Ruthenium(III)] or [Osmium(VIII)]} where k′ and k″ (having different values in case of ruthenium(III) and osmium(VIII)) are the rate constants for uncatalyzed and catalyzed path respectively. The suitable mechanism consisting with the kinetic data is proposed in each case and discussed.     

Curing kinetics and mechanism of bisphenol S epoxy resin with 4,4′‐Diaminodiphenyl ether or phathlic anhydride

The kinetics of the cure reaction for systems of bisphenol‐S epoxy resin with 4,4′‐diaminodiphenyl ether or phthalic anhydride as a curing agent were investigated with a differential scanning calorimetry. Autocatalytic behavior was shown in the first stages of the cure for the systems, which could be well described by the model proposed by Kamal [Polym Eng Sci 1973, 13, 59–64] that includes two rate constants k₁ and k₂ and two reaction orders, m and n. k₁ and k₂ values are observed to increase with the increasing temperature. With the proceeding of the cure reaction, the cross‐linking structure appears, and the reaction is mainly controlled by diffusion in the latter stages. The molecular mechanism of the curing system was discussed. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 558–563, 2001     

Curing Kinetics and Thermal Property Characterization of Bisphenol-F Epoxy Resin and MeTHPA System

The curing kinetics of bisphenol-F epoxy resin (BPFER) and curing agent 3-methyl-1,2,3,6-tetrahydrophthalic anhydride (MeTHPA), with N,N-dimethyl-benzylamine as an accelerator, were studied by differential scanning calorimetry (DSC). Analysis of DSC data indicated that an autocatalytic behavior showed in the first stages of the cure for the system, which could be well described by the model proposed by Kamal, which includes two rate constants, k ₁ and k ₂, and two reaction orders, m andn. The curing reaction at the later stages was practically diffusion-controlled. To consider the diffusion effect more precisely, diffusion factor, d(a), was introduced into Kamal's equation. The glass transition temperatures (T _gs) of the BPFER/MeTHPA samples were determined by means of torsional braid analysis (TBA). The thermal degradation kinetics of cured BPFER were investigated by thermogravimetric analysis (TG). This revised version was published online in August 2006 with corrections to the Cover Date.     

Correction for instrument time constant and baseline in determination of reaction kinetics

Rates of reactions can be expressed as dn/dt = kf(n), where n is moles of reaction, k is a rate constant, and f(n) is a function of the properties of the sample. Instrumental measurement of rates requires c(dn/dt) = ckf(n), where c is the proportionality constant between the measured variable and the rate of reaction. When the product of instrument time constant, τ, and k is ? 1, the reaction is much slower than the time response of the instrument and measured rates are unaffected by instrument response. When τ k < 1, = 1, or >1, the reaction rate and instrument response rate are sufficiently comparable that measured rates are significantly affected by instrument response and correction for instrument response must be done to obtain accurate reaction kinetics. This paper describes a method for simultaneous determination of τ, k, c, and instrument baseline by fitting equations describing the combined instrument response and rate law to rates observed as a function of time. When τ cannot be neglected, correction for instrument response has previously been done by truncating early data or by use of the Tian equation. Both methods can lead to significant errors that increase as τk increases. Inclusion of instrument baseline as a fitting parameter significantly reduced variability in k and c compared with use of measured instrument baselines. The method was tested with data on the heat rate from acid‐catalyzed hydrolysis of sucrose collected with three types of calorimeters. In addition, to demonstrate the generality of this method of data analysis, equations including τ, k, c, and instrument baseline are derived for the relation between the reaction rate and the observed rate for first order, second order (first in each reactant), nth order in one reactant, autocatalytic, Michaelis–Menten kinetics, and the Ng equation. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 43: 53–61, 2011     

A novel approach to measure all rate constants in the simplest enzyme kinetics model

Enzymes play vital roles in life processes. Almost all biochemical reactions are mediated by enzymes. The rate constants of enzyme kinetics are the most important parameters for the reactions catalyzed by enzymes. In 1902, Adrian Brown proposed a simple single-substrate-single-product model which contains only three rate constants k ₁, k ₋₁ and k ₂. So far, biologists can measure the Michaelis constant K _M and the catalytic constant k _cat , which actually is equal to k ₂, according to Michaelis–Menten equation. Using temperature jump method or transient state kinetics, k ₁, k ₋₁ and k ₂ can be determined. However, these methods are complicated. In this article, we design a novel simple method that could determine the rate constants k ₁ and k ₋₁ based on knowing k _cat and K _M . Our numerical experiments show that the three rate constants can be calculated rather precisely. Hence, we believe that biochemists could design experiments to measure the rate constants based on our method. This work was partially supported by the National Natural Science Foundation of China (NSFC) under Grant No. 10771206 and partially by 973 project (2004CB318000) of P. R. China.     

A Mechanistic Study on the Oxidative Degradation of Dibenzazepine Derivatives by Manganese(III) Complexes in Acidic Sulfate Media

The oxidative degradation of tricyclic antidepressants (TCA) was studied in the presence of a large excess of the oxidizing agent manganese(III) and its reduced form manganese(II) sulfate in acidic media. The products were detected and identified using UV–vis, ESI‐MS, IR, and EPR methods. The mechanism of the reaction was studied for the following two classes of TCA: 10,11‐dihydro‐5H‐dibenz[b, f]azepines and dibenz[b, f]azepines. The oxidative degradation between dibenz[b, f]azepines and the manganese(III) ions resulted in the formation of substituted acridine with the same substituent as in the origin dibenz[b, f]azepine derivative. The pseudo–first‐order rate constants (k_obs) were determined for the degradation process. The dependences of the observed rate constants on the [Mn^III] with a zero intercept were linear. The reaction between 10,11‐dihydro‐5H‐dibenz[b, f]azepines, and the manganese(III) sulfate ion resulted in oxidative dehydrogenation, which proceeded via the formation of the following two intermediates: a free organic radical and a dimer. Further oxidation of the second intermediate led to a positively charged radical dimer as the single final product. Linear dependences of the pseudo–first‐order rate constants (k_obs) on the [Mn^III] with a zero intercept were established for the degradation of 10,11‐dihydro‐5H‐dibenz[b, f]azepines. The observed rate constants were dependent on the [H⁺] and independent of the [TCA] within the excess concentration range of the manganese(III) complexes used in the isolation method. The radical product of the degradation of 10,11‐dihydro‐5H‐dibenz[b, f]azepines was not stable in the aqueous solution and was subsequently transformed to a nonradical dimer in the next slower step. The observed rate constants were independent of the [Mn^III], independent of the [H⁺] and increased slightly with increasing TCA concentrations when TCA was used in excess. The mechanistic consequences of all of these results are discussed.     

Kinetics and mechanism of the quaternization of poly(4-vinyl pyridine) with 1-bromopropane

The kinetics of the quaternization of poly(4-vinyl pyridine) with 1-bromopropane in sulfolane has been studied in the temperature range 308–348°K with data points covering the whole conversion range. The results have been analyzed according to the neighbouring-group model with rate constants k₀, k₁, and k₂ for reaction of pyridyl groups with zero, one, and two already reacted neighbors. Allowing for limiting reaction at about 95%, the experimental results substantiate the model with K = k₁/k₀ = 0.80 ± 0.03, and L = k₂/k₀ = 0.37 ± 0.03, which are independent of temperature. The temperature dependence of k₀ values gives an activation energy of 66.22 ± 4.20 kJ mol^?1. It is still not possible to decide whether steric or electrostatic factors are responsible for K and L values less than unity. Other systems are mentioned where side reactions occur.     

On the (im)possibility of evaluating correct individual rate constants of chain propagation kp and chain termination kt by combining kp2/kt and kp/kt data for chain‐length dependent termination

On the basis of simulated data two ways of evaluating individual rate constants by combining k_p²/k_t and k_p /k_t (k_p , k_t = rate constants of chain propagation and termination, respectively) were checked considering the chain‐length dependence of k_t. The first way tried to make use of the fact that pseudostationary polymerization yields data for k_p²/k_t as well as for k_p /k_t referring to the very same experiment, in the second way k_p²/k_t (from steady state experiments) and k_p/k_t data referring to the same mean length of the terminating radical chains were compared. In the first case no meaningful data at all could be obtained because different averages of k_t are operative in the expressions for k_p /k_t and k_p²/k_t. In spite of the comparatively small difference between these two averages (≈15% only) this makes the method collapse. The second way, which can be regarded as an intelligent modification of the “classical” method of determining individual rate constants, at least succeeded in reproducing the correct order of magnitude of the individual rate constants. However, although stationary and pseudostationary experiments independently could be shown to return the same k_t for the same average chain‐length of terminating radicals within extremely narrow limits no reasonable chain‐length dependence of k_t could be derived in this way. The reason is an extreme sensitivity of the pair of equations for k_p/k_t and k_p²/k_t towards small errors and inconsistencies which renders the method unsuccessful even for the high quality simulation data and most probably makes it even collapse for real data. This casts a characteristic light on the unsatisfactory situation with respect to individual rate constants determined in the classical way, regardless of a chain‐length dependence of termination. As a consequence, all efforts of establishing the chain‐length dependence of k_t are recommended to avoid this way and should rather resort to methods based on inserting a directly determined k_p into the equations characteristic of k_p²/k_t or k_p/k_t, properly considering the chain‐length dependent character of k_t.     

Calculation of the elementary rate constants of polymer-analogous reactions and sequence analysis of products

A method has been developed for the calculation of elementary rate constants of deceleration and acceleration reactions on polymers in which the reactivity of the group is influenced only by the character of the closest adjacent groups. It is suggested that this method may be valid if the calculation yields a rate constant k′₃, which is independent of conversion. In this case, the sequence analysis of products can be performed by using Markovian first-order statistics, and the rate constants thus obtained can be used for calculating the relative frequencies of variously long sequences of reacted and unreacted groups and their number-average length. For markedly accelerated reactions, a simplified method of estimation of the average sequence length involving use of two of the three elementary rate constants, i.e., k₁ and k′₂, has been suggested.     

Ruthenium(III), osmium(VIII) and ruthenium(III) + osmium(VIII) catalysed oxidations ofi-propanol by N-bromosuccinimide in basic solution

Summary The oxidation ofi-propanol (IPA) by N-bromosuccinimide (NBS) in basic solution was investigated separately in the presence of Ru^III, Os^VIII and Ru^III + Os^VIII ions. The order in [IPA] was found to be 0.7, 0.5 and 0.3 respectively in the above three cases in the concentration range studied. The order in [NBS] was unity in the presence of Ru^III chloride but was found to be zero in the case of Os^VIII and Ru^III+Os^VIII catalysis. The order in [metalion] was found to be nearly unity in all the three catalysed reactions. Increase in [^–OH] increased the rate of reaction while addition of succinimide retarded the rate of reaction. Decrease in dielectric constantsof the medium decreased the rate of oxidation. The pseudo first order rate constants (k), zero order rate constants (k₀) and the formation constants (k_f) of the substrate-catalyst complexes and the thermodynamic parameters have been evaluated. Suitable mechanisms in conformity with the experimental observations have been proposed for the three catalysed reactions.     

An improved method to measure all rate constants in the simplest enzyme kinetics model

Since Adrian Brown and Victor Henri’s work, the simplest enzyme kinetics model, which contains only three rate constants k ₁, k ₂ and k ₋₁ in 1902, has been thoroughly explored in many directions. By using the Michaelis–Menten equation, K _M and k ₂ can be measured quickly. All the three rate constants can be derived by temperature jump method or transient state kinetics, but both methods need more complicated techniques and equipments. In our previous paper (Li et al. in J Math Chem 46:290–301, 2009), we gave a method to measure all the rate constants which does not require any additional equipment other than those needed for measuring K _M and k ₂. Here, we propose a new one which needs no additional equipment either. This method is based on a study of inflection points of integral curves. Numerical results show that the new one is much better than the previous one in two aspects: near the end of the reaction, the new one gives more accurate estimation; during the quasi-steady state of the reaction, it also gives good estimations while the previous one can not. Hence, this method not only advances the estimation accuracy, but also has more choices for measuring.     

Kinetics and stereoregulation in the isotactic-specific and living polymerization of methyl methacrylate

Kinetic studies on the isotactic-specific living polymerization of methyl methacrylate with t-C₄H₉MgBr were carried out in toluene at −78°C and the kinetic orders with respect to the monomer and initiator were found to be unity. Propagation rate in the early stage of polymerization and the initiation rate were studied by kinetic measurement and analysis of oligomer distribution. The rate constants for the propagation of the unimer (k₁), dimer (k₂), and trimer anions (k₃) were found to be in the following order; k₁ >> k₂ > k₃. ¹³C NMR spectra of the oligomer anions indicated the coordination of penultimate and antepenultimate ester groups to Mg counterion. Possible mechanism for stereoregulation in the early stage of polymerization was discussed.     

Kinetics and Products of the Reactions of Ethyl and n‐Propyl Nitrates with OH Radicals

The kinetics of the reactions of ethyl (1) and n‐propyl (2) nitrates with OH radicals has been studied using a low‐pressure flow tube reactor combined with a quadrupole mass spectrometer. The rate constants of the title reactions were determined under pseudo–first‐order conditions from kinetics of OH consumption in high excess of nitrates. The overall rate constants, k₁ = 1.14 × 10^?13 (T/298)^2.45 exp(193/T) and k₂ = 3.00 × 10^?13 (T/298)^2.50 exp(205/T) cm³ molecule^?1 s^?1 (with conservative 15% uncertainty), were determined at a total pressure of 1 Torr of helium over the temperature range (248–500) and (263–500) K, respectively. The yields of the carbonyl compounds, acetaldehyde and propanal, resulting from the abstraction by OH of an α‐hydrogen atom in ethyl and n‐propyl nitrates, followed by α‐substituted alkyl radical decomposition, were determined at T = 300 K to be 0.77 ± 0.12 and 0.22 ± 0.04, respectively.     

Comment on the evaluation of the arrhenius parameters by the least squares method

Arrhenius parameters are frequently evaluated incorrectly by applying the least squares method to the logarithmic form of the Arrhenius equation without simultaneously transforming the statistical weights as required for the change of variable from k to ln k. This has been mentioned briefly in an earlier paper. In the present communication the correct procedures are discussed and illustrated by several examples of evaluations. In particular, Arrhenius parameters calculated by the Taylor series expansion of the exponential form of the Arrhenius equation are compared with those calculated from the logarithmic form, using an exact and two approximate transformations of the statistical weights. The comparisons indicate thatthe preferred procedure for obtaining Arrhenius parameters is either the Taylor series method or the logarithmic method with proper transformation of the experimentally determined statistical weights of the rate constants k_i. The common approximation of assuming equal statistical weights of ln k_i when the logarithmic form of the Arrhenius expression is used is shown not to be always appropriate, and reasons forthis are given.     

Curing Kinetics of Diglycidyl Ether of Bisphenol A and Diaminodiphenylmethane Using a Mechanistic Model

Summary: The curing kinetics of diglycidyl ether of bisphenol A (DGEBA) and 4,4′‐diaminodiphenylmethane (DDM) was analyzed using isothermal differential scanning calorimetry (DSC) modes by using a simple mechanistic model which includes two rate constants, k₁ and k₂, two reaction orders, n₁ and n₂, and the ratio of initial concentration of hydroxyl group to initial epoxy concentration, c₀. Analyses of DSC data indicated that an autocatalytic reaction existed in the curing process. The mechanistic model proposed in this paper fits the experimental data exactly. Rate constants, k₁ and k₂ have been found to increase with rising curing temperature. The activation energies for the relative reactions were determined to be 66.00 ± 4.21 and 50.74 ± 8.92 kJ/mol, respectively. The complex equivalent constant, K, decreased with increasing temperature. Diffusion control was incorporated to describe the cure in the latter stages.

Comparison of experimental data with the mechanistic model for the curing kinetics of DGEBA with DDM.     

Kinetics of the reaction of 4,4′‐biphenol with bromoethane and 1‐bromobutane by phase‐transfer catalysis

The reaction of 4,4′‐biphenol and two species of bromoalkanes (e.g., bromoethane and 1‐bromobutane) to synthesize two symmetric products (4,4′‐diethanoxy biphenyl and 4,4′‐dibutanoxy biphenyl) and one asymmetric product (4‐ethanoxy, 4′‐butanoxy biphenyl) was successfully carried out under two‐phase phase‐transfer catalysis conditions. A rational mechanism and kinetic model were built up by considering the reactions both in aqueous phase and in organic phase. The first active catalyst (QO(Ph)₂OQ) was also synthesized under two‐phase reaction and was identified by instruments. The experimental data were explained satisfactorily by the pseudo‐steady‐state hypothesis. Two sets of rate constants of organic reactions, i.e. primary (k₁ and k₂) and secondary (k₁₁, k₁₂, k₂₁, and k₂₂) rate constants participate in the kinetic model. The two primary rate constants were obtained individually via experimental data for synthesizing the symmetric products. The ratios of the other four secondary rate constants were obtained from the reaction of synthesizing asymmetric products and determined from the initial yield rates of symmetric products. The effects of the ratio of bromoethane and 1‐bromobutane, temperature, organic solvents, amount of catalyst, and amount of sodium hydroxide on the reaction rate and the selectivity of products were investigated in detail. The results were explained satisfactorily by the interaction between the reactants and the environmental species. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 139–153, 2003     

Kinetic study of OH radical reaction with n‐heptane and n‐hexane at 240–340K using the relative rate/discharge flow/mass spectrometry (RR/DF/MS) technique

The kinetics of reactions of OH radical with n‐heptane and n‐hexane over a temperature range of 240–340K has been investigated using the relative rate combined with discharge flow/mass spectrometry (RR/DF/MS) technique. The rate constant for the reaction of OH radical with n‐heptane was measured with both n‐octane and n‐nonane as references. At 298K, these rate constants were determined to be k_{1, octane} = (6.68 ± 0.48) × 10^?12 cm³ molecule^?1 s^?1 and k_{1, nonane} = (6.64 ± 1.36) × 10^?12 cm³ molecule^?1 s^?1, respectively, which are in very good agreement with the literature values. The rate constant for reaction of n‐hexane with the OH radical was determined to be k₂ = (4.95 ± 0.40) × 10^?12 cm³ molecule^?1 s^?1 at 298K using n‐heptane as a reference. The Arrhenius expression for these chemical reactions have been determined to be k_{1, octane} = (2.25 ± 0.21) × 10^?11 exp[(?293 ± 37)/T] and k₂ = (2.43 ± 0.52) × 10^?11 exp[(?481.2 ± 60)/T], respectively. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 489–497, 2011