Optimizing the use of the Kezdy–Mangelsdorf–Swinbourne method for analysis of data following a exp(–kt) + Z

The use of the KMS method for the evaluation of the exponent by the experimentalist requires that a lag or retardation be chosen. The best choice of lag is discussed quantitatively. Its dependence upon the decade range of the data, the relative magnitude of the background, the level and character of the noise, the number and distribution of the data, and the weighted least-squares method of analysis are all detailed. A table of lags and error factors is given, for various ranges, backgrounds, and kinds of noise. Bias in the extracted rate (k), due to noise and treatment of the data, is also discussed.     

Comparison between the analysis of the asymptotic wavepacket and the associated flux for the calculation of kinetic-energy-releases function

The kinetic-energy-releases (KER) distribution function of the fragment is an important observable in the molecular dynamics. In theory, there are several different methods to calculate the KER distribution function or spectrum, which could be generally divided into two classes: One is based on the analysis of the asymptotic wavepacket (“projection method”) and the other is on the analysis of the associated flux (“flux method”). By taking the above-threshold dissociation of the HeH⁺ (v = 8) molecule as an example, we compared these two classes of methods. Based on evenly separated Fourier grid representation, the KER distribution calculated via the projection method F_Proj(E_k) is the same as the one calculated via the flux method F_Flux(E_k) . The relationship between F_Proj(E_k) and the distribution of the projection of the asymptotic wavepacket onto the energy eigenstates of the quasicontinuum, P_Proj(E_k) , and the relationship between F_Flux(E_k) and the distribution of the dissociation probability P_Flux(E_k) from the cumulation of the associated flux, are determined.     

Kinetics and mechanism of the aminolysis of O‐phenyl 4‐nitrophenyl dithiocarbonate in aqueous ethanol

The reactions of the title substrate (1) with a series of secondary alicyclic amines are subjected to a kinetic investigation in 44 wt% ethanol‐water, at 25.0°C, ionic strength 0.2 M (KCl). Under amine excess over the substrate, pseudo‐first‐order rate coefficients (k_obs) are obtained. Plots of k_obs against [NH], where NH is the free amine, are nonlinear upwards, except the reactions of piperidine, which show linear plots. According to the kinetic results and the analysis of products, a reaction scheme is proposed with two tetrahedral intermediates, one zwitterionic (T^±) and another anionic (T⁻), with a kinetically significant proton transfer from T^± to an amine to yield T⁻ (k₃ step). By nonlinear least‐squares fitting of an equation derived from the scheme to the experimental points, the rate microcoefficients involved in the reactions are determined. Comparison of the kinetics of the title reactions with the linear k_obs vs. [NH] plots found in the same aminolysis of O‐ethyl 4‐nitrophenyl dithiocarbonate (2) in the same solvent shows that the rate coefficient for leaving group expulsion from T^± (k₂) is larger for 2 due to a stronger push by EtO than PhO. The k₃ value is the same for both reactions since both proton transfers are diffusion controlled. Comparison of the title reactions with the same aminolysis of phenyl 4‐nitrophenyl thionocarbonate (3) in water indicates that (i) the k₂ value is larger for the aminolysis of 1 due to the less basic nucleofuge involved and the small solvent effect on k₂, (ii) the k₃ value is smaller for the reactions of 1 due to the more viscous solvent, (iii) the rate coefficient for amine expulsion from T^± (k₋₁) is larger for the aminolysis of 1 than that of 3 due to a solvent effect, and (iv) the value of the rate coefficient for amine attack (k₁) is smaller for the aminolysis of 1 in aqueous ethanol, which can be explained by a predominant solvent effect relative to the electron‐withdrawing effect from the nucleofuge. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 839–845, 1999     

Transient kinetic studies involving exciplex formation. Methods of analysis

In this paper, rate parameters are extracted from fluorescene decay data in the framework of Feedback-Type Kinetics (k₈ < k₄). The exciplex dissociation (k₄) and fluorescene decay rate constants (k₈) have been obtained for the five following systems: For this task we have added to the straight line method of Ware which is valid in certain cases only at high perturber concentrations, a new but similar Taylor series method applicable at low concentrations. Thereafter, a safer and more general method of kinetic analysis based on a quasi-linear χ² minimization procedure has been developed and applies to data in any range of concentration.     

Computational aspects of Laplace transform inversion of thermal unimolecular rate constant

The thermal limiting high-pressure unimolecular rate constant k∞ represents, operationally, the Laplace transform of the product of microcanonical rate constant for decomposition of molecules having specified energy E [k(E)] and the density of states [N(E)]. By inversion, it is possible to recover k(E)N(E), from which one can obtain the energy dependence of k(E) and the pressure dependence of k_uni, the thermal general-pressure unimolecular rate constant. This article examines numerical aspects of three methods of inversion, their reliability and dependence on sampling, i.e., on the number of available experimental data points, by comparing exact k(E) and k_uni with those obtained by inversion. It turns out that the method of steepest descents is the best all-round performer.     

Cathodic reduction of oxygen on PdCo/C catalyst synthesized based on commercial Pd/C catalyst

The data on the cathodic PdCo/C catalyst prepared by high-temperature synthesis from 20 wt % Pd/C (E-TEK) are shown. According to XRD data, the catalyst represents an alloy with the preferential composition of Pd₂Co. The kinetics and mechanism of oxygen reduction on the PdCo/C catalyst are studied by the methods of rotating disk electrode, rotating ring-disk electrode, and electrochemical impedance. It is shown that oxygen is reduced preferentially to water (k ₁) but in the potential range more negative than 0.6 V, the ratio of constants k ₁/k ₂ decreases, which suggests that the contribution of the reaction that proceeds through the formation of H₂O₂ (k ₂) increases. The activity of PdCo/C catalyst under model conditions in 0.5 M H₂SO₄ was assessed to be 15 mA/mg_cat at a potential of 0.7 V.     

Kinetics of the reactions of the hydroxyl radical with dimethyl ether and diethyl ether

Absolute rate coefficients for the reactions of the hydroxyl radical with dimethyl ether (k₁) and diethyl ether (k₂) were measured over the temperature range 295–442 K. The rate coefficient data, in the units cm³ molecule^?1 s^?1, were fitted to the Arrhenius equations k₁ (T) = (1.04 ± 0.10) × 10^?11 exp[?(739 ± 67 cal mol^?1)/RT] and k₂(T) = (9.13 ± 0.35) × 10^?12 exp[+(228 ± 27 kcal mol^?1)/RT], respectively, in which the stated error limits are 2σ values. Our results are compared with those of previous studies of hydrogen-atom abstraction from saturated hydrocarbons by OH. Correlations between measured reaction-rate coefficients and C? H bond-dissociation energies are discussed.     

Schiff bases of pyridoxal and polyallylamine. The formation rate determining step

The apparent rate constants of formation (k₁) and hydrolysis (k₂) of the Schiff bases formed between pyridoxal and polyallylamine has been fitted to a kinetic scheme that involve the different protonated species in the reaction medium and the individual rate constants of formation (k₁ⁱ) and hydrolysis (k₂ⁱ). The (k₁ⁱ) values precludes an acid catalyzed intramolecular process. The effects of hydrophobic medium due to the presence of the macromolecule on the reaction is also discussed. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet: 30: 1–6, 1998.     

Determination of the Glass Electrode Parameters by Means of Potentiometric Titration of Acetic Acid in Aqueous Sodium or Potassium Chloride Solutions at 25°C

Single-ion activity coefficient equations are presented for the calculation of stoichiometric (molality scale) dissociation constants K _m for acetic acid in aqueous NaCl or KCl solutions at 25°C. These equations are of the Pitzer or Hückel type and apply to the case where the inert electrolyte alone determines the ionic strength of the acetic acid solution considered. K _m for a certain ionic strength can be calculated from the thermodynamic dissociation constant K _a by means of the equations for ionic activity coefficients. The data used in the estimation of the parameters for the activity coefficient equations were taken from the literature. In these data were included results of measurements on galvanic cells without a liquid junction (i.e., on cells of the Harned type). Despite the theoretical difficulties associated with the single-ion activity coefficients, K _m can be calculated for acetic acid in NaCl or KCl solutions by the Pitzer or Hückel method (the two methods give practically identical K _m values) almost within experimental error at least up to ionic strengths of about 1 mol-kg^–1. Potentiometric acetic acid titrations with base solutions (NaOH or KOH) were performed in a glass electrode cell at constant ionic strengths adjusted by NaCl or KCl. These titrations were analyzed by equation E = E _o + k(RT/F) ln[m(H⁺)], where m(H⁺) is the molality of protons, and E is the electromotive force measured. m(H⁺) was calculated for each titration point from the volume of the base solution added by using the stoichiometric dissociation constant K _m obtained by the Pitzer or Hückel method. During each base titration at a constant ionic strength, E _o and k in this equation were observed to be constants and were determined by linear regression analysis. The use of this equation in the analysis of potentiometric glass electrode data represents an improvement when compared to the common methods in use for two reasons. No activity coefficients are needed and problems associated with liquid junction potentials have been eliminated.     

Rate coefficients for the reactions of chlorine atoms with methanol and acetaldehyde

Rate coefficients have been measured for the reactions of Cl atoms with methanol (k₁) and acetaldehyde (k₂) using both absolute (laser photolysis with resonance fluorescence) and relative rate methods at 295 ± 2 K. The measured rate coefficients were (units of 10⁻¹¹ cm³ molecule⁻¹ s⁻¹): absolute method, k₁ = (5.1 ± 0.4), k₂ = (7.3 ± 0.7); relative method k₁ = (5.6 ± 0.6), k₂ = (8.4 ± 1.0). Based on a critical evaluation of the literature data, the following rate coefficients are recommended: k₁ = (5.4 ± 0.9) × 10⁻¹¹ and k₂ = (7.8 ± 1.3) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ (95% confidence limits). The results significantly improve the confidence in the database for reactions of Cl atoms with these oxygenated organics. Rate coefficients were also measured for the reactions of Cl₂ with CH₂OH, k₅ = (2.9 ± 0.6) × 10⁻¹¹ and CH₃CO, k₆ = (4.3 ± 1.5) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹, by observing the regeneration of Cl atoms in the absence of O₂. Based on these results and those from a previous relative rate study, the rate coefficient for CH₃CO + O₂ at the high pressure limit is estimated to be (5.7 ± 1.9) × 10⁻¹² cm³ molecule⁻¹ s⁻¹. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 776–784, 1999     

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.     

Comparison of the catalogues of thek 0-and thek Zn single comparator methods for standardization in INAA

The independently measured catalogues of two single comparator methods for standardization in INAA, i.e., thek _Zn-and thek ₀-method, were compared. Many reactions were listed only in thek _Zn-catalogue; in these cases other literature data were used to supplement thek ₀-catalogue. The agreement between thek _Zn-and thek ₀-catalogue was found to be much better than the agreement between thek _Zn-catalogue and other literature data. It is therefore suggested to use the convertedk _Zn-catalogue as a supplement of the previously publishedk ₀-catalogue.     

Kinetics and mechanism of the aminolysis of O-ethyl S-phenyl dithiocarbonate in aqueous ethanol

The reactions of secondary alicyclic amines with the title substrate (PDTC) are subjected to a kinetic study in 44 wt.% aqueous ethanol, 25.0°C, ionic strength 0.2 M (KCl). Pseudo-first-order rate coefficients (k_obs) are found under amine excess. Linear plots of [N]/k_obs against 1/[N], where N is the free amine, are obtained for the reactions with piperidine, piperazine, 1-(2-hydroxyethyl)piperazine, and morpholine. The reaction with 1-formylpiperazine exhibits a linear plot of k_obs against [N]². These results are interpreted through a mechanism consisting of two tetrahedral intermediates: a zwitterionic ( T ^±) and an anionic ( T ^?), where the amine catalyzed proton transfer from T ^± to T ^? is partially rate determining for the four former reactions and is fully rate determining for the reaction of 1-formylpiperazine. The rate microcoefficients involved in the reaction scheme are either determined experimentally or estimated. Comparison with the corresponding microcoefficients reported for the same reactions in water reveals that the rate coefficient for formation of T ^± from reactants (k₁) is smaller and that for the reversal of this (k_?1) is larger in aqueous ethanol compared to water, in agreement with the expected structure of the corresponding transition state. Bronsted-type plots are obtained for k₁, k_?1, and K₁ (=k₁/k_?1) with slopes ca. 0.4, ?0.6, and 1.0, respectively. Comparison of the present stepwise reactions with the concerted ones found in the same aminolysis of O-ethyl 2,4,6,-(trinitrophenyl) dithiocarbonate indicates that T ^± is so destabilized by the change of PhS by the 2,4,6-trinitrobenzenethio group that T ^± no longer exists and becomes a transition state. © 1995 John Wiley & Sons, Inc.     

New aspects of chain-length dependent termination

A survey is given on a selection of recently developed methods for the evaluation of the rate coefficient k_t of termination and its chain-length dependence. In particular these are the time-resolved single-pulse pulsed laser polymerization (TR-SP-PLP), the single pulse pulsed laser polymerization in combination with the analysis of the molecular weight distribution produced (SP-PLP-MWD), the methods yielding an average k_t either from the second moment of the chain-length distribution (CLD) or from the rate of polymerization, and a method focusing on the chain-length dependence of k_t consisting in an analysis of the CLD resulting from PLP experiments carried out at low pulse frequencies (LF-PLP). The results obtained by these methods are compared and discussed. The role of the shielding of the two radical chains by their appendant coils is emphasized.     

Evidences for temperature-dependent mechanism of host-guest complexation

Summary High-performance liquid chromatography and ultraviolet spectroscopy methods were applied to the studies on the influence of temperature on the complexation of β-cyclodextrin with naphthalene and its derivatives. The strong nonlinearity of Van't Hoff plots suggests, that the retention mechanism of hydrocarbons investigated might be different in high and low temperature region. The total lack of correlation (r=−0.230) between chromatographic data (capacity factors ratio:k _PAH/k _PAH×CD) and spectrophotometric data (ΔA) at high temperature (60°) as well as a significant correlation (r=0.922) at subambient temperature (15°C) suggest, that the inclusion mechanism starts to be important at low temperature region and the predominant mechanism for chromatographic retention is the formation of an inclusion complexes in the mobile phase.     

Linearization of second-order reaction data

Reaction data described by the second-order growth function A(t) = A_∞(αt) (1 + αt)^?1, where A_∞ is the ultimate value of the product concentration A(t), can be linearized by plotting a suitable function F(t) against the time (t). The slope of the straight line obtained is (2α), where α is the product of the rate constant (k₂) and the initial concentration of either reactant, with the result that k₂ can be determined without knowledge of A?. Optimal determination of the parameter α requires that data taking be limited to the interval 0 ≤ t ≤ T, where (αT) is approximately 4.0. Numerical data derived from an experiment on the exchange of lead by zinc ions in the enzyme carbonic anhydrase are analyzed to illustrate the method. The effects of small errors in the initial concentrations and of small deviations from second-order kinetics are briefly discussed.     

Graft polymers: Chain transfer and branching

The vinyl monomers, methyl methacrylate, ethyl methacrylate, and methyl acrylate were polymerized in the presence of chlorinated rubber or poly(vinyl chloride) in homogeneous solution with benzoyl peroxide as catalyst. A graft polymer was formed by a chain-transfer reaction involving the growing polymer radicals to the backbone of chlorinated rubber or poly(vinyl chloride), in addition to homopolymer from the monomer. The homopolymer was isolated from the polymer mixture by fractional precipitation from methyl ethyl ketone solution with methanol as precipitant. The chain-transfer constants for the branching reactions were evaluated. The ratios k_p/(k_t)^1/2 for the grafting reactions were obtained by a correlation of chain-transfer constants with the extent of branching. The chain-transfer data were correlated on the basis of an extension of the Q–e scheme of Alfrey and Price to polymer–polymer transfer reactions. Specific effects due to the backbone are found to have considerable influence on the course of the chaintransfer reactions and k_p/(k_t)^1/2 of the grafting reactions.     

Kinetics of the reaction of sodium arylthiolates with nitro-carboxybenzyl halide derivatives

The rate constants for the reactions of 4-halomethyl-3-nitrobenzoic acids, the nonnitro derivatives, and their ethyl esters with arylthiolates were measured at different temperatures. It was found that the retardation in rate constants compared to benzyl halides is due to the electrostatic repulsion between the electronegative substituents (COO⁻ and/or NO₂) in the substrates and thiolate ions. Good correlations between log k₂ values of the acids and carbon basicities of thiolates were found while log k₂ values of the esters show good straight lines with Hammett σ constants, pk_a, and carbon basicities of arylthiolates. © 1996 John Wiley & Sons Inc