Isokinetic Relation Research Articles

Breakdown of kinetic compensation effect in physical desorption

The kinetic compensation effect (KCE), observed in many fields of science, is the systematic variation in the apparent magnitudes of the Arrhenius parameters $E_a$, the energy of activation, and $\nu$, the preexponential factor, as a response to perturbations. If, in a series of closely related activated processes, these parameters exhibit a strong linear correlation, it is expected that an isokinetic relation will occur, then the rates $k$ become the same at a common compensation temperature $T_c$. The reality of these two phenomena continues to be debated as they have not been explicitly demonstrated and their physical origins remain poorly understood. Using kinetic Monte Carlo simulations on a model interface, we explore how site and adsorbate interactions influence the Arrhenius parameters during a typical desorption process. We find that their transient variations result in a net partial compensation, due to the variations in the prefactor not being large enough to completely offset those in $E_a$, both in plots that exhibit a high degree of linearity and in curved non-Arrhenius plots. In addition, the observed isokinetic relation arises due to a transition to a non-interacting regime, and not due to compensation between $E_a$ and $\ln{\nu}$. We expect our results to provide a deeper insight into the microscopic events that originate compensation effects and isokinetic relations in our system, and in other fields where these effects have been reported.

Enthalpy-Entropy Compensation (EEC) Effect: A Revisit.

A short account of the developments and perspectives of IKR (iso-kinetic relation) and EEC (enthalpy (H) - entropy (S) compensation) has been presented. The IKR and EEC are known to be extra thermodynamic or empirical correlations though linear H-S correlation can be thermodynamically deduced. Attempt has also been made to explain the phenomena in terms of statistical thermodynamics. In this study, we have briefly revisited the fundamentals of both IKR and EEC from kinetic and thermodynamic grounds. A detailed revisit of the EEC phenomenon on varied kinetic and equilibrium processes has been also presented. Possible correlations among the free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) changes of different similar and nonsimilar chemical processes under varied conditions have been discussed with possible future projections.

Oxidative Cleavage of β-Lactam Ring of Cephalosporins with Chloramine-T in Alkaline Medium: A Kinetic, Mechanistic, and Reactivity Study

Cephalosporins are β-lactam antibiotics, and the important drugs of this group are cephalexin, cefadroxil and cephradine. In the present research, the kinetics and mechanism of oxidation of cephalexin (CEX), cefadroxil (CFL), and cephradine (CPD) with chloramine-T (CAT) in alkaline medium were investigated at 301 K. All the three oxidation reactions follow identical kinetics with a first-order dependence each on [CAT]o and [substrate]o. The reaction is catalyzed by hydroxide ions, and the order is found to be fractional. The dielectric effect is negative. Proton inventory studies in H2O-D2O mixtures with CEX as a probe have been made. Activation parameters and reaction constants have been evaluated. Oxidation products were identified by mass spectral analysis. An isokinetic relation was observed with β = 378 K, indicating that enthalpy factors control the rate. The rate increases in the following order: CPD > CFL > CEX. The proposed mechanism and the derived rate law are consistent with the observed kinetics.

Comment on “The mathematical origins of the kinetic compensation effect” Parts 1 and 2 by P. J. Barrie, Phys. Chem. Chem. Phys., 2012, 14, 318 and 327

The concept of kinetic compensation and the associated isokinetic relation continue to be subject to debate, despite the fact that the conditions under which they are to be expected are now well established, and the criteria for deciding that they have been observed are known. We present these conditions and criteria, and the reality of these relations, and stress their importance for catalysis. We then discuss the fact that statistical arguments against their reality continue to be presented. Recently two articles, based upon the statistical point of view have been published in this Journal. We show that, despite the fact that the mathematics of these articles is error free, they present a distorted image of the present understanding of the subject.

Activation parameters of supercritical and gas-phase β-pinene thermal isomerization

New data on enthalpy and entropy contributions to the energy barrier of β-pinene thermal isomerization were obtained. The rate of β-pinene conversion is higher in supercritical EtOH (P = 120 atm) than in the gas phase (P ≤ 1 atm, without solvent, or for inert carrier gas N2) at equal temperatures. The highest activation energy EΣ of total β-pinene conversion is also observed in reactions in the supercritical (sc) condition. Activation parameters ΔHΣ#, ΔSΣ#, and ΔGΣ# depend strongly on the reaction pressure. Thus, at P ≤ 1 atm (gas-phase reaction) the values of ΔSΣ# are negative, while at sc conditions at P = 120 atm is positive. The linear dependences lnkΣ0 − EΣ and ΔSΣ# − ΔSΣ# indicate an isokinetic relation (IKR) and enthalpy-entropy compensation effect (EEC). The isokinetic temperature was calculated (Tiso = 605.5 ± 22.7 K). It was shown that elevation of temperature reduces the value of ΔGΣ#(T) upon sc thermolysis only, whereas in all gas-phase reactions ΔGΣ#(T) increases. At equal reaction temperatures, the greatest values of Keq#(T) proved to be typical for thermolysis in sc-EtOH. We hypothesize that the rate of total β-pinene conversion increases dramatically due to a considerable shift in equilibrium toward higher concentrations of activated complex yTS#. A detailed analysis of activation parameters shows that the IKR and EEC coincide, evidence of a common mechanism of β-pinene conversion observed under different reaction conditions, including thermolysis in sc-EtOH.

Os(VIII)-Catalyzed Oxidation of Some Aliphatic Ketones by Sodium N-Chlorobenzenesulfonamide (Chloramine-B) in the Presence of Sodium Hydroxide: Kinetic Mechanistic Chemistry

Kinetics of oxidation of 2-propanone, 2-butanone, and 2-pentanone by chloramine-B (CAB) in presence of NaOH and OsO4 catalyst has been investigated at 303 K. The reaction rate shows a first–order dependence each on [CAB]o and [Os(VIII)], fractional-order on [NaOH], and zero-order on [ketone]o. The solvent isotope effect k/(H2O) / k/(D2O) = 0.58. Activation parameters have been deduced. An isokinetic relation is obtained with β = 340 K. The rate of oxidation of ketones follows the order: 2-pentanone > 2-butanone > 2-propanone. The Os(VIII) catalyzed reactions are 7 to 9 fold faster than the uncatalyzed reactions. Suitable mechanism and rate law have been proposed.

Oxidative decolorization of triphenylmethane dyes by chloramine-T in alkaline medium catalyzed by Pd(II): A comparative spectrophotomeric kinetic and mechanistic approach

Triphenylmethane dyes viz., p-rosaniline, crystal violet and ethyl violet (henceforth abbreviated as Dye) have been extensively used as colorants in textile industries. Effluents containing these dyes released by the industry causes significant environmental problems. Hence decolorization of dye effluents has acquired increasing attention. The oxidative decolorization of these dyes is of greater significance one understanding of their kinetic and mechanistic aspects in redox reactions is important. Consequently, Pd(II) catalyzed kinetics and oxidative decolorization of p-rosaniline, crystal violet and ethyl violet dyes by chloramine-T (CAT) in NaOH medium were studied spectrophotometrically. The oxidation reaction follows the identical kinetics for all the three dyes and obeys the rate law: rate = k[CAT] a [Dye] b [OH −] c [Pd(II)] d where a and b are unity, and c and d are less than unity. Addition of p-toluenesulfonamide, the reduction product of CAT, retards the rate and the order was found to be less than unity. The reaction rate increased with increasing ionic strength of the medium. Addition of chloride ions show negligible effect on the rate of reaction. Oxidation products were characterized by GC–MS analysis. Proton-inventory studies with ethyl violet as a probe have been made in H 2O–D 2O mixtures. Activation parameters and decomposition constants have been deduced. An isokinetic relation is observed with β = 423 K indicating enthalpy as a controlling factor. The rate of oxidation of triphenylmethane dyes follows the order: p-rosaniline > crystal violet > ethyl violet. This trend may be attributed to inductive effects of alkyl amino groups. Further, the kinetics of Pd(II)-catalyzed oxidation of these dyes have been compared with uncatalyzed reactions (in the absence of Pd(II) catalyst) and found that the catalyzed reactions are nearly four times faster. The catalytic constant ( K C) for Pd(II) was also calculated for each dye at different temperatures and the values of activation parameters with respect to the catalyst have been evaluated. Chlorite ion (OCl −) has been postulated as the reactive oxidizing species. The observed results have been explained by a general mechanism, and the related rate law has been obtained. Furthermore, the simple and elegant method developed for the decolorization of triphenylmethane dyes in the present work can be adopted for treating the aforesaid dyes present in industrial effluents to minimize the toxicity caused by these dyes.

Kinetics of the reaction of substituted 4-nitrophenyl benzoates with benzenethiol in the presence of potassium carbonate in dimethylformamide

The effect of the substituent nature on the rate and activation parameters of transesterification of a series of 4-nitrophenyl benzoates with benzenethiol in dimethylformamide in the presence of potassium carbonate was studied by the competing reaction method. In all cases, change of the Gibbs energy of activation is determined mainly by variation of the enthalpy of activation. 4-Nitrophenyl benzoates having electron-withdrawing substituents in the benzoyl fragment were found to fit an isokinetic relation with an isokinetic temperature β of 318 K. Enthalpy-entropy compensation effect was observed in the reactions with all the examined 4-nitrophenyl benzoates. The relation between the reactivity and polarizability of nucleophilic center in S-and O-nucleophiles is discussed.

Temperature-dependent Mn-diffusion modes in CoFeB- and CoFe-based magnetic tunnel junctions: Electron-microscopy studies

We show that Mn atoms diffuse with two different mechanisms at high and low temperatures in CoFeB- and CoFe-based magnetic tunnel junctions. By combining high resolution and scanning transmission electron microscopy, we reveal that below 300 ° C, the amorphous CoFeB and the textured CoFe are equally effective in blocking the diffusion of Mn, contradicting the conventional wisdom that the diffusion occurs primarily along grain boundaries. Below 300 ° C, Mn diffusion in crystalline CoFe occurs through the bulk and is assisted by oxygen atoms which only diffuse parallel to the bcc close-packed 110 plane. Above 300 ° C, Mn diffuses through vacancies along the grain boundaries of CoFe and in the bulk of amorphous CoFeB. A universal diffusion temperature is proposed based on an isokinetic relation.

The gas phase reaction between CO2 and lanthanide atoms. A test of a model for the isokinetic effect

Using literature data on the gas phase reaction between free lanthanide atoms and carbon dioxide, we have found an isokinetic relation for seven of the twelve investigated elements with an isokinetic temperature, Tiso, of 2500±330 K. This value is analyzed in the framework of the model of selective energy transfer, SET, indicating that metal-CO2 complexes are formed as pre-reaction states. The result is in accordance with the fundamental concepts of SET.

Temperature and Solvent Effects on the Reactions of o-Positronium with Nitroso Spin Traps in Methanol−Water Mixed Solvents

Positron annihilation lifetime spectroscopy (PALS) is used to study the reactions of the ortho-positronium (o-Ps) atom with the following nitroso spin traps: nitrosobenzene (NOB), N,N-dimethyl-4-nitroso-aniline (DMNA), and tert-nitroso-butane (t-NOBu). The reaction rate constants (k) are close to the range that corresponds to that of diffusion-controlled reactions and exhibit a similar trend to those reported in the literature for the analogous nitro compounds. The differences between the aromatic and aliphatic nitroso and nitro compounds and the observed substituent effect are in good correlation with the calculated LUMO energies of the molecules. The nucleophilic o-Ps attacks the molecules at their electron deficient aromatic ring. Solvent effects on the reaction rates in methanol−water solvent mixtures exhibit a complex and solute-dependent nature. The reactions are strongly affected by solvent viscosity; however, the expected 1/η versus k variation is valid only for limited ranges of solvent compositions. The dielectric permittivity effect on the reaction rate constants does not follow the expected trend; k values in water are significantly greater than in the less polar methanol. The average activation enthalpies (ΔH⧧ and entropies (ΔS⧧) evaluated for the reaction of o-Ps with DMNA exhibit maxima at a solvent composition which corresponds to the most rigid solvent structure, where the activation energies of the transport processes such as viscosity and self-diffusion have extremes too. The validity of the isokinetic relation between ΔH⧧ and ΔS⧧ shows that the mechanism of the reaction of o-Ps does not depend on the solvent composition. ΔH⧧ exhibits an “Onsager reaction field” type (ε − 1)/(ε + 2) dependence on solvent permittivity. The results are compared to literature data for the reactions of o-Ps with stable nitroxide free radicals and reaction of solvated electron with nitrobenzene (NO2B) in methanol−water mixtures. The observed similarities and differences are discussed.

Oxidation of aliphatic am ides by N-chlorobenzenesulfonamide in acid medium catalyzed by ruthenium(III) : a kinetic and mechanistic study

The kinetics of the ruthenium(III)-catalyzed oxidation of urea and substituted ureas, namely, methylurea, ethylurea and propylurea by sodium N-chlorobenzenesulfonamide or chloramine-B (CAB) in HCI medium have been studied at 30°. The reaction rate shows a first order dependence each on CAB, amide and RuIII and fractional order on H+. Additions of halide ions and the reaction product of CAB (benzenesulfonamide) and the variation of ionic strength and dielectric constant of the medium do not have any significant effect on the reaction rate. Activation parameters have been evaluated. The rate increases in D2O medium. Proton inventory studies were made in H2O-D2O mixtures for both the amides. A Taft linear free energy relationship is observed for the reaction with I�* = -0.88 and -3.20 and I´ = -0.33, indicating that electron-donating groups enhance the rate. An isokinetic relation is observed with I² = 372 K confirmed by the Exner criterion. The protonation constant of monochloramine-B has been evaluated to be 8.6. A mechanism consistent with the observed kinetic data has been proposed. The rate of oxidation increases in the order: propylurea > ethylurea > methylurea > urea.

Thermolysis of tert-butyl phenylperacetates: delicate control of the rates through contributions from translational and rotational entropy.

The first-order rate constants (k(Y)) at several temperatures in CDCl(3) were measured for thermal decompositions of YC(6)H(4)CH(2)CO(3)C(CH(3))(3) with Y being p-OCH(3), p-OPh, p-CH(3), p-Ph, p-H, p-Cl, m-Cl, and p-NO(2). The relative rates (k(Y)/k(H)) exhibit excellent rho(+)/sigma(+) Hammett correlations with rho(+) < 0, indicating a polar TS. Activation parameters (DeltaH()(Y) and DeltaS()(Y)) and their differential terms (DeltaDeltaH()(Y)(-)(H) and DeltaDeltaS()(Y)(-)(H)) were obtained from the Eyring plot. Differential activation terms (DeltaDeltaH()(Y)(-)(H) and DeltaDeltaS()(Y)(-)(H)) disclose an isokinetic relation with p-CH(3), p-Ph, p-H, p-Cl, and m-Cl (isokinetic temp, 230 K). However, p-OCH(3), and p-OPh show negative deviations, and a positive deviation occurs with p-NO(2). Plot of DeltaDeltaH()(Y)(-)(H) vs sigma(+) exhibits a good linear relation (r = 0.95) with a slope (alpha(1) = -3.34). A better linear correlation (r = 0.97) and steeper slope (alpha(2) = -5.22) were observed for TDeltaDeltaS()(Y)(-)(H) vs sigma(+). Negatively larger slope (alpha(2) = -5.22) may point to entropy control of rates. Differential activation parameters (DeltaDeltaH()(Y)(-)(H) and DeltaDeltaS()(Y)(-)(H)) reflect variations of activation process. Differential activation entropies (DeltaDeltaS()(Y)(-)(H)) are discussed in terms of contributions of translational and rotational entropies. Similar deviation behaviors of p-OCH(3), p-OPh, and p-NO(2) were again observed for the both plots. p-NO(2) can strongly destabilize the cationic site of the polar TS but serves an eminent spin delocalizer for the homolytic TS.

Kinetics of thermal bleaching reaction of the photomerocyanine form of spironaphthooxazine

The thermal bleaching reactions of photomerocyanine (PMC) form of spironaphthooxazine (SNO) were investigated in various temperatures and solvents using laser flash photolysis. The thermal decay rate of PMC for SNO markedly decreases as temperature decreases and generally increases with solvent polarity. The solvent effect on the rate constant was well explained by using the π ∗-scale. The activation energy and activation entropy also increase with the solvent polarity and the isokinetic relation has been observed. The combined results are interpreted in terms of dissociation of solvated PMC complex and/or ordered solvent structure around PMC molecules. Based on the experimental results, the potential energy surface along the reaction path in the ground state has been proposed.

Ruthenium(III)-catalyzed oxidation of amides by sodium N-bromobenzenesulphonamide in hydrochloric acid: a kinetic and mechanistic study

The kinetics of the RuIII-catalyzed oxidation of urea and substituted ureas namely: methylurea, ethylurea and propylurea, to the corresponding hydrazines by sodium N- bromobenzenesulphonamide or bromamine-B (BAB) in HCl medium has been studied at 303K. The reaction rate shows a first order dependence each upon [BAB], [amide] and [RuIII] and is dependent on [H+]. Addition of halide ions and benzenesulphonamide do not significantly affect the rate. Proton inventory studies were made in H2O-D2O mixtures for urea and methylurea. A Taft linear free energy relationship is observed for the reaction with ρ*=−2.95 and δ=−0.25, showing that electron-donating groups enhance the rate. An isokinetic relation is observed with β=370K, indicating that enthalpy factors control the rate; this result is also confirmed by Exner Criterion which showed a linear plot for the logarithms of rate constants at the highest and lowest temperatures employed. The protonation constant of monobromamine-B has been evaluated and equals 7.5. A mechanism consistent with the observed kinetic data has been proposed.

Kinetic Analysis of Thermogravimetric Data XXXI. Derivation of a non-linear kinetic compensation law

The kinetic compensation effect observed in heterogeneous non-isothermal kinetics is only an apparent effect. In general, the correlation derived between the kinetic parameters E and log A from TG curves can be described by means of a non-linear compensation law, expressed by Eq. (14). This equation may become approximately linear in certain particular cases, i.e. it may change into an isokinetic relation. The validity of the non-linear compensation law has been tested by using over 1000 sets of kinetic parameters reported earlier.

Compensation effect in heterogeneous non-isothermal kinetics

A number of 1145 sets of kinetic parameters derived in our earlier papers from TG curves have been worked up. The apparent activation energy and pre-exponential factor values have been found to obey a linear compensation law (isokinetic relation) if the thermal decomposition begins in the same temperature interval, irrespective of the nature of the chemical reaction. The isokinetic temperatureT i has been found to be very close to the mean value of the temperaturesT 0.1 at which the conversion becomes equal to 0.1 and atT i the rate constant has been found to be approximately equal to 10−3s−1 in allT 0.1 intervals investigated. It is concluded that the kinetic compensation effect observed in heterogeneous non isothermal TG kinetics is not a true one.

Ruthenium(III) catalyzed kinetics of chloroacetic acids oxidation by sodium N‐bromobenzenesulfonamide in hydrochloric acid medium

AbstractKinetics of uncatalyzed and Ru(III)‐catalyzed oxidations of mono‐, di‐, and tri‐chloroacetic acids by the title compound (bromamine‐B or BAB) in HCl medium has been studied at 40°C. The uncatalyzed reaction shows a first‐order dependence of the rate on [BAB], and fractional and zero orders in [acid] at low and high [HCl] ranges, respectively. The Ru(III)‐catalyzed reaction, on the other hand, shows a first‐order behavior on each of [BAB] and [substrate], second‐order dependence on [Ru(III)], and inverse fractional and inverse first orders in [acid] at low and high [HCl] ranges. Addition of halide ions and the reduction product of BAB, benzenesulfonamide, has no effect on the reaction rate. Variation of ionic strength of the medium has no influence on the reaction. Solvent isotope effect was studied using D2O. Activation parameters have been evaluated from the Arrhenius plots. Mechanisms consistent with the above kinetic data have been proposed. The protonation constant of monobromamine‐B evaluated from the uncatalyzed reaction is 12.4 while that evaluated from Ru(III) catalyzed reaction is 12.7. A Taft linear free‐energy relationship is noted for the catalyzed reaction with ρ* = 1.2 and 0.07 indicating that electron withdrawing groups enhance the rate. An isokinetic relation is observed with β = 338 K indicating that enthalpy factors control the reaction rate. © 1993 John Wiley &amp; Sons, Inc.

Oxidation of α-Amino Acids by Permanganate: Isokinetic Relation

The oxidation of three α-amino acids by permanganate under neutral conditions has been studied at various temperatures. The use of Exner's statistical method shows no existence of an isokinetic relation in the heterogeneous process but for the homogeneous process such a relation has been found. Moreover, the existence of linear free energy relations was confirmed for the homogeneous process.

Oxidation of secondary alcohols by sodium N-chlorobenzenesulphonamide in aqueous solution. A kinetic study

The kinetics of oxidation of five secondary alcohols by sodium N-chlorobenzenesulphonamide (chloramine-B) has been studied in acid medium at 40°C. The reaction is first order with respect to the oxidant and alcohol and fractional order in [H+]. The influence of added halide ions and of reaction product and the effects of varying ionic strength and dielectric constant of the medium have also been studied. The solvent isotope effects k’(H2O)/k’(D2O) were determined. The rates were studied at four different temperatures and the activation parameters were evaluated. Attempts have been made to arrive at a linear free energy relation through the Taft treatment. An isokinetic relation is observed with β = 248 K, indicating the entropy of activation as the rate controlling factor. Protonated chloramine-T (monochloramine-T) has been postulated as the reactive oxidizing species, the main product of oxidation being the corresponding ketone. A mechanism involving the interaction of protonated haloamine species and the alcohol in a rate limiting step has been proposed.