Modified Arrhenius Equation in Materials Science,Chemistry and Biology

The Arrhenius plot (logarithmic plot vs. inverse temperature) is represented by a straight line if the Arrhenius equation holds. A curved Arrhenius plot (mostly concave) is usually described phenomenologically, often using polynomials of T or 1/T. Many modifications of the Arrhenius equation based on different models have also been published, which fit the experimental data better or worse. This paper proposes two solutions for the concave-curved Arrhenius plot. The first is based on consecutive A→B→C reaction with rate constants k₁ ≪ k₂ at higher temperatures and k₁ ≫ k₂ (or at least k₁ > k₂) at lower temperatures. The second is based on the substitution of the temperature T the by temperature difference T − T₀ in the Arrhenius equation, where T₀ is the maximum temperature at which the Arrheniusprocess under study does not yet occur.     

Reduction of acetophenone using supercritical 2-propanol: the substituent effect and the deuterium kinetic isotope effect

The reductions of several substituted acetophenones using supercritical 2-propanol were carried out to estimate the Hammett's reaction constant (ρ=0.33). Also, the reduction of acetophenone using supercritical deuteriated 2-propanol was carried out to determine the rate-determining step. The kinetic isotope effects were observed in the reduction using 2-deuterio-2-propanol (k_H/k_D=1.6) and O-deuterio-2-propanol (k_H/k_D=2.0). These findings suggest that the reaction proceeds via a cyclic transition state between acetophenone and 2-propanol similar to that of the Meerwein-Ponndorf-Verley reduction.     

Selective extraction of antioxidants with molecularly imprinted polymers

Molecular imprinting technology can be used to generate specific artificial polymeric receptors, i.e., high affinity stationary phases, as already shown for peptides and many other food ingredients. In this work, polymers have been molecularly imprinted with three exemplary antioxidants, butylated hydroxyanisole (BHA), butylated hydroxytoluene (BHT) and propyl gallate (PG). Results of chromatographic evaluations are presented, demonstrating the specificity of the imprinted polymers (MIP) compared to non-specific control polymers (CP). For a BHA imprinted polymer and the respective analyte BHA a separation factor of α=k_BHA-MIP′/k_CP′=1.12 was found, whereas for the BHT-MIP a higher selectivity was determined with α=k_BHT-MIP′/k_CP′=1.47. Using the PG selective MIP for PG as analyte a value of α=k_PG-MIP′/k_CP′=1.24 could be achieved. Furthermore, results of extraction procedures based on MIP and CP phases are presented, demonstrating for instance a higher selectivity of the BHA-MIP in comparison with its CP when using methanol or acetonitrile as analyte solvent, and of the PG-MIP when performing the extraction in acetonitrile.     

Investigation of trialkoxysilane hydrolysis kinetics using liquid chromatography with inductively coupled plasma atomic emission spectrometric detection and non-linear regression modeling

A novel approach is demonstrated for measuring rates of the consecutive acid-base catalyzed hydrolysis reactions of (3-glycidoxypropyl)trimethoxysilane (GPTMS) and (3-aminopropyl)triethoxysilane (APTES) in dilute aqueous solution using liquid chromatography with inductively coupled plasma atomic emission spectrometric (ICP-AES) detection. The hydrolysis reactions are monitored by sampling kinetic solutions in a timewise manner and performing liquid chromatographic separations of the parent silane and organosilicon hydrolysis products. The column effluent is fed into the ICP through a direct injection nebulizer for online monitoring of silicon atomic emission at 251.611 nm, producing a series of silicon chromatograms for each kinetic run. Reversed phase separations are effected using acetonitrile-water gradients and are complete in 6 min or less. The systematic changes in peak areas provide information from which the rate constants of the consecutive hydrolysis reactions (k₁, k₂, and k₃) are obtained by non-linear regression modeling. Using a quenching scheme, hydrolysis half-lives as brief as 3 min for the parent silane can be monitored. For each compound, a series of rate constants are obtained over a range of pH and buffer concentration, permitting estimation of the catalytic constants k_H3O⁺ and k_OH⁻ for the consecutive acid-base catalyzed hydrolysis reactions by multiple regression analysis.     

Pulse polarography: Part V. on the theory for the kinetic currents with an ece mechanism

We have derived an equation for the instantaneous limiting current in pulse polarography with an ECE mechanism. That equation has been derived for the expanding sphere electrode model (and also for the expanding plane electrode model) with the condition (k₁+k₂)>>1, k₁ and k₂ being the rate constants of the chemical reaction. We show that by an adequate choice of the time of application of the potential and time of the drop growth prior to potential application, it is possible — if the equilibrium constant for chemical reaction is known — to widen the interval of values for k₁ and k₂ that may be determined using this technique. At the same time, we also show that if the electrode sphericity is not taken into account, the values obtained for k₁ and k₂ are always lower than the real ones.     

The 2012 recommended k 0 database

Many overview papers have been published with recommended nuclear data for use in the k ₀ method of NAA and made available in scientific journals or in the form of a downloadable database. In September 2009, the k ₀-International Scientific Committee formed the k ₀-Nuclear Data Committee (k ₀-NDC) whose first task was to collect all these data at a single place to facilitate updating and to correct any evident errors. This task of the k ₀-NDC was successfully completed in March 2012 when the 2012 recommended k ₀ database was published in the form of an Excel file.     

Kinetic studies of the photodecomposition of dipyridamole in solution: Interaction with lysophosphatidylcholine and bovine serum albumin

Photoirradiation of dipyridamole (DIP) solution at λ ⪢ 390 nm leads to a reduction of the intensity of the absorption band without change in its appearance. This reduction is due to the breaking of the π-conjugation chain of the DIP molecule. The experimentally measured rate constant k is proportional to the concentration of oxygen and to the ratio of the rates of photoreaction, k_r, and of radiation, k_o. In homogeneous solutions the values of k_r and k_o are three-times greater at pH 5.0 than at pH 7.0. So, the photoreaction is more effective when the DIP molecules are completely protonated. In alcoholic and alkaline solutions (pH 13.5), the deprotonation of DIP molecules is responsible for a significant reduction of k_r. In the presence of microheterogeneous systems, lysophosphatidylcholine (L-PC) micelles and bovine serum albumin (BSA), a significant reduction of k_r is observed. The value of k_r in this case depends on the pH of the solution as well as on the concentration of L-PC and BSA. In the presence of L-PC or BSA, different values of k could be associated to free and bound DIP molecules. A kinetic procedure is proposed which permits the evaluation of the binding constants as well as the kinetic constants. The binding constant of DIP to L-PC micelles is estimated as 1.28 × 10⁴ M⁻¹ and the value of the limiting effective rate constant k is similar to the value obtained in ethanol. This is evidence for the localization of DIP molecules in the polar region of L-PC micelles. The value of k in this case is three-times greater at pH 5.0 than at pH 7.0 as occurs in homogeneous solutions. The binding to BSA was also studied and binding constants of (1.8±0.2) × 10⁴ M⁻¹ and (7.8±0.9) × 10⁴ M⁻¹ were obtained at pH 7.0 and pH 5.0, respectively. In this case the ratio k_{(ph 5.0)}/k_{(ph 7.0)} is also equal to three, the same as in homogeneous solutions or in the presence of L-PC micelles. This implies that DIP molecules maintain their protonation form in the presence of microheterogeneous systems.     

Non-and near-resonant (vv) energy transfer between the isotopes of N2 and of CO in liquid Ar and in the gas phase at 85 k

Rate constants for vibrational energy transfer have been measured in the system N₂(v= 1) +CO(v=0) as a function of energy mismatch by using isotopic derivatives of N₂ and of CO. These rate constants have been determined both in the gas phase and in liquid argon solution at 85 K. For non-resonant processes we find k_L=k_G for the nearest to resonant system we find k_L <k_G. This result is considered to arise because long range forces important in near-resonant energy transfer operate to a lesser extent in the liquid phase.     

The question of a pressure effect in the reaction OH + HNO3. A laser flash-photolysis resonance-absorption study

Absolute rate constants, k, of the reaction OH + HNO₃ were determined using a pulsed laser photolysis-resonance absorption technique. The measured values, in cm³ mol^-1 s^-1 at ±3σ, 10^-10k(1–16 Torr HNO₃) = 7.57 ± 0.64, k(500 Torr N₂) = 7.20 ± 0.66 and k(600 Torr SF₆) = 8.37 ± 0.45, indicate that any pressure effect on k at 297 K is less than the experimental uncertainty of 10%.     

Reversal of coupling in intermetallic compounds containing two rare earth elements

The reversal in coupling (from antiferromagnetic to ferromagnetic order with increasing x) in Eu_xLa_1−xAl₂ ternaries is successfully analyzed in terms of the RKKY formalism. The Fermi wavevector k required to account for the behavior of these ternaries is k = 0.94 k₀, which is in close agreement with the k-value previously obtained for GdAl₂ and GdAl₂-based ternaries from NMR work. The similarity of behavior of Gd_0.1La_0.9Al₂ and Eu_0.1La_0.9Al₂ and their observed Curie temperatures can also be understood using the same theoretical framework and approximately the same k-values.     

Linear expansion of the eigenvalues of a Hermitian matrix and its application to the analysis of the electronic spectra of 3d ions in crystals

It is shown that the eigenvalues E_i of a Hermitian matrix H with matrix elements H_ij = Σ_kA^k_ija_k, where A^k_ij are known numbers and a_k a set of parameters, can be exactly expanded as $\text{E}{}_{\mathrm{i}}\text{= Σ}{}_{\mathrm{k}}\text{(}\text{?E}{}_{\mathrm{i}}\text{?a}{}_{\mathrm{k}}\text{)a}{}_{\mathrm{k}}$. This property is applied to the analysis of the optical spectra of transition metal ions in crystals proposed by L. Pueyo, M. Bermejo, and J. W. Richardson (J. Solid State Chem.31, 217, 1980), and it is shown that this method represents the best fit of the Hamiltonian eigenvalues to the observed (or calculated) spectrum. Further advantages of using this property, in connection with the spectral analysis, are the minimization of the errors associated with the numerical approximations and a reduction in computer time. In the molecular orbital calculation of the optical or uv spectra of these systems, this linear expansion of the eigenvalues give a detailed interpretation of the improvements produced by refined calculations, such as those including configuration interaction. In particular, the changes in one-electron energy and in open-shell repulsion interactions associated with the refinement can be clearly and easily formulated. As examples, the computed spectra of CrF^4?₆ and CrF^3?₆ are discussed.     

Mechanism of atomization at constant temperature in capacitive discharge graphite furnace atomic absorption spectrometry

At constant temperature (isothermal) maintained throughout in the capacitive discharge technique, the measured absorbance at any time t due to concentration of analyte atoms can be given by: absorbance = p[A]₀{k₁/(k₁?k₂)}[exp(?k₂t)-exp(?k₁t)], where p is a function of the oscillator strength (a constant) and the efficiency with which the analyte atoms are produced, [A]₀ is the initial concentration of the analyte atoms, k₁ and k₂ are first-order rate constants for formation and decay of analyte atoms, respectively. This technique yields k₁?k₂ and k₁t?k₂t; and so the above equation reduces to: absorbance ?p[A]₀, resulting in large enhancement in sensitivity. In the case of lead, the immediate precursor of the gaseous lead monomer is the gaseous lead dimer, which is partly lost by diffusion of the lead dimer with a first-order rate constant, k₃. The kinetic parameters k₁, k₂ and k₃ have been evaluated, and the values of k₁ at different temperatures used to draw the Arrhenius plots, from which activation energies of the rate-determining steps have been determined. The activation energies have been used to elucidate atomization mechanisms by extensive correlation of the experimental energy values with the literature values.     

A time-resolved lif study of the kinetics of OH(ν = 0) and OH(ν = 1) with HCl and HBr

The kinetics of OH(ν = 0) and OH(ν = 1) have been followed using pulsed photolysis of H₂O or HNO₃ to generate hydroxyl radicals, and time-resolved, laser-induced fluorescence to observe the rates of their subsequent removal in the presence of HCl or HBr. The experiments yield the following rate constants (cm³ molecule^?1 s^?1) at 298 ± 4 K: OH(ν = 0) + HCl: k_o = (6.8 ± 0.25) × 10^?13; OH(ν = 0) + HBr: k_o = (11.2 ± 0.45) × 10^?12; OH(ν = 1) + HCl: k₁ = (9.7 ± 1.0) × 10^?13; OH(gn = 1) + HBr; k₁ = (8.1 ± 1.05) × 10^?12 For OH(ν = 1), the measurements do not distinguish between loss by reaction and relaxation, and the fact that k₁ > k_o for HCl is tentatively attributed to relaxation, probably by near-resonant vibrational—vibrational energy transfer. Clearly, neither of these exothermic, low-activation-energy reactions is enhanced to any great extent, if at all, by vibrational excitation of the OH radical.ft]*|Present address: Battelle/Pacific Northwest Laboratories, P.O. Box 999, Richland, Washington 99352, USA.     

Product distribution in preparative scale electrolysis: Part VI. Competition between dimerization and first-order deactivation

The dependence of product distribution from the various experimental parameters (rates, concentration diffusion layer thickness, current density) is analyzed for a reaction scheme involving the competition between dimerization and first-order deactivation of the intermediate resulting from the first electron uptake (or removal). Two cases are considered, corresponding to the product of the first-order deactivation being either electroinactive or undergoing a further electron transfer at the electrode or in the solution. It is shown that the dimer yield is not very sensitive to the further fate of the deactivation product. It is in all cases a function of the competition parameter σ=k₁k₂^?3/2D^1/2 c⁰ δ^?1 in potentiostatic conditions and σ^Δ=k₁k₂^?3/2D^?1/2(i⁰/FS) in galvanostatic conditions (k₁, k₂ rate constants of the dimerization and deactivation reactions respectively; D diffusion coefficient; c⁰ concentration of substrate; δ diffusion layer thickness; (i⁰/S) current density). The reduction of CO₂ in DMF with competitive formation of oxalate and formate is taken as an example illustrating the theoretical analysis.     

Electrochemical and quantum-chemical studies of chromium(III,II) fluoride complexes in alkali chloride melts

The standard rate constants (k _s) of charge transfer on a glass carbon electrode were determined for the Cr(III)/Cr(II) redox pair in the NaCl-KCl-K₃CrF₆, KCl-K₃CrF₆, and CsCl-K₃CrF₆ systems at 973–1173 K by cyclic voltammetry. The k _s constant was found to increase at elevated temperatures and the following nonmonotonic dependence of k _s on the nature of the outer-spheric cation was found: k _s (CsCl) > k _s (NaCl-KCl) > k _s (KCl). On the basis of quantum-chemical data for the M₃CrF₆ + 18MCl (M = Na, K) model systems, it was shown that the complex chromium particles with four or five outer-spheric sodium or potassium cations had maximum thermodynamic stability. Quantum-chemical calculations were performed to interpret the experimental data on the effect of the second coordination sphere of the complexes on the standard charge transfer rate constants.     

Temperature effects on the relaxation parameters of the 1-methylnaphthalene excimer

The excimer lifetime τ_D and the excimer fluorescence efficiency for 1-methylnaphthalene in ethanol have been determined between −30 and 60°C. Expressing the rate constant for excimer deactivation. k_D, in terms of radiative k_FD) and nonradiative (k_ID) processes as k_D = k_FD + k_ID it is found that k_FD is independent of tempeature and k_ID = 5 × 10⁶ + 3.2 × 10¹¹ exp (-ΔE/RT) sec⁻¹, where ΔE = 6.7 kcal mole⁻¹. The behaviour of k_FD and k_ID with temperature and the appearance of isoemissive points in a limited region of temperature are discussed.     

Electron self-exchange reaction of viologen and its derivatives in poly(ethylene glycol)

The electron self-exchange rates (k_ex) of viologen and its derivatives are estimated by using microelectrode voltammetry in poly(ethylene glycol) films. The dependences of supporting electrolyte concentration and sizes of viologen and its derivatives on k_ex and diffusion coefficients (D) are discussed. Results show that k_ex increases with the decrease of supporting electrolyte concentration and sizes of reactants.     

Decomposition of cyclic acetone peroxides in acid media

The kinetics and stoichiometry of the formation of active oxygen (AO) in the acidic decomposition of trimeric (TATP) and dimeric (DADP) cyclic acetone peroxides are considered. Fe(III) produced as a result of Fe(II) oxidation with active oxygen has been determined using rhodanide procedure. The kinetics of the formation of active oxygen is described by a first order equation. The effective rate constant of TATP decomposition depends on the Hammett acidity function H ₀: log k _eff = ?H ₀ ? 2.6 (k _eff is in s^?1). Consequently, the decomposition rate of TATP is limited by protonation. In the HCl and H₂SO₄ concentration range from 0.006 to 2.9 mol/L, the decomposition of DADP occurs with k _eff = 0.0010 ± 0003 s^?1 at a Fe(II) concentration of 3.5 mmol/L and k _eff depends linearly on the concentration of Fe(II).     

The rate constants of the gas-phase reactions K + Cl ⇆ K+ + Cl− and KCl + M ⇆ K+ + Cl− + M from measurements in atmospheric pressure flames

Mass spectrometric studies of the ions present in H₂/O₂/N₂ flames with potassium and chlorine added have demonstrated that ionization can occur in the forward steps of K + Cl ? K⁺ + Cl^? (II), KCl + M ? K⁺ + Cl^? + M (IV), where M is any third body. Variations of [K⁺] with time in these systems have been measured and establish that the rate coefficients (in ml molecule^?1 s^?1) of the ion-producing steps are k₂ = 5 × 10^?10T^{?$\text{1}\text{2}$} exp(?10 500/T) and k₄ = 2.2 × 10⁷T^?3.5 × exp(?60 800/T). Coefficients for ion-ion recombination have been obtained from k₂ and k₄ using the equilibrium constants of (II) and (IV) and are k_?2 = 1.7 × 10^?9T^{?$\text{1}\text{2}$} and k_?4 = 1.1 × 10^?17T^?3, with each one in the ml molecule^?1 s^?1 system of units. Replacement of the N₂ in one of these flames with sufficient Ar to maintain the temperature constant leaves the measured k₂ and k_?2 unchanged, but lowers the observed k₄ and k_?4. This confirms that ion-recombination in the backward step in (II) is a two-body process, whereas in (IV) it is termolecular.     

Interpretation of static and dynamic responses of a dissolved oxygen electrode in viscous broths

The response of an amperometric oxygen electrode is studied theoretically and experimentally for the case of significant liquid film resistance at the outer side of the membrane. The behaviour of the probe in a gas stream is predicted by using a transfer function which involves an electrode model including oxygen diffusion within the electrode. The effects of the liquid film which exists at the membrane surface when dissolved oxygen concentrations are measured, are taken into account by modifying the transfer function. The new expression obtained is used to model the step response of the probe in a 2-1 stirred tank fermentor filled with water or xanthane solutions at different concentrations. First, the results are used to correct automatically the steady-state voltage readings of the probe. Secondly, the probe transfer function is used to evaluate k₁a by dynamic measurements: the response to a step change in the gas concentration is transformed via the fast Fourier transform algorithm and k₁a is identified in the Fourier domain by a Gauss-Newton algorithm. Data acquisition, Fourier transform and k₁a identification are implemented on-line on a HP-87 computer. This method of obtaining k₁a values appears to be a generalized moment method. It is shown that it is necessary to consider the liquid film dynamics around the probe in the actual fermenting conditions to evaluate k₁a successfully.