Pulse polarography: Part VII. Theoretical relationships for electrode processes with an ECE mechanism

A theoretical study of the pulse polarographic response for the instantaneous limiting current with an ECE mechanism is presented. Thus, equations for the current have been derived under the following conditions: (a) Both the expanding plane electrode and the expanding sphere electrode models have been accounted. (b) The steady-state approximation was not used. (c) All species are initially present in the solution. With these conditions we have: (a) proposed a method for the calculation of the rate constant values through measurements of instantaneous limiting currents; (b) shown that the interval of the rate constant values that can be determined is about 10³ times larger than in dc polarography; (c) checked the validity of the steady-state approximation.     

Determination of the diffusion coefficients from sintering data of ultrafine oxide particles

Many kinetic equations derived from a simple geometrical model can account for the shrinkage rate of pellets of particles. Nevertheless, even when a kinetic equation is followed the calculation of the apparent diffusion coefficient may not be meaningful if the system under study and the theoretical model does not fit closely. This is shown by the experimental results on sintering of fine particles of anatase and alumina. When the system closely fits the model, the predicted sintering equation is observed and the calculated diffusion coefficients are close to the cation diffusion coefficients. But when the system (polyhedral particles) does not fit the model, an apparent agreement is found between the experimental results and the theoretical law corresponding to an unrelated model so that the calculated diffusion coefficient is meaningless.     

钪和钇二价离子跃迁几率和振子强度的理论计算

利用最弱受约束电子势模型理论计算了二价钪离了和二价钇离子的能级间跃迁几率和振子强度的数值．二价钪离子的计算结果与美国国家标准技术研究院（NIST）所给出的可接受值吻合良好二价钇离子的计算结果也与现有的其他理论方法的计算结果十分接近．     

Phenomenological description of transport properties of three-phase composites

The possibility is discussed of estimating the values of conductivity and dielectric permeability of three-phase composites using the modified mixing equation similar to the equation suggested earlier for two-phase systems. It is shown that the choice of theoretical mixing equation parameters for three-phase composites of the conductor–electrolyte–insulator type can be controversial; variants of solving this problem are suggested. According to the equation, three percolation thresholds can exist in this three-phase system; their position can be estimated on the basis of the maximum of dielectric permeability. The value of the maximum is determined by the ratio of conductivities of the conducting and dielectric phases. The equation can be extended to the case when interaction exists between the individual phases of the composite and a highly conducting layer is formed at the interface between these phases. The calculation of three-phase composites of the conductor–composite solid electrolyte–insulator type is calculated for the first time. It is shown that the mixing equation also allows calculating electric properties of composites in this case.     

烷基自由基β位裂解反应类反应势垒与速率常数的精确计算

提出反应类等键方法并用于高温燃烧机理中一类重要反应——烷基自由基β位裂解反应的反应势垒和速率常数的精确校正计算. 通过10种不同从头算水平对类反应中5个代表反应的反应势垒的计算发现, 用反应类等键反应方法和直接从头算方法获得的5 个代表反应的反应势垒最大绝对偏差的平均值分别为5.32 和16.16 kJ·mol^-1, 表明反应类等键反应方法计算的反应势垒对不同水平从头算方法的依赖性小, 可在较低从头算水平计算得到精确的反应势垒, 解决大分子体系反应势垒的精确计算问题. 此外应用反应类等键反应方法在BHandHLYP/cc-pVDZ 从头算水平计算了3 个代表反应的速率常数, 并与文献报道的实验值进行了比较, 其在500-2000 K温度区间内计算速率常数与实验速率常数中较大值与较小值的比值k_max/k_min的平均值为1.67, 最大值也仅有2.49. 表明应用反应类等键反应方法在较低从头算水平即可对同类反应的速率常数进行精确计算.最后在BHandHLYP/cc-pVDZ从头算水平用反应类等键反应方法计算了13个烷基自由基β位裂解反应的速率常数.     

Nonisothermal decomposition kinetics and computational studies on the properties of 2,4,6,8-tetranitro-2,4,6,8-tetraazabicyclo[3,3,1]onan-3,7-dione (TNPDU)

The thermal decomposition and the nonisothermal kinetics of the thermal decomposition reaction of 2,4,6,8-tetranitro-2,4,6,8-tetraazabicyclo[3,3,1]onan-3,7-dione (TNPDU) were studied under the nonisothermal condition by differential scanning calorimetry (DSC) and thermogravimetry-derivative thermogravimetry (TG-DTG) methods. The kinetic model function in differential form and the value of Ea and A of the decomposition reaction of TNPDU are f(alpha) = 3(1 - alpha)[-ln(1 - alpha)](2/3), 141.72 kJ mol(-1), and 10(11.99) s(-1), respectively. The critical temperature of thermal explosion of the title compound is 232.58 degrees C. The values of DeltaS(++), DeltaH(++), and DeltaG(++) of this reaction are -15.50 J mol(-1) K(-1), 147.65 kJ mol(-1), and 155.26 kJ mol(-1), respectively. The theoretical investigation on the title compound as a structure unit was carried out by the DFT-B3LYP/6-311++G** method. The IR frequencies and NMR chemical shift were performed and compared with the experimental results. The heat of formation (HOF) for TNPDU was evaluated by designing isodesmic reactions. The detonation velocity (D) and detonation pressure (P) were estimated by using the well-known Kamlet-Jacobs equation, based on the theoretical densities and HOF. The calculation on bond dissociation energy suggests that the N-N bond should be the trigger bond during the pyrolysis initiation process.     

Improved methods of estimating monomer reactivity ratios in copolymerization by considering experimental errors in both variables

Existing methods of calculating monomer reactivity ratios in copolymerization are reviewed briefly, evaluated, and classified according to their mathematical and computational similarities. More attention is paid to procedures based on the integrated copolymer equation with which calculation of r values is performed most often by electronic computer. Unfortunately, until now all procedures have shown shortcomings because the real-error structure of the observations has not been taken into account. A new algorithm that does account correctly for measurement errors in both variables is described. A computational method is illustrated for copolymerization data obtained from quantitative gas chromatographic analysis of the monomer feed throughout the reaction. It is shown that the actual error structure of the variables corresponds to the assumed error structure. Reliability of the estimates is substantially increased, compared with the existing methods. Standard deviations of the monomer reactivity ratios are given and appear to be in good agreement with reality.     

A method,based on statistical moments,to evaluate the kinetic parameters involved in unstable enzyme systems

The evaluation of individual rate constants involved in any reaction mechanism of an enzymatic systems first requires experimental monitoring of the time course of the concentration or product rate creation or of any enzyme species. The experimental progress curves obtained must then be fitted to the corresponding theoretical symbolic equation. Nevertheless, in some cases, e.g. when the equation involves two or more exponential terms, this fit is not easy and sometimes impossible. Simplification of the equation is usually required by assuming, for example, that the system has reached the steady-state, assuming an initial steady-state of a segment in the scheme of the reaction mechanism or assuming rapid equilibrium in one or more of the reversible steps, if there are any. But, obviously, simplified equations produce either fewer individual rate constants or global constants consisting of algebraic associations of individual rate constants or individual rate constants or global constants that might considerably differ from the real ones due to the approaches made. In this contribution, we suggest an alternative procedure for evaluating the rate constants of enzyme reactions corresponding to enzyme systems where one or more of the species involved is unstable or where one or more of the enzyme species is irreversibly inhibited, or both. The procedure is based on the numerical determination of statistical moments from experimental time progress curves. The fitting of these experimentally obtained moments to the corresponding theoretical expressions allows us, in most cases, to evaluate of all of the rate constants involved, with only a small error. To verify the goodness of the suggested procedure, it was applied to an unstable enzyme system which had previously been analysed with other methods. Finally, it is indicated how this procedure could also be extrapolated for application to any stable or unstable enzyme system.     

The Kissinger law and the IKP method for evaluating the non-isothermal kinetic parameters

The following problems concerning the apparent compensation effect (CE) (lnA=a+bE, where A is the pre-exponential factor, E is the activation energy, a and b are CE parameters) due to the change of the conversion function and on which the invariant kinetic parameters method (IKP method) is based, are discussed: (1) the explanation of this kind of CE; (2) the choice of the set of conversion functions that checks CE relationship; (3) the dependencies of CE parameters on the heating rate and the temperature corresponding to the maximum reaction rate. Using the condition of maximum of the reaction rate suggested by Kissinger (Kissinger law), it is pointed out that, for a certain heating rate, the CE relationship is checked only for reaction order (Fn) and Avrami-Erofeev (An) kinetic models, and not for diffusion kinetic models (Dn). Consequently, IKP method, which is based on the supercorrelation relationship between CE parameters, can be applied only for the set Fn+ An of kinetic models. The dependencies of a and b parameters on the heating rate and T _m (temperature corresponding to maximum reaction rate) are derived. The theoretical results are discussed and checked for (a) TG simulated data for a single first order reaction; (b) TG data for PVC degradation; (b) the dehydration of CaC₂O₄·H₂O.     

Die bestimmung kinetischer parameter endothermer zersetzungsreaktionen unter nicht-isothermen bedingungen

By using the kinetic parameters calculated from non-isothermal measurements according to Freeman and Carroll a computer programm is given, which permits the determination of the more probable reaction mechanism by use of 17 different kinetic equations. The computer programm includes the kinetic equation for chemical reaction, nucleation, phase boundary reaction and diffusion and can easily be extended to other equations. The evaluation of the experimental values by a distinct kinetic equation is quantitatively characterized by means of the correlation coefficient.The kinetic parameters are calculated on the basis of a regression analysis. By dividing the thermogravimetric curve in different reaction intervals a differential calculation is possible.Decomposition of CaCO₃, MgCO₃ and CaSO₄·2H₂O is discussed from the results of the computer calculation. It is seen that the kinetic parameters and the reaction mechanism are not constant during the reaction. Further experiments for a physical interpretation are being carried out.     

A new integral method for the kinetic analysis of thermogravimetric data

Methods for the calculation of activation energies, pre-exponential factors and reaction orders from thermogravimetric data are briefly reviewed. A new integral method is proposed for the determination of these kinetic parameters, using data from pairs of TG curves produced at different heating rates. Employing accurate values of the temperature integral of the Arrhenius equation, tabulated over a range ofE andT, and a simple graphical procedure, the method offers advantages of speed and accuracy over those previously reported. It is suggested that at least one of the kinetic parameters should be allowed to move freely in order to achieve the best possible fit between calculated and experimental traces.     

The upper limit pH in the dye-binding method for the determination of serum protein via measurements of the absorbance increase produced by protein error.

In the dye-binding method for determining the albumin concentration, the absorbance increase due to the change of the color shade by protein error of a pH indicator can be measured by a spectrophotometer. This absorbance increase is observed only in a restricted pH region, but this pH region is not theoretically studied yet. Thus, the author investigated the upper limit pH (pHUL) at which the absorbance increase occurs by the theoretical calculation, and compared these results with those obtained experimentally using four pH indicators. The pHUL is not affected by the dye or protein concentrations, or by the formation constant of the dye-protein complex; but the value changes according to the acid-dissociation constant of the dye (KD) and the ratio of the molar absorptivities of the proton-dissociated dye anion (epsilonD) and the dye-protein complex (epsilonPD). The pHUL value can be calculated by the equation, found theoretically. The calculated pHUL values of BPB, BCG, BCP and BTB were 5.1, 4.8, 6.2 and 5.5, respectively. These values correlated with the experimental results of 4.5 for BPB, 4.7 for BCG, 5.9 for BCP and 5.2 for BTB, but were not associated with the pKD values of each dye. The pHUL of these dyes did not change significantly for various dye and protein concentrations, as was expected from the thoretical calculation.     

Spectrophotometric method for the determination of europium with 2,2′-biquinoxalyl

A selective and sensitive method for the determination of europium was developed. Other lanthanides and oxidants do not require separation. The method is based on the redox reaction of Eu(III) with 2,2′-biquinoxalyl. It was checked for the range of 0.5 to 10 μg/Eu/mL. Sm(III) does not interfere in 1000-fold excess.     

Kinetic and theoretical studies on the mechanism of alkaline hydrolysis of DNA

The reaction mechanism of alkaline hydrolysis of DNA has been investigated by kinetic analysis and density-functional-theory calculation. The rates of hydrolysis of thymidine 3'-monophosphate esters (including thymidylyl(3'-5')thymidine (Tp-OT)) monotonically decrease as the leaving groups get poorer. According to the theoretical calculation in which the solvent effects are incorporated, no intermediate is formed in the course of the reaction. In the alkaline hydrolysis of the activated Tp-OT analogues having good leaving groups, the 3',5'-cyclic monophosphate of thymidine is concurrently formed through the intramolecular attack by the 5'-alkoxide ion. In the hydrolysis of the native dinucleotide, however, this side reaction does not occur, since the transition state leading to the departure of its poor leaving group cannot be formed due to conformational restraint. These arguments are supported by the theoretical analysis on the hydrolysis of both dimethyl phosphate and its O(bridging)-->S substituted analogue.     

离子选择电极电位法中结果计算方法(Ⅱ)——电位滴定三参数拟合法

提出了离子选择电极电位法中用于计算结果的三参数拟合法。该法可用于各种类型的电位滴定。本法的优点是精度较高,同时可确定C_x,E′_o、S。法特别适用于自动滴定分析。     

The non-Markovian quantum master equation in the collective-mode representation: application to barrier crossing in the intermediate friction regime

The calculation of chemical reaction rates in the condensed phase is a central preoccupation of theoretical chemistry. At low temperatures, quantum-mechanical effects can be significant and even dominant; yet quantum calculations of rate constants are extremely challenging, requiring theories and methods capable of describing quantum evolution in the presence of dissipation. In this paper we present a new approach based on the use of a non-Markovian quantum master equation (NM-QME). As opposed to other approximate quantum methods, the quantum dynamics of the system coordinate is treated exactly; hence there is no loss of accuracy at low temperatures. However, because of the perturbative nature of the NM-QME it breaks down for dimensionless frictions larger than about 0.1. We show that by augmenting the system coordinate with a collective mode of the bath, the regime of validity of the non-Markovian master equation can be extended significantly, up to dimensionless frictions of 0.5 over the entire temperature range. In the energy representation, the scaling goes as the number of levels in the relevant energy range to the third power. This scaling is not prohibitive even for chemical systems with many levels; hence we believe that the current method will find a useful place alongside the existing techniques for calculating quantum condensed-phase rate constants.     

Mechanism reduction of chemical reaction based on sensitivity analysis: development and testing of some new procedure

This paper proposes a procedure for simplifying the mathematical model of a chemical reaction by reducing the number of steps and species in the reaction scheme. This procedure is based on the sensitivity analysis of the model functional to the change in the model parameters. The application of this procedure makes it possible to accelerate and improve the construction of mathematical models for chemical reactions, as this does not require the calculation of sensitivity coefficients at various time points or sensitivity matrix analysis. This scheme was predicted the same behavior of the main reaction components as the detailed reaction scheme but includes much fewer steps. The efficiency of using this procedure was demonstrated by comparative results of modeling of formaldehyde oxidation and hydrogen oxidation in terms of detailed and reduced schemes. The sensitivity analysis was performed by Sobol’s method.     

Thermodynamic consistency of data banks

Data sets originated from different sources are typically used simultaneously either in data banks or in data bases of flowsheeting programs. If these data sets concern different kinds of data, they ought to be in accordance with the laws of thermodynamics. This is not assured, however, and in many cases it is not even checked. Methods used for data compilation rely on approximate models, which may bias the residuals.

Two model-free methods are proposed, where the residuals of the thermodynamic differential equations are investigated.

The first method is a χ² test based on a quadratic form of the f residuals, involving variances of the elementary measurements, if they are available.

The second method is a rather sensitive trend/shift analysis of residuals, which does not require the knowledge of error variances.

The examples are the Clausius-Clapeyron equation, a binary vapor-liquid equilibrium data set and a simultaneous treatment of PVT and caloric data.     

pKa of acetate in water: a computational study

Several computational methods including the conductor-like polarizable continuum model, CPCM with both UAKS and UAHF cavities, Cramer and Truhlar's generalized Born solvation model, SM5.4(AM1), SM5.4(PM3), and SM5.43R(mPW1PW91/6-31+G(d)), and mixed QM/MM-Ewald simulations were used to calculate the pK(a) values of acetate and bicarbonate anions in aqueous solution. This work provided a critical and comprehensive assessment of the quality of these theoretical models in the calculation of aqueous solvation free energies for the singly charged acetate and bicarbonate ions, as well as the doubly charged acetate dianion and carbonate dianion. It was shown that QM/MM-Ewald simulations could give an accurate and consistent evaluation of the pK(a) values of acetate and bicarbonate based on both the relative and absolute pK(a) formulas, while other methods could yield satisfactory results only for certain calculations. However, this does not mean that the current QM/MM-Ewald protocol is superior to other methods. The useful information obtained in this investigation is that both the absolute and relative pK(a) formulas should better be tested in accurate calculations of pK(a) values based on any methods.     

Hamilton-Jacobi equation for the least-action/least-time dynamical path based on fast marching method

Classical dynamics can be described with Newton's equation of motion or, totally equivalently, using the Hamilton-Jacobi equation. Here, the possibility of using the Hamilton-Jacobi equation to describe chemical reaction dynamics is explored. This requires an efficient computational approach for constructing the physically and chemically relevant solutions to the Hamilton-Jacobi equation; here we solve Hamilton-Jacobi equations on a Cartesian grid using Sethian's fast marching method. Using this method, we can--starting from an arbitrary initial conformation--find reaction paths that minimize the action or the time. The method is demonstrated by computing the mechanism for two different systems: a model system with four different stationary configurations and the H+H(2)-->H(2)+H reaction. Least-time paths (termed brachistochrones in classical mechanics) seem to be a suitable chioce for the reaction coordinate, allowing one to determine the key intermediates and final product of a chemical reaction. For conservative systems the Hamilton-Jacobi equation does not depend on the time, so this approach may be useful for simulating systems where important motions occur on a variety of different time scales.