Determination of kinetic parameters from TG curves by non-linear optimization

The results obtained so far by kinetic analysis of non-isothermal experiments indicate that the kinetic parameters found by the conventional methods, in general, do not describe the experimental curve in an optimum manner. This is due to the fact that the initial differential equation is transformed into the logarithmic and, consequently, linear form and that the initial and final weights of the conversion curve cannot be determined exactly, which may falsify the slope of the curve.Investigations have shown that the determination of the kinetic parameters by non-linear optimization (simplex method) results in a better fit of the theoretical conversion curve to the experimental one. But this procedure gives optimum results only when the initial and final weights of the reaction can be determined exactly. If this is impossible, exact parameters can be obtained only by the use of the non-standardized TG curve.Examples are cited to prove that it is possible to evaluate overlapping reactions by the formation of intervals. However, the evaluation of conversion curves merely by the use of mathematical methods can easily result in an erroneous interpretation of the reaction course investigated. Therefore, it is necessary to check the mathematical results as to their physical and chemical meaning.     

General equation for determining the dissociation constants of polyprotic acids and bases from additive properties. Part II. Applications

Dissociation constants of some polyprotic acids and bases are determined from spectrophotometric and reversed-phase high performance liquid chromatographic data. A general equation relating additive properties of acids and bases to the pH of the solution is used for this purpose. The method is tested by applying it to the calculation of overlapping pK_as without the prerequisite of measuring the limiting values of the property for the individual species that result from the dissociation of the solute. The possibility of applying the same method to hyperpolarizability measurements is pointed out, and a procedure, based on the general equation, for obtaining the activity coefficients of the ionic species as a function of the ionic strength is also suggested.     

On the estimation of the reaction mechanisms of thermal decomposition of solids from the fraction reacted at the maximum reaction rate

A procedure is developed for determining equilibrium constants of reactions of the type: A (solid) ? B (solid) + C (gas) from TG data. The method is based upon the overlapping of both formation and decomposition TG diagrams when an appropriate heating rate is applied.     

Study of the one-channel resonance states. Method without a stabilization procedure in the framework of the optical potential model

The resonances of some one-dimensional systems are studied in the framework of the optical potential model. Analysis of the discrepancies between the observed and exact resonance energy values shows that these differences come from the partial waves reflected upon the optical potential wall. When these disturbing waves have a small amplitude, an autocorrective procedure enables one to accurately determine the resonance energy if one only knows two approximate values of it deduced from a finite representation and the corresponding complex incoming and outgoing wave amplitudes.     

基于积分渐进展开的气相色谱重叠峰快速解析法

论文提出用积分渐进展开解析气相色谱重叠峰,该方法有3个主要步骤：首先将谷峰或肩峰分成两个积分区域,得到一个子区域的积分方程和一个重叠峰面积的代数方程;然后用数值积分求出这两个方程计算中所需要的峰面积,再用积分渐进公式将积分方程展开成代数方程;最后,将这两个方程与峰高约束方程联立后,得到一个非线性代数方程组,用Gauss-Seidel迭代可以快速求解方程组,方程收敛的最大迭代次数不超过20次。仿真和实验结果表明,解析的峰高和峰面积误差均很小,峰面积最大误差低于6.44%,峰高的最大误差约为6.80%。由于该算法精度高,效率高,所以这个方法可以用于气相色谱重叠峰和一般色谱峰的实时在线解析。     

Quantitative analysis of undefined mixtures - "fishing net" algorithm

An approach for quantitative analysis of mixtures with unknown individual responses of the components is discussed. Although it is based on a resolution of overlapping bands technique, the main emphasis is not given to the computational facets of curve fitting. A logical procedure is described, allowing estimation of the unknown concentrations in the mixture, and both the number of overlapping bands and their assignment to the components in the solution to be determined automatically. A general conclusion about the precision of the method cannot be defined, because it depends on the extent of overlapping of the individual spectra of the components and their complexity. Using this procedure a complicated three-component acid-base equilibrium of a halochromic dye in solution is studied.     

Overcoming stiffness in stochastic simulation stemming from partial equilibrium: a multiscale Monte Carlo algorithm

In this paper the problem of stiffness in stochastic simulation of singularly perturbed systems is discussed. Such stiffness arises often from partial equilibrium or quasi-steady-state type of conditions. A multiscale Monte Carlo method is discussed that first assesses whether partial equilibrium is established using a simple criterion. The exact stochastic simulation algorithm (SSA) is next employed to sample among fast reactions over short time intervals (microscopic time steps) in order to compute numerically the proper probability distribution function for sampling the slow reactions. Subsequently, the SSA is used to sample among slow reactions and advance the time by large (macroscopic) time steps. Numerical examples indicate that not only long times can be simulated but also fluctuations are properly captured and substantial computational savings result.     

Spectrophotometric evaluation of acidity constants of tetra-step overlapping equilibria

The simultaneous evaluation of acidity constants of tetra-step overlapping equilibria from spectrophotometric data may be carried out if the absorbance versus pH graph of a tetra-protic acid at a given wavelength shows two maxima and a minimum of two minima and a maximum. In such cases, a tetraprotic acid may be treated like a monoprotic one by substituting the pH values with a function of the pH values which have corresponding absorbances.     

Optimisation of data handling and detection conditions for automated chromatographic assay software

Summary The principle of automated chromatographic peak detection and analysis software is summarized, and critical steps are systematically studied. As the only parameter to be entered is the acquisition frequency, evaluation of its effect on software performance is discussed. In the case of relatively noisy chromatograms, it is shown experimentally that numerous points per peak have to be taken, leading to quite fast computer acquisition procedures. The use of discrete Fourier transform filtration techniques can modify peak shapes and a comparative study evaluates the relative errors induced in the shapes and characteristics of the chromatographic profiles. Optimisation of filtering conditions is achieved and it is shown that for a filter position only 2% of the Nyquist frequency no deformation occurs in the chromatographic profile. Detection of the start and finish of chromatographic peaks is optimized according to a simple four step iterative procedure. In the case of simulations, the difference between the values used to simulate peaks and those calculated by the software are less than 1%.     

Standardisierung quantitativer Analysenverfahren

After defining the term standardization the necessity of standardized planning, execution, and evaluation in quantitative analysis is illustrated. From the working steps: sampling, preliminary treatment of the sample, determination, and evaluation only the last two steps are standardizable in an universal way, because they can be examined and checked up independently from the actual object of inquiring. These steps are designated as analytical procedure in a narrow meaning. The quantitative analytical message is obtained by way of a chain of signal S, information I, and of an absolute quantity of the determinated substance, called working quantity A. The transitions should be described by a signal function I=f(S) and by an analytical function A=F(I). The important demand for a standard procedure is the realization of a lineary analytical function in a defined working range. A classification of standard working ranges as “complete” ranges of powers of ten for amounts of substances in the SI-unit Mol leads to new general designations for all kinds of analytical procedures. By fixing a general scheme of measurement execution and result evaluation an identically set of characteristic data can be obtained for a critical examination and an objective comparison of procedures. The base of the standard evaluation is the method of least squares, applicated to a set of 24 blocks of data arranged in standardized 6 groups of a size of 4 blocks. Details of standard measurements and standard evaluation are presented in paper II.     

Significance of fluid regime and wetted area in biofilm reactors

Mass transfer within microbial films was described using Monod-type biological kinetics in terms of properties of filter media and feed solution. The performance characteristics of a trickling filter were thus modeled. The model enables one to consider the effect of inlet substrate concentration and flow rate upon the removal efficiency. For this purpose a second-order partial differential equation describing the dispersion phenomena inside the liquid layer was solved under special boundary conditions and used to determine substrate flux into the biofilm. A uniform biofilm thickness was considered. The model is based on computer techniques and the numerical evaluation of the normalized biofilm mathematical model. A design procedure was also given to calculate biological filters. The numerical model was also applied to experimental data to demonstrate its validity.     

Kinetic analysis of second order reactions using UV-VIS spectroscopy

A new method was recently developed for the spectroscopic kinetic analysis of reactions with two linearly independent concentration variables. Firstly, the results of this theory applied to experimental data are represented. For this investigation, reactions of the mechanism type A + Bk (1)--> C + D and A + E uc-->|k(2)|F + G were chosen since both reaction steps can be studied separately. The evaluation of the reaction system consisting of both reaction steps gives satisfactory results when the methods of "formal integration" and "singular value decomposition" (SVD) are used. Absorption coefficients of absorbing species are not needed for the evaluation. Only time dependent spectroscopic measuring values and initial concentrations are used in the presented practical example.     

Geometrical energy derivative evaluation with MRCI wave functions

The theory of MCSCF and CI energy derivatives with respect to geometrical variations is briefly reviewed with special attention given to the MCSCF and MRCI energy gradients. A computational procedure is proposed for MRCI energy gradients that does not require the solution to any “coupled-perturbed MCSCF ” equations, it does not require any expensive direct-CI matrix-vector products involving derivative integrals, and it does not require any derivative integrals to be transformed from the AO basis to the MO basis. An additional feature is that it does not require any changes to existing MCSCF gradient evaluation programs in order to compute MRCI gradients. The only difference in the two cases is the exact nature of the data passed to the gradient evaluation program from the previous steps in the computational procedure. The additional effort required to compute the entire MRCI energy gradient vector is approximately that required for one additional iteration of the MRCI diagonalization procedure and for one additional MCSCF iteration. For large scale MRCI wave functions, the MRCI energy gradient evaluation should only require about 10% of the effort of computing the wave function itself. This computational procedure removes a major computational botleneck of potential energy surface evaluation.     

Parameters of ultrasonic dispersion of polymer-composite solutions

Conditions allowing the formation of three types of characteristic cavities in liquid via ultrasonic cavitations have been considered. The effect of the ultrasonic-field parameters on the dispersion efficiency has been analyzed, and the choice of criteria for the evaluation of the quality of steering and dispersion of a polymer-composite material (PCM) for reconstruction of body parts of automotive engineering has been grounded. The conditions for effective dispersion of a PCM solution have been established on the basis of the sound-pressure amplitude upon ultrasonic treatment and based on the maximum permissible level of the solution in an ultrasonic bath.     

Computer simulation of dissociative equilibrium in aqueous NaCl electrolyte with account for polarization and ion recharging. Model of interactions

Comparative analysis of different models applied in theoretical studies of electrolytes points to the considerable role of polarization interactions. In order to study aqueous electrolytes on the molecular level, a detailed model is presented of intermolecular interactions that accounts in explicit form, apart from Coulombic, exchange, and dispersion interactions, also many-body interactions caused by polarization of solvent molecules in the field of ions and ion polarization in the field of solvent molecules, and also many-body covalent interactions, effects of excess charge transfer and effects of partial counterion recharging. Numeric values of parameters for an aqueous NaCl solution are obtained by correlation of the calculated values of free energies and entropy of the first reactions of vapor molecule addition to hydrate ion shells with the corresponding experimental values and also from the experimental data on the dissociation energy and IR vibration frequencies of the ion pair and quantum-chemical calculation of the energy of stable configurations of a hydrated ion pair. A special form of describing many-body interactions allows by more than an order of magnitudes reducing the extent of the required calculations and makes it possible to apply the developed model for computer simulation of aqueous electrolytes at the room temperatures.     

Polyaniline films containing palladium microparticles for electrocatalytic purposes

The deposition of palladium as microparticles on electrogenerated polyaniline (PAni) films accomplished by metal electroless precipitation or by electrodeposition has been used to prepare stable polymer-modified electrode systems. Its general morphology, metal particles size and distribution were obtained by AFM analysis. The PAni/Pd microparticles electrodes have been evaluated for their catalytic activity towards hydrogenation reactions upon organic compounds reduction using 4-nitro-benzaldehyde. Studies on rotating ring-disk electrodes have shown that relatively low Pd loadings are required to obtain effective electrocatalytic activity, provided a good metal particles dispersion of about 100 nm diameter is observed. Dedicated to Professor M. A. Vorotyntsev on the occasion of his 60th birthday     

Computational modeling of the mechanisms of the free radical-chain reaction of alkanes with oxygen. The oxidation of isobutane,n-butane,and isopentane

A general computational method for obtaining complete solutions of time-dependent kinetic equations has been developed and applied to free radical-initiated reactions of alkanes with oxygen. The method has been applied to the low-temperature, peroxide-initiated oxidations of isobutane and isopentane. Using available independently measured and estimated values for the rate constants and activation parameters for each of the 20 proposed reaction steps for the oxidation of isobutane, the rates and products have been calculated for both the liquid phase and gas phase in the range of 100°–155°C. The calculated rates and products of oxidation agree with published experimental values. The oxidation of isopentane was examined by a 32-reaction model. The rate constants were estimated using values for the appropriate rate steps in the oxidation of n-butane and isobutane. The calculation of the oxidation rate and products agree with our experiments.     

Evaluation of analytical interlaboratory comparisons and certification of reference materials

A procedure for the evaluation of results of interlaboratory comparisons of trace multi-component determinations is presented. The distribution of interlaboratory comparison data may differ significantly from the normal distribution and, therefore, various types of median and modal values approximate their central values better than the mean. The simple median and its confidence interval, calculated on the basis of a nonparametric distribution after the rejection of outlying results, is shown to be the optimal indicator of the central values. The total procedure consists of three parts: statistical evaluation of the data, classification of the results according to a special set of analytical criteria, and graphic presentation of the data. The application of the results of such comparisons for certification of analytical reference materials is discussed.     

Screening methods for the detection of thirteen common mycotoxins

A study of screening methods for thirteen mycotoxins showed that they can be separated as neutral and acidic metabolites. RF values were determined in several solvent systems. The reactions of the mycotoxins with well known spray reagents were investigated, and their detection limits were established. A general procedure for the extraction of mycotoxins from contaminated samples is described.