New aspects of time interval analysis method for the determination of artificial alpha-nuclides

A new determination equipment combined with the time interval analysis (TIA) has been developed for the simultaneous determination of concomitant alpha–emitting nuclides, such as Pu, Am, Cm and natural alpha–emitters in dust samples. This discrimination technique for the determination of artificial alpha–nuclides is based on the selective subtraction of natural alpha–nuclides contribution to the total pulses by analysing the time interval distributions due to the successive alpha- and beta decay events within millisecond or microsecond orders.     

Constant rate thermal analysis for thermal stability studies of polymers

This paper explores the relationship between the shapes of temperature-time curves obtained from experimental data recorded by means of constant rate thermal analysis (CRTA) and the kinetic model followed by the thermal degradation reaction. A detailed shape analysis of CRTA curves has been performed as a function of the most common kinetic models. The analysis has been validated with simulated data, and with experimental data recorded from the thermal degradation of polytetrafluoroethylene (PTFE), poly(1,4-butylene terephthalate) (PBT), polyethylene (PE) and poly(vinyl chloride) (PVC). The resulting temperature-time profiles indicate that the studied polymers decompose through phase boundary, random scission, diffusion and nucleation mechanisms respectively. The results here presented demonstrate that the strong dependence of the temperature-time profile on the reaction mechanism would allow the real kinetic model obeyed by a reaction to be discerned from a single CRTA curve.     

A reduction method for multiple time scale stochastic reaction networks

In this paper we develop a reduction method for multiple time scale stochastic reaction networks. When the transition-rate matrix between different states of the species is available, we obtain systems of reduced equations, whose solutions can successively approximate, to any degree of accuracy, the exact probability that the reaction system be in any particular state. For the case when the transition-rate matrix is not available, one needs to rely on the chemical master equation. For this case, we obtain a corresponding reduced master equation with first-order accuracy. We illustrate the accuracy and efficiency of both approaches by simulating several motivating examples and comparing the results of our simulations with the results obtained by the exact method. Our examples include both linear and nonlinear reaction networks as well as a three time scale stochastic reaction-diffusion model arising from gene expression.     

Spectrophotometric reaction rate method for determination of barbituric acid by inhibition of the hydrochloric acid-bromate reaction

A new kinetic-spectrophotometric method was developed for the determination of barbituric acid. The method is based on its inhibition effect on the reaction between hydrochloric acid and bromate. The decolorization of methyl orange by the reaction products was used to monitor the reaction spectrophotometrically at 510 nm. The variable affecting the rate of the reaction was investigated. The method is simple, rapid, relatively sensitive and precise. The limit of detection is 7.9x10(-7) M and calibration rang is 1x10(-6)-6.0x10(-4) M barbituric acid. The linearity range of the calibration graph is depends on bromate concentration. The relative standard deviation of seven replication determination of 5.6x10(-6) M barbituric acid was 1.8%. The influence of potential interfering substance was studied.     

Simultaneous determination of reaction order and rate constant by rank annihilation factor analysis from kinetic-spectral data

Rank annihilation factor analysis combined with the optimization of kinetic parameter is adopted to resolve the two-way kinetic-spectral data measured online from chemical reactions. To a multi-step reaction whose intermediate process is complicated and reaction order is fractional, the reaction order and rate constant of the first step can be determined without the knowledge of the kinetic model of the reaction. Taken a three-step reaction as an example, the synthetic data has been resolved and its effectiveness was proved. When the approach is applied to the analysis of practical reaction systems such as alkaline hydrolysis of phenyl benzoate, oxidization of sodium bromide by potassium permanganate and electro-degradation of sunset yellow, reliable results are obtained.     

Dwell time analysis of a single-molecule mechanochemical reaction

Force-clamp spectroscopy is a novel technique for studying mechanochemistry at the single-bond level. Single disulfide bond reduction events are accurately detected as stepwise increases in the length of polyproteins that contain disulfide bonds and that are stretched at a constant force with the cantilever of an atomic force microscope (AFM). The kinetics of this reaction has been measured from single-exponential fits to ensemble averages of the reduction events. However, exponential fits are notoriously ambiguous to use in cases of kinetic data showing multiple reaction pathways. Here we introduce a dwell time analysis technique, of widespread use in the single ion channel field, that we apply to the examination of the kinetics of reduction of disulfide bonds measured from single-molecule force-clamp spectroscopy traces. In this technique, exponentially distributed dwell time data is plotted as a histogram with a logarithmic time scale and a square root ordinate. The advantage of logarithmic histograms is that exponentially distributed dwell times appear as well-defined peaks in the distribution, greatly enhancing our ability to detect multiple kinetic pathways. We apply this technique to examine the distribution of dwell times of 4488 single disulfide bond reduction events measured in the presence of two very different kinds of reducing agents: tris-(2-carboxyethyl)phosphine hydrochloride (TCEP) and the enzyme thioredoxin (TRX). A different clamping force is used for each reducing agent to obtain distributions of dwell times on a similar time scale. In the case of TCEP, the logarithmic histogram of dwell times showed a single peak, corresponding to a single reaction mechanism. By contrast, similar experiments done with TRX showed two well-separated peaks, marking two distinct modes of chemical reduction operating simultaneously. These experiments demonstrate that dwell time analysis techniques are a powerful approach to studying chemical reactions at the single-molecule level.     

Rapid data analysis method for differential mobility cytometry

Differential mobility cytometry (DMC) has recently been established as a powerful method to capture cells and study adhesion processes. DMC uses an oscillation system and cell affinity chromatography to monitor cells as they adhere to a surface. In the past, differential images had to be created individually which limited the throughput of the method. A new method to create differential images is presented. The method involves the subtraction of short movies from each other to create a stack of differential images that can be easily analyzed. In the future, this method will make DMC more accessible and improve throughput.     

Differential method for the determination of the order of reaction and the rate constants

A method is proposed whereby the orders and rate constants for processes obeying the rate law ?dA/dt = kAⁿ may be determined. The method is illustrated in two ways. First, simulated data for processes of various orders are treated, and the treatment is shown to be capable of reproducing orders and rate constants to a high degree of accuracy. The factors affecting the accuracy with which n and k can be determined are considered. These are inaccuracy in the determination of concentration values, irregularity of the time intevals between concentration determinations, and the length of those time intervals. It is shown that if concentrations are determined at times that are close together, the effect of the other two factors is small, but if the time intervals are made longer, the errors due to the other two factors affect the calculated values of n and k much more seriously. Second, the method was applied to two homogeneous reactions, of which one was first-order and one was second order, and three heterogeneous reactions, of which one was found by the original workers to be first order, one to be zero order, and one to vary between zero and first order, depending on the initial pressure. The present method gives results in agreement with these conclusions and reproduces the rate constants to within ±5% in all cases.     

Temperature dependence of the rate of reaction in thermal analysis

Special problems are encountered in modeling the temperature dependence of the kinetics of heterogeneous, condensed phase systems. In the division of the model for the reaction rate into two parts, a)f() which is physical (translational) and b)k(T) which is chemical (vibrational), complications arise in defining the temperature dependence of part a) which may take various mathematical forms and then in coupling it with the Arrhenius temperature dependence of part b). The role off() in thermal analysis systems is discussed. The concept of rate-controlling step is applied to the simplification of the temperature dependent term. The significance of the compensation effect in these systems is described and an heuristic rationalization for it is suggested. Maximum practical temperature ranges for thermal analysis experiments and the effect of temperature measurement imprecision on obtaining meaningful Arrhenius parameters are discussed. The WLF and other equations used to describe the temperature dependence off() are not found to couple compatibly with the Arrhenius equation.

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Zusammenfassung Bei der Modellierung der TemperaturabhÄngigkeit der Kinetik bei heterogenen, kondensierten Phasen treten spezielle Probleme auf. In der Unterteilung des Modelles für die Reaktionsgeschwindigkeit in zwei Teile: a)f() ist physikalisch (Translation) und b)k(T) ist chemisch (Vibration) treten bei der Definierung der TemperaturabhÄngigkeit von Teil a) und dann bei der Verknüpfung mit der Arrhenius-schen TemperaturabhÄngigkeit von Teil b) Komplikationen auf. Es wird die Rolle vonf() in thermoanalytischen Systemen besprochen. An einer Vereinfachung des temperaturabhÄngigen Termes wurde das Konzept des geschwindigkeitsbestimmenden Schrittes angewendet. Es wird die Bedeutsamkeit des Kompensationseffektes in diesen Systemen beschrieben und dafür eine heuristische Vereinfachung vorgeschlagen. Praktisch gesehen maximale Temperaturbereiche für thermoanalytische Experimente sowie der Einflu\ der Ungenauigkeit der Temperaturmessung für die erhaltenen Arrhenius-Parameter wird diskutiert. Die zur Beschreibung der TemperaturabhÄngigkeit vonf() benutzten WLF und anderen Gleichungen stellen keine KompatibilitÄt mit der Arrhenius-schen Gleichung her.

     

Sensitive reaction rate method for the determination of low levels of formaldehyde with photometric detection

A simple and rapid method is proposed for the determination of ultra trace amounts of formaldehyde. It is based on the catalytic effect of formaldehyde on the oxidation of Brilliant cresyl blue by bromate. The reaction is monitored photometrically by measuring the decrease in absorbance of the dye. Formaldehyde in the range of 0.005–2.300 μg/mL can be determined with a limit of detection of 0.003 μg/mL. The relative standard deviation for ten replicate measurements of 1.5 μg/mL formaldehyde is 0.1%. The method was used for the determination of formaldehyde in real samples with satisfactory results. Received: 26 May 1998 / Revised: 30 September 1998 / Accepted: 3 October 1998     

Sensitive reaction rate method for the determination of low levels of formaldehyde with photometric detection

A simple and rapid method is proposed for the determination of ultra trace amounts of formaldehyde. It is based on the catalytic effect of formaldehyde on the oxidation of Brilliant cresyl blue by bromate. The reaction is monitored photometrically by measuring the decrease in absorbance of the dye. Formaldehyde in the range of 0.005–2.300 μg/mL can be determined with a limit of detection of 0.003 μg/mL. The relative standard deviation for ten replicate measurements of 1.5 μg/mL formaldehyde is 0.1%. The method was used for the determination of formaldehyde in real samples with satisfactory results.     

Comparative sensitivity analysis of transport properties and reaction rate coefficients

Transport properties of chemical species are required for many combustion models. A sensitivity analysis is conducted to assess the significance of transport properties and their underlying molecular parameterizations for atmospheric pressure premixed laminar flames for three different fuels and two different approaches to transport property calculations. The analysis is performed at both the macroscopic level of Arrhenius A-factors and transport coefficients as well as at the molecular scale. First- and second-order sensitivities of reactant, intermediate, and product species concentrations, temperature, and flame velocity were calculated with respect to various parameters, all within the mixture approximation using ADIFOR 2.0, a software package that supports exact differentiation. Parameters considered were the binary diffusion coefficients, pure species thermal conductivity coefficients, and thermal diffusion ratios. The more fundamental molecular parameters: collision diameters, well depths, dipole moments, polarizabilities, and the rotational relaxation collision numbers were also considered. Influential transport properties are found to be as important in flame modeling as influential reaction rates, and both should be taken into account when building chemical mechanisms. Transport parameter importance was found to vary according to the independent variable being considered and the flame type. Magnitudes of sensitivities appear to be more influenced by the underlying molecular parameters than the approach used to compute the transport properties. The number of significant sensitivities to transport parameters increases for the progression: flame temperature, flame velocity, reactant species, product species, and intermediate radical species. Many dependent variables have significant sensitivities to the pure species thermal conductivities of N₂, O₂, and the fuel. At the molecular level, large sensitivities to the collision diameters of several species are also observed, but significant sensitivity to well depths, although observed is less and more rare. Large sensitivities are not observed to the rotational relaxation collision number, the dipole moment, or to the molecular polarizability. Second-order sensitivities are significant for a number of dependent variables. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 538–553, 2005     

A reduction method for multiple time scale stochastic reaction networks with non-unique equilibrium probability

We develop a reduction method for general closed multiple time scale stochastic reaction networks for which the fast subsystem may have non-unique equilibrium probability. We obtain a reduced ODE system with nonhomogeneous terms whose solutions can approximate the solutions of the full system accurately. We then apply this reduction method to general linear network and nonlinear networks for which the state diagram can be constructed. We illustrate the accuracy of the reduction method by comparing computational results of the full systems with the reduced ODE systems for several examples. Finally, we show how the reduction method may be extended to three or more time scale reaction networks.     

Determination of naturalα-radionuclides related to millisecond order lives in environmental samples using the time interval analysis (TIA) method

The time files due to radioactive decay events were analyzed for the selective extraction of successive alpha-decay pulse events in millisecond orders, such as²¹⁶Po (145 ms, thorium series),²¹⁷At (32.3 ms, neptunium series), and²¹⁵Po (1.78 ms, actinium series) after respective preceding parents decay, using a multiple time interval analysis (TIA-MTA) technique from both theoretical and experimental viewpoints. In the theoretical treatments, the detection sensitivities of each correlated event in natural decay series was compared with more generalized conditions. It was noteworthy that the evaluated detection sensitivity had increased proportionally with shorter half-lives in the following order:²¹⁴Po>²¹⁵Po>²¹⁷At>²¹⁶Po.Finally, the present TIA was applied to the clarification of thorium series disequilibrium states in Tamagawa (Akita, Japan) Hot Spring waters. Activities of²²⁴Ra were evaluated to be 3.41±0.38 and 0.60±0.08 Bq/l at the upper and lower stream, respectively. The results from activity ratios of radium to thorium isotopes showed a preferential precipitation of radium isotopes in comparison with thorium, reflecting the sensitivity to the lowering acidity of strongly acidic hot spring waters in the lower end of the stream.     

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.     

Rank annihilation factor analysis method for spectrophotometric study of second-order reaction kinetics

In this study several methods are described to determine the rate constant of a second-order reaction in the form of A+B→C. These approaches allow circumventing a rank deficiency inherent of a second-order reaction when the spectroscopic data is influenced by additional source of variance. Classically, to determine the unknown rate constant in this kind of systems, one needs to have extra knowledge about the system, including the spectra of the reactants or product and the exact kinetics. In the case of the presence of an unknown phenomenon in the data set that cannot be explained by the model, such as baseline drift, the estimated rate constant might be erroneous. Present work is a modification of the rank annihilation factor analysis (RAFA) algorithm by inclusion of I) pure spectra of reactants, or IIA) mean centering step, or IIB) mean spectrum. The proposed methods can interestingly be applied on a single kinetic run. The performances of the new methods have been evaluated by applying them to analysis of simulated and experimental data.     

A program system for computer integration of multistep reaction rate equations using the gear integration method

A program system is described for the integration of the rate equations resulting from large systems of elementary reactions. The Gear integration method is used for this problem, which frequently may exhibit stiffness instability when other integration methds are employed. No usage of the quasi-steady-state approximation is necessary. Ease in varying the reaction mechanism and simplicity of input structure are coupled with efficient execution and minimal demands for program storage as key features. The input–output structure, method of operation, and implementation are summarized, along with core storage requirements and execution times for trials using an IBM 360/44 computer.     

'One-pot' Hammett plots: a general method for the rapid acquisition of relative rate data

A general 'one-pot' method for determining relative rates of reaction in complex mixtures has been established using free energy relationships to demonstrate its utility. Competition experiments involving as many as seven species gave relative rate constants that are in good agreement to those obtained from individual kinetic analyses.