Linearized non-equilibrium and non-isothermal two-dimensional model of liquid chromatography for studying thermal effects in cylindrical columns

A non-equilibrium and non-isothermal two-dimensional lumped kinetic model (2?D-LKM) is formulated and analytically solved to study the influence of temperature variations along the axial and radial coordinates of a liquid chromatographic column. The model includes convection-diffusion partial differential equations for mass and energy balances in the mobile phase coupled with differential equations for mass and energy in the stationary phase. The solutions are derived analytically through sequential implementation of finite Hankel and Laplace transformations using the Dirichlet inlet boundary conditions. The coupling between the thermal waves and concentration fronts is demonstrated through numerical simulations and important parameters are recognized that influence the column performance. For a more comprehensive study of the considered model, numerical temporal moments are obtained from the derived solutions. Several case studies are conducted and validity ranges of the derived analytical solutions are identified. The current analytical results will play a major role in the improvements of non-equilibrium and non-isothermal liquid chromatographic processes.     

About compensation effect by thermal decomposition of some catalyst precursors

Summary In order to obtain catalysts, the thermal decomposition of the precursors is a compulsory step. However, kinetic analysis of the decomposition data obtained under non-isothermal conditions lead very seldom to the intimate reaction mechanism. There is also a lack of information because in non-isothermal kinetics, the compensation effect, is rather a rule and unfortunately a source of debate. In order to discriminate between these processes, and the influence of conversion, respectively temperature on the reaction rate, the NPK (non-parametric kinetic - Sempere and Nomen) method was used. This method is based on the singular value decomposition algorithm (SVD) applied on the matrix of reaction rate at corresponding conversion and temperature. This method allows a less speculative determination of the conversion functions and of the kinetic parameters.     

Kinetic behaviour of non-isothermal lime hydration

The rate of the solid—liquid reaction between lime and water depends on the physicochemical properties of lime and on the solid-to-liquid ratio. The hydration is usually carried out under non-isothermal conditions and at high solid-to-liquid ratios, leading to a first reaction step in which the solid breaks down with a fast increase in temperature. The second step is much slower. In this work a mathematical model based on the structural properties of the solid was used to describe the second step of the hydration leading to the interfacial reaction and diffusion parameters and activation energies for both parameters.The kinetic model was able to simulate the non-isothermal results of the adiabatic system in the range of variables studied.     

Kinetic Analysis of Single or Multi-Step Decomposition Processes; Limits introduced by statistical analysis

A kinetic study on decomposition processes of some penicillin and some commercial drugs was carried out. As expected by the complex structures of penicillins, several steps with different activation energies occurred in their decomposition processes. Model-fitting and model-free kinetic approach were applied to non-isothermal and isothermal data. In the model-fitting methods the kinetic triplets (f(α), A and E _a) that defines a single reaction step resulted in being at variance with the multi-step nature of penicillins decomposition. The model-free approach represented by isothermal and non-isothermal isoconversional methods, gave dependences of the activation energies on the extent of conversion. The complex nature of the multi-step process of the studied compounds was more easily revealed using a broader temperature range in non-isothermal isoconversional method. The failure in the model fitting method did not allow calculating storage times. Model-fitting and model-free methods, both isothermal and non-isothermal, showed that F1 mechanism is able to describe decomposition processes for drugs (having Phosphomycin salts as active component) for which a single decomposition process occurs. Statistical analysis allowed us to select reliable kinetic parameters related to the decomposition processes for these last compounds. This procedure showed that the values obtained by extrapolation, outside the temperature range where the processes occurred must be used with caution. Indeed half-life and shelf-life values, commonly extrapoled at room temperature, seemed to be unrealistic. This revised version was published online in August 2006 with corrections to the Cover Date.     

Modelling of natural graphite oxidation using thermal analysis techniques

A natural graphite recommended for use in nuclear applications was analyzed using thermogravimetric analysis. The oxidation behaviour was unlike that expected for flake-like particles. The dynamic data displayed an apparent bimodal reaction rate curve as a function of temperature and degree of conversion. Nevertheless, it was possible to model this behaviour with a single rate constant, i.e. without the need for a parallel reaction type of kinetic mechanism. The approach used in this paper to model the gas–solid reaction of graphite and oxygen, provides a consistent framework to test the validity of complementary isothermal and non-isothermal data for a specific solid state reaction.     

Kinetic study of the multistep thermal behaviour of barium titanyl oxalate prepared via chemical precipitation method

This study describes the physico-geometrical mechanism and overall kinetics for the multistep thermal dehydration of barium titanyl oxalate tetrahydrate (BTO). The thermal dehydration kinetics of BTO was studied at four different linear heating rates under non-isothermal conditions. The reaction kinetics was performed using differential scanning calorimetry (DSC) and the curves obtained were analysed using different isoconversional model-free equations and the values are found to be compatible with each other. The kinetic deconvolution principle is used for identifying the partially overlapped kinetic processes of the thermal dehydration of BTO, and it occurs in two stages. The overall reaction kinetics parameters calculated via kinetic deconvolution of the sample indicate the multistep nature of the process and the kinetic analysis of the non-isothermal data of this reaction model shows that the reaction is best described by Sestak–Berggren (m, n) empirical kinetic model. The prepared sample was identified and characterized by means of FT-IR, XRD, SEM, and TEM.

     

Kinetic Analysis of Non-isothermal DSC Data. Computer-aided test of its applicability

The applicability of the kinetic analysis of data obtained by non-isothermal differential scanning calorimetry (DSC) is discussed. The Johnson-Mehl-Avrami (JMA) model was used for the computer simulation of DSC traces subsequently analysed by common methods of kinetic analysis of non-isothermal data. For the temperature-independent kinetic exponent n of the JMA equation, the kinetic analysis was shown to provide correct results, e.g. a correct kinetic model and apparent activation energy. On the other hand, for the temperature-dependent kinetic exponent, there is a great possibility of erroneous determination of the correct kinetic model and apparent activation energy, especially at higher heating rates. Since the temperature dependence of n cannot be determined on the basis of non-isothermal DSC experiments, conclusions must be drawn with appropriate caution. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermal analysis of Beypazari lignite

Beypazari lignite was investigated by differential scanning calorimetry (DSC), thermogravimetry (TG), high pressure thermogravimetry (HPTG) and combustion cell experiments. All the experiments were conducted at non-isothermal heating conditions with a heating rate of 10°C min^?1, in the temperature range of 20–700°C. DSC-TG data were analysed using an Arrhenius-type reaction model assuming a first-order reaction. For the HPTG data the Coats and Redfern equation was used for kinetic analysis. In the combustion cell experiments the Fassihi and Brigham approach was used in order to calculate kinetic data. Finally a comparison is made between the kinetic results.     

Numerical solution of nonlinear and non-isothermal general rate model of reactive liquid chromatography

Abstract

A nonlinear general rate model (GRM) of liquid chromatography is formulated to analyze the influence of temperature variations on the dynamics of multi-component mixtures in a thermally insulated liquid chromatographic reactor. The mathematical model is formed by a system of nonlinear convection–diffusion reaction partial differential equations (PDEs) coupled with nonlinear algebraic equations for reactions and isotherms. The model equations are solved numerically by applying a semi-discrete high-resolution finite volume scheme (HR-FVS). Several numerical case studies are conducted for two different types of reactions to demonstrate the influence of heat transfer on the retention time, separation, and reaction. It was found that the enthalpies of adsorption and reaction significantly influence the reactor performance. The ratio of density time heat capacity of solid and liquid phases significantly influences the magnitude and velocity of concentration and thermal waves. The results obtained could be very helpful for further developments in non-isothermal reactive chromatography and provide a deeper insight into the sensitivity of chromatographic reactor operating under non-isothermal conditions.     

Thermokinetic parameters and thermal hazard evaluation for three organic peroxides by DSC and TAM III

The thermokinetic parameters were investigated for cumene hydroperoxide (CHP), di-tert-butyl peroxide (DTBP), and tert-butyl peroxybenzoate (TBPB) by non-isothermal kinetic model and isothermal kinetic model by differential scanning calorimetry (DSC) and thermal activity monitor III (TAM III), respectively. The objective was to investigate the activation energy (E _a) of CHP, DTBP, and TBPB applied non-isothermal well-known kinetic equation to evaluate the thermokinetic parameters by DSC. We employed TAM III to assess the thermokinetic parameters of three liquid organic peroxides, obtained thermal runaway data, and then used the Arrhenius plot to obtain the E _a of liquid organic peroxides at various isothermal temperatures. In contrast, the results of non-isothermal kinetic algorithm and isothermal kinetic algorithm were acquired from a highly accurate procedure for receiving information on thermal decomposition characteristics and reaction hazard.     

A unified theory for the kinetic analysis of solid state reactions under any thermal pathway

The Ozawa concept of generalized time has been used for developing master plots for the different kinetic models describing solid state reactions. These plots can be indistinctly used for analysing isothermal or non-isothermal experimental data. It is demonstrated that it is not possible to discriminate the kinetic model from a single non-isothermal curve without a previous knowledge of the activation energy. However, it has been shown that the ln [(da/dt)/f(a)] data taken from a set of DTG curves obtained at different heating rates lie on a single straight line when represented as a function of 1/T only if the kinetic model really obeyed by the reaction is considered. Moreover, the true values of E and A are obtained from the slope and the intercept of this straight line. This revised version was published online in July 2006 with corrections to the Cover Date.     

邻氨基酚萃取催化光度法测定痕量钒及其催化反应机理

研究了在ｐＨ３．５的弱酸性介质中，痕量钒（Ｖ）能催化溴酸钾氧化邻氨基酚的指示反应，用萃取平衡控制反应时间和水相中邻氨基酚的浓度及反应程度，通过测量４２４ｎｍ下有机相的吸光度，建立了萃取催化光度法测定钒的新方法，方法的线性范围为０．００１０～０．３０ｍｇ／Ｌ检出限为１．０×１０＾－６ｇ／Ｌ用于人发，煤和岩石中痕量钒的测定，结果满意，此外，还探讨了反应机理，建立了动力方程。     

Improved Iterative Version of the Coats-Redfern Method to Evaluate Non-Isothermal Kinetic Parameters

An improved version of the Coats-Redfern method of evaluating non-isothermal kinetic parameters is presented. The Coats-Redfern approximation of the temperature integral is replaced by a third-degree rational approximation, which is much more accurate. The kinetic parameters are evaluated iteratively by linear regression and, besides the correlation coefficient, the F test is suggested as a supplementary statistical criterion for selecting the most probable mechanism function. For applications, both non-isothermal data obtained by theoretical simulation and experimental data taken from the literature for the non-isothermal dehydration of Mg(OH)₂ have been processed.This revised version was published online in November 2005 with corrections to the Cover Date.     

KBrO_3-邻氨基酚体系催化动力学光度法测定微量Cu(Ⅱ)

在pH为4.5的HAc-NaAc缓冲溶液介质中,Cu(Ⅱ)能催化KBrO_3氧化邻氨基酚而显色,据此建立了测定微量Cu(Ⅱ)的新方法。方法的测定波长为430nm,反应温度为60℃时控制反应时间为6min,Cu(Ⅱ)在0.10~1.2μg/mL范围内吸光度与Cu(Ⅱ)的浓度呈良好的线性关系,相关系数r为0.9971。方法用于测定冶炼厂电解银废液中铜含量,相对标准偏差为2.49%(n=6),加标回收率在91.6%~99.4%之间。     

Flow-injection analysis of nitrate by reduction to nitrite and gas-phase molecular absorption spectrometry

Two flow-injection manifolds have been investigated for the determination of nitrate. These manifolds are based on the reduction of nitrate to nitrite and determination of nitrite by gas-phase molecular absorption spectrophotometry. Nitrate sample solution (300 microL) which is injected to the flow line, is reduced to nitrite by reaction with hydrazine or passage through the on-line copperized cadmium (Cd-Cu) reduction column. The nitrite produced reacts with a stream of hydrochloric acid and the evolved gases are purged into the stream of O2 carrier gas. The gaseous phase is separated from the liquid phase using a gas-liquid separator and then swept into a flow-through cell which has been positioned in the cell compartment of an UV-visible spectrophotometer. The absorbance of the gaseous phase is measured at 204.7 nm. A linear relationship was obtained between the intensity of absorption signals and concentration of nitrate when Cd-Cu reduction method was used, but a logarithmic relationship was obtained when the hydrazine reduction method was used. By use of the Cd-Cu reduction method, up to 330 microg of nitrate was determined. The limit of detection was 2.97 microg nitrate and the relative standard deviations for the determination of 12.0, 30.0 and 150 microg nitrate were 3.32, 3.87 and 3.6%, respectively. Maximum sampling rate was approximately 30 samples per hour. The Cd-Cu reduction method was applied to the determination of nitrate and the simultaneous determination of nitrate and nitrite in meat products, vegetables, urine, and a water sample.     

Kinetics analysis for non-isothermal decomposition γ-irradiated indium acetate

Kinetics analysis for non-isothermal decomposition of un-irradiated and pre-γ-irradiated anhydrous indium acetate was studied in the temperature range (298–1273 K) in static air using dynamics thermogravimetric techniques. The data were analyzed using various solid state reaction models. Integral method using Coats–Redfern equation was applied in dynamic data analysis. The results showed that the kinetic of non-isothermal (dynamic) decomposition was controlled by phase boundary process. The activation energies for un-irradiated and pre-γ-irradiated anhydrous indium acetate were calculated and evaluated.     

Polymerization kinetics of acrylic bone cements by differential scanning calorimetry

Bone cements are widely used for the fixation of metallic prostheses in orthopaedics and to form replacements for skull defects in neurosurgery. Acrylic bone cements are based on a mixture of methyl methacrylate (MMA) and a fine powder of polymethyl methacrylate (PMMA). The polymerization of the bone cement occurs in contact with the bone and the prosthesis which act as the boundaries of a bulk polymerization reactor. The kinetic behaviour of the bone cement plays a fundamental role for the final performance of the implant. In this paper, the isothermal and non-isothermal polymerization behaviour of a commercial bone cement is described. A simple phenomenological model, accounting for the autoacceleration ffect, for a diffusion controlled termination mechanism and for the reaction between inhibitor and initiator, is proposed. The reaction kinetics is analysed by DSC. DSC data are used for the determination of the rates of polymerization under isothermal and non-isothermal conditions. The experimental data are processed to calculate the parameters of the proposed phenomenological kinetic model. The analytical and numerical details related to the integration of the model are discussed.     

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.