Kinetics study of propyl acetate synthesis reaction catalyzed by Amberlyst 15

The reaction kinetics of esterification of acetic acid with n‐propanol was investigated. The reaction was catalyzed by the commercial cation‐exchange resin Amberlyst 15, and the kinetic data were obtained in a batch reactor within the temperature range 338–368 K. The chemical equilibrium constant, K_eq, was first determined experimentally; the result shows that K_eq is about 20 and slightly temperature dependent. Altogether 14 sets of kinetic data were then measured. The influences of operating parameters such as temperatures, initial molar ratios, and catalyst concentrations were checked. The pseudo‐homogeneous (PH), Rideal–Eley (RE), and Langmuir–Hinshelwood–Hougen–Watson (LHHW) kinetic models were developed to interpret the obtained kinetic data. The parameters of the kinetic models were identified by the software DIVA, and the confidence interval of each parameter was also estimated. Both the chemical equilibrium constant and kinetic models were formulated in terms of the liquid phase activity, which was described by the nonrandom two‐liquid (NRTL) model. The LHHW model gives the best fitting result, followed by the RE model and the PH model, whereas the confidence intervals rank in the reverse order. In addition, an effective solution was proposed to overcome a convergence problem occurring in the LHHW model parameter identification, which has been reported several times in the literature. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 245–253, 2007     

Parameter identification of thermophilic anaerobic degradation of valerate

The considered mathematical model of the decomposition of valerate presents three unknown kinetic parameters, two unknown stoichiometric coefficients, and three unknown initial concentrations for biomass. Applying a structural identifiability study, we concluded that it is necessary to perform simultaneous batch experiments with differenitial conditions for estimating these parameters. Four simultaneous batch experiments were conducted at 55°C, characterized by four different initial acetate concentrations. Product inhibition of valerate degradation by acetate was considered. Practical identification was done optimizing the sum of the multiple determination coefficients for all measured state viariables and for all experiments simultaneously. The estimated values of kinetic parameters and stoichiometric coefficients were characterized by the parameter correlation matrix, the confidence interval, and the student's t-test at 9% significance level with positive results except for the saturation constant, for which more eperiments for improving its identifiability should be conducted. In this article, we discussekinetic parameter estimation methods.     

Kinetic model of poly(3-hydroxybutyrate) thermal degradation from experimental non-isothermal data

The non-isothermal data given by TG curves for poly(3-hydroxybutyrate) (PHB) were studied in order to obtain a consistent kinetic model that better represents the PHB thermal decomposition. Thus, data obtained from the dynamic TG curves were suitably managed in order to obtain the Arrhenius kinetic parameter E according to the isoconversional F-W-O method. Once the E parameters is found, a suitable logA and kinetic model (f(α)) could be calculated. Hence, the kinetic triplet (E±SD, logA±SD and f(α)) obtained for the thermal decomposition of PHB under non-isothermal conditions was E=152±4 kJ mol⁻¹, logA=14.1±0.2 s⁻¹ for the kinetic model, and the autocatalytic model function was: f(α)=α^m(1−α)ⁿ=α^0.42(1−α)^0.56.     

Comparative kinetic study of decomposition of some diazepine derivatives under isothermal and non-isothermal conditions

Thermal analysis is one of the most widely used methods for studying the solid state of pharmaceutical substances. TG/DTG and DSC curves provide important information regarding the physical properties of the pharmaceutical compounds (stability, compatibility, polymorphism, kinetic analysis, phase transitions etc.). The purpose of a kinetic investigation is to calculate the kinetic parameters and the kinetic model for the studied process. The results are further used to predict the system’s behaviour in various circumstances. A kinetic study regarding the diazepam, nitrazepam and oxazepam thermal decomposition was performed, under non-isothermal and isothermal conditions and in a nitrogen atmosphere, for the temperature steps: 483, 498, 523, 538 and 553 K. The TG/DTG data were processed by three methods: isothermal model-fitting, Friedman’s isothermal-isoconversional and Nomen-Sempere non-parametric kinetics. 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 diazepines decomposition. The model-free approach represented by isothermal and non-isothermal isoconversional methods, gave dependences of the activation energies on the extent of conversion. It is very difficult to obtain an accord with the similar data which resulted under non-isothermal conditions from a previous work. The careful treatment of the kinetic parameters obtained in different thermal conditions was confirmed to be necessary, as well as a different strategy of experimental data processing.     

Combined kinetic analysis of solid-state reactions: The integral method (ICKA)

In this work, we propose the first Integral method for the Combined Kinetic Analysis (ICKA) of solid-state reactions typically performed in a thermogravimetric analyzer. The ICKA method prevents the systematic inaccuracies inherent to all the differential methods, including the standard CKA method. Two main achievements have been made for implementing the method: (1) the most accurate approximation for the general temperature integral yet developed, and (2) a general integral form of the kinetic model of the type g (α) = (abcZ)⁻¹ [1 − (1 − α^a)^b]^c, where Z is a parameter evaluated together with the preexponential factor and a, b, and c are fitting parameters. This expression allows any known kinetic model to be exactly or very closely reproduced. Together, the two developments yield an equation for the conversion, α, that has been successfully fitted to simulated conversion values of single-step reaction processes following different kinetic models. The curve fitting resulted in the same values of the kinetic and model parameters as those from which the simulated conversion curves were originally built, proving the validity of the ICKA method.     

The flying ice cube: Velocity rescaling in molecular dynamics leads to violation of energy equipartition

This article describes an unexpected phenomenon encountered during MD simulations: velocity rescaling using standard protocols can systematically change the proportion of total kinetic energy (KE) found in motions associated with the various degrees of freedom. Under these conditions, the simulation violates the principle of equipartition of energy, which requires a mean kinetic energy of RT/2 in each degree of freedom. A particularly pathological form of this problem occurs if one does not periodically remove the net translation of (and rotation about) the center of mass. In this case, almost all of the kinetic energy is converted into these two kinds of motion, producing a system with almost no kinetic energy associated with the internal degrees of freedom. We call this phenomenon “the flying ice cube.” We present a mathematical analysis of a simple diatomic system with two degrees of freedom, to document the origin of the problem. We then present examples from three kinds of MD simulations, one being an in vacuo simulation on a diatomic system, one involving a low resolution model of DNA in vacuo, and the third using a traditional all-atom DNA model with full solvation, periodic boundary conditions, and the particle mesh Ewald method for treating long-range electrostatics. Finally, we discuss methods for avoiding the problem. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 726–740, 1998     

Analytical models for state-specific diatomic dissociation rate coefficients

Two analytical models are presented to approximate the temperature dependent, rotationally-averaged vibrational-state-specific dissociation rate coefficient for collisions between diatomic molecules and rare gas atoms at combustion temperatures. The new models are derived by making simplifying approximations to a more detailed theoretical model recently reported in the literature. For accuracy, the first model requires, for a given collision pair, knowledge of the maximum vibrational quantum number, a single vibrational-rotational energy and an interaction parameter for dissociation, all of which are tabulated in this article for collisions of Ar with p-H₂, O₂, N₂, and CO. This is in contrast to the recently reported theoretical model, which requires knowledge of all vibrational-rotational energies below the dissociation threshold, in addition to the interaction parameter for dissociation. The second model is simpler and more general than the first, but less accurate. To completely specify this model, knowledge of only the hard sphere cross section, and the characteristic temperatures for vibration and dissociation is required. The two analytical models are shown to agree well with the published theoretical values, with the accuracy of each model increasing with increasing temperature. The present models provide an accurate and efficient means of computing thousands or millions of rate coefficients for use in numerical simulations of combustion processes that couple kinetic equations with the governing equations of fluid dynamics. © 1997 John Wiley & Sons, Inc.     

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 On-line Evaluation of Chemical Reactions

A computer program was developed for kinetic evaluations of calorimetric experiments to predict the further reaction run under adiabatic conditions. Kinetic modeling is based on elementary reaction steps whose rate laws form a set of differential equations. For the continuous parameter optimization time-temperature data and their derivatives are used. A special calorimeter of the ACTRON series with safety equipment was applied to investigate the kinetics of chemical reactions and to test kinetic on-line evaluations. In the paper, examples for the reaction of n-propanol with o-chlornitrobenzene and for the alcoholysis of phenyl isocyanate are given.This revised version was published online in November 2005 with corrections to the Cover Date.     

A Novel Kinetic Approach for Photocatalytic Degradation of Azo Dye with CdS and Ag/CdS Nanoparticles Fixed on a Cement Bed in a Continuous‐Flow Photoreactor

Azo dyes are one of the synthetic dyes that have been used in many textile industries. Azo dye and their intermediate products are toxic, carcinogenic, and mutagenic to aquatic life. Removal of azo dyes is one of the main challenges before releasing the wastes discharged by textile industries. Photocatalytic degradation of azo dyes by nanoparticles is one of the environment‐friendly methods used for the removal of dyes from textile effluents. Therefore, this study focused on degradation of azo dye, Direct Red 264. Photocatalytic degradation of DR 264 azo dye was investigated using CdS and Ag/CdS nanoparticles immobilized on a cement bed in a continuous‐flow photoreactor under UV‐C exposure. The effect of the parameters of type and mass of catalyst, temperature, flow rate, dye concentration, and light intensity were evaluated for azo dye removal. Under optimal conditions, photocatalytic degradation of DR 264 azo dye using Ag/CdS nanoparticles immobilized on a cement bed in a continuous‐flow photoreactor obtained an efficiency of 99.99%. A developed kinetic model was proposed based on the intrinsic elementary reactions. The proposed model is in a good agreement with the Langmuir–Hinshelwood (L–H) equation. The pseudo–steady‐state approximation has considered for the concentration of hydroxyl radicals associated with the L–H model under certain conditions and explains consistently the dependence of the apparent kinetic parameter, k_obs (the reaction rate constant), and K_R (the adsorption equilibrium constant) with the light intensity. Based on the model, k_obs for Ag/CdS was greater than the CdS nanoparticles.     

Numerical analysis for characterizing the sorption/desorption of cesium in crushed granite

The reactive mechanism of cesium in crushed granite was demonstrated in this study through a numerical analysis or a model of the results of sorption/desorption kinetic tests. To employ such numerical analysis, this study applied batch kinetic tests with different solid to liquid ratios (1: 20 and 1: 30) for the characterization of sorption/desorption reaction of Cs and the calibration/validation of hypothesized reactive models. Based on the least square errors (LSE) between numerical analysis and results of batch tests, the two-site sorption models, which are corresponding to two decay constants (λ ₁ and λ ₂), might be more adequate than one-site sorption models in characterizing Cs sorption/desorption. Moreover, a two-site Langmuir kinetic model has been found to be capable of appropriately describing Cs sorption/desorption under test conditions.     

The Adsorption Kinetics of Cethyltrimethylammonium Bromide (CTAB) onto Powdered Active Carbon

This study investigates the adsorption kinetics of CTAB (cethyltrimethylammonium bromide), a cationic surfactant, onto PAC from aqueous solution with respect to the initial CTAB concentration at 20C. The pseudo-first-order, second-order kinetic models and intraparticle diffusion model were used to describe the kinetic data and the rate constants were calculated. The rate parameter, k_i, of intraparticle diffusion, the rate parameter, k₂, of the pseudo-second-order and k₁, the rate parameter for the pseudo-first-order mechanism were compared. It was found that the pseudo-second-order adsorption mechanism is predominant and the overall rate of the CTAB adsorption process appears to be controlled by more than one step, namely both the external mass transfer and intraparticle diffusion mechanisms.     

A LFER Kinetic Study of The Reaction of 5‐Substituted Orotic Acids with Diazodiphenylmethane

Linear free energy relationships (LFER) were applied to the kinetic data for the reaction of 5‐substituted orotic acids, series 1 , with diazodiphenylmethane (DDM) in N,N–dimethylformamide and compared with results obtained for 2‐substituted benzoic acids, series 2 . The correlation analysis of the kinetic data with σ substituent parameters was carried out using SSP (single substituent parameter) methods. From the sign and value of proportinality constant ρ, lower sensitivity to the substituent effect was obtained in series 1 , 0.876, than in the series 2 , 1.877. Evaluation of substituent “ortho‐effect” was performed using the Charton model, which includes the steric substituent parameter, and Fujita and Nishioka's model, which describes the total ortho‐effect as contribution of ordinary polar effect, the ortho‐steric and ortho‐polar effects. Results of correlations, obtained by using the Charton model, showed highest contribution of the polar effect, 0.861 vs. 2.101, whereas the steric effect is of lowest significance, 0.117 vs. 0.055, for series 1 and 2 , respectively. Also, a low negative value of coefficient with the steric effect, –0.08, obtained from the Fujita–Nishioka model indicated low steric effect, influencing a decrease of the reaction rate in series 1 . The structural and substituent effects were also studied by using the density functional theory method, and together with kinetic data, it gave a better insight into the influence of the effect of both geometry and substituent on the π?electron density shift induced reactivity of investigated acids.     

Non-isothermal kinetic study on the decomposition of Zn acetate-based sol-gel precursor

The paper presents a non-isothermal kinetic study of the decomposition of Zn acetate-based gel precursors for ZnO thin films, based on the thermogravimetric (TG) data. The evaluation of the dependence of the activation energy (E) on the mass loss (Δm) using the isoconversional methods (Friedman (FR), Flynn-Wall-Ozawa (FWO) and Kissinger-Akahira-Sunose (KAS)) has been presented in a previous paper. It was obtained that the sample dried at 125°C for 8 h exhibits the activation energy independent on the heating rate for the second decomposition step. In this paper the invariant kinetic parameter (IKP) method is used for evaluating the invariant activation parameters, which were used for numerically evaluation of the function of conversion. The value of the invariant activation energy is in a good agreement with those determined by isoconversional methods. In order to determine the kinetic model, IKP method was associated with the criterion of coincidence of the kinetic parameters for all heating rates. Finally, the following kinetic triplet was obtained: E=91.7 (±0.1) kJ mol⁻¹, lnA(s⁻¹)=16.174 (±0.020) and F1 kinetic model.     

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.     

Kinetic parameters determination in non-isothermal conditions for the crystallisation of a silica-soda-lead glass

Two integral isoconversional methods (Flynn–Wall–Ozawa and Kissinger–Akahira–Sunose) and the invariant kinetic parameters method (IKP) were used in order to examine the kinetics of the non-isothermal crystallisation of a silica-soda-lead glass. The objective of the paper is to show the usefulness of the IKP method to determine both the activation parameters and the kinetic model of the investigated process. Thismethod associated with the criterion of coincidence of kinetic parameters for all heating rates and some procedures of the evaluation of the parameter from Johnson–Mehl–Avrami–Erofeev–Kolmogorov (JMAEK) equation led us to the following kinetic triplet: activation energy, E=170.5±2.5 kJ mol^–1 , pre-exponential factor, A=1.178±0.350·10 10 min^–1 and JMAEK model (A _m) m=1.5.     

Features of the initiated oxidation mechanism of n-heptadecane at low concentrations of oxygen

The oxidation of n-heptadecane was studied at various partial pressures of oxygen in an oxygen-argon mixture from 100 to 10% and various initiation rates W _i in the range (1–5)·10⁻⁶ mol L⁻¹ s⁻¹ at 413 K. The kinetic curves of oxygen uptake and hydroperoxide buildup were obtained under the indicated conditions. The observed features of n-heptadecane oxidation at low concentrations of oxygen may qualitatively be explained and quantitatively described if the oxidation scheme takes into account the cross termination of alkyl and peroxyl radicals R · + RO₂ · \underrightarrow k₅ \underrightarrow {k_5 } ROOR along with the square termination of peroxyl radicals. A method for determination of the corresponding kinetic parameter by the dependence of the initial oxidation rate on the partial oxygen pressure was proposed. A method for identification of the key reactions and determination of the kinetic parameters by the kinetics of oxygen uptake at lowered oxygen concentrations was developed. The kinetic model of the process was obtained, which quantitatively describes the kinetic curves of oxygen uptake and hydroperoxide buildup at the initial steps of initiated oxidation of n-heptadecane.     

A relationship between macroradical decay kinetics and α-segmental dynamics in glassy amorphous polymers

For a series of five amorphous polymers with a broad range of T_g values the kinetics of macroradical decay was measured by ESR technique and evaluated by the second-order kinetic model. It was found that the temperature T_tr of the transition between two regions of different reactivity in free radical decay reaction agrees quite well with the temperature parameter T₀ of the Vogel-Fulcher-Tamman-Hesse (VFTH) equation for α-segmental dynamics. This parameter represents the onset of α-segmental mobility in glassy state below T_g. A nontraditional way of the estimation of T₀ values for α-segmental dynamics through study of the macroradical decay in glassy state of amorphous polymers has been suggested. © 1996 John Wiley & Sons, Inc.     

Optimization of the nitroxide‐mediated radical polymerization conditions for styrene and tert‐butyl acrylate in an automated parallel synthesizer

Automated parallel synthesizers provide fast and comparable screening of different polymerization parameters under similar conditions. In addition, these robotic systems eliminate handling errors, which may affect the results of a kinetic experiment more than the effect of an important parameter. The polymerization temperature and N,N‐tert‐butyl‐N‐[1′‐diethylphosphono‐2,2′‐dimethylpropyl]nitroxide concentration were optimized for the homopolymerization of both styrene and tert‐butyl acrylate to improve the control over the polymerization while reasonable polymerization rates were retained. Subsequently, polystyrene and poly(tert‐butyl acrylate) macro initiators were synthesized according to the knowledge obtained from the screening results. These macroinitiators were used for the preparation of block copolymers consisting of styrene and tert‐butyl acrylate. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6202–6213, 2006