Prout-Tompkins Model Research Articles

Modeling Polystyrene Nanoplastics Degradation in Water via Photo-Fenton Treatment: A Shrinking-Particle Approach

In this study, kinetic models for the photo-Fenton oxidation of polystyrene nanoplastics (NPs) in water were developed, considering particles with decreasing diameters. Various reaction parameters affecting the oxidation rate, such as particle size (140−909nm), agitation speed (250−1000rpm), and operating temperature (25 and 60 °C) were investigated. Oxidation progress was evaluated through turbidity measurements, TEM, and FTIR analysis, while leached intermediates were identified via Pyr-GC-MS and IC. Due to changes in NPs surface reactivity, the overall reaction rate was divided into two stages, following a free-radical mechanism. Using equations derived from the classic Shrinking Core Model, the oxidation of NPs was determined to proceed under chemical reaction control, with negligible mass transfer limitations. Additionally, the Prout-Tompkins model was found to accurately represent the degradation process. The proposed mechanisms and models provide valuable insights for describing and predicting the advanced oxidation of NPs under different operating conditions and treatment methods.

Pyrolysis of natural rubber–cellulose composites: isoconversional kinetic analysis based on thermogravimetric data

Despite the current growing interest in rubber composites with natural organic fillers, there is a lack of kinetic analyses that describe the decomposition of these materials during pyrolysis. For this reason, the main objective of this study was the kinetic analysis and determination of formal kinetic parameters for the pyrolytic decomposition of NR–CEL composites with different cellulose content (0, 30, 45, and 55 phr). Thermogravimetric measurements were made at heating rates of 2, 4, 6, 8, 10, and 20 °C min–1 in the temperature range of 20–600 °C. First, Friedman and KAS model-free methods were applied. Therefore, model-based methods and the model-fitting procedure were used to find the optimal multi-step kinetic model. The proposed final model consists of two parallel processes, which are kinetically independent: A → B → C and D → E → F. For each step, a kinetic triplet was calculated: the apparent activation energy, the pre-exponential factor, and the kinetic parameters of the extended empirical Prout–Tompkins model. The master plots method was used to determine the kinetic decomposition mechanism of the individual steps. It was found that step A → B has the shape of an nth-order model, step B → C mainly follows the diffusion model, the mechanism of step D → E transfers from a random scission kinetics model to an nth-order model with an increasing amount of CEL, and step E → F obeys the chain scission mechanism.

Development of a new approach for the kinetic modeling of the lithium reactive hydride composite (Li-RHC) for hydrogen storage under desorption conditions

Among some promising candidates for high-capacity energy and hydrogen storage is the Lithium-Boron Reactive Hydride Composite System (Li-RHC: 2 LiH + MgB2/2 LiBH4 + MgH2). This system desorbs hydrogen only at relatively high temperatures and presents a two-step series of reactions occurring in different time scales: first, MgH2 desorbs, followed by LiBH4. Hitherto, the dehydrogenation kinetic behavior of such a system has been described for different temperatures at specific values of operative pressure. However, a comprehensive model representing its dehydrogenation kinetic behavior under different operative conditions has not yet been developed. Herein, the separable variable method is applied to develop a comprehensive kinetic model, including the two-step dehydrogenation series reaction. The MgH2 decomposition is described with the one-dimensional interface-controlled reaction rate Johnson-Mehl-Avrami-Erofeyev-Kholmogorov (JMAEK) with a (Pequilibrium/Poperative) pressure functionality and an Arrhenius temperature dependence activation energy of 63 ± 3 kJ/mol H2. The LiBH4 decomposition is modeled applying the autocatalytic Prout-Tompkins model. A novel approach to describe the Prout-Tompkins t0 parameter as a function of the operative temperature and pressure model is proposed. This second reaction step presented a (Pequilibrium – Poperative/Pequilibrium)2 pressure dependence and an Arrhenius temperature dependence with activation energy 94 ± 13 kJ/mol H2. The proposed approach is experimentally and computationally validated, successfully describing the decomposition kinetic behavior of MgH2 and LiBH4 under three-phase gas, liquid and solid environment and shows good agreement between experimental and modeled curves.

The Prediction of CMDB Propellant lifetime Based on Arrhenius accelerated model, Berthelot’s equation and Multi-step Prout-Tompkins Model

Different models were provided to predict the storage lifetime of propellants more accurately. The stabilizer was recognized as a vital parameter for double based propellants’ storage lifetime estimation. The stabilizer contents of a certain RDX-CMDB propellant were traced during the accelerated aging tests. Based on that, the safe storage lifetime of this propellant were predicted using the Berthelot’s equation, Arrhenius accelerated equation and the advanced kinetic model, respectively. The predicted results were compared and the causes were analysed. It found that the biggest disadvantage of Berthelot’s equation and Arrhenius accelerated equation is that the predicted results are significantly affected by the original data. In details, the minor difference of original data will bring tremendous errors when extrapolating to normal temperature. The general model which can be used to depict complex reactions adopted in AKTS software was preferred compared to reaction order (RO) model and Prout-Tompkins (PT) model.

A study of ofloxacin and levofloxacin photostability in aqueous solutions

Introduction. The photostability is one of the most important properties of drugs. A comprehensive study of ofloxacin (OFX) and levofloxacin (LVX) photostability in aqueous solutions was performed. Ofloxacin is a chemotherapeutic agent belonging to the second generation fluoroquinolones and is a racemate of (R)-(+)-ofloxacin and (S)-(-)-ofloxacin (LVX).Material and Methods. Samples of OFX and LVX were subjected to stress conditions of UV irradiation using a mercury-vapor lamp. The study involved development of enantioselective high-performance liquid chromatography (HPLC) and high-performance capillary electrophoresis (HPCE) methods for separation of OFX enantiomers and their degradation products. These methods were used to monitor the degradation process of OFX and LVX under irradiation and to determine the kinetics of degradation of these antibacterial agents. Moreover, the identification of photoproducts was also attempted. The structure of the main photoproducts was examined by mass spectrometry (MS).Results and Conclusions. Using HPLC method it was possible to observe two products of OFX degradation and only one for LVX, while using HPCE method eight products of OFX degradation and six of LVX were observed. Some of the photoproducts retain character of optically active compounds. The trend of the photodegradation of both tested compounds was described by autocatalytic reaction proceeding according to the Prout-Tompkins model. Some of the products of the decomposition catalyze this reaction. The rate of degradation was similar for both enantiomers but t0.5 was slightly longer for LVX than OFX. Based on MS experiments the photodegradation products of the studied fluoroquinolones and possible pathways of UV induced decay were identified.

Production of the Spherical Nano-Al/AP Composites by Drowning-Out/Agglomeration and Their Solid-Reaction Kinetics

Spherical nano-Al/AP composites were produced by a drowning-out/agglomeration (D/A) process and characterized as a function of the amount of bridging liquid, agitation rate, agitation time, and time interval. Experimental data showed that the amount of bridging liquid plays an important role in agglomeration because it affects directly the content of wetted particles leading to the coalescence between them. Agitation rate and agitation time were found to have optimal points above which the agglomerates begin to collapse. In particular, an increasing number of injection time intervals of bridging liquid turned out to promote further growth of agglomerates. Thermogravimetric curves showed that decomposition of AP could be well described by the Prout–Tompkins model and the geometrical contraction model at low- and high-temperature area, respectively. Furthermore, the nano-Al/AP composites by the D/A process clearly revealed that thermal stability of AP is enhanced and the decomposition rate is increased at h...

Reduction and oxidation kinetic modeling of NiO-based oxygen transfer materials

Abstract This study investigates the redox kinetics of four NiO-based oxygen transfer materials (OTMs) supported on Al 2 O 3 , TiO 2 , SiO 2 and ZrO 2 . The OTMs were tested and evaluated under twenty consecutive methane reduction/air oxidation cycles. Several solid-state kinetic models were consecutively and optimally screened for each OTM at different redox cycles. The use of different supports resulted in different forms of the redox kinetics. NiO/Al 2 O 3 and NiO/TiO 2 reduction kinetics were rate-determined by chemical reaction and fitted via the Unreacted Shrinking Core Model. On the other hand, NiO/ZrO 2 and NiO/SiO 2 reduction was found to proceed via nucleation and subsequent nuclei growth and was suitably described with Avrami-Erofeev models. The use of different types of kinetic models is attributed to differences in strength of metal-support interactions. Specifically, the strong interaction between NiO and Al 2 O 3 and TiO 2 creates NiO-support interfaces where Ni nuclei are formed very fast, rendering the chemical reaction the governing step of the reduction process. When NiO is supported on SiO 2 and ZrO 2 , the interaction is weak and NiO basically behaves like free NiO, reducing via the slow formation of homogeneous nuclei on the surface and the subsequent faster growth of Ni domains. Regarding Ni oxidation kinetics, all OTMs were rate-determined by nucleation and nuclei growth. NiO/Al 2 O 3 and NiO/TiO 2 OTMs followed an Avrami-Erofeev model approach for all considered cycles, while NiO/ZrO 2 oxidation kinetics were described via a Prout-Tompkins model that considered a short but still, significant nucleation period.

Use and misuse of logistic equations for modeling chemical kinetics

A generalized logistic function has been proposed as a kinetic analysis method that is superior to traditional methods. In fact, the parameter τ in the generalized logistic function has an effect on the reaction profile similar to the parameter n in the extended Prout–Tompkins model for autocatalytic reactions. Furthermore, the comparisons made in some papers to traditional methods were made by using the discredited method of determining kinetic parameters from a single heating rate, so they are misleading compared to proper kinetic analysis methods that simultaneously analyze multiple thermal histories. In addition, the current implementation of the generalized logistic function of fitting each experiment individually is prone to introduce errors in the kinetic parameters. Guidance is given on how the generalized logistic function might be used for proper chemical kinetic analysis.

Thermal degradation studies of poly(urethane–siloxane) thermosets based on co-poly(dimethyl)(methyl, hydroxypolyoxyethylenepropyl) siloxane

• The thermal decomposition of the poly(urethane–siloxane) thermosets based on siloxane was investigated. • The TGA–FTIR of evolved gases during degradation were performed. • The thermal degradation kinetic parameters were determined. • The possible degradation model f(α) was proposed. A series of crosslinked hybrid poly(urethane–siloxane) networks based on comb-like structure co-poly(dimethyl)(methyl, hydroxypolyoxyethylenepropyl) siloxane cured with aliphatic diicocyanates hexamethylene diisocyanate (HDI), isophorone diisocyanate (IPDI), and 4,4′-methylenebis(cyclohexyl isocyanate) (H 12 MDI), were obtained. The samples have been submitted to thermal stability investigations at non-isothermal conditions in nitrogen and air. The thermal degradation behavior was investigated by evolved gas analysis, using coupled TG–FTIR technique. The kinetic parameters of the degradation process were determined both by isoconversional methods of Friedman and Ozawa–Flynn–Wall as well as by model fitting multivariate non-linear regression method. It was observed that the thermal stability of the poly(urethane–siloxane) thermosets depends on employed diisocyanate. The best fit of the f ( α ) function with the experimental data was found for two-step degradation mechanism. Successive stages of thermal decomposition occurred by diffusion and by the expanded Prout–Tompkins model, respectively.

The effect of pre-heating on the kinetics of the thermal decomposition of pure and chloride and phosphate doped sodium oxalate

The effect of pre-heating on the kinetics of the thermal decomposition of pure and chloride and phosphate doped sodium oxalate has been studied, as a function of the time of pre-heating, at a temperatures of 783K under isothermal conditions by thermogravimetry (TG). The model fitting analysis of the TG data shows that no single kinetic model describes the whole α versus t curve with a single rate constant throughout the decomposition reaction; Prout–Tompkins model best describes the acceleratory stage of the decomposition while the decay region is best fitted with the contracting cylinder model. The rates of both stages were decreased by pre-heating for 24–36h and then remained constant. Pre-heating of sodium oxalate resulted in a significant decrease in the rate of thermal decomposition and the general nature of the effects of dopants remains unaffected in both stages of the thermal decomposition reaction.

Effect of pre-compression on the kinetics of thermal decomposition of pure and doped sodium oxalate under isothermal conditions

Pure and doped samples of sodium oxalate (Na2C2O4) were subjected to pre-compression and their thermal decomposition kinetics was studied at five different temperatures in the range 783–803 K under isothermal conditions by thermogravimetry. The pre-compressed samples decomposed in two stages governed by different rate laws; the Prout–Tompkins model best describes the acceleratory stage of the decomposition while the decay region is best fitted with the contracting cylinder model as in the case of uncompressed sodium oxalate samples. The rate constants k1 and k2 of the acceleratory and deceleratory stages of the thermal decomposition were dramatically decreased on pre-compression. However, the activation energies, evaluated by model fitting kinetic method, E1 and E2 for the respective stages of decomposition remained unaltered by pre-compression. The results favor ionic diffusion mechanism proposed earlier on the basis of doping studies.

Effect of chloride dopant on the kinetics of the thermal decomposition of sodium oxalate

The thermal decomposition kinetics of sodium oxalate (Na2C2O4) has been studied as a function of concentration of dopant, chloride, at five different temperatures in the range 783–803 K under isothermal conditions by thermogravimetry (TG). The TG data were subjected to both model free and model fitting methods of kinetic analysis. The results obtained from model fitting methods of kinetic analysis shows that no single kinetic model describes the whole α versus t curve with a single rate constant throughout the decomposition reaction. Separate kinetic analysis shows that Prout–Tompkins model best describes the acceleratory stage of the decomposition while the decay region is best fitted with the contracting cylinder model, and corresponding activation energy values were evaluated. The diffusion of Na+ ions occupying normal lattice sites and interstitial sites was greatly affected by a change in the concentration of defects.

Kinetic studies on the thermal decomposition of aluminium doped sodium oxalate under isothermal conditions

The kinetics of thermal decomposition of sodium oxalate (Na2C2O4) has been studied as a function of concentration of dopant, aluminium, at five different temperatures in the range 783–803K under isothermal conditions by thermogravimetry (TG). The TG data were subjected to both model fitting and model free kinetic methods of analysis. The model fitting analysis of the TG data shows that no single kinetic model describes the whole α versus t curve with a single rate constant throughout the decomposition reaction. Separate kinetic analysis shows that Prout–Tompkins model best describes the acceleratory stage of the decomposition while the decay region is best fitted with the contracting cylinder model. Activation energy values were evaluated by model fitting and model free kinetic methods for both stages of decomposition. As proposed earlier the results favours a diffusion controlled mechanism for the isothermal decomposition of sodium oxalate.

Kinetic studies on the thermal decomposition of phosphate-doped sodium oxalate

The thermal decomposition kinetics of sodium oxalate (Na2C2O4) has been studied as a function of concentration of dopant, phosphate, at five different temperatures in the range 783–803 K under isothermal conditions by thermogravimetry (TG). The TG data were subjected to both model-fitting and model-free kinetic methods of analysis. The model-fitting analysis of the TG data of all the samples shows that no single kinetic model describes the whole α versus t curve with a single rate constant throughout the decomposition reaction. Separate kinetic analysis shows that Prout–Tompkins model best describes the acceleratory stage of the decomposition, while the decay region is best fitted with the contracting cylinder model. Activation energy values were evaluated by both model-fitting and model-free kinetic methods. The observed results favour a diffusion-controlled mechanism for the thermal decomposition of sodium oxalate.

Modeling of Autocatalytic Hydrolysis of Adefovir Dipivoxil in Solid Formulations

The stability and hydrolysis kinetics of a phosphate prodrug, adefovir dipivoxil, in solid formulations were studied. The stability relationship between five solid formulations was explored. An autocatalytic mechanism for hydrolysis could be proposed according to the kinetic behavior which fits the Prout-Tompkins model well. For the classical kinetic models could hardly describe and predict the hydrolysis kinetics of adefovir dipivoxil in solid formulations accurately when the temperature is high, a feedforward multilayer perceptron (MLP) neural network was constructed to model the hydrolysis kinetics. The build-in approaches in Weka, such as lazy classifiers and rule-based learners (IBk, KStar, DecisionTable and M5Rules), were used to verify the performance of MLP. The predictability of the models was evaluated by 10-fold cross-validation and an external test set. It reveals that MLP should be of general applicability proposing an alternative efficient way to model and predict autocatalytic hydrolysis kinetics for phosphate prodrugs.

Effects of dopants on the isothermal decomposition kinetics of potassium metaperiodate

The isothermal decomposition and kinetics of potassium metaperiodate (KIO4) were studied by thermogravimetry as a function of the concentration of dopants. The thermal decomposition of KIO4 proceeds mainly through two stages: an acceleration period up to ? = 0.50 and a decay stage. The thermal decomposition data for both doped and untreated KIO4 were found to be best described by the Prout-Tompkins Equation. The ? - t data of doped and untreated samples of KIO4 were subjected to isoconversional studies for the determination of the activation energy values. The isoconversional studies of the isothermal decomposition of untreated and doped samples of KIO4 indicated that the thermal decomposition of KIO4 proceeds through a single kinetic model, the Prout-Tompkins model, throughout the entire range of conversion, as opposed to earlier observations.

A different approach for the study of the crystallization kinetics in polymers. Key study: poly(ethylene terephthalate)/ SiO2 nanocomposites

Polymer crystallization is complex and difficult to model, especially when it is non-isothermal and even more so when describing cold crystallization. In most cases, two different processes occur, so-called primary and secondary crystallization. In the literature, two assumptions are generally made. Firstly, the validity of the Avrami model is assumed a priori. Secondly, for calculations of the kinetic parameters and activation energy, data from a single differential scanning calorimetry scan at a given heating rate are used. The other popular model, that of Ozawa, is also based on similar assumptions. In the study reported here, a different approach was adopted, which uses multiple scans at various heating rates simultaneously. Here the experimental data of the non-isothermal cold crystallization of an in situ-prepared poly(ethylene terephthalate)/1% SiO2 nanocomposite were used. Data were analysed following both the ordinary procedure and the method proposed in this work. Findings showed that when the Avrami model is a priori supposed to hold and the data of different heating rates are analysed separately, results are not acceptable. The new approach involves calculation of the activation energy through use of the isoconversional methods of Ozawa–Flynn–Wall and Friedman over the whole range of the crystallization conversion. The reaction model f(a) was determined after the evaluation of 16 different models. The best fitting was achieved for the Prout–Tompkins model or for a mechanism involving two steps described by respective Avrami equations with different activation energies. Copyright © 2010 Society of Chemical Industry

Effect of pre-treatments on isothermal decomposition kinetics of potassium metaperiodate

The effect of pre-compression, pre-heating and particle size on the thermal decomposition kinetics of potassium metaperiodate (KIO 4) to potassium iodate (KIO 3) has been investigated by thermogravimetric analysis under isothermal conditions. Although the effect of pre-compression was negligible up to an applied pressure of 5 × 10 3 kg cm −2, the rate increased drastically on a further increase in pressure. Results of pre-heating indicate that gross imperfections are not as easily annealed as point defects. Studies on the effect of particle size emphasize the need for fixing the particle size to enable a meaningful interpretation of the effects of pre-treatment on solid-state reactions. The rate law (Prout–Tompkins model) as well as the mechanism (electron-transfer) for the decomposition of KIO 4 remained unaffected by these pre-treatments. The α– t data of uncompressed and compressed samples of pure KIO 4 were also subjected to isoconversional studies for the determination of activation energy values.

Determination of factors affecting kinetics of solid-state transformation of fluconazole polymorph II to polymorph I using diffuse reflectance Fourier transform spectroscopy

Background: It was of interest to investigate the factors affecting kinetics of transformation of fluconazole polymorph II (the metastable form) to fluconazole polymorph I (the stable form) using diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). Method: Fluconazole polymorphs I and II both were prepared by crystallization in dichloromethane. The two forms were characterized using differential scanning calorimetry, thermogravimetric analysis, powder X-ray diffraction, solubility, and DRIFTS. Transformation of polymorph II to polymorph I was also studied under different isothermal temperatures using DRIFTS. Kinetic analyses of the data were done using model-dependent and model-independent methods. Eighteen solid-state reaction models were used to interpret the experimental results. Results: Based on statistics, the Prout–Tompkins model provided the best fit for the transformation. The activation energy (Ea) value derived from the rate constants of the Prout–Tompkins model was 329 kJ/mol. Model-independent analysis was also applied to the experimental results. The average values calculated using both methods were not significantly different. Factors affecting kinetics of transformation such as mechanical factors, relative humidity, and the effect of seeding were also studied. Mechanical factors, which included trituration and compression, proved to enhance transformation rate significantly. Relative humidity proved to transform both polymorphs to monohydrate form. The presence of seed crystals of polymorph I was proved not to affect the transformation process of polymorph II to polymorph I. Effect of solvent of crystallization (dichloromethane) was studied. A significant change of the rate of transformation was proved in the presence of solvent vapors, and a change on the mechanism was proposed.

Effect of metal oxide additives on the thermal decomposition kinetics of potassium metaperiodate

Abstract The effect of additives (CuO, MnO2 and TiO2) on the thermal decomposition kinetics of potassium metaperiodate (KIO4) to potassium iodate (KIO3) has been studied in air by thermogravimetry under isothermal conditions. Irrespective of whether p- or n-type, the metal oxides show only a little or no influence on the rate of the decomposition except for the small decrease when the oxide concentration is as high as 10 wt%. The rate law for the decomposition of KIO4 (Prout–Tompkins model) remained unaffected by the additives.