Prout-Tompkins Model Research Articles

Application of Global Kinetic Models to HMX β−δ Transition and Cookoff Processes

The reduction of the number of reactions in kinetic models for both the HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) beta-delta phase transition and thermal cookoff provides an attractive alternative to traditional multi-stage kinetic models due to reduced calibration effort requirements. In this study, we use the LLNL code ALE3D to provide calibrated kinetic parameters for a two-reaction bidirectional beta-delta HMX phase transition model based on Sandia instrumented thermal ignition (SITI) and scaled thermal explosion (STEX) temperature history curves, and a Prout-Tompkins cookoff model based on one-dimensional time to explosion (ODTX) data. Results show that the two-reaction bidirectional beta-delta transition model presented here agrees as well with STEX and SITI temperature history curves as a reversible four-reaction Arrhenius model yet requires an order of magnitude less computational effort. In addition, a single-reaction Prout-Tompkins model calibrated to ODTX data provides better agreement with ODTX data than a traditional multistep Arrhenius model and can contain up to 90% fewer chemistry-limited time steps for low-temperature ODTX simulations. Manual calibration methods for the Prout-Tompkins kinetics provide much better agreement with ODTX experimental data than parameters derived from differential scanning calorimetry (DSC) measurements at atmospheric pressure. The predicted surface temperature at explosion for STEX cookoff simulations is a weak function of the cookoff model used, and a reduction of up to 15% of chemistry-limited time steps can be achieved by neglecting the beta-delta transition for this type of simulation. Finally, the inclusion of the beta-delta transition model in the overall kinetics model can affect the predicted time to explosion by 1% for the traditional multistep Arrhenius approach, and up to 11% using a Prout-Tompkins cookoff model.

Kinetics of isothermal thermooxidative degradation of poly(vinyl chloride)/chlorinated polyethylene blends

The thermooxidative degradation of poly(vinyl chloride)/chlorinated polyethylene blends of different compositions was investigated by means of isothermal thermogravimetry in flowing atmosphere of synthetic air at temperatures 240–270 °C. The main degradation processes are dehydrochlorination of PVC and CPE. For calculation of the apparent activation energy and apparent pre-exponential factor two kinetic methods were used: isoconversional method and Prout–Tompkins method. True compensation dependency between Arrhenius parameters, obtained using Prout–Tompkins model, was found. Calculated kinetic parameters of isothermal thermooxidative degradation are close to those from non-isothermal degradation and confirm the assumption of the main degradation process in PVC/CPE blends.

Competition between kinetic models in thermal decomposition: analysis by artificial neural network

A new approach, based on neural networks, was developed to describe thermal decomposition process. In this method the activation function for the neurons in the hidden layer are substituted by kinetic models functions. Within this framework it was possible to measure the individual importance of the models under consideration. The rhodium (II) acetate system was used as a prototype to test the efficiency of the neural network. Four models, the Prout–Tompkins model and the Avrami–Erofeev model with m=2, 3 and 4, were selected in a preliminary least square analysis. This will provide the present neural network architecture with an important chemical aspect. The competition between models was possible to be quantified by the weights in the output layer. Although this thermal decomposition process was, in general, dominated by the Prout–Tompkins model, other models were also important to correctly describe the mechanism. The accuracy of the computed values of decomposition fraction is shown to be greater when compared with the models separately. The present method is of general applicability proposing an alternative efficient way to describe solid thermal decomposition data.

Some remarks on the use of isothermal thermogravimetric data for the evaluation of kinetic parameters. Applications for degradation of polymeric materials

AbstractA critical analysis of the isoconversional methods for evaluating kinetic parameters of decomposition of solids from isothermal thermogravimetric data is presented. An isoconversional integral method to evaluate the activation energy is suggested. This method allows removing the errors due the correction of the degradation time by subtracting the induction period to onset of the main reaction (also including the time required to heat the sample to the temperature at which the isotherm is recorded). This procedure was used to study the degradation of two series of polymeric materials, (a) poly(vinyl chloride)/acrilonitrile–butadiene–styrene (PVC/ABS) blends and (b) poly(vinyl chloride)/chlorinated poly(ethylene) (PVC/CPE) blends. The values obtained for the activation energy are in fairly good agreement with those obtained from the Prout–Tompkins model in case (a) and from nonisothermal data in case (b). © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 355–360, 2003

Kinetic analysis of the thermo-oxidative degradation of poly(vinyl chloride) in poly(vinyl chloride)/methyl methacrylate-butadiene-styrene blends1 Isothermal degradation

The thermal degradation of poly(vinyl chloride)/poly(methyl methacrylate-butadiene-styrene) (PVC/MBS) blends was investigated by means of isothermal thermogravimetry in air. During 120 min the main process in the blends is the dehydrochlorination of PVC. The reaction rate constants were determined by applying the Prout–Tompkins model, which assumes autocatalytic degradation. Their values are about three times higher in air than in nitrogen. MBS in such conditions retards the thermo-oxidative dehydrochlorination of PVC in the blends. Applying the Arrhenius equation, apparent activation energies and pre-exponential factors were calculated. Their relationship through compensation effect was discussed and a false compensation effect was found.

Kinetic study of the solid-state photolytic degradation of two polymorphic forms of furosemide

In this paper some aspects influencing the solid-state photolytic degradation of two polymorphic forms of furosemide were investigated. Powder samples of the two polymorphic forms were exposed to prolonged UV irradiation, direct sunlight, in a normal and nitrogen atmosphere. The solid-state photolytic degradation of furosemide followed apparent first-order kinetics as described by a model consisting of nucleation and growth periods with eventual deceleration as it reached a maximum fraction degraded. Kinetic calculations revealed that this bilateral first-order degradation process was best described by a power law dependence ( n = 2) of the fraction decomposed (α) on time ( t) for the nucleation period and first-order kinetic degradation with an asymptote for the growth and deceleration period (Prout-Tompkins model). Overall, the rate constants during the nucleation period were significantly smaller than the growth period. Form I was photochemically more stable than form II, especially under a nitrogen atmosphere ( t 1 2 50 h ). The photolytic degradation of form II was not influenced by the presence of oxygen ( t 1 2 35 h under normal atmospheric conditions and 38 h in a nitrogen atmosphere). After exposure to sunlight 4-chloro-5-sulphamoylanthranilic acid (CSA) was found in significant concentrations in samples taken from both forms I and II. Photolytic degradation of furosemide form II led to the formation of mainly CSA in the presence of nitrogen and CSA and other unidentified products in the presence of oxygen.

Study on the rate of decomposition of amoxicillin in solid state using high-performance liquid chromatography

AbstractAmoxicillin sodium salt degradation in solid state relies on a sequential reaction consisting of two pseudo-first-order processes. Amoxicillin trihydrate, now used in pharmaceutical formulations, is significantly more stable than sodium amoxicillin. It degrades according to Prout-Tompkins model. We studied the stability of amoxicillin at temperatures of 37°, 50°, 80°, 90°, 100° y 110° C. HPLC was chosen as the analytical method. Amoxicillin and its decomposition products are separated by reversed-phase (C18) HPLC with gradient elution.

Influence of chromium on the oxidation kinetics of annealing spinels (Fe 2+Al 3+2− xCr 3+x)O 2−4

The oxidation of annealing spinels (Fe 2+Al 3+ 2− x Cr 3+ x )O 2− 4 in metastable deficient spinels γ-( Fe 3+ 8 9 Al 3+ 8 9 (2−x) Cr 3+ 8x 9 □ 1 3 ) O 2− 4 at temperatures in the range 350–450°C and over the pressure range 50-10 4 Pa has been studied with special emphasis on the effect on chromium content. When particle size is increased by annealing crystals of more than approximately 200 to 500 nm, the kinetic curves are sigmoidal, but only for spinels with high chromium content. Although the kinetic results are well interpreted by the Prout-Tompkins model (E. G. Prout and F. C. Tompkins, Trans. Faraday Soc. 40, 488 (1944)), the morphological observations and the X-ray diffraction data suggest an autocatalytic process.

Isothermal DSC study of the thermal decomposition of potassium permanganate

Potassium permanganate decomposes on heating in two stages. The first stage (−290 °C) is exothermic overall and the second (620 °C) is endothermic. The Prout-Tompkins model is often used to describe the kinetics of the first stage. Isothermal DSC studies show that the first stage of the decomposition does not give the symmetrical exotherm expected for the Prout-Tompkins model, but consists of several overlapping exotherms, as well as a final endothermic contribution when product oxygen is removed by an inert carrier gas. The effects of atmosphere, temperature and particle-size on the DSC curves are reported and electron micrographs reveal some details of the decomposition mechanism.

Isothermal DSC study of the thermal decomposition of potassium permanganate

Potassium permanganate decomposes on heating in two discrete stages. The first stage (∼ 290°C) is exothermic overall and the second (∼ 620°C) is endothermic. Kinetic studies of the first stage of the decomposition in vacuum led to the introduction of the Prout—Tompkins equation (ln(α/(1 − α)) = kt + c) and a mechanism involving branching nuclei to account for this autocatalytic behaviour. Isothermal DSC studies show that the first stage of the decomposition does not give the symmetrical exotherm expected for the Prout—Tompkins model, but consists of several overlapping exotherms, as well as a final endothermic contribution when product oxygen is removed by an inert carrier gas. The effects of atmosphere, temperature and particle size on the DSC curves are reported and discussed in relation to the Prout—Tompkins model. Electron micrographs reveal some details of the decomposition mechanism.