The study of decomposition reactions through the exchange of thermal energy

In many decomposition reactions, the reaction velocity can be described as a product of two functions: a temperature dependent part K(T) and the kinetic function f(1 – α), where T designates the temperature and α the fraction of reactant that has decomposed. The physical interpretation of these functions is discussed for both solid and homogeneous systems. A method is described by which f(1 – α) and K(T) can be determined from kinetic data. The mechanism of decomposition can subsequently be identified which should be consistent with the derived kinetic parameters. The method has been applied to analyze the kinetics of the thermal decomposition of nitromethane. © 1994 John Wiley & Sons, Inc.     

Analysis of dynamic kinetic data from solid-state reactions

The kinetics of heterogeneous reactions, involving one reactant in the solid phase, usually follow the lawα=K _∞ exp(?E/kT)f(1?α), where α is the degree of conversion of the solid, andK _∞ andE are the kinetic constants. A critical examination is given of the various methods which are currently used to analyse dynamic experimental data. The limitations of these methods and their insensitivity to the form off(1-α) are pointed out. An alternative approach free from these limitations is suggested. In this,f(1?α) is determined from isothermal experiments, and then the dynamic data are accurately analyzed to obtain the values of the kinetic constants. A case study is given to elucidate the applicability of the approach.     

Hydrothermal synthesis and characterization of (Na,K)Ti2(PO4)3 solid solutions

Na_1?x K_xTi₂(PO₄)₃ (0 ≤ x ≤ 1) solid solutions are synthesized through ion exchange under hydrothermal conditions and a sol-gel process. The unit cell parameters are calculated for (Na,K) titanium phosphates. Cation-exchange reactions in the NaTi₂(PO₄)₃-KTi₂(PO₄)₃-NaCl-KCl-H₂O system are studied at T = 973 K and p = 200 MPa. The solid phase with compositions in the range 0 ≤ x ≤ 0.7 is enriched with sodium; in the range 0.7 ≤ x ≤ 1.0, it is enriched with potassium. The excess functions of mixing for the solid solutions are described in terms of the Margules model. Titanium phosphates Na_1?x K_xTi₂(PO₄)₃ show greater nonideality than zirconium phosphates Na_1?x K_xZr₂(PO₄)₃ and lower thermodynamic stability in decay into pure components at high pressures and temperatures.     

Simulation of the curing process of an unsaturated polyester resin in adiabatic conditions

The exothermal process of curing of thermoset resins in adiabatic conditions cannot be monitored by differential thermal analysis techniques such as DSC. Starting from the specific reaction rate, heat capacity as function of the temperature and the heat of reaction at some reference temperature, it is possible to design any adiabatic operation. In this paper we apply the energy balance to the curing process in adiabatic conditions and solve the basic rate law for the two empirical kinetic functionsf(α) usually used:n ^th-order kinetics [f(α)=(1?α)ⁿ], and autocatalytic kinetics [f(α)=α^m(1?α)ⁿ], where α is the degree of conversion andn andm the reaction orders, in order to obtain the heat generation curve (dH/dt) as a function of time, as well as the change of temperature with time, the explosion time, the maximum adiabatic temperature and the rate of reaction as a function of the degree of conversion.     

Researches on Thermal Decomposition Kinetics of Composite Modified Double-base Propellants

The thermal decomposition kinetics of composite modified double‐base (CMDB) propellants with a series of contents of hexogeon (RDX) was investigated by using parameters of T_eo, T_i, T_p, T_f, T_b, T_a, E, lg A and ΔH, which were obtained from using a CDR‐4P differential scanning calorimeter (DSC) and Perkin‐Elmer Pyris 1 thermogravimetric analyzer (TG) analyses with heating rates of 5, 10, 15 and 20 K/min. Reliable activation energy was calculated using Flynn‐Wall‐Ozawa method before analyzing the thermal decomposition mechanism. TG‐DTG curves were treated with Malek method in order to obtain the reaction mechanisms. The obtained results show that the thermal decomposition mechanisms with the conversion from 0.2 to 0.4 was f(α)?1/2α, and with the conversion from 0.5 to 0.7 was f(α)?(1/4)(1?α)[?ln(1?α)]^?3.     

Analysis of (NH4)6Mo7O24·4H2O thermal decomposition in argon

Nanometric carbides of transition metals and silicon are obtained by using precursors. Control of the course of these processes require data concerning transformations of single precursor, transformations of precursor in the presence of reducing agent and synthesis of the carbide. In this work, the way of investigating such processes is described on the example of thermal decomposition of (NH₄)₆Mo₇O₂₄·4H₂O (precursor) in argon. The measurements were carried out by TG–DSC method. The solid products were identified by XRD method, and the gaseous products were determined by mass spectrometry method. There was demonstrated that the investigated process proceeded in five stages. Kinetic models (forms of f(α) and g(α) function) most consistent with experimental data and coefficients of Arrhenius equation A and E were determined for the stages. The Kissinger method and the Coats–Redfern equation were applied. In case of the Coats–Redfern equation, the calculations were performed by analogue method. In this way good consistency between the calculated and determined conversion degrees α(T) at practically constant values of A and E were obtained for distinguished stages and different sample heating rates.     

Application of the ISM EoS for polymer melts

A method for predicting an analytical equation of state for polymer melts from surface tension and liquid state density at the freezing temperature (γ_f,ρ_f), as scaling constants, is presented. B₂(T) follows a promising corresponding-states principle. Calculation of α(T) and b(T), the two other temperature-dependent constants of the equation of state, are made possible by scaling. As a result, γ_f and ρ_f are sufficient for the calculation of thermophysical properties of polymer melts. We applied the procedure to predict specific volumes of polyethylene glycol (PEG), polypropylene glycol (PPG), polypropylene (PP) and polyvinylchloride (PVC) at compressed state with temperature range from 298.15 to 423.15 K and pressures up to 200 MPa. The experimental specific volumes were correlated satisfactorily with our procedure and the results are within 3%.     

Simultaneous determination of the activation energy and the reaction kinetic model from the analysis of a single curve obtained by a novel method

It has been demonstrated that a single plot of the values of Δlnα^1/2/Δln(1-α) (taken from a single α?T curve obtained under a controlled linear increase of the reaction rate) as a function of the corresponding values of Δ(1/T)/Δln(1?α) permits the simultaneous determination of both the activation energy and the kinetic model in accordance with a solid state reaction.     

Study on thermal decomposition and oxidation kinetics of cation exchange resins using non-isothermal TG analysis

Kinetics of two successive thermal decomposition reaction steps of cationic ion exchange resins and oxidation of the first thermal decomposition residue were investigated using a non-isothermal thermogravimetric analysis. Reaction mechanisms and kinetic parameters for three different reaction steps, which were identified from a FTIR gas analysis, were established from an analysis of TG analysis data using an isoconversional method and a master-plot method. Primary thermal dissociation of SO₃H⁺ from divinylbenzene copolymer was well described by an Avrami–Erofeev type reaction (n = 2, g(α) = [?ln(1 ? α)]^1/2]), and its activation energy was determined to be 46.8 ± 2.8 kJ mol^?1. Thermal decomposition of remaining polymeric materials at temperatures above 400 °C was described by one-dimensional diffusion (g(α) = α ²), and its activation energy was determined to be 49.1 ± 3.1 kJ mol^?1. The oxidation of remaining polymeric materials after thermal dissociation of SO₃H⁺ was described by a phase boundary reaction (contracting volume, g(α) = 1?(1 ? α)^1/3). The activation energy and the order of oxygen power dependency were determined to be 101.3 ± 13.4 and 1.05 ± 0.17 kJ mol^?1, respectively.     

Thermodynamic Studies on NdFeO3(s)

The enthalpy increments and the standard molar Gibbs energy of formation of NdFeO₃(s) have been measured using a high-temperature Calvet microcalorimeter and a solid oxide galvanic cell, respectively. A λ-type transition, related to magnetic order-disorder transformation (antiferromagnetic to paramagnetic), is apparent from the heat capacity data at ∼687 K. Enthalpy increments, except in the vicinity of transition, can be represented by a polynomial expression: {H°_m(T)−H°_m(298.15 K)}/J·mol⁻¹ (±0.7%)=−53625.6+146.0(T/K) +1.150×10⁻⁴(T/K)² +3.007×10⁶(T/K)⁻¹; (298.15≤T/K ≤1000). The heat capacity, the first differential of {H°_m(T)−H°_m(298.15 K)} with respect to temperature, is given by C^o_{p, m}/J·K⁻¹·mol⁻¹=146.0+2.30×10⁻⁴(T/K)−3.007×10⁶(T/K)⁻². The reversible emf's of the cell, (−) Pt/{NdFeO₃(s) +Nd₂O₃(s)+Fe(s)}//YDT/CSZ//{Fe(s)‘FeO’(s)}/Pt(+), were measured in the temperature range from 1004 to 1208 K. It can be represented within experimental error by a linear equation: E/V:(0.1418±0.0003)−(3.890±0.023)×10⁻⁵(T/K). The Gibbs energy of formation of solid NdFeO₃ calculated by the least-squares regression analysis of the data obtained in the present study, and data for Fe_0.95O and Nd₂O₃ from the literature, is given by Δ_fG°_m(NdFeO₃, s)/kJ·mol⁻¹(±2.0)=−1345.9+0.2542(T/K); (1000≤T/K ≤1650). The error in Δ_fG°_m(NdFeO₃, s, T) includes the standard deviation in emf and the uncertainty in the data taken from the literature. Values of Δ_fH°_m(NdFeO₃, s, 298.15 K) and S°_m(NdFeO₃, s, 298.15 K) calculated by the second law method are −1362.5 (±6) kJ·mol⁻¹ and 123.9 (±2.5) J·K⁻¹·mol⁻¹, respectively. Based on the thermodynamic information, an oxygen potential diagram for the system Nd-Fe-O was developed at 1350 K.     

P–V–T properties of polymer melts based on equation of state and neural network

An accurate and efficient analytical equation of state (EOS) and artificial neural network (ANN) methods are developed for the prediction of volumetric properties of polymer melts. To apply EOS, the second virial coefficients B₂(T), effective van der Waals co-volume, b(T) and correction factor, α(T) were determined. The second virial coefficient was calculated from a two-parameter corresponding states correlation, which is constructed with two constants as scaling parameters, i.e., temperature (T_f) and density at melting (ρ_f) point. The new correlations were used to predict the specific volumes of polypropylene glycol (PPG), polyethylene glycol (PEG), polypropylene (PP), polyvinylchloride (PVC), poly(1-butene)(PB1), poly (?-caprolactone) (PCL), polyethylene (PE) and polyvinylmethylether (PVME) at compressed state in the temperature range of 298.15–634.6 K. The obtained results show that the two models have good agreement with the experimental data with absolute average deviation of 0.28% and 0.39% for ANN and EOS, respectively. The Comparison of the results with ISM model shows that the proposed models represent an efficient method and are more accurate.     

Kinetic data from DTA measurements

The theory of Borchardt and Daniels for the determination from the DTA curve of the fraction decomposed (α) is used. The probable mechanism, activation energy (E) and frequency factor (Z) can be found by the trial and error method from the plot ofα vs.T for a decomposition reaction which can be expressed by the equation $$\log g(\alpha ) = \log p(E/RT) + \frac{{ZE}}{{Rq}}$$ The use of tables of log g(α) for different mechanisms, and plots of the function logp(E/RT _α) vs. temperature for different activation energies is described. The influence is shown of the mechanism of the process, activation energy, frequency factor and heating rate (q) on the shape of the DTA curve. The kinetic data for the decomposition of several solids obtained by the described method are in good agreement with those obtained from literature sources.     

Application of the modified van der waals equation for unsaturated vapour and liquid states

The Law-Lielmezs (L-L) modification of the Van der Waals equation of state: P = RT/(V-b)-a(T)/V² where: a(T) = a(T_c)·a(T_c·a(T¹) and: a(T¹) = 1 + pT^1q has been extended to include unsaturated states in terms of a correcting function C_f(such that the α(T¹) term becomes: a(T¹) = 1 + _pC_fT^1q The proposed extension has been compared with the results obtained by the use of the original Van der Waals equation of state.     

Reevaluation of neutron flux characterization parameters for NIST RT-2 facility

It has been difficult to characterize the thermal to epithermal neutron flux ratio (f) and the measure of the nonideal epithermal neutron flux distribution (α) for the RT-2 pneumatic rabbit facility at the NIST National Bureau of Standards Reactor (NBSR). In a previous paper, only cadmium-covered irradiations yielded physically reasonable parameters. New measurements were performed using chromium, manganese, cobalt, zinc, zirconium, molybdenum, antimony, gadolinium, lutetium, and gold. The neutron temperature (T _n ) in RT-2 measured using bare lutetium and gold foils gave unphysical values. The bare foil methods for measuring f and α gave inconsistent results. The underlying reasons are demonstrated via MCNP simulation results for cumulative reaction rates of selected isotopes. To determine expected intervals for f, α and T, parametric methods were explored. Measured reaction rate probability per target atom (R _p ) values for the listed elements were fitted to a modified Westcott curve using an iterative least-squares method to verify consistency of measurements and nuclear data. An advanced parametric approach using a detailed MCNP model of the NBSR was used to calculate neutron flux characterization parameters.     

Kinetic model of the evaporation process of benzylbutyl phthalate from plasticized poly(vinyl chloride)

The kinetic model of the physical process of evaporation of plasticizer from plasticized PVC foils was developed from the results of isothermal thermogravimetric investigation of evaporation of benzyl-butyl phthalate in the temperature range 120-150 °C under nitrogen flow. The kinetic parameters were estimated by integral method of analysis. Mathematical modeling of the kinetic of plasticizers evaporation was performed on the basis of function c=f(T,t) and kinetic equation of evaporation −dc/dt=f(T,c₀,c(t)). The developed mathematical model was described by the general kinetic equation . The differential quotients δ(−dc/dt)/δT=f(T,c₀,c(t))=f(T,c₀,t) and δ(−dc/dt)/δc₀=f(T,c(t))=f(T,c₀,t) were performed, and mathematical definition of the changes of the evaporation rate constant with the change of temperature and the change of the initial plasticized concentration were discussed.     

Non-radiative pathways of anilino-naphthalene sulphonates: Twisted intramolecular charge transfer versus intersystem crossing

The effect of solvent polarity and external heavy atom (ethyl iodide) on the fluorescence properties of 2-tolouidino-6-naphthalene-sulphonate (TNS) and 1-anilino-8-naphthalene-sulphonate (ANS) have been studied. For ANS with rise in polarity, a monotonic decrease of fluorescence yield (α_f) and lifetime (τ_f) is observed while ethyl iodide was found to have negligible effect. For TNS at low polarity α_f and τ_f are found to increase with rise in polarity, while ethyl iodide causes a decrease in τ_f. At high polarity [E_T(30) > 51] behaviour of TNS is more or less similar to that of ANS. It is proposed that polarity-dependent, twisted intramolecular charge transfer is the main non-radiative process for ANS at all polarities [E_T(30) = 36–63] and for TNS only at high polarity. At low polarity intersystem crossing is the main non-radiative pathway for TNS.     

Systems Ln-Fe-O (Ln=Eu, Gd): thermodynamic properties of ternary oxides using solid-state electrochemical cells

The standard molar Gibbs energies of formation of LnFeO₃(s) and Ln₃Fe₅O₁₂(s) where Ln=Eu and Gd have been determined using solid-state electrochemical technique employing different solid electrolytes. The reversible e.m.f.s of the following solid-state electrochemical cells have been measured in the temperature range from 1050 to 1255 K.Cell (I): (−)Pt / {LnFeO₃(s)+Ln₂O₃(s)+Fe(s)} // YDT/CSZ // {Fe(s)+Fe_0.95O(s)} / Pt(+);Cell (II): (−)Pt/{Fe(s)+Fe_0.95O(s)}//CSZ//{LnFeO₃(s)+Ln₃Fe₅O₁₂(s)+Fe₃O₄(s)}/Pt(+);Cell (III): (−)Pt/{LnFeO₃(s)+Ln₃Fe₅O₁₂(s)+Fe₃O₄(s)}//YSZ//{Ni(s)+NiO(s)}/Pt(+);andCell(IV):(−)Pt/{Fe(s)+Fe_0.95O(s)}//YDT/CSZ//{LnFeO₃(s)+Ln₃Fe₅O₁₂(s)+Fe₃O₄(s)}/Pt(+).The oxygen chemical potentials corresponding to the three-phase equilibria involving the ternary oxides have been computed from the e.m.f. data. The standard Gibbs energies of formation of solid EuFeO₃, Eu₃Fe₅O₁₂, GdFeO₃ and Gd₃Fe₅O₁₂ calculated by the least-squares regression analysis of the data obtained in the present study are given byΔ_fG°_m(EuFeO₃, s) /kJ mol⁻¹ (± 3.2)=−1265.5+0.2687(T/K)   (1050 ? T/K ? 1570),Δ_fG°_m(Eu₃Fe₅O₁₂, s)/kJ mol⁻¹ (± 3.5)=−4626.2+1.0474(T/K)   (1050 ? T/K ? 1255),Δ_fG°_m(GdFeO₃, s) /kJ mol⁻¹ (± 3.2)=−1342.5+0.2539(T/K)   (1050 ? T/K ? 1570),andΔ_fG°_m(Gd₃Fe₅O₁₂, s)/kJ·mol⁻¹ (± 3.5)=−4856.0+1.0021(T/K)   (1050 ? T/K ? 1255).The uncertainty estimates for Δ_fG°_m include the standard deviation in the e.m.f. and uncertainty in the data taken from the literature. Based on the thermodynamic information, oxygen potential diagrams for the systems Eu-Fe-O and Gd-Fe-O and chemical potential diagrams for the system Gd-Fe-O were computed at 1250 K.     

Adsorption properties of GaAs-CdS system

The adsorption properties of GaAs-CdS solid solutions and the constituent binary systems with respect to CO and NH₃ were studies by piezoquartz microweighing, temperature-programmed desorption, and IR spectroscopy. On the basis of an analysis of the measured α _p = f(T), α _T = f(p), and α _T = f(t) dependences, the thermodynamic and kinetic characteristics of adsorption, earlier obtained acid-base and other physicochemical characteristics of adsorbents, and the electronic properties of the adsorbate molecules, the mechanism and regularities of the adsorption processes at various conditions and compositions of the system were established. A comparison of the adsorption properties of the GaAs and CdS individual binary compounds with their (GaAs)_x(CdS)_1?x solutions, multicomponent systems, revealed common and distinctive features. Optimal compositions of adsorbents suitable for manufacturing primary transducers in sensors for medical and environmental purposes were determined.     

Adsorption properties of CdS-CdTe system semiconductors

The adsorption of carbon(II) oxide and ammonia on nanofilms of solid solutions and binary compounds of the CdS-CdTe system is studied by means of piezoquartz microweighing, FTIR IR, and measuring electroconductivity. Allowing for the conditions and composition of semiconductor systems, we determine the mechanisms and principles of adsorption processes by analyzing the α _p = f(T), α _T = f(p), and α _T = f(t) experimental dependences; IR spectra; the thermodynamic and kinetic characteristics of adsorption; the acid-base, electrophysical, and other characteristics of adsorbents; the electron nature of adsorbate molecules; and the obtained acid-base characteristics: the composition and adsorption characteristics and composition state diagrams. Previous statements on the nature and retention of local active centers responsible for adsorption and catalytic processes upon changes in their habitus and composition (as components of systems of the A^IIIB^V-A^IIB^VI and A^IIB^VI-A^IIB^VI types) on the surface of diamond-like semiconductors are confirmed. Specific features of the behavior of (CdS) _x (CdTe)_{1 ? x} solid solutions are identified in addition to general features with binary compounds (CdS, CdTe), as is demonstrated by the presence of critical points on acid-base characteristics-composition and adsorption characteristics-composition diagrams. On the basis of these diagrams, the most active adsorbents (with respect to CO and NH₃) used in designing highly sensitive and selective sensors are identified.