Computer-determined kinetic parameters from TG curves. Part IX

By applying the restriction that α (conversion) = constant to non-isothermal TG (NITG), isothermal TG (ITG) and a combination of both (NITG/ITG), various corresponding expressions have been derived for the evaluation of the activation energy, E. By means of a computer, all the expressions developed were tested against data which was generated from theoretical equations. Also, changes were made in the number of significant figures (s.f.) of data in order to ascertain their effects on values of E. Data were generated and tested for the three theoretical mechanisms, A₂, F₁ and R₂.     

The effect of experimental methods and measurement conditions on values of the kinetic parameters of [Co(NH3)6]2(C2O4)3·4H2O

Using the thermal decomposition of [Co(NH₃)₆]₂(C₂O₄)₃·4H₂O as a basis, the paper presents results which show how computed values of kinetic parameters are influenced by experimental conditions (ambient atmosphere, sample mass, linear heating rate) when using the non-isothermal methods and the Coats-Redfern (CR) modified equation. It also illustrates the influence of the experimental methods i.e. non-isothermal and isothermal (conventional) methods and also a quasiisothermal-isobaric one which can be recognised as equivalent to Constant Rate Thermal Analysis (CRTA). The results obtained have confirmed the significant influence of the experimental parameters as well as that of the experimental method used on the estimated values of kinetic parameters. The correlation between activation energy (E) and sample mass (m) or heating rate (β) is generally of a linear nature:E=a+bx     

Devitrification kinetics of PbGeO3

The devitrification of glassy PbGeO₃ was studied and interpreted by means of isothermal and non-isothermal Johnson-Mehl-Avrami equations. In the case of the non-isothermal approach, several approximated equations proposed by various authors were considered in order to obtain both the activation energy E _a and the Avrami morphological coefficient n of the crystallisation process. A critical discussion of the Avrami coefficient on the basis of experimental morphological evidence is also presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Crystallization kinetics of Ti20Zr20Cu60 metallic glass by isoconversional methods using modulated differential scanning calorimetry

The study of crystallization kinetics of amorphous alloys has been a matter of great interest for material researchers for past few decades, since it provides information about the kinetic parameters i.e., activation energy of crystallization and the frequency factor. These kinetic parameters can be calculated by model-free isoconversional methods. Isoconversional methods allow calculating the activation energy as a function of degree of conversion, α. Hence, these methods provide accurate results for multistep processes like crystallization. Model-free methods are categorized as linear and non-linear isoconversional methods. Linear methods are further classified as linear differential and linear integral isoconversional methods. In present work, we have used these isoconversional methods to study the effect of non-linear heating rate, employed by modulated differential scanning calorimetry (MDSC), on the non-isothermal crystallization kinetics of Ti₂₀Zr₂₀Cu₆₀ metallic glass. For Ti₂₀Zr₂₀Cu₆₀, MDSC curves clearly indicate a two-step crystallization process. Both crystallization peaks were studied based on the modified expressions for isoconversional methods by non-linear heating rate. The term corresponding to non-linearity comes out to be (A _T ω/2β)². The effect of non-linear heating rate on measurement of kinetic parameters by isoconversional methods is studied. The activation energy of crystallization is calculated for Ti₂₀Zr₂₀Cu₆₀ metallic glass for various degrees of conversion by linear integral isoconversional methods i.e., Ozawa–Flynn–Wall, Kissinger–Akahira–Sunose, and also with Friedman method which is a linear differential isoconversional method.     

Application of model-free and multivariate non-linear regression methods for evaluation of the thermo-oxidative endurance of a recent manufactured parchment

The thermo-oxidative degradation of a parchment recent manufactured from a goat skin has been investigated by TG/DTG, DSC simultaneous analysis performed in static air atmosphere, at six heating rates in the range 3–15 K min⁻¹. At the progressive heating in air atmosphere, the investigated material exhibits three main successive processes occurring with formation of volatile products, namely the dehydration followed by two thermo-oxidative processes. The processing of the non-isothermal data corresponding to the first process of thermo-oxidation was performed by using Netzsch Thermokinetics—a Software Module for Kinetic Analysis. The dependence of activation energy, evaluated by isoconversional methods suggested by Friedman, and Ozawa, Flynn and Wall, on the conversion degree and the relative high standard deviations of this quantity show that the investigated process is a complex one. The mechanism and the corresponding kinetic parameters were determined by Multivariate Non-linear Regression program. Three mechanisms, one consisting in four successive steps and two others in five successive steps, exhibit the best F-test Fit Quality for TG curves. It was also used the previously suggested criterion, according to which the most probable process mechanism correspond to the best agreement between E _FR  = E _FR (α) (E _FR is the activation energy evaluated by isoconversional method suggested by Friedman; α is the conversion degree) obtained from non-isothermal experimental data and activation energy values, E _iso , obtained by applying the differential method to isothermal data simulated using non-isothermal kinetic parameters. According to this last criterion, the most probable mechanism of parchment oxidation consists in four successive steps. The contribution of the thermo-oxidation process in the parchment damage by natural aging is discussed.     

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.     

Model-free method for isothermal and non-isothermal decomposition kinetics analysis of PET sample

Pyrolysis, one possible alternative to recover valuable products from waste plastics, has recently been the subject of renewed interest. In the present study, the isoconversion methods, i.e., Vyazovkin model-free approach is applied to study non-isothermal decomposition kinetics of waste PET samples using various temperature integral approximations such as Coats and Redfern, Gorbachev, and Agrawal and Sivasubramanian approximation and direct integration (recursive adaptive Simpson quadrature scheme) to analyze the decomposition kinetics.The results show that activation energy (E_α) is a weak but increasing function of conversion (α) in case of non-isothermal decomposition and strong and decreasing function of conversion in case of isothermal decomposition. This indicates possible existence of nucleation, nuclei growth and gas diffusion mechanism during non-isothermal pyrolysis and nucleation and gas diffusion mechanism during isothermal pyrolysis. Optimum E_α dependencies on α obtained for non-isothermal data showed similar nature for all the types of temperature integral approximations.     

Simulation of isothermal cure of A powder coating

The curing of a thermosetting powder coating was studied by means of differential scanning calorimetry (DSC). The isothermal cure was simulated by non-isothermal experiments. The results of the simulation were compared with experimental isothermal data. From non-isothermal isoconversional procedures (free model), it was concluded that these permit simulation of the isothermal cure but do not enable us to determine the complete kinetic triplet (A preexponential factor, E activation energy, f(a) and/or g(a) function of conversion). Non-isothermal procedures based on a single heating rate or on master curves present difficulties for determination of all the kinetic parameters, due to the compensation effect between preexponential factor and activation energy. The kinetic triplet can be determined by a combination of various non-isothermal methods or by using experimental isothermal data in addition to non-isothermal data. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Computer Program for the Evaluation of Non-isothermal Kinetic Parameters

A program for the evaluation of non-isothermal kinetic parameters is presented. The program allows evaluation of the kinetic parameters under constant heating rate or constant reaction rate conditions. The simulation of temperature vs. conversion curves is also possible. A regression method is included, which allows a discrimination between various conversion functions and also evaluation of the activation parameters. The program was tested with various simulated decomposition curves and the non-isothermal decomposition curves of calcium oxalate. The program is written in Visual BASIC 4.0 and can be run under Windows 95 ©.     

Estimation of the curing rate of acrylamide used as a consolidant in heritage sandstone conservation

An investigation of the curing (polymerisation) rate of acrylamide was carried out using isothermal and non-isothermal DSC in order to estimate the time for complete conversion of monomer at ambient temperatures. The non-isothermal data were used to model the rate using integral isoconversional and incremental isoconversional kinetic methods. Applying the equations for integral isoconversional methods and extrapolating to ambient temperatures resulted in non-sensical conversion–time curves, where the time estimated decreased for increasing degree of conversion to be reached. This odd behaviour was attributed to the incorrectness of the integration where the kinetic parameters (e.g. the activation energy) are a function of conversion. The problem was addressed by applying incremental methods which provided more reasonable results as the integration is carried out over small conversion increments where the kinetic parameters are assumed to be constant. Estimates of the conversion were compared to isothermal measurements and, although isothermal DSC produced significant variability in the data, extrapolated estimates from non-isothermal kinetic analysis produced, at best, an upper boundary for the estimation of the time to reach a fixed degree of conversion.     

A simple method of evaluating non-isothermal crystallization kinetics in multicomponent polymer systems

A new simple method of evaluating non-isothermal crystallization kinetics is proposed. The procedure based on mathematical treatment of DSC cumulative crystallization curves at their inflection point provides three kinetic parameters: temperature of start of crystallization (T_s), temperature of maximum crystallization rate (T_i) and numerical value of the maximum crystallization rate (s_i), and also final crystallinity after cooling (CR_c). The method is demonstrated on the system poly(ɛ-caprolactone)/poly(lactic acid)/clay C15 and related microfibrillar composite. The method provides the values of T_s and T_i with standard deviation σ = 0.3 and 0.4 °C, respectively. The coefficient of variation v of s_i and CR_c is 5.8 and 1.5%, respectively. The proposed method does not refer to any crystallization model and does not require exact determination of the starting time. It is particularly useful for characterizing a series of samples derived by modification of the neat polymer.     

Thermal decomposition study of bismuth (III) trichloride complex with 1,10-phenanthroline as the ligand

The complex BiCl₃·L (L = 1,10-phenanthroline) was synthesized and characterized by elemental analysis and infrared spectroscopy (IR). Infrared spectroscopy data suggested that the nitrogen atom of the aromatic ring is bonded to the bismuth atom. The kinetic study of thermal degradation was determined by non-isothermal thermogravimetry. Two methods based on integral equation of Coats-Redfern, were necessary for determining the kinetic trip: the fitting method, known as the checking model and an iso-conversional method. The latter gives the activation energy for each degree of conversion and the first, the kinetic model gives activation energy and the pre-exponential factor for thermal decomposition processes that occur through a single simple mechanism. The kinetic parameters, E _a and log A for the heating rates of 5, 10, and 15 min K⁻¹, were determined considering the decomposition model denoted by F0/R1 in the range of degree of conversion between 0.065 and 0.71.     

非等温反应过程中新的动力学方程

对于非等温过程中的动力学方程，正确的Arrhenius方程的温度积分应该是从T₂到T₁，但是许多动力学方程中的温度积分是从T到0 K，例如Ozawa等方程。我们的研究指出对于某些反应，这些方程中的活化能存在较大的误差，因此我们提出了一个新的动力学方程。凭借等转化率法，应用新的方程可以精确求解线性或非线性加热过程中化学反应的活化能。用新方程对2个经典反应（聚酰胺的热裂解和一水草酸钙的热分解）的研究表明：Ozawa方程的活化能有时是精确的，有时偏差太大。     

Thermal decomposition kinetics of PrMO<Subscript>3</Subscript> (M = Ni or Co) ceramic materials via thermogravimetry

Thermogravimetric data using the non-isothermal kinetic models of Flynn and Wall and “Model-free Kinetics” were used to determine the activation energy to study the decomposition kinetics of the ligand groups with system’s metallic ions that takes part in the synthesis of PrMO₃ (M = Ni or Co). This activation energy was determined for the stage of highest decomposition of the organic matter to establish parameters in synthesis condition optimization and application of the proposed material.     

A simple and precise linear integral method for isoconversional data

A simple and precise linear integral method to evaluate the activation energy dependence on the extent of conversion has been proposed. The method leads to consistent results with those from differential and integral non-linear procedure (Vyazovkin method). Moreover, the new procedure yields the pre-exponential factor and the kinetic model. The method was evaluated from isothermal, non-isothermal and non-linear non-isothermal data (CRTA).     

Ultimate resolution in open tubular columns

The expression for the resolution function, R, in terms of operating parameters for open tubular columns has been extended to include inlet contributions to the peak variance. Subsequent optimization has revealed the existence of optima in the column radius, the stationary phase thickness and the diffusion coefficient ratio in the stationary and mobile phases-in addition to the well-known optimum in the flow velocity. This implies that R at optimum becomes R=f(K)L^0.6V_i^?0.2, i.e. a function only of the column length, L, the inlet volume, V_i, and the concentration distribution coefficient, K. For given K, L and V_i all other parameters such as retention time and pressure drop can thus be directly computed. The information is finally consolidated in the form of contour diagrams. The text itself is cast in the form of a science fantasy.     

Prediction of poly(oxymethylene) non-isothermal crystallization behaviour from isothermal data

The spherulite growth, nucleation-related,K _g, parameter values obtained from isothermal data (by DSC or optical microscopy) and two other adjustable parameters (the spherulite growth rate preexponential factor and the Avrami's or Tobin's exponent,n) have been used with Nakamura's and Tobin's modified non-isothermal equations to model the kinetics of polymer non-isothermal crystallization. Malkin's model was also tested, for comparison. It is shown that, for polymers that crystallize on cooling almost entirely at temperatures higher than the maximum growth rate temperature, this Tobin's-like non-isothermal model accurately describes the experimental behaviour with only 2 parameters.