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AKTS-Thermokinetics - Thermal Aging License - Version 3

Determination of kinetic parameters (activation energy E and pre-exponential factor in Arrhenius equation A) of complex multistage overlapped reactions based on multi-curves methods from HFC, DSC, nanoDSC, microDSC, C-80, DTA, TG and/or DTG, TG-MS, TG-FTIR measurements and prediction of the reaction progress and thermal stability of materials under any temperature mode.

• Advanced kinetic analysis :
• automatic baseline construction and use of the differential isoconversional method of Friedman (model free) for an advanced baseline optimization
• smoothing of data (Savitzky-Golay) and spikes correction
• differential isoconversional method of Friedman (model free)
• integral isoconversional method of Ozawa-Flynn-Wall (model free)
• standard procedure of ASTM A698
• model fitting method applying all commonly used equations for the description of the decomposition reactions e.g. n-th order reactions (Fn), nucleation (Avrami-Erofeev, An, A2, A1.5), diffusion (parabolic law D1, Valesi D2, Jander D3, Brounshtein D4) movement of the phase boundary (shrinking core model, Rn, R1, R2), autocatalysis
• calculations using any type of kinetic equation introduced by a user

e.g. da/dt =1e10 * exp(-100000/8.314/(T+273.15)) * (1-a)
or da/dt = A(a) * exp(-E(a)/8.314/(T+273.15)) * (1-a)

• Prediction of the reaction progress and thermal stability of materials under any temperature mode:
• isothermal and non-isothermal, stepwise
• modulated temperature or periodic temperature variations
• rapid temperature increase (temperature shock)
• real atmospheric temperature profiles for investigating properties of e.g. low-temperature decomposed substances under different climates (yearly temperature profiles with daily minimal and maximal fluctuations. 50 climates available in the default version).
• NATO norm STANAG 2895 temperature profile: Zones A1, A2, A3, B1, B2, B3, C0, C1, C2, C3, C4, M1, M2, M3.
• customized temperature profiles: possibility to compare the reaction progress of substances at any temperature profile
• combination of mass loss TG, heat flow signal e.g. DSC/DTA and MS data in multi-projects for simultaneous comparison of the mass loss, heat flow and volatiles species evolution at any temperature profile
• confidence interval of the prediction
• viewing data in form of overall conversion alpha(T(t)) , dalpha(T(t))/dt
• viewing data in natural form Q(T(t)), dQ(T(t))/dt, P(T(t)), dP(T(t))/dt, M(T(t)), dM(T(t))/dt
• extended features for High Sensitivity Isothermal Heat Flow Calorimetry (HFC): Ability to calculate the thermokinetics from long term isothermal HFC data for very precise lifetime prediction on the first percent of degradation (quality control)

Introduction

Application of thermokinetics for the determination of materials’ behaviour

The main goal of AKTS-Thermokinetics Software Package [1] is to facilitate kinetic analysis of any type of thermoanalytical data (DSC, DTA, TGA, TG-MS or TG-FTIR) for the study of raw materials and products within the scope of research, development and quality. In the present help, it is discussed how advanced numerical techniques can be applied for the interpretation of DSC signals of a reaction mixture after the reduction of an ester with a Lithium aluminium hydride solution. If DSC monitors the evolution of the reactions, signals can be used not only for qualitative and quantitative analysis but also for kinetic description. The main challenge is the prediction of thermal stability for substances submitted to extended temperature ranges and temperature conditions for which experimentation is difficult or impossible. These difficulties are prevalent at low temperatures (requiring a very long investigation time), as well as under specific temperature fluctuations. The goal of this advanced numerical approach is :

• a deeper insight into the reaction course of any material ;
• and an early detection of the stability/reactivity.

Analysis Process

A full kinetic analysis of a solid state reaction has at least three major stages :

• (1) experimental collection of data ;
• (2) computation of kinetic parameters using the data from stage 1 ;
• (3) prediction of the reaction progress for required temperature profiles applying determined kinetic parameters.

Using experimental DSC measurements performed on the examined samples (stage 1) AKTS-Thermokinetics software determines kinetic characteristics of the reaction (stage 2). The calculated kinetic parameters are subsequently employed to predict the reaction progress of the investigated samples under any given temperature mode (stage 3).

Experimental Part

Selection of the evaluation range and determination of the baseline (stage 1)

Example : For the examination of a reaction mixture after the reduction of an ester with a Lithium aluminium hydride solution, the DSC technique can be used. The measured data are subsequently exported in ASCII format and entered into AKTS-Thermokinetics Software for further thermokinetic interpretation. Temperature programs run from about 30 to 350°C. Experiments are performed in high pressure sealed crucibles (http://www.swissi.ch/index.cfm?rub=1010) at different heating rates ranging from 0.5 to 8K/min with a sample mass of about 20 mg. Fig. 1 show DSC signals at different heating rates of the examined material used for thermokinetic evaluation.

The selection of the evaluation range should contain the signal before and after the occurrence of the measured thermal event as depicted in Fig. 1 for the examined substance.

Generally the application of straight-line form for the baseline is incorrect [2]. The recorded signal results not only from the heat of the reaction but is additionally affected by the change of the specific heat of the mixture reactant-products during the progress of the reaction.

With :

B(t) the baseline

and S(t) the differential signal,

the reaction rate

and the reaction progress α(t) [-] can be expressed as

with

(0 < α(t) < 1) and B(t) = (1- α(t))*(a1+b1*t) + α(t)*(a2+b2*t)

where
(a1+b1*t) : tangent at the beginning of the signal S(t).
(a2+b2*t) : tangent at the end of the signal S(t).

The tangential area-proportional baseline is the most universal type because of its correction possibilities. It is created at α(t)   0 and at α(t)   1by the appropriate tangents at the beginning or the end of the measured DSC signal. It allows compensation of not only changes in the size of Cp of the reactant and product, but also of changes in their temperature dependency. This type of baselines can be described by the following equation :

B(t) = (1-α(t))*(a1+b1*t) + α(t)*(a2+b2*t)

with
(a1+b1*t) : tangent at the beginning of the signal S(t).
(a2+b2*t) : tangent at the end of the signal S(t).

B(t) can be calculated iteratively. The convergence is achieved as soon as the relative average deviations between two iterations are smaller than an arbitrarily chosen value (for example 1e-6). An area-proportional baseline has been calculated using arbitrarily 300 iteration loops in Fig. 2.

Fig. 2 : DSC curve of the examined substance and the baseline calculation illustrated for a heating rate of about 1 K/min.

In addition to the sigmoid baseline types, AKTS-Thermokinetics Version III enables advanced baseline construction ten (10) different baseline types (tangential sigmoid, tangential first point, tangential last point, sigmoid, spline, straight, horizontal first point, horizontal last point, equal to zero baseline, staged) because the correct baseline selection is one of the most critical parts of data treatment. Baselines selection can be done automatically and also optimized visually using the zoom functionality. Standard baseline treatments are also accessible, but the software offers the more precise options for the treatment of the data.

It is obvious that the baseline determination can significantly influence the determination of the kinetic parameters of the reaction. Moreover, the correct baseline determination should be intimately combined with the computation of the kinetic parameters for the investigated reaction. Advanced mathematical procedures are therefore necessary for an objective calculation of the most appropriate baseline for each DSC signal.

Determination of the Kinetic Characteristics (Stage 2)

Single kinetic triplet

The noticeable weakness of the ‘single curve’ methods (determination of the kinetic parameters from single run recorded with one heating rate only) has led to the introduction of the ‘multi curve’ methods over the past few years, as discussed in the International ICTAC Kinetics project [3-6]. Only series of non-isothermal measurements carried out at different heating rates can give a data set which in general contains the necessary amount of information required for full identification of the complexity of a process [4].

If the decomposition follows a single mechanism then the reaction can be described in terms of a single pair of Arrhenius parameters and the commonly used set of reaction models. In such cases the dependence of the logarithm of the reaction rate over 1/T is linear with the same slope ofm = E/R for all conversion degrees α(t). The reaction rate can be described by only one value of the activation energy E and one value of the pre-exponential factor A by the following expression :

However, decomposition reactions are often too complex to be described in terms of a single pair of Arrhenius parameters and the commonly applied set of reaction models (table 1).

Autocatalytic :  (1-a)^n a^m F1 : 1-α F2 : (1-α)^2 F3 : (1-α)^3 Fn : (1-α)^n P1 : α^0 P2 : 2 α^(1/2) P3 : 3 α^(2/3) P4 : 4 α^(3/4) Pn : n α^(1-1/n)

A1.5 : 1.5 (1-α) [-ln(1-α)]^(1/3) A2 : 2 (1-α) [-ln(1-α)]^(1/2) An : n (1-α) [-ln(1-α)]^(1-1/n) R2 : 2 (1-α)^(1/2) R3 : 3 (1-α)^(2/3) Rn : n (1-α)^(1-1/n) D1 : 1/(2α) D2 : [-ln(1-α)]^-1 D3 : 1.5 [1-(1-a)^(1/3)]^-1 (1-α)^(2/3) D4 : 1.5 [(1-α)^(-1/3)-1]^-1

Table 1 : forms of the f(α) function dependent on the reaction model.

As a general rule, decomposition reactions demonstrate profoundly multi-step characteristics. They can involve several processes with different activation energies and mechanisms. In such situation the reaction rate can be described only by complex equations, where the apparent activation energy term is no longer constant but is dependent on the reaction progress a (E≠const but E=E(α), see Fig. 2). Thus a simplified kinetic analysis can no more lead to an accurate description of the experimental data. For multistage overlapped reactions the prediction of the thermal behavior under any new temperature profile, without taking into account the dependence of the activation energies E(α) on the conversion degree a, is of little value.

Isoconversional methods - Concept

The kinetic parameters can be evaluated by the isoconversional method. This is a numerical method which involves determination of temperatures corresponding to certain, arbitrarily chosen values of the conversion extent α recorded in the experiments carried out at e.g. different heating rates β. Isoconversional methods are based on the so called isoconversional principle saying that the reaction rate dα/dt at constant reaction progress α is only a function of temperature and that the temperature dependence is contained only in the Arrhenius expression. These methods can be applied for determination of the activation energy (or dependence E on α) without assuming the explicit form of f(α).

The thermoanalytical data set usually contains:

• the relationship between specific conversion, αi, and temperatures for different heating rates (non-isothermal mode).
• the relationship between specific conversion, αi, and time for different temperatures (isothermal mode).

Commonly applied are the following three isoconversional methods known as: Friedman [7], Ozawa-Flynn-Wall [8-9] and the ASTM E698 analysis [10].

Friedman Analysis

The Friedman method is a so-called differential isoconversional method. Based on the Arrhenius equation

with

α :	reaction progress	[α] = -
f(α) :	model function	[f(α)] = -
A :	preexponential factor	[A] = 1/s
E :	activation energy	[E] = kJ/mol
T :	temperature	[T] = K
t :	time	[t] = s

Friedman proposed to apply the logarithm of the conversion rate dα/dt as a function of the reciprocal temperature at any conversion α:

f(α) is a constant in the last term of at any fixed α, the logarithm of the conversion rate dα/dt over 1/T shows a straight line with the slope m = E/R.

By extension 

with

So, having determined and we can predict the reaction rate or reaction progress using the following expression:

at any temperature profile:

• isothermal, non-isothermal, stepwise
• modulated temperature or periodic temperature variations
• rapid temperature increase (temperature shock)
• real atmospheric temperature profiles for investigating properties of e.g. low-temperature decomposed substances under different climates (yearly temperature profiles with daily minimal and maximal fluctuations. 50 climates available in the default version).
• STANAG 2895 temperature profile: Zones A1, A2, A3, B1, B2, B3, C0, C1, C2, C3, C4, M1, M2, M3.
• customized temperature profiles
• possibility to compare the reaction progress of substances at any temperature profile
• confidence interval of the prediction

The extended features of AKTS-Software applied to High Sensitivity Isothermal Heat Flow Calorimetry enable

• the calculations of the thermokinetics from long term isothermal Heat Flow Calorimetry data for very precise lifetime prediction, generally on the first few percents of degradation (quality control)

Ozawa-Flynn-Wall Analysis

The Ozawa-Flynn-Wall analysis is a so-called integral isoconversional method. The activation energies obtained as a function of the reaction progress are less precise than with the differential isoconversional method of Friedman because the details of decomposition are buried by the integration.

Independent of each other Ozawa, Flynn and Wall developed a method for the determination of the activation energy, which is based on several curves measured at different, but constant heating rates. Starting from the Arrhenius equation:

with constant heating rate β
dT/dt = β = constant

the integration leads to:

with 
f(α) : the model function, A: the preexponential factor, E: the activation energy, β: the heating rate, T : the temperature and t: the time.

If ‘To’ lies below the temperature at which the reaction is noticeable, then one can set the lower limit of integration to To = 0, so that the following equation is obtained after integration and using a logarithm expression form:

with: and

By using the approximation given by DOYLE [11] 
ln p(z) = 5.3305 - 1.052·z  and transposing, ones obtains:

It can be seen from the above equation that with a series of measurements at fixed heating rates β and at fixed degrees of conversion a the graph ln(β) versus 1/T shows straight lines with a slope m = - 1.052·E/R (see figure below). The temperatures T are those at which the conversion α is reached at a heating rate β. As a result, the slope of the straight lines enables to calculate the activation energy as a function of the reaction progress α.

ASTM E698

The analysis according to ASTM E698 is based on the assumption that the maximum (for example maximum of the DSC or DTG curve) of a single step reaction is reached at the same conversion degree independent of the heating rate. Although this assumption is only partly right, the resulting errors are small [12]. In this method, the logarithm of the heating rate is plotted over the reciprocal temperature of the maximum. The slope of the yielded straight line is proportional to the activation energy, just as in the Ozawa-Flynn-Wall analysis.

General information about isoconversional methods

A detailed analysis of the various isoconversional methods (i.e. the isoconversional differential and integral methods) for the determination of the activation energy has been reported in the literature by Budrugeac [13]. The convergence of the activation energy values obtained by means of a differential method like Friedman method [7] with those resulted from using integral methods with integration over small ranges of reaction progressa comes from the fundamentals of the differential and integral calculus. In other words, it can be mathematically demonstrated that the use of isoconversional integral methods (for example: Ozawa-Flynn-Wall [8-9]) can yield systematic errors when determining the activation energies. These errors depend directly on the size of the small ranges of reaction progress Δα over which the integration is performed. These errors can be avoided by using infinitesimal ranges of reaction progress Δα. As a result, isoconversional integral methods turn back to the differential isoconversional methods formerly proposed by Friedman [7].

The differential methods for the calculation of the kinetic parameters are based on the use of the following reaction rate equation:

where β is the heating rate, T the temperature, E(α) the activation energy, A(α) the preexponential factor and f(α) is the differential conversion function.

As far as isoconversional integral methods are considered, these techniques are based on the equation:

where g(α) is the integral conversion function.

The isoconversional integral methods with the integration over low ranges of the degree of conversion and respectively temperature, are based on the equation:

which is derived by supposing that in the range of the variation of the conversion degree Δα, the activation energy E can be assumed constant. Obviously, the use of such an approach leads to a plot of E versus the degree of conversion α. However, the activation energy as a function of the conversion progress looks like a stair function in which the low ranges of Δα where E keeps a constant value are clearly marked. The number of stairs depends directly on the size of Δα.

In order to evaluate the integrals from the previous equation, one can use the theorem of the average value, we obtain:

where

Since the number of stairs (where the activation energy E is assumed constant in the isoconversional integral methods) depends directly on the range of chosen Δα, then an unlimited number of stairs can be reached by making Δα infinitesimal. For Δα → 0, we have Tξ → T and f(αξ) → f(α). As a consequence, the previous equation turns back into its differential form:

This means that the isoconversional integral methods return to isoconversional differential method which corresponds to the Friedman approach. More generally, the conversion rate expression can be adapted to an arbitrary variation of temperature (as well as to isothermal conditions) by replacing β(dα/dT) with dα/dt. Friedman analysis, based on the Arrhenius equation, applies the logarithm of the conversion rate dα/dt as a function of the reciprocal temperature at different degrees of the conversion α.

with i: index of conversion, j: index of the curve and f(αi,j) the function dependent on the reaction model that is assumed to be constant for a given reaction progress αi,j for all curves j. As f(α) is constant at each conversion degree αi, the method is named ‘isoconversional’ and the dependence of the logarithm of the reaction rate over 1/T is linear with the slope of m = E/R and the intercept A as presented in figures 1 and 2.

The reaction rate can now be described as following:

Prediction of the reaction progress under any temperature mode (Stage 3)

The DSC data collected during non-isothermal reaction of the examined materials with different heating rates were used for determination of the kinetic parameters and thereafter applied for prediction of the reaction extent. More generally, kinetic parameters calculated from the non-isothermal experiments make possible the prediction of the reaction progress for any other heating rate and more generally for any temperature mode [14-21] such as:

• isothermal
• non-isothermal
• stepwise
• modulated temperature or periodic temperature variations
• rapid temperature increase (temperature shock)
• real atmospheric temperature profiles for investigating properties of e.g. low-temperature decomposed substances under different climates (yearly temperature profiles with daily minimal and maximal fluctuations. 50 climates available in the default version).
• NATO norm STANAG 2895 temperature profile: Zones A1, A2, A3, B1, B2, B3, C0, C1, C2, C3, C4, M1, M2, M3.
• customized temperature profiles
• possibility to compare the reaction progress of substances at any temperature profile
• combination of mass loss TG, heat flow signal e.g. DSC/DTA and MS data in multi-projects for simultaneous comparison of the mass loss, heat flow and volatiles species evolution at any temperature profile
• confidence interval of the prediction
• viewing data in form of overall conversion α(T(t)) and conversion rate dα(T(t))/dt
• viewing data in natural form as e.g. Q(T(t)), dQ(T(t))/dt, P(T(t)), dP(T(t))/dt, M(T(t)), dM(T(t))/dt
• integration according Runge-Kutta, important for stiff systems of differential equations
• extended features for High Sensitivity Isothermal Heat Flow Calorimetry (HFC): Ability to calculate thermokinetics from long term isothermal HFC data for very precise lifetime prediction at the first few percents of degradation (quality control)

Thermal Stability Predictions

Isothermal

Kinetic parameters calculated from non-isothermal experiments allow prediction of the reaction progress at any temperature mode: isothermal, non-isothermal and intermediate intervals in the heating rate, expressed, e.g. in oscillatory temperature modes. The prediction of the reaction progress in various temperature modes is for example given below.

Non-Isothermal

In general, non-isothermal scans with different heating rates are carried out within a much wider temperature range than is possible, for experimental reasons, in isothermal conditions. This allows discernment between the different reaction paths involved in the kinetic process because the data contain the necessary information on the time-temperature dependence of particular processes which is a prerequisite for the correct identification of the complex nature of the investigated reaction. Computations are usually made with the results obtained from at least 5 heating rates such as 8, 4, 2, 1, 0.5 K/min. This method insures a ratio of 8/0.5 = 16 between the highest and lowest heating rates. The application of heating rates too close to each other should be avoided. If they are very close, they become tantamount to a model-fitting analysis using single heating-rate methods. Consequently, they may fail the required purpose as amply reported in the literature (see international ICTAC kinetic project [3-6]). Our general tip for experimental data: start with e.g. 4 K/min. It enables to rapidly examine the shape of the signals over the whole temperature range. Then continue by 8 K/min and 2 K/min. If signal to noise ratio is not good for 2 K/min add more sample mass and continue with 1 K/min and continue with 0.5 K/min. The information required for each scan is: Temperature, Time, Thermal property. Please find at the link below such an example of data for a better illustration of the required measurements (ASCII data = Notepad format = *.txt format) : http://www.akts.ch/faq/format-example.zip

Note:

• the DSC data should be set-up to record the maximum number of data points possible (i.e. do not limit the data collection in any way)
• for isochoric conditions (required for the determination of e.g. the Time to Maximum Rate under adiabatic conditions), we recommend to use the high pressure sealed crucibles of the Swiss Institute of Safety and Security : http://www.swissi.ch/index.cfm?rub=1010

Stepwise

Modulated

The kinetic parameters calculated from the non-isothermal experiments allow prediction of the reaction progress at any temperature mode: isothermal, non-isothermal and intermediate intervals in the heating rate, expressed, e.g. in an oscillatory temperature mode. Examples of predictions of the reaction progress in an oscillatory temperature mode (widely applied in temperature-modulated calorimetry) are given below. A temperature-modulated mode increases the basic understanding of the characterization of materials in different ways. Presented examples indicate that the prediction of some of the thermal aging strongly depends on the exact temperature profile of the sample.

In the next figures, the arithmetic mean temperature (30°C) of the oscillatory temperature modes is the same for all calculations, however, the differences in the amplitudes greatly influence the reaction progress and rate. The prediction of the decomposition at 30°C with ± 30°C amplitude and 24h period indicates that after one month the sample will reach a reaction progress of about 80%. For the same mean temperature (30°C, isothermal conditions), the substance will decompose much less in this period of time (reaction progress is about 20%, respectively).

Worldwide

REAL ATMOSPHERIC TEMPERATURE MODE: Prediction of the reaction rate and progress for real atmospheric temperature profiles which allows the investigation of the properties of low-temperature decomposed substances under different climates (yearly temperature profiles with daily minimal and maximal fluctuations). The important goal of the investigation of thermal decomposition kinetics is the need to determine the thermal stability of substances, i.e. the temperature range over which a substance does not decompose with an appreciable rate. The correct prediction of the reaction progress of materials which are unstable under ambient conditions (food, drugs, some polymers, etc.) requires accurate application in the calculations of both:

• the kinetic parameters
• the exact temperature profile for a given climate

Calculations can be achieved for any fluctuation of the temperature which makes possible the predictions of thermal stability properties for varying climates. Exact consideration in the calculations of daily minimal and maximal temperature variations of worldwide climates provides very valuable insight when interpreting and quantifying the reaction progress of materials subjected to atmospheric conditions.

STANAG 2895

The application of kinetics makes possible the precise prediction of the reaction progress under temperature mode corresponding to real atmospheric changes according to STANAG 2895. During their production, storage or final usage, chemicals often undergo temperature fluctuations. Due to the fact that the reaction rate varies exponentially with the temperature it is important that predictive tools could enable the simulation of the reaction progress in the real conditions, as a small temperature jump can induce a significant increasing reaction rate.

Since thermokinetics allows a precise description of the decomposition process, the reaction rate can be predicted for any temperature profile, such as stepwise variations, oscillatory conditions, temperature shock, or even real atmospheric temperature profiles. To illustrate the importance of the influence of the temperature fluctuations on the reaction rate, the simulations of the reaction progress were carried out for the high temperature climatic category A1 according to STANAG 2895.

This document describes the principal climatic factors which constitute the distinctive climatic environments found throughout the world and provides guidance on the drafting of the climatic environmental clauses of requirement documents. The temperature profiles according to STANAG 2895 are important the prediction of the influence of the temperatures on the slow decomposition of e.g. high energetic materials such as propellants. The precise prediction of the reaction rate and progress requires the knowledge of the diurnal and annual variations of the meteorological and storage /transit temperatures.

The meteorological temperature is the ambient air temperature measured under standard conditions, whereas storage and transit temperature represents the air temperature measured inside temporary unventilated field shelter e.g. in railway boxcar which is exposed to direct solar radiation. The time dependences of the diurnal minimal and maximal meteorological and storage / transit temperatures for two temperature profiles of climatic category A1 are presented in the next figure.

Applying the advanced kinetic software it is possible to calculate the reaction progress for all propellants using the kinetic parameters determined from thermoanalytical signal and taking into account the dependence of the temperature changes depicted in STANAG 2895. Presented results indicate the very significant dependence of the thermal stability of the investigated propellants on the storage conditions even in the same climatic category.

Customized

The experimental data collected by means of DSC enables the prediction of the shelf life of substances at any temperature mode and even the precise simulation of the reaction at any temperature profile close to the ambient temperature. To illustrate the importance of the influence of the temperature fluctuations on the reaction course, the simulations of the reaction progress can be carried out even for storage temperature profile corresponding temperature fluctuations measured during the sample storage as presented in the next figure.

References

[1] AKTS AG, http://www.akts.com (AKTS-Thermokinetics software and AKTS-Thermal Safety software)
[2] Hemminger W. F., Sarge, S. M., J. Therm. Anal., 37 (1991), 1455.
[3] M.E. Brown et al. Computational aspects of kinetic analysis. The ICTAC Kinetics project data, methods and results. Thermochim. Acta, 355 (2000) 125.
[4] M. Maciejewski, Computational aspects of kinetic analysis. The ICTAC Kinetics Project - The decomposition kinetics of calcium carbonate revisited, or some tips on survival in the kinetic minefield. Thermochim. Acta, 355 (2000) 145.
[5] A. Burnham, Computational aspects of kinetic analysis. The ICTAC Kinetics Project - multi-thermal-history model-fitting methods and their relation to isoconversional methods. Thermochim. Acta, 355 (2000) 165.
[6] B. Roduit, Computational aspects of kinetic analysis. The ICTAC Kinetics Project - numerical techniques and kinetics of solid state processes. Thermochim. Acta, 355 (2000) 171.
[7] H. L. Friedman, J. Polym. Sci, Part C, Polymer Symposium (6PC), 183 (1964).
[8] T. Ozawa: Bull. Chem. Soc. Japan, 38 (1965) 1881.
[9] J.H. Flynn, L.A. Wall, J. Res. Nat. Bur. Standards, 70A (1966), 487.
[10] http://www.astm.org
[11] C. D. Doyle: J. Appl. Anal., 27 (1962) 639
[12] J.P.Elder: J. Thermal Anal., 30 (1985) 657
[13] P. Brudugeac, J. Therm. Anal., Vol. 68 (2002) 131.
[14] B. Roduit, Thermochim. Acta, 388 (2002) 377.
[15] B. Roduit, Ch. Borgeat, B. Alonso, J.N. Aebischer, P. Pollien, A. Raemy and I. Blank, 32nd NATAS CONFERENCE, Williamsburg Marriott, Williamsburg, VA October 4-6, 2004. 
[16] B. Roduit, W. Dermaut, A. Lunghi, P. Folly, B. Berger and A. Sarbach, J. Therm. Anal. Cal., Vol. 93 (2008) 1, 163–173, 
Advanced Kinetics-Based Simulation of Time to Maximum Rate Under Adiabatic Conditions
http://dx.doi.org/10.1007/s10973-007-8866-1
[17] B. Roduit, Ch. Borgeat, B. Berger, P. Folly, B. Alonso, J.N. Aebischer and F. Stoessel, J. Therm. Anal. Cal., ICTAC special issue, 80 (2005) 229–236.
[18] B. Roduit, Ch. Borgeat, B. Berger, P. Folly, B. Alonso, J.N. Aebischer, J. Therm. Anal. Cal., ICTAC special issue, 80 (2005) 91–102.
[19] U. Ticmanis, G. Pantel, S. Wilker, M. Kaiser, Precision required for parameters in thermal safety simulations, 32nd Internationl Annual Conference of ICT July, (2001), 135.
[20] B. Roduit, Ch. Borgeat, U. Ticmanis, M. Kaiser, P. Guillaume,B. Berger, P. Folly, 35th International Annual Conference of ICT, June 29 - July 2, 2004, 37-1. 
[21] P. Folly, Chimia, 58 (2004), 394.
[22] F. Stoessel, J. Steinbach, A. Eberz: Plant and process safety, exothermic and pressure inducing chemical reactions, In: Ullmann's encyclopedia of industrial chemistry. Weise E (Eds), VCH, Weinheim (1995):343-354.
[23]  A. Keller, D. Stark, H. Fierz, E. Heinzle, K. Hungerbuehler: Estimation of the TMR using dynamic DSC experiments. Journal of Loss Prevention in the Process Industries (1997) 10(1):31-41.
[24] D.A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, Plenum Press, New York, London, 1969.
[25] J.M. Dien, H. Fierz, F. Stoessel, G. Killé: The thermal risk of autocatalytic decompositions: a kinetic study. Chimia (1994) 48(12):542-550.
[26] D.W. Smith, Assessing the hazards of runaway reactions, Chem. Eng., 14, (1984) 54.
[27] T. Grewer, Thermochim. Acta, 225 (1993) 165.
[28] R. Gygax, International Symposium on Runaway reactions, March 7-9, 1989, Cambridge, Massachusetts, USA, 52.
[29] F. Stoessel, Thermal Safety of Chemical Processes, Risk Assessment and Process Design, 1. Auflage - Februar 2008, WILEY-VCH Verlag GmbH & Co. CGaA.
[30] A heat transfer textbook Third Edition, John H. Lienhard IV / John H. Lienhard V, Phlogiston Press, Cambridge Massachusetts, 2008
[31] H. Fierz, Journal of Hazardous Materials A96 (2003) 121–126 
[32] 2003, Recommendations on the Transport of Dangerous Goods, Manual of Tests and Criteria, 4 revised edition, United Nations, ST/SG/AC.10/11/Rev.4 (United Nations, New York and Geneva).
[33] 2003, Globally Harmonized System of Classification and Labelling of Chemicals (GHS), United Nations, New York and Geneva
[34] B. Roduit, P. Folly, B. Berger, J. Mathieu, A. Sarbach, H. Andres, M. Ramin and B. Vogelsanger, J. Therm. Anal. Cal., 93 (2008) 1, 153–161.
Evaluating SADT By Advanced Kinetics-Based Simulation Approach
http://dx.doi.org/10.1007/s10973-007-8865-2
[35] B. Roduit, L. Xia, P. Folly, B. Berger, J. Mathieu, A. Sarbach, H. Andres, M. Ramin, B. Vogelsanger, D. Spitzer, H. Moulard and D. Dilhan, J. Therm. Anal. Cal., Vol. 93 (2008) 1, 143–152.
Advanced Kinetics-Based Simulation of Time to Maximum Rate Under Adiabatic Conditions
http://dx.doi.org/10.1007/s10973-007-8864-3