AKTS-Thermokinetics

AKTS-Thermokinetics
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Click here to see our video webinar and learn the basics of AKTS-Thermokinetics software.

A brief description

The main goal of AKTS-Thermokinetics Software Package is to facilitate kinetic analysis of DSC, DTA, TGA, EGA (TG-MS, TG-FTIR) data for the study of the thermal behaviour of raw materials and products within the scope of research, development and quality assurance.

The software provides a means to infer additional characteristics and thermal properties of examined substances based on conventional thermoanalytical measurements. The procedure begins with the determination of the kinetic parameters for a given substance. These parameters are then used to predict reaction progress under various temperature ranges and modes. In certain cases, the direct investigation of some reactions would be very difficult at low temperatures (requiring very long scanning times), as well as under complex temperature profiles. Using AKTS-Thermokinetics Software, the rate and the progress of the reactions can be predicted for the variety of temperature profiles such as: isothermal, non-isothermal, stepwise, modulated temperature or periodic temperature variations, rapid temperature increase (temperature shock) and real atmospheric temperature profiles (up to 7000 climates).


       

 

AKTS-Thermokinetics - Thermal Aging License

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 as 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 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/dt (T(t))
  • viewing data in raw format Q, dQ/dt, P, dP/dt, m, dm/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 based on the first percent of degradation (quality control)
Thermal Aging and Thermal Safety

1. INTRODUCTION

1.1 Application of thermokinetics for 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. 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.

1.2. Analysis Process

A full kinetic analysis of a solid state reaction has at least three major steps [1-17]:

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

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

AKTS-Thermokinetics, TMRad calculation in 5 steps

Fig. 1.1: Description of the steps to calculate the kinetics and to determine the reaction progress and rate at any temperature profile.

2. EXPERIMENTAL PART (STEP 1)

Selection of the evaluation range and determination of the baseline

For this examination the DSC data were used. The measured data were subsequently exported in ASCII format for further thermokinetic interpretation with AKTS-Thermokinetics Software. Experiments were performed in gold plated high pressure sealed crucibles at a heating rate of 0.5, 1, 2, 4 and 8 K/min (non-isothermal) with a sample masses between 6.66 and 11.28 mg (AKTS recommends to use the high pressure sealed crucibles of the Swiss Institute for the Promotion of Safety and Security http://www.tuev-sued.ch/ch-en/activity/testing-equipment/dsc). Figures 2.1 show DSC signals at different heating rates of the examined material used for thermokinetic evaluation.

Typical DSC curve at 0.5 K/min

Typical DSC curve at 1 K/min

Typical DSC curve at 2 K/min

Typical DSC curve at 4 K/min

Typical DSC curve at 8 K/min

Fig. 2.1: DSC curve of the examined material recorded at 0.5, 1, 2, 4 and 8 K/min (black curves: simulations after differential isoconversional analysis).

The selection of the evaluation range should contain the signal before and after the occurrence of the measured thermal event as depicted in Fig. 2.1 for the examined substance.

Generally the application of straight-line form for the baseline is incorrect [18]. 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:

symbolnameunits
B(t)The baselineWatts per Gram
S(t)The differential signalWatts per Gram
The reaction rate

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

Reaction progress

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) Around 0 and at α(t) Around 1 by 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 Cof 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. 2.2.

Baseline calculation, reaction rate and progress.

Fig. 2.2: DSC curve of the examined substance, baseline calculation, reaction rate and progress illustrated for a heating rate of 8 K/min.

AKTS-Thermokinetics Software enables advanced baseline construction ten (10) different baseline types (tangential sigmoid, tangential first point, tangential last point, sigmoid, spline, straight, horizontal last point, equal to zero baseline, staged) because the correct baseline selection is one of the most critical parts of data treatment. Constructed baselines can be optimized numerically.

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.

3. DETERMINATION OF THE KINETIC CHARACTERISTICS (STEP 2)

3.1. Kinetic analysis of thermally stimulated processes

Chemical reaction rates are most often considered to be a function of only two time-dependent variables, temperature T and chemical conversion α (which varies from 0 to 1 from initiation to completion). The usual relationship incorporating the Arrhenius expression is

Usual relationship incorporating Arrhenius expression

This equation relates the reaction rate dα/dt to three distinct kinetic parameters: the pre-exponential factor A, the activation energy E, and the reaction model f(α). As a set, these three parameters are referred to as the "kinetic triplet". Determination of the kinetic triplet is a common way to establish a mathematical relationship between the reaction rate dα/dt, the extent of conversion α, and the temperature (or time). The extent of the conversion α is determined experimentally as a fraction of the overall change in a physical quantity that represents the reaction progress as a function of time t or temperature T. If the reaction process is accompanied by heat flow, such as measured in a DSC or other heat flow device, then the extent of conversion at T or t is given as the ratio of the amount of evolved (or consumed) heat to the total amount of heat released (or absorbed) in the process. Mass loss/gain (for TG) is treated in a similar way. For adiabatic conditions the conversion can be related to the observed temperature rise relative to the total adiabatic temperature rise. A wide variety of the reaction models f(α) is applied in the solid-state kinetics, some of which are presented in Table 3.

Reaction model Abbreviation: f(α) Reaction model Abbreviation: f(α)
first order F1 : 1-α Avrami-Erofeev A1.5 : 1.5 (1-α) [-ln(1-α)]^(1/3)
second order F2 : (1-α)^2 Avrami-Erofeev A2 : 2 (1-α) [-ln(1-α)]^(1/2)
third order F3 : (1-α)^3 Avrami-Erofeev An : n (1-α) [-ln(1-α)]^(1-1/n)
nth order Fn : (1-α)^n contracting cylinder R2 : 2 (1-α)^(1/2)
power law P1 : α^0 contracting sphere R3 : 3 (1-α)^(2/3)
power law P2 : 2 α^(1/2)   Rn : n (1-α)^(1-1/n)
power law P3 : 3 α^(2/3) 1-dimensional diffusion D1 : 1/(2α)
power law P4 : 4 α^(3/4) 2-dimensional diffusion D2 : [-ln(1-α)]^-1
power law Pn : n α^(1-1/n) 3-dimensional diffusion D3 : 1.5 [1-(1-α)^(1/3)]^-1 (1-α)^(2/3)
    autocatalytic (1-α)^n α^m

Table 3.1. Typical reaction models f(α) applied in the solid-state kinetics

Although there is a significant number of various reaction models f(α), they all can be reduced to three major types when considering the dependence of the reaction progress on the time: accelerating, decelerating and autocatalytic. Each of these types has a characteristic reaction profile or kinetic curve, the terms frequently used to describe a dependence of α or dα/dt on t or T. Such profiles are readily recognized for isothermal data. The respective α or dα/dt vs. t reaction profiles are shown in Figure 3.1.

Relationship of the reaction progress α vs time for decelerating, autocatalytic and accelerating reaction models.

Fig. 3.1: Relationship of the reaction progress α vs time for decelerating, autocatalytic and accelerating reaction models.

(1) Models of the decelerating type represent processes whose rate has maximum at the beginning of the process and decreases continuously as the extent of conversion increases. The most common example here is a reaction-order model:

Reaction-order model.

where n is the reaction order. Diffusion models (Table 3.1) belong also to the decelerating models.

(2) Sigmoidal reaction models may be thought of as accelerating at the beginning (when α is close to 0) and decelerating at the end (when α is close to 1) so that the process rate reaches its maximum at some intermediate values of the extent of the conversion. The Prout-Tompkins autocatalytic model is a typical example of sigmoidal reaction models. It can be described by the following equation:

Sigmoidal reaction model.

These reactions typically have a long induction period at the beginning, so that thermal history of the sample may develop small but significant conversion α prior to detection of a signal, a possibility that must be considered during kinetic analysis. Therefore, for such chemistries, beyond the usual kinetic triplet, it is necessary to introduce the initial conversion α0 as an essential parameter in predictive calculations.

(3) Accelerating models represent processes whose rate increases continuously with increasing the extent of conversion α and reaches its maximum at the end of the process. Models of this type can be exemplified by a power-law model:

Power-law model.

where n is a constant.

Only those kinetic methods that allow considering all three types of the conversion dependencies can be recommended as reliable methods. Sestak and Berggren (SB) have introduced an empirical model:

Empirical model.

in which the values of the exponents m, n, and p characterize the contribution of the different reaction models in the observed reaction rate. The SB model is generally used in truncated form (p=0) being equivalent to the so called Prout-Tompkins autocatalytic model.

The motivation for kinetic evaluation of experimental data is the prediction of process rate and reaction progress at arbitrarily chosen values of temperature T or time t under any thermal mode (isothermal, non-isothermal, adiabatic, etc.). At lab scale the most common non-isothermal mode is one with an imposed heating rate dT/dt = Β = constant, while for long-term storage diurnal and seasonal temperature variations might be experienced. Predictions in either case are reliable only when sound kinetic analysis methods are used. It is however very important to note that a common difficulty in the correct interpretation of experimental data for such purposes is that even an apparently simple one-step process may in reality contain multiple steps and may require more complex elaboration of the experimental results. This remark is illustrated in Figure 3.2 where unknown amount of reactions can contribute to the observed, apparently simple, shape of the heat flow signal.

Uncertainity of thermokinetics analysis.

Fig. 3.2: Thermokinetic analysis of heat flow signals: the stages and physico-chemical reaction pathways are generally unknown.

With the approach proposed in AKTS software it is possible to analyze several observed thermal events that can be the combination of not always known chemical sub-stages of the reaction. For simplest reactions like A->B or for reactions of several consequent steps like:

A->B->C->D->E

AKTS software uses so called unique advanced differential isoconversional techniques for analysis and for predictions. The differential isoconversional approach allows determination of several values of kinetic parameters as the apparent activation energy as a function of the conversion. This unique feature enables to describe very precisely processes combining parallel or consecutive steps because at each time point several elementary (usually unknown) processes take place simultaneously. Therefore AKTS Software avoids cumbersome, time consuming and sometimes very arbitrary approach introducing the assumption of existence of several reaction models and activation energy values necessary for the kinetic analysis of the investigated process.

More generally, the differential isoconversional method does not require an explicit assumption of the form of f(α), and additionally does not assume the constancy of A and E during the course of the process (see Fig. 3.3). It is therefore generally more precise than presupposing knowledge of f(α) and assuming that A and E are constant over the range of α from 0 to 1.

Since differential isoconversional methods do not make use of any approximations about reaction models they are potentially very accurate and avoid the risk of wrong model assumptions which are not correct from chemical point of view and can have very dangerous consequences for e.g. thermal aging or hazards evaluation. Another advantage is that with the differential isoconversional approach it is possible to correctly describe kinetics of complex reactions within few minutes only.

The isoconversional principle states that the reaction rate at a constant conversion α (i.e., the isoconversional rate) is only a function of temperature. This can be easily demonstrated by taking the logarithmic derivative of the reaction rate at α = constant:

Isoconversional Principle.

where the subscript α indicates isoconversional values, i.e., the values related to a given extent of the conversion α. Because at α =const, f(α) is also constant therefore the second term in the right hand side of the previous equation is zero. Thus:

Isoconversional Principle.

It follows that the temperature dependence of the isoconversional rate can be used to evaluate isoconversional values of the activation energy, E(α) without assuming or determining any particular form of the reaction model f(α). For this reason, isoconversional methods are frequently called model-free methods. However, one should not take this term literally. Although the methods do not need to identify the reaction model, they do assume that the conversion dependence of the rate obeys some f(α) model. This is visible with the most common differential isoconversional method of Friedman. Friedman proposed to apply the logarithm of the conversion rate dα/dt as a function of the reciprocal temperature at any conversion α:

Isoconversional Principle.

Isoconversional Principle.

f(α) is a constant in the last term at any fixed value of α and the dependence of the logarithm of the conversion rate dα/dt on 1/T shows a straight line with the slope m = -E/R and intercept equal to ln(A(α)·f(α)) as presented in Figures 3.3 to 3.5. By extension

Isoconversional Principle.

with A'(α) = A(α)f(α)

Differential isoconversional analysis.

Fig. 3.3: Differential isoconversional analysis

Differential isoconversional analysis.

Fig. 3.4: Differential isoconversional analysis of the examined material

Activation Energy.

Fig. 3.5: Activation energy and pre-exponential factor as a function of the reaction progress for decomposition of the examined material.

Consider for example α = 0.5. A series of DSC experiments might be performed at different scan rates or different isothermal temperatures. At the point in each experiment when α = 0.5 the corresponding isoconversional rate and temperature are measured. Thus from a limited but sufficiently diverse set of small scale experiments one can establish the temperature dependence of the isoconversional reaction rate. This can in turn be used to evaluate isoconversional values of the activation energy E(α) and a modified pre-exponential factor A(α) without explicitly assuming a particular form of the reaction model f(α). Finally, the differential isoconversional results can be applied to accurately simulate the reaction rate dα/dt and progress α as illustrated in Figures 3.6 for the examined substance (or the time tα to reach a given reaction progress α = thermal aging) using the expressions:

Reaction rate and progress.

By extension above equation can be applied to calculate the reaction rate dα/dt and progress α for milligram, kilo, and ton scales under any thermal conditions, where T(t) is determined by applying appropriate heat balance equations.

Reaction progress.

Reaction rate.

Figures 3.6. Reaction rates and progress (normalized DSC-signals after correctly calculated baselines and kinetics) for the decomposition of the examined material. Experimental data are represented as color lines; black lines represent the calculated signals. The values of the heating rates are marked on the curves.

3.2. Remarks 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 [19]. The convergence of the activation energy values obtained by means of a differential method like Friedman method [20] with those resulted from using integral methods with integration over small ranges of reaction progress a 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 [21-22]) 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 [20].

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

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:

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:

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:

Equation

where Equation

and Equation

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:

Equation

It means that the isoconversional integral methods return to isoconversional differential method which corresponds to the Friedman approach that is described in the previous chapter. The conversion rate expression can now be adapted to an arbitrary variation of temperature by replacing β(dα/dT) with dα/dt.

Nomenclature
Apre-exponential factor
Amodified pre-exponential factor A(α)=A(α)·f(α)
Eactivation energy
k(T)rate constant
Rideal gas constant
ttime
TTemperature
αreaction progress
α0initial reaction progress at t=0
βimposed heating rate dT/dt
DSCDifferential Scanning Calorimeter

4. KINETICS AND THERMAL AGING - SHELF LIFE (STEP 3)

4.1 Prediction of the reaction progress under any temperature mode

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. 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). 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 [1, 8-17] 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
  • Sample Controlled Thermal Analysis

4.2 Isothermal, modulated, stepwise and real atmospheric temperature mode

4.2.1 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.

AKTS-Thermokinetics, Prediction Window

Isothermal Predictions

Isothermal Predictions

Figure 4.1. Calculated reaction rate and progress (normalized signals) of the decomposition of the examined material as a function of time under isothermal conditions. The values of the temperature in C are marked on the curves.

4.2.2 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 [2-7]). 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.

AKTS-Thermokinetics, Prediction Window

Non-Isothermal Predictions

Figure 4.2. Calculated reaction rate and progress (normalized signals) of the decomposition of the examined material as a function of time under non-isothermal conditions. The values of the heating rates in K/min are marked on the curves.

4.2.3 Stepwise

AKTS-Thermokinetics, Prediction Window

Stepwise Predictions

Figure 4.3. Stepwise mode. Reaction rate and progress α (normalized signals) of the examined substance as a function of time for combined isothermal and non-isothermal temperature modes (stepwise mode).

4.2.4 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 decomposition 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 ± 20°C amplitude and 24 h period indicates is presented below.

AKTS-Thermokinetics, Prediction Window

Modulated Predictions

Figure 4.4. Calculated reaction progress (normalized signals) of the decomposition of the examined substance as a function of time under isothermal (30°C) and oscillatory (30°C±20°C, 24 h period) temperature conditions. Presented figure illustrates the influence of the oscillatory temperature mode on the reaction progress.

4.2.5 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. This feature is interesting for low temperature decomposed substance.

AKTS-Thermokinetics, Prediction Window

Worldwide Predictions

Figure 4.5. Top: Average daily minimal and maximal temperatures recorded for each day of the year between 1961 and 1990 (Zurich and Miami). Middle and bottom: Reaction rate and progress (DSC, normalized signals) of the examined substance as a function of time for the Zurich and Miami temperature profiles.

4.2.6 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 can be carried out for climatic categories 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 cam represent e.g. the ambient 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. Applying the advanced kinetic software it is possible to calculate the reaction progress using the kinetic parameters determined from thermoanalytical signal and taking into account the dependence of the temperature changes depicted in STANAG 2895. This feature is interesting for low temperature decomposed substance.

AKTS-Thermokinetics, Prediction Window

STANAG Predictions

Figure 4.6 Predictions of the reaction rate and progress of the examined substance as a function of time due to the temperature variations represented by the diurnal storage temperature profiles of climatic category A2 of STANAG 2895.

4.2.7 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.

AKTS-Thermokinetics, Prediction Window

Customized Predictions

Figure 4.7 Example of prediction of the reaction rate and progress of the examined substance for measured temperature profiles.

4.2.8 Sample Controlled Thermal Analysis

AKTS-Thermokinetics Software can optimize temperature program in such a way that it allows to obtain the value of the reaction rate set by the user. It is often the case in industrial applications, that in order to achieve a certain characteristic profile, high quality or specific sample properties, thermal reaction rates should be very carefully controlled, not exceeding e.g. a certain critical value. This method of controlling reaction rate is known as Sample Controlled Thermal Analysis.

Sample Controlled Thermal Analysis

Significant is the control of a reaction rate by constantly increasing Partial Area between a signal and the baseline (for DSC and DTA), in order to force e.g. the uniform curing of epoxy resins. Therefore, as powerful tool for the solution of such problems, AKTS-Thermokinetics contains simulation through kinetic analysis of rate controlled mass change for thermogravimetric signals, rate controlled conversion and/or rate controlled partial area for DSC measurements. The target of this analysis is to provide such temperature profiles for achieve e.g. TGA-curves with constant mass loss rates or DSC-curves with rate controlled heat release (or consumption).

Example of prediction of rate controlled conversion

Example of prediction of rate controlled conversion

Figure 4.8 Example of prediction of rate controlled conversion (Sample Controlled Thermal Analysis) of the examined substance.

References

[1] AKTS AG, http://www.akts.com AKTS-Thermokinetics software)
[2] M.E. Brown et al. Computational aspects of kinetic analysis. The ICTAC Kinetics project data, methods and results. Thermochim. Acta, 355 (2000) 125.
[3] 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.
[4] 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.
[5] B. Roduit, Computational aspects of kinetic analysis. The ICTAC Kinetics Project - numerical techniques and kinetics of solid state processes. Thermochim. Acta, 355 (2000) 171.
[6] S. Vyazovkin, A.K. Burnham, J.M. Criado, L.A. Prez-Maqueda, C. Popescu, N. Sbirrazzuoli, ICTAC Kinetics Committee recommendations for performing kinetic computations on thermal analysis data, Thermochim. Acta, 520 (2011) 1-19.
[7] S. Vyazovkin, K. Chrissafis, M.L. Di Lorenzo, N. Koga, M. Pijolat, B. Roduit, N. Sbirrazzuoli, J.J. Suñol, ICTAC Kinetics Committee recommendations for collecting experimental thermal analysis data for kinetic computations, Thermochim. Acta, 590 (2014) 1-23.
[8] B. Roduit, W. Dermaut, A. Lunghi, P. Folly, B. Berger and A. Sarbach, J. Therm. Anal. Cal., 93 (2008) 1, 163-173.
[9] 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.
[10] 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., 93 (2008) 1, 143-152.
[11] B. Roduit, M. Hartmann, P. Folly, A. Sarbach, P. Brodard, R. Baltensperger, J. Therm. Anal. Calorim., 117(2014) 1017-1026.
[12] B. Roduit, M. Hartmann, P. Folly, A. Sarbach, P. Brodard, R. Baltensperger, Thermochim. Acta, 621 (2015) 6-24.
[13] B. Roduit, M. Hartmann, P. Folly, A. Sarbach, R. Baltensperger, Thermochim. Acta, 579 (2014) 31-39.
[14] 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.
[15] B. Roduit, Ch. Borgeat, B. Berger, P. Folly, B. Alonso, J.N. Aebischer, J. Therm. Anal. Cal., ICTAC special issue, 80 (2005) 91-102.
[16]P. Folly, Chimia, 58 (2004), 394.
[17] M. Dellavedova, C. Pasturenzi, L. Gigante, A. Lunghi, Chem. Ing. Trans., Vol
[18] Hemminger W. F., Sarge, S. M., J. Therm. Anal., 37 (1991), 1455.
[19] P. Brudugeac, J. Therm. Anal., 68 (2002) 131.
[20] H. L. Friedman, J. Polym. Sci, Part C, Polymer Symposium (6PC), 183 (1964).
[21] T. Ozawa: Bull. Chem. Soc. Japan, 38 (1965) 1881.
[22] J.H. Flynn, L.A. Wall, J. Res. Nat. Bur. Standards, 70A (1966), 487.
[23] 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.
[24] 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.
[25] 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.
[26] D.A. Frank-Kamenetskii, 2nd Ed., Translated from Russian by J.P. Appleton, Plenum Press, New York-London (1969) 375.
[27] N.N. Semenov, Prog. Phys. Sci. U.S.S.R., 23 (1940) 251-292; National advisory committee for aeronautics, Technical memorandum, 1024 Washington (1942) 1-57.
[28] J.M. Dien, H. Fierz, F. Stoessel, G. Kill: The thermal risk of autocatalytic decompositions: a kinetic study. Chimia (1994) 48(12):542-550.
[29] D.W. Smith, Assessing the hazards of runaway reactions, Chem. Eng., 14, (1984) 54.
[30] T. Grewer, Thermochim. Acta, 225 (1993) 165.
[31] R. Gygax, International Symposium on Runaway reactions, March 7-9, 1989, Cambridge, Massachusetts, USA, 52.
[32] F. Stoessel, Thermal Safety of Chemical Processes, Risk Assessment and Process Design, 1. Auflage - Februar 2008, WILEY-VCH Verlag GmbH & Co. CGaA.
[33] A heat transfer textbook Third Edition, John H. Lienhard IV / John H. Lienhard V, Phlogiston Press, Cambridge Massachusetts, 2008.
[34] H. Fierz, J. Hazard. Mater., A96 (2003) 121126.
[35] UN Recommendations on the Transport of Dangerous Goods, Manual of Tests and Criteria, 5th revised edition. United Nations, New York and Geneva, (2009) 297-316.
[36] M. Steensma, P. Schuurman, M. Malow, U. Krause, K.D. Wehrstedt, J. Hazard. Mater., A117 (2005) 89-102.

Possibilities of analysis offered

Abbreviations:        
TA: AKTS-Thermal Analysis (Calisto Software)        
TK: AKTS-Thermokinetics Software        
TS: AKTS-Thermal Safety Software        
RC: AKTS-Reaction Calorimetry Software TA TK TS RC
  Possibilities of analysis offered
Temperature modes allowed        
isothermal yes yes yes yes
non-isothermal linear, non-linear, arbitrary heating or cooling rates yes yes yes yes
isoperibolic (various constant oven temperatures) yes yes yes yes
Evaluation of the data collected by the following thermoanalytical techniques at conventional and/or specific conditions:        
Differential Scanning Calorimetry (DSC) yes yes yes yes
Differential Thermal Analysis (DTA) yes yes yes yes
Simultaneous Thermogravimetry & Differential Scanning Calorimetry / Differential Thermal Analysis yes yes yes yes
Pressure monitoring / Gas generation: P and dP/dt yes yes yes yes
TG (m(t)) and DTG (dm/dt) yes yes yes yes
Hyphenated Techniques: TG-EGA (MS or FTIR) yes yes yes yes
Dilatometry / Mechanical Analysis: TMA, DMA yes yes yes yes
Non Destructive Assay: NDA for e.g. Nuclear Waste Characterization (e.g.Setaram LVC-3013) yes yes yes yes
Gas Humidity Monitoring (e.g. Setaram Wetsys) yes yes yes yes
Microcalorimetry (e.g.TA Instruments TAM, Setaram C80, MicroSC and many others) yes yes yes yes
Reaction Calorimetry (e.g. Mettler RC1, Setaram DRC, HEL Simular, ChemiSens CPA 102, 202 and many others) yes yes yes yes
Thermal Conductivity of liquids and solids (e.g. C-Therm TCI) yes yes yes yes
Adiabatic Data (THT ARC, Fauske VSP, Omnical DARC and many others) yes yes yes yes
Additional Thermal hazard data: Radex, Sedex, Sipcon (Grewer, Ltolf, Miniautoclave, Hot storage test), CO-Monitoring and A16-Test, Deflagration-Test yes yes yes yes
Data collected discontinuously by e.g. HPLC with only few points for each temperature yes yes yes yes
Simultaneously collected data from the same or different instruments and units as e.g. yes yes yes yes
Heat flow DSC (W) and reaction calorimetry data of RC1 (W) yes yes yes yes
Heat flow DSC (W) and mass loss TG (mg) yes yes yes yes
Heat flow DSC (W) and temperature T(C) and pressure P(bar) in adiabatic conditions (e.g. ARC) yes yes yes yes
Features offered        
Subtraction of experimental base line (blank) yes yes yes yes
Reconstruction of the "under peak" base line (BL) for reaction rate data e.g DSC, DTA, DTG, etc. yes yes yes yes
Baseline types considered: Sigmoid, Tangential Sigmoid, Linear, Horizontal First Point, Horizontal Last Point, Horizontal, Staged, Spline & Polynomial with variable order, Tangential First Point, Tangential Last Point yes yes yes yes
Possible adjustments of temperature onset and offset yes yes yes yes
Baseline Subtraction with or without normalization (setting the integration value of the signal to one) yes yes yes yes
Smoothing data (allows the user to smooth partially or entirely a curve. Methods: Savitzky & Golay or Gaussian) yes yes yes yes
Custom Interpolation and Spikes Correction (designed to interpolate a portion of the signal to remove the bad or noisy data points). Interpolation modes: Straight line, Horizontal, tangential first or last points, Spline or Polynomial with variable orders yes yes yes yes
Dragging Data Points (for moving a data point in order to manually smooth the noisy part of the signal) yes yes yes yes
Removing Vertical Displacement (Signal Step) (allows the user to bring the zone of displacement to the same level as the left limit point) yes yes yes yes
Cutting externals, separate points, internal fragments (allows the user to cut a part of a signal which is not required) yes yes yes yes
Building complementary responses (integral from derivative and vice versa) yes yes yes yes
Derivation with adjustable "Derivative Filter" (the derivative of a curve at a certain point is the slope of the tangent to the curve at that point) yes yes yes yes
Integration (generates the integrated curve of a subtracted or normalized subtracted signal) yes yes yes yes
Viewing data in form of over-all conversion α(t) or dα(t)/dt yes yes yes yes
Viewing data in original form (Q(t), dQ/dt, m(t), dm/dt) raw mass or heat data considered instead of reaction extent α yes yes yes yes
Deconvolution and/or Temperature Adjustment by Inverse Filtering of DSC, heat flux or any type of thermoanalytical data (allows the user to consider the time constant of the temperature sensor in order to reconstruct the real response of the sample on the temperature change) yes yes yes yes
Automatic unit management by changing axis units: from e.g. W to mW, mW, Cal/s, mCal/s, mCal/s (and/or normalization: e.g. W/g, W/mol, etc.) yes yes yes yes
Customizable axis unit menu with any signals of user defined units: e.g. count/g, mg/ml, etc. yes yes yes yes
Automatic unit management by signal derivative and/or integral: e.g. J, W or K, K/s or K/min, etc. yes yes yes yes
Peak separation based on the application of Gaussian and/or Fraser-Suzuki (asymmetric) types signals (Position; Amplitude; Half-width; Asymmetry) yes yes yes yes
Thinning out data (reducing number of points without loss of information) yes yes yes yes
Statistical analysis of results of parallel runs via Customizing Equation (allows the user to apply a mathematical formula to one or more signals) yes yes yes yes
Heat capacity determination via two methods: Continuous Cp or Cp by Step (Both methods with or without reference) yes yes yes yes
Phase transition parameters determination yes yes yes yes
Glass transition (Tg) determination according to IUPAC procedure yes yes yes yes
Thermal conductivity determination of both solids and liquids yes yes yes yes
Converting to Natural Logarithm (especially useful when addressing the exponential Heat Flow signals obtained during isothermal studies) yes yes yes yes
Crystallinity evaluation of semi-crystalline materials yes yes yes yes
Oxidation Induction Time calculation based on the ISO 11357-6 norm yes yes yes yes
Purity determination calculated with Van`t Hoff equation yes yes yes yes
Setting Signal to Zero (allows the user to set to zero on the Y-axis the value of a selected point of a signal) yes yes yes yes
Slope Correction (adjusting the slope of a signal to remove its drift for a better presentation) yes yes yes yes
Temperature Correction (allows calibration of the apparatus to adjust the measured and the real temperatures of the sample) yes yes yes yes
Temperature Segmentation (generates from an experimental temperature curve a new temperature profile built up from an arbitrarily chosen number (between 1 and 2000) of segments) yes yes yes yes
TMA-True and Average Alpha and TMA Correction yes yes yes yes
Data Loading (Importing data in the form of ASCII files from files created by any type of apparatus via general interface yes yes yes yes
User Rights Management (Controls access to the software's features. The administrator can create the list of the users and decide about their rights) yes yes yes yes
Managing the Connection to the Database in which the data are stored in "ressource.adb" file yes yes yes yes
Deletion Management (allows to definitively remove zones and experiments (single or series) stored in the database) yes yes yes yes
Customizing Menus (to change the visible icons shown on the toolbars) yes yes yes yes
Copying Signals, Moving Axes, Merging Axes, Scrolling, Zooming, Magnifying Glass Option, Autoscaling, Cursor Tool, . yes yes yes yes
Chart Size Adjustment, Selecting Default Temperature, Merging Multiple Signals yes yes yes yes
Drag-and-drop a signal (from treeview to chart (and vice versa), from chart to chart, from treeview to treeview) yes yes yes yes
Saving and Loading Macros (recorded actions performed by the user to be applied again quickly) yes yes yes yes
Exporting Chart (available formats: *.png, *.gif, *.bmp, *.jpg, *.emf, automated exportation to MSWord) yes yes yes yes
Exporting Points (with or without interpolation, *.txt and *.csv, Excel *.xls) yes yes yes yes
Customizing Chart: Background, Border and Margins, Legend, Titles, Themes, Axes, Series, Adding and Customizing Notes and Images, etc. yes yes yes yes
Supported languages and translation for all Calisto features: English, French, Chinese yes yes yes yes
Types of kinetic analyses supported        
Isoconversional (model-free) kinetic analysis   yes yes yes
Custom arbitrary chosen formal kinetic models and reaction rates introduced manually   yes yes yes
e.g. da/dt =1e9 * exp(-100000/8.314/(T+273.15)) * (1-a)^1 + 1e10 * exp(-100000/8.314/(T+273.15)) * (1-a)^2*a^0.5   yes yes yes
Formal one- or multi-stage model-based kinetic analysis for discontinuously collected data   yes yes yes
Formal one- or multi-stage and concentration model-based kinetic analysis       yes
Data types and their combinations used for kinetic evaluation        
Discontinuous data composed from only few points (sparse data points, e.g. GC, HPLC data collected e.g. at three temperatures only)   yes yes yes
Continuous data:   yes yes yes
Tr-controlled data   yes yes yes
heat flow (e.g. DSC)   yes yes yes
pressure P (dP/dt) data   yes yes yes
mass loss and its rate (TG, DTG)   yes yes yes
all other thermoanalytical data collected continuously such as TG-EGA, TMA, etc.   yes yes yes
all microcalorimetric data such as TAM, C80, etc.   yes yes yes
non-isothermal - set of runs at various heating rates   yes yes yes
isothermal - set of runs at various temperatures   yes yes yes
set of runs at various heating rates and temperatures (combination of non-isothermal and isothermal data)   yes yes yes
Adiabatic data (e.g. THT ARC, Fauske VSP, Omnical DARC)     yes yes
Tj-controlled data (isoperibolic) and cascade controlled (PID controller) data of reaction Calorimetry (both batch or semi-batch) (e.g.: Mettler RC1, Setaram DRC, HEL Simular, ChemiSens CPA 102, 202 and many others)       yes
Combination of Tr-controlled data of different types (e.g. DSC and TG data)   yes yes yes
Combination of Adiabatic and Tr-controlled data (e.g. ARC and DSC for calculation of the kinetic parameters) for determination of safety hazard indicators (e.g. TMRad24, SADT)     yes yes
Combination of Tr- and Tj-controlled data for thermal safety and process optimization purpose (e.g. DSC and Mettler RC1)       yes
Methods for estimation of the kinetic parameters        
Arrhenius-type dependence of the reaction rate on temperature   yes yes yes
Linear optimization suitable for single stage models   yes yes yes
Non-linear optimization; applicable to data collected discontinously (sparse data points)   yes yes yes
Model ranking (Akaike's Information Criterion (AIC), Bayesian Information Criterion (BIC) and weighted scores (w)) for comparing and discriminating best kinetic models based on information theory   yes yes yes
Non-linear optimization method; applicable to complex multi stage models       yes
Simulation of thermal behavior in mg, kg and ton scales        
Temperature profiles applicable for thermal behavior predictions        
Isothermal   yes yes yes
Non-isothermal   yes yes yes
Stepwise   yes yes yes
Modulated temperature or periodic temperature variations   yes yes yes
Rapid temperature increase (temperature shock)   yes yes yes
Real atmospheric temperature profiles for investigating properties (50 climates by default with yearly temperature profiles with daily minimal and maximal fluctuations)   yes yes yes
Customized temperature and humidity profiles: possibility to compare the reaction progress of substances at any temperature and relative humidity (useful in combination with datalogger)   yes yes yes
NATO norm STANAG 2895 temperature profile: Zones A1, A2, A3, B1, B2, B3, C0, C1, C2, C3, C4, M1, M2, M3   yes yes yes
Specific features        
Extended option for High Sensitivity Isothermal Heat Flow Microcalorimetry (e.g. TAM data of propellants, surveillance of ammunitions, quality control) allowing to calculate the kinetic parameters from long term isothermal data for very precise lifetime prediction applying data collected during the first percent of degradation   yes yes yes
Sample Controlled Thermal Analysis: possibility to optimize temperature program in such a way that it allows obtaining the value of the constant reaction rate set by the user (allows creating temperature profiles for achieving e.g. TGA-curves with constant mass loss rates or DSC-curves with rate controlled heat release (or consumption))   yes yes yes
Combination of Tr-controlled data e.g. TG & DSC/DTA & MS data in multi-projects for simultaneous comparison of mass loss, heat flow and volatiles species evolution   yes yes yes
Bootstrap method for evaluation of prediction band (e.g. 95, 97.5 or 99 % confidence intervals), particularly important for long-term predictions (e.g. stabilizers in propellants, vaccines, etc.)   yes yes yes
Heat Accumulation, Thermal Runaway and Explosion     yes yes
Simulation of transient heat conduction systems such as thermal explosion in solids (this analysis considers the variation of temperature with time and position in one- and multidimensional systems)     yes yes
Simulation of lumped systems such as thermal explosion in low viscous liquids (this analysis considers that the temperature of a body varies with time but remains uniform throughout at any time)     yes yes
Influence of packaging geometry, material properties and insulations in simulation of the storage of dangerous materials     yes yes
Infinite slab     yes yes
Infinite axis-symmetrical cylinder     yes yes
Limited cylinder with given H/D ratio (H:height, D:diameter) and flat lids (e.g. drums, containers,etc.)     yes yes
Sphere (application of volume equivalent sphere radius and surface-to-volume ratio S/V, useful for the characterization of any package regardless its specific shape and size)     yes yes
Comparative thermal explosion analysis (e.g. cylinder with given H/D ratio vs sphere with equivalent surface-to-volume ratio S/V)     yes yes
Others geometries (after exportation of the kinetic parameters into codes like Abaqus, Ansys dedicated for the more complex geometries)     yes yes
Inert shell and partitions, multilayer packaging materials (different layers of insulation with different thicknesses)     yes yes
Different properties for separate part of an object     yes yes
Possibility of considering temperature dependence of physical properties     yes yes
Export of material data properties from database (with possible customization of the material property list)     yes yes
Heat sources in an object     yes yes
Possibility of application of specific kinetic parameters for separate parts of an object     yes yes
Heat-generated by a reaction and or non-reactive heat sources     yes yes
Time-dependent boundary conditions:     yes yes
1st kind - Prescribed temperature at the surface (Dirichlet condition)     yes yes
2nd kind - Heat flux at the surface (Neumann condition)     yes yes
3rd kind - Heat transfer at the surface (Newton law, convective heat transfer, mixed boundary conditions)     yes yes
Determination of hazard indicators     yes yes
Time to Maximum Rate under adiabatic conditions (TMRad) for any chosen starting temperature     yes yes
Safety diagram: runaway time as a function of process temperature under adiabatic conditions (TMRad = f(T))     yes yes
Automatic determination of the starting temperatures corresponding to TMRad of 7 days, 24h, 8h and 4h     yes yes
Self heat rate curves dT/dt, dQ/dt and dalpha/dt (dP/dt possible in combination with e.g. ARC data for pressure/gas generation and ventsizing calculations)     yes yes
Influence of the different Phi factors (Phi=1 and Phi>1) on the TMRad and on dT/dt, dQ/dt, dalpha/dt and dP/dt     yes yes
Total energy release under adiabatic conditions     yes yes
Total pressure release under adiabatic conditions (possible in combination with e.g. ARC data)     yes yes
Temperature corresponding to ARC detection limit such as 0.02 K/min for any Phi factors     yes yes
Automatic determination of the Self-Accelerating Decomposition Temperature (SADT) according to the recommendations of Manual of Tests and Criteria of the United Nations on the transport of dangerous goods     yes yes
Automatic determination of the critical hot discharge temperature 'Tin' in e.g. a container or critical surrounding temperature 'Tout'     yes yes
Automatic determination of the critical radius 'r' of e.g. a container and the critical thickness 'd' of an insulation layer of such a container     yes yes
Determination of the relationship between the input factor Xi (thermal conductivity, density and specific heat) and the output Y (time to thermal explosion) for identifying the physical property of a material (chemical or packaging layer) which will mostly influence the time to thermal explosion     yes yes
Setting of time steps, spatial mesh and numerical precision and computation speed     yes yes
Variable adaptive time step     yes yes
Uniform and Non-uniform spatial mesh     yes yes
Second order accuracy in both space and time and numerical stability even for large time steps (to ensure high precision and decreases by orders of magnitudes the calculation time)     yes yes
Display of results     yes yes
Evolution of the temperature profile T(t) and reaction progress a(t) in the cross-section or in a selected point of an object     yes yes
Temperature and conversion distribution on isolines (2-D) and/or 3-D graphs     yes yes
Animated isolines (2-D) and/or 3-D views of both temperature and reaction progress distribution     yes yes
Chemical reactors considered       yes
Batch       yes
Semi-Batch       yes
Continuous Stirred Tank Reactor (CSTR)       yes
Plug-Flow (PFR)       yes
Cascade of reactors including       yes
Stream (continuous or discontinuous with or without dosing conditions for optimization of feed rate dosing profile)       yes
Mixing       yes
Splitting       yes
Heating       yes
Temperature modes       yes
Adiabatic       yes
Tr-control       yes
Tj-control (isoperibolic)       yes
Cascade control (PID controller)       yes
Customizable temperature profiles (isothermal, non-isothermal, stepwise, own profile, etc.)       yes
Process Flow Diagram (PFD) modules for an easy saving of various reactor types       yes
Process optimization (e.g. adjustment of the best feed or temperature profiles for maximum yield and selectivity)       yes
Specific process control (process parameters (e.g. feed or temperature) can be constraint to remain below or above some critical values at all time during the reaction for achieving inherent safety process)       yes