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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 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)

1. INTRODUCTION - ANALYSIS PROCESS

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. 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. Analysis Process

A full kinetic analysis of a solid state reaction has at least three major steps [1-8]:

• (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).

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, 2, 4 and 8 K/min (non-isothermal) with a sample masses between 6.66 and 9.69 mg (AKTS recommends to use the high pressure sealed crucibles of the Swiss Institute for the Promotion of Safety and Security http://www.swissi.ch/index.cfm?rub=1010). Figures 2.1 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 [9]. 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)  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 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.

In addition to the sigmoid baseline types, AKTS-Thermokinetics Version 3 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. Constructed baselines can be optimized numerically. 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.

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

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 vs. t reaction profiles are shown in Figure 3.1.

(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:

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:

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:

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:

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 experimental signal (bold line).

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. 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 ageing 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 (eq. 1) at α = constant:

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:

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:

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

with A'(α) = A(α)f(α)

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:

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 (Figure 3.7).

Nomenclature
A	pre-exponential factor
A’	modified pre-exponential factor A’(α)=A(α)·f(α)
E	activation energy
k(T)	rate constant
R	ideal gas constant
t	time
T	Temperature
α	reaction progress
α0	initial reaction progress at t=0
β	imposed heating rate dT/dt
DSC	Differential Scanning Calorimeter

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 [10]. The convergence of the activation energy values obtained by means of a differential method like Friedman method [6] 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 [7-8]) 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 [6].

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:

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.

4. KINETICS AND MILLIGRAM SCALE - 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. 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, 11-18] 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
• etc.

4.2 Isothermal, modulated, stepwise and real atmospheric temperature modes

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.

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 [2-5]). 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)

4.2.3 Stepwise

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

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.

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 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. This feature is interesting for low temperature decomposed substance.

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.

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.

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).

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