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 raw materials and products within the scope of
research, development and quality assurance. The
technique provides a means to infer additional
characteristics and behaviour of examined substances
based on conventional thermoanalytical measurements. The
method 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 conditions. By comparison, direct
investigation of such 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
following temperature profiles: isothermal,
non-isothermal, stepwise, modulated temperature or
periodic temperature variations, rapid temperature
increase (temperature shock) and real atmospheric
temperature profiles (up to 7000 climates).
Fig.1: Non-isothermal
conditions: DSC scans of multi-step a
Nitrocellulose-Nitroglycerine based compound at 0.5, 1, 2
and 4 Kmin-1. Black dots are experimental, baseline
corrected data. Pink, green, blue and red curves are model
free simulated curves.
Fig.2:Friedman analysis with advanced
baseline optimization for an accurate determination of the
activation energy:
If the decomposition follows a single mechanism then the
reaction can be described in terms of a single pair of
Arrhenius parameters and the commonly used set of reaction
models. In such cases the dependence of the logarithm of
the reaction rate over 1/T is linear with the same slope
of E/R for all conversion degrees xn. The reaction
rate can be described by only one value of the activation
energy E and one value of the pre-exponential factor A by
the following expression:
with n: index of conversion,
k: index of heating rate
However, this approach is not acceptable for most of the
decomposition reactions because, as presented in the
Friedman analysis plot and in the next figure for the
examined samples, the activation energy is often strongly
dependent on the reaction progress.
Thus, fulfilling both conditions
(I: Arrhenius type reaction rate and II: Gaussian-type
distributed errors) makes possible the iterative
calculation and objective determination of the correct
baseline for each signal measured under different heating
rates. This objective determination is done by the
iterative calculation of all tangent parameters for each
heating rate:
ai,k, bi,k, aj,k, bj,k for each heating rate k
with
i = indices of the slope and intercept of the tangent at
the beginning of the signal S(T) with the heating rate 'k'
j = indices of the slope and intercept of the tangent at
the end of the signal S(T) with the heating rate 'k', where
B(T) the baseline Bk(T) = (1-x(T))*(ai,k+bi,k*T)
+ x(T)*(aj,k+bj,k*T),
S(T) the differential signal,
x(T) the reaction progress
The baselines are no longer arbitrarily chosen by the
users but objectively optimized taking into account:
- statistics, for the consideration of the experimental
noise and shape of the signals. - the kinetic parameters,
for the consideration of reaction rates following
Arrhenius relationship:
Fig.3:Activation energy
:
Activation energy as a function of the
reaction progress for decomposition of the examined
material.
Fig.4:Isothermal
conditions: Calculated
reaction progress (DSC, normalized signals) of the
decomposition of the Nitrocellulose/Nitroglycerine
compound as a function of time under isothermal
conditions. The values of the temperature in °C are marked
on the curves. The predictions are in good agreement with
two subsequent measurements for control under isothermal
conditions (82% decomposition at 120°C after 10 days, 0.7%
decomposition at 80°C after 20 days). The confidence
interval (with d = 4s = 0.5%) for a temperature of 120°C
is indicated after 10 days. These values indicate that
there is a 95% probability that the reaction progress
after 10 days exposure at 120°C is greater than 77 and
lower than 93%.
Fig. 5: Modulated temperature or
periodic temperature variations:
reaction extent of the decomposition of the examined
energetic material in isothermal 50°C and oscillatory
temperature modes (24 h period, Temperature variations
50°C
±40°C).
Fig. 6: Modulated temperature or
periodic temperature variations: reaction
progress (DSC, normalized signals) of the Nitrocellulose/Nitroglycerine
substance as a function of time for the temperature shock
mode (24 h period, Temperature variations 100°C+
50°C; isothermal: 50°C and 150°C).
Fig. 7: Real atmospheric temperature mode: Influence of the temperature profile changes (Moscow and Riyadh) on the reaction extent of the Nitrocellulose / Nitroglycerine compound.
Benefits
