KINETIC ANALYSIS OF THE THERMAL DECOMPOSITION OF AMITRIPTYLINE HYDROCHLORIDE BY NONISOTHERMAL THERMOGRAVIMETRY
Laila Tosson Kamel*
Narcotic Department, National Centre for Social and Criminal Research
Zamalek , 11561, Cairo, Egypt
Key Words: Amitriptyline hydrochloride, isoconversional methods, DAEM method, master plots
ABSTRACT
The nonisothermal thermogravimetric decomposition of amitriptyline hydrochloride was investigated under pure nitrogen atmosphere at four different heating rates (β =5, 10, 15, 20oC min-1). Friedman, Flynn-wall-Ozawa, and Tang isoconversional methods were used to calculate the activation energy Ea. The results obtained was compared with that obtained by the distributed activation energy model, Miura procedure. Activation energy, Ea, results showed that the isoconversional kinetic methods used (Friedman, Flynn-Wall-Ozawa and Tang methods) were in good agreement with each other, together with the distributed activation energy model. It was found that the activation energy Ea was not really changed and was almost independent with respect to the level of conversion (α). This result suggests that the nonisothermal decomposition process of amitriptyline hydrochloride follows a single-step reaction. The master-plots were used to obtain the reaction kinetic model, which was confirmed by the integral composite I method. The kinetic triplet determined was, activation energy, Ea = 74.68 kJmol-1 , pre-exponential factor, A= 3.71×103 min-1 and the reaction kinetic model follows the Avrami-Erofeev model, (nucleation and growth) , A4, f(α)= 4(1-α)[-ln(1-α)]3/4 , g(α) =[-ln(1-α)]1/4 . 1- INTRODUCTION Amitriptyline hydrochloride (AMT), with trade names, Vanatrip, Elavil, Endep, is an antidepressant drug under tricyclic antidepressant group. AMT has been widely used in the treatment of chronic pain, regardless of the presence of depression (Burke et al.,2015). It is used to treat many psychological disorder including major depressive disorder, anxiety, attention-deficit hyperactivity disorder, and bipolar disorder (Dipalma and Katzung,1983).
The thermal decomposition study, has received considerable attention all along the modern history, especially in the pharmaceutical field. Thermogravimetry, derivative thermogravimetry (TG/DTG) and differential thermal analysis (DTA), are analytic tools of high importance that helps in identifying the polymorphic forms, phase transitions, active–excipients
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interactions, shelf life determinations, evaluation of the validity, thermal stability, products formed during decomposition, thermal decomposition kinetics and identification of drugs. (Silva et al, (2015); Rodante et al (2002), Wang and You (2014); Salama et al (2015); Mohamed and Attia (2017) and Wang and You (2016))
Thermal decomposition of AMT has important theoretical significance for further understanding its chemical properties. To our knowledge, the thermal decomposition of amitriptyline hydrochloride is not yet studied. In this paper the complete kinetic triplet of amitriplyline hydrochloride decomposition under nonisothermal conditions was calculated using multiple heating rates. Differential (Freidman method) and integral (Flynn Wall Ozawa and Tang methods), isoconversional (model-free) methods, mater plots and integral composite I method were used. The distributed activation energy model (DAEM) the Miura’s procedure was also used for the investigation decomposition process.
2- EXPERIMENTAL
2.1. Materials
Amitriptyline hydrochloride (AMT) of at least 98% purity was purchased from Sigma Chemical Co. (St. Louis, MO, USA).
2.2. Instrument
The TG, DTG, and DTA curves were obtained by Shimadzu TGA-50 thermobalance, under nitrogen atmosphere gas at a flowing rate of 20 mL/min, at heating rates 5, 10, 15 and 20 °C min-1 with an average mass of samples, 3.584, 5.227, 5.445 and 5.496 mg, respectively, contained in an alumina crucible . Temperature range was from ambient one to 400°C.
3- Theoretical
The governing equation for kinetic analysis of solid state decomposition can be expressed as: (1)
Where α is the degree of conversion and it increase from 0 to 1.
where, mt represents the mass of the sample at time t (or temperature T), whereas mo and mf are the mass of the sample at the beginning and at the end of the process, respectively. T is the absolute temperature, K(T) represents the temperature – dependent rate constant, is the conversion rate. f(α) is the differential conversion function (reaction model). The reaction models may take various analytical forms.
The temperature dependent rate constant is introduced by replacing K(T) with the Arrhenius equation, which gives
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(2)
Where A is the pre-exponential (frequency) factor (min-1), Ea is the apparent activation energy (kJmol-1) and R is the gas constant (8.314 kJmol-1).
For the nonisothermal measurement at constant heating rate of β = dT/dt Eq. (2) may be transferred to (3)
Equations (2 and 3) are the fundamental expressions of analytical methods to calculate kinetic parameters on the basis of TG data. Integration of eq. (3) leads to (4)
Where g(α) is the function of the reaction model in the integral form. and the right-hand side of Eq.(4) is a function known as the temperature integral that has no analytical solution but can be resolved either by numerical methods or by different approximations.
3.1. Isoconversional methods
The isoconversional methods are model independent that estimates the apparent activation energy at progressive degree of conversion by conducting multiple experiments at different constant heating rates are highly recommended for obtaining the reliable kinetic description of the investigated process. (Jankovic and Mentus, 2009)
In order to determine the apparent activation energy Ea and the pre exponential factor, ln A, the following methods are used.
3.1.1. Friedman method (FR) (Friedman,1964)
FR method, a linear differential isoconversional method based on Eq. (3) in the logarithmic form , (5)
The apparent activation energy, Ea ,and the pre exponential factor ,lnA, are determined from the slope and intercept of the plot of ln(dα/dt) vs 1/T at a constant α value respectively.
3.1.2. Flynn–Wall–Ozawa method (FWO) (Flynn et al ,1966 and Ozawa ,1965)
FWO method, a linear integral method uses the following equation: (6)
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Plotting ln β vs 1/T should give straight lines, the slope of which is directly proportional to the activation energy and the intercept to the pre exponential factor lnA, at a constant α value .
3.1.3. Tang method (Tang, 2003)
Tang method, a linear integral method based on the following equation:
Plotting vs 1/T should give straight lines, the slope of which is directly proportional to the activation energy and the intercept to the pre- exponential factor lnA, at a constant α value.
These plots are model independent since the estimation of the apparent activation energy does not require selection of particular kinetic model.
3.2- The Distributed Activation Energy model (DAEM) (Miura ,1995; Miura and Maki,1998)
Generally, the DAEM model may be written as the following expression (8)
where a distribution function f(Ea) is used to represent the difference in activation energies for an infinite number of irreversible first-order parallel reactions. V and V* are the amount of volatile formed by time t, and the total volatile amount of the AMT sample, respectively.
Under linear non-isothermal conditions, Eq. (8) can be rewritten as follows: (9)
Where (10)
In the DAEM models, the activation energy function f(Ea) can be conventionally described by a Gaussian distribution with a mean activation energy, E0, and a standard deviation, σ. (11)
Recently, Miura and Maki (Miura and Maki,1998) have proposed a new simplified DAEM model. In their study, the temperature integral has been approximated with the following expression: (12)
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And with this approximation, the double exponential function φ(Ea ,T) becomes (13)
Further , the function φ(Ea , T ) can be approximated by a step function at
Ea = Es for a selected temperature T so that the activation energy Es can be chosen to satisfy φ(Ea ,T ) ≅ 0.58 using this approximation, Eq. (13) gives (14)
In the meantime, Eq. (9) can be simplified to (15)
Obviously, this treatment approximates that only a reaction having Ea occurs at the specific temperature T and the heating rate β.
Finally, the related Arrhenius equation can be written as follows (16)
Thus, the Arrhenius plot of ln(β/T2) versus 1/T at the same α conversion levels should be a straight line, and its slope and intercept can be used to determine the values of Ea and lnA, respectively. The activation energy distribution function f(Ea) can be obtained by differentiating the V/V* versus Ea relationship. In this method, the compensation effect between lnA and Ea was assumed to be ln A =ln a + bEa ; and no assumption is required for the functional form of f(Ea). For simplicity, the symbol α, the degree of conversion, is used here for conversion in place of V/V*. The calculating procedure to estimate f(Ea) and A using the above-mentioned DAEM method, is given as follows:
(1) Obtain α versus T relationships at least three different heating rates;
(2) Calculate the values of ln(β/T2) at selected a values for different heating rates;
(3) Plot ln(β/T2) versus 1/T at selected α values, and determine the Ea and lnA values from the Arrhenius plots at different a values using Eq. (16);
(4) Plot the α versus Ea;
(5) Differentiate the α versus Ea relationship to obtain f(Ea).
3.3- Master Plots (Pedro et al, 2010)
The generalized kinetic equation introduced by Ozawa, (1965) was used for the proposal of universal master plots that were valid for
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experimental data recorded under any heating profile. (Gotor et al , 2000)
Thus, if the generalized time is defined as: (Ozawa, 1986) (17)
where, considering the integral of Eq. (2), it is clear that θ represents the time needed to reach a certain α value at infinite temperature. By differentiating Eq. (17) the following equation can be obtained:
(18)
The combination of eqs. (2 and 18) leads to (19)
which can also be expressed in the following way: (20)
dα/dθ being the generalized reaction rate that, according to Eqs. (2, 19 and 20), represents the reaction rate extrapolated at infinite temperature as previously shown by Ozawa, (1986). Since the previous knowledge of the activation energy allows for the extrapolation to infinite temperature of experimental data recorded under any heating profile, Eq. (20) should be valid for the analysis of any data, independently of the temperature profile under which they were obtained. From Eq. (19) and taking α = 0.5 as a reference we get: (21)
As f(0.5) is constant for a certain kinetic model, Eq. (21) indicates that for a given α, the reduced-generalized reaction rate, (dα/dθ)/(dα/dθ) α=0.5, would be equivalent to f(α)/f(0.5) when the proper f(α) is selected to describe the process. From Eq. (20 and 21), the relationship between the generalized reaction rate and the experimental data can be established: (22)
where T0.5 represents the temperature corresponding to α = 0.5.
The previous knowledge of the activation energy is required in order to construct the experimental master plots. By plotting together the generalized reaction rate, as calculated from Eq. (22), and the fraction f(α)/f(0.5), corresponding to different theoretical kinetic models, versus α, it is possible to deduce by comparison the kinetic model followed by the process. Table (1) shows the algebric expressions for the most frequently used mechanisms of solid state process.
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It must be noted that, according to Eq. (22), for non-isothermal experiments a single activation energy value is assumed. Therefore, for this analysis procedure to be valid, the studied process must obey single step kinetics. isoconversional analysis, must be used to check that the activation energy does not vary with α in a significant way.
Table (1) Algebric expression for the most frequently used mechanisms of solid state process
No
Mechanism
S*
Differential form
Integral form
Sigmoidal Curves ( Nucleation and nuclei growth , Avrami-Erofeev equ.)
1
N and G (n=1)
A1
(1-α)
[-ln(1-α)]
2
N and G (n=1.5)
A1.5
[-ln(1-α)]2/3
3
N and G (n=2)
A2
[-ln(1-α)]1/2
4
N and G (n=3)
A3
[-ln(1-α)]1/3
5
N and G (n=4)
A4
[-ln(1-α)]1/4
Deceleration curves
6
Diffusion,1D
D1
α2
7
Diffusion, 2D
D2
8
Diffusion,3D
D3
9
Diffusion,3D
D4
10
Diffusion,3D
D5
11
Diffusion,3D
D6
12
Contracted geometry shape (cylindrical symmetry)
R2
13
Contracted geometry shape (sphere symmetry)
R3
Acceleration curves
14
power law
(n=2)
P2
2α1/2
α1/2
15
power law
(n=3)
P3
3/2α2/3
α1/3
16
power law
(n=4)
P4
4α3/4
α1/4
17
power law
(n=2/3)
P3/2
2/3α-1/2
α3/2
18
Mample power law
(n=3/2)
P2/3
3/2α1/3
α2/3
19
Mample power law
(n=4/3)
P3/4
4/3α-1/3
α3/4
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4- RESULTS AND DISCUSSION
4.1- Characterization Results
The TG and DTG curves of the thermal decomposition process of AMT samples obtained at different heating rates (5, 10, 15, 20oC min-1) under nitrogen atmosphere are shown in Figs (1 and 2) respectively. As shown in Fig. (1) TG curves are shifted to higher temperatures as the heating rates increases from 5 to 20oC min-1. The shapes of the curves are quite similar, all curves showed one decomposition step. There is no mass loss up to 206oC, as temperature increases the TG curves exhibit a total mass loss in the temperature range 274.47-327.97oC. Fig. (2) shows the DTG peaks of the thermal decomposition of AMT. Peaks become stronger and wider as the heating rate increases from 5 to 20oCmin-1 and the peak temperature is promoted from 242.15 to 281.72oC.
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It is evident from both curves (TG/DTG) that the thermal decomposition of AMT exhibited only one single step reaction. Fig. (3) shows the DTA curve of AMT at 10oC min-1. The curve presents a first strong peak at 198oC, which corresponds to the melting process of the AMT. The second broad peak, in the temperature range 289-320oC, shows the endothermic nature, of the decomposition process.
Amitriptyline hydrochloride (AMT), (3-(10,11-dihydro-5H-dibenzo [a,d]cycloheptane-5-ylidene)-N,N-dimethyl-1-1-propanamine), has a dibenzocycloheptadiene structure with rigid, almost planar tricyclic ring system and a short hydrocarbon chain carrying a terminal nitrogen atom attached to cycloheptadiene through methylene groups with an exocyclic double bond substituted with N,N-dimethyl 1,1 propane amino side chain. The structure of amitriptyline is shown in Fig.(4).
Fig.(4) The structure of AMT
Thermal decomposition of organic molecules is due to the molecular kinetic energy increasing during heating. These include atomic oscillations that rupture the weaker chemical bonds. The fragmentation of tricyclic antidepressants is similar to that of phenothiazines (Kollroser
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and Schober , 2002). Fig.(5) shows the proposed mechanism of the
thermal decomposition of AMT. The bond between the tricyclic ring and
the dimethylamine group in the side chain is broken, which results in the
formation of iminium ion (H2C=N(CH3)2)+ with complete decomposition
in one step.
CH2
+
N
H3C CH3
iminium ion
N
+
CH3
CH3
C
H
H
(Complete decomposition)
Fig.(5) The proposed mechanism of the thermal decomposition of AMT
4.2. - Calculation of Activation Energy Ea
4.2.1- Isoconversional methods
The conversion values, α, range from (0.2 ≤ α ≤ 0.8) were used in
this work rather than the entire range. This range is strongly
recommended because solid-state reactions are not stable at the
beginning and ending periods. Solid-state reaction usually contains a
diffusion process (Koga and Criado 1998a&b), as it generates
temperature and partial pressure gradient. Consequently, it generates
reaction gradient from the outer to the inner surface of the solid sample.
As a result, the real activation energy values at this period are different
from the ones at the middle period (0.2 to around 0.8). (Jankovic et al,
2009)
Figs (6, 7 and 8) show a typical FR , FWO and Tang
isoconversional methods plots which are constructed according to eq. (5,
6, 7) respectively to evaluate the slopes of ln (dα/dt) vs. 1/T , ln (β/T2)
vs. 1/T and vs 1/T respectively . Figs. (6, 7 and 8) show
that the conversional lines at all considered conversion levels have
almost the same slopes . The apparent activation energy was determined:
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(FR) Ea, FR = 70.24 kJmol-1 , (FWO) Ea,FWO = 78.61kJmol-1 , (Tang),
Ea,Tang = 75.12 kJmol-1 .
It should be noted that these results are obtained without any
knowledge of the reaction model function.
4.2.2. The distributed activation energy model (DAEM)
The Arrhenius plot of ln(β/T2) vs 1/T at the same α conversion
levels was constructed according to eq. (16) is shown in Fig. (9). All
lines have almost the same slopes, the apparent activation energy was
determined (DAEM) Ea, DAEM = 74.76 kJmol-1.
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It is clear that the apparent activation energy Ea values calculated using different methods are in good agreement with each other. It is observed that the value of Ea calculated by means of FR method is slightly lower than those calculated by means of (Tang and FWO) methods, and the DAEM method. It is also shown that the Ea determined by FWO is slightly higher. These differences may be attributed to different ways to derive the relations being the back ground of these methods. Kinetic parameters of thermal decomposition of AMT corresponding to different degrees of conversion α calculated by Freidman (FR), Flynn Wall Ozawa (FWO), Tang and DAEM equations respectively are shown in Table (2). The dependence of the apparent activation energy Ea on the extent of conversion, α, (Ea-α plot) (Budrugeac et al, 2001a&b; Sbirrazuoli et al, 1997) for the nonisothermal decomposition process of AMT is shown in Fig. (10). It is observed that regardless of the calculation procedure used the activation energy Ea remain partially constant ie. does not depend on α, the relative error is less than 6%. This suggests that the nonisothermal decomposition process of AMT follows a single step reaction.
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Table (2) The Ea and lnA values of thermal decomposition of AMT corresponding to different degrees of conversion α
FR method
FWO method
Tang method
DAEM method
α
Ea
lnA
R2
Ea
lnA
R2
Ea
lnA
R2
Ea
lnA
R2
0.2
72.92
9.08
0.996
81.02
10.19
0.993
81.18
8.69
0.995
80.84
10.38
0.995
0.25
72.56
9.19
0.999
82.65
9.89
0.999
78.62
7.87
0.999
78.28
9.56
0.999
0.3
72.78
9.37
1
82.59
10.38
0.998
79.55
7.95
0.993
79.2
9.64
0.993
0.35
70.86
8.77
0.998
80.68
10.15
0.999
77.49
7.34
0.999
77.14
9.02
0.999
0.4
70.67
8.417
0.999
80.31
10.16
0.999
78.10
7.36
0.998
77.75
9.05
0.998
0.45
72.23
9.19
0.980
78.67
9.50
0.998
76.34
6.85
0.999
75.99
8.53
0.999
0.5
69.45
8.34
0.995
78.38
9.90
0.999
76.00
6.66
0.999
75.64
8.34
0.999
0.55
69.99
7.99
0.993
78.38
9.65
0.999
73.83
6.00
0.998
73.46
7.67
0.998
0.6
68.54
8.08
0.987
78.52
9.65
0.999
73.96
6.01
0.999
73.6
7.68
0.997
0.65
69.85
8.45
0.991
77.23
9.52
0.999
72.56
5.59
0.999
72.19
7.27
0.999
0.7
67.56
7.58
0.987
75.59
9.32
0.999
70.80
5.10
0.999
70.43
6.77
0.999
0.75
67.86
7.88
0.991
74.83
9.23
0.999
69.99
4.86
0.999
69.61
6.52
0.995
0.8
67.84
7.48
0.999
73.12
9.03
0.995
68.12
4.30
0.999
67.74
5.96
0.999
Av
70.24
8.45
78.61
9.73
75.12
6.51
74.76
8.18
4.3. Determination of the most probable reaction mechanism
Master plots are reference theoretical curves that depend on the kinetic model but are independent of the kinetic parameters. Experimental data can easily be transformed into experimental master plots and compared with the theoretical ones determined for the different kinetic models. Comparing various kinetic models with the experimental master plot, the appropriate kinetic model can be easily selected.
Fig.(11) shows the comparison between the master plots constructed from the experimental data eq. (22) at the four heating rates (5, 10, 15, 20oCmin-1) using the average value of the apparent activation energy Ea (74.68kJ mol-1) in conversion fraction, α, (0.20 ≤ α ≤ 0.80) with the plots constructed from the most usual kinetic models Table (1). It is clear that the thermal decomposition of AMT has a very close resemblance to the nucleation and growth kinetic models, Avrami-Erofeev model, A4, f(α)= 4(1-α)[-ln(1-α)]3/4, g(α) =[-ln(1-α)]1/4 .
The observed displacement of the curve is attributed to the difference between the real process and the ideal conditions.
In order to confirm the established reaction mechanism, the integral I composite method, was applied. The composite method presuppose one single set of activation parameters for all conversions and heating rates. In this way, all the experimental data can be superimposed in one single master curve.
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The composite integral method I (Budrugeac and Segal, 2005; Gabal, 2003) is based on the Coats–Redfern equation (Coats and Redfern , 1964) which is rewritten as follows:
For each form of g(α), the curve vs 1/T was plotted for the experimental data obtained at different heating rates. The kinetic model that gives the best correlation coefficient where the data falls in a single master straight line is chosen.
From Fig.(12), it is clear that A4 model, f(α)= 4(1-α)[-ln(1-α)]3/4 , g(α) =[-ln(1-α)]1/4, best fits the decomposition process because all the different heating rate data are in only one master curve.
4.4. Calculation of pre-exponential factor
The pre-exponential factor lnA is estimated from the intercepts of the plots of Figs (6, 7, 8), by inserting the obtained most probable kinetic function model, A4, in the eqs. (5,6,7. f(α) 4(1-α)((-ln(1-α))3/4 was inserted in eq.( 5),where the g(α) =[-ln(1-α)]1/4 was inserted in eqs. (6 and 7). Results show that the pre-exponential factor ,A, values range from 103 to 104 min-1 and the average value of ,A, is 3.71 × 103min-1.
Fig. (13) shows the functional dependence between lnA and Ea of AMT. The linear relationship between lnA and activation energy Ea could possibly be written as
207 Egypt. J. of Appl. Sci., 34 (9) 2019
lnA = 0.3085Ea -13.136. lnA versus Ea relationship indicates that there is a kinetic compensation effect, that is to say, there exist a compensatory increase of lnA with an increasing activation energy Ea. The kinetics compensation effect is due to the change in reactant properties during the sample decomposition reaction, which becomes more difficult to occur as the conversion increases, subsequently presenting a higher activation energy (Zhen H. et al, 2015). Obviously, the pre exponential factor lnA is not a constant because of the change in the reacted component
4.5 Miura –Maki DAEM model
The distributed activation energy model (DAEM) is applied to study the thermal decomposition kinetics. According to eq. (16), a new simple method was used. The Ea and A values of thermal decomposition of the AMT corresponding to different degrees of conversion α are obtained simultaneously. Results are shown in Table 2.
The variation of the pre-exponential factor lnA with activation energy Ea is given in Fig. (13). A functional dependence between the pre-exponential factor, lnA, with activation energy, Ea , can be obtained as the following empirical equation: lnA =0.3349Ea – 18.603
The distribution curve f(Ea) for AMT decomposition is obtained by differentiating α with respect to Ea and the results are shown in Fig.(14). It can be observed from the Fig.(14) that the estimated curve for the investigated process represents a sharp peak and does not show a broad peak and the apparent activation energy does not spread in the large Ea interval. The peak position is placed in a single point at Ea =
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73.45kJ/mol. It can be pointed out that the value of Ea is very similar to the value of Ea calculated by the isoconversional methods. CONCLUSION
The kinetics of the nonisothermal decomposition of AMT was accurately determined from a series of thermo analytical experiments at four constant heating rates (5, 10, 15, 20oCmin-1). The apparent activation energy (Ea) was calculated by the differential isoconversional
209 Egypt. J. of Appl. Sci., 34 (9) 2019
(Friedman) and integral isoconversional (FWO and Tang) methods without a previous assumption of the kinetic model of the reaction.
It was found that:
The apparent activation energy ,Ea , was not really changed and was nearly independent with respect to the level of conversion (α). This suggests that the nonisothermal decomposition process of AMT follows a single-step reaction.
The master plots method was used to define the most probable mechanism, f(α), for the investigated decomposition process. From the obtained results, it was found that the most probable reaction mechanism belongs to the mechanism of the nucleation and growth kinetic models , Avrami-Erofeev model, A4, f(α)= 4(1-α)[-ln(1-α)]3/4 , g(α) =[-ln(1-α)]1/4, the integral I composite method, was applied to confirm the established reaction mechanism.
Miura procedure, (DAEM) was applied, the experimental distribution curve of the apparent activation energies, f(Ea), was estimated. The value of Ea determined was very similar to that calculated by the isoconversional methods.
As a final conclusion ,the kinetic triplet of the nonisothermal thermogravimetric decomposition of amitriptyline hydrochloride was ,Ea = 74.68 kJmol-1 , A= 3.71×103 min-1 (ln A= 8.22), reaction model follows the Avrami-Erofeev model, A4, f(α)= 4(1-α)[-ln(1-α)]3/4, g(α) =[-ln(1-α)]1/4, (nucleation and growth) .
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01 05 01 5
EaEaαmaster plotsIEa = 74.68 kJmolA = 3.71 × 103 0 Avrami-Erofeev
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