untitled European Journal of Chemistry 6 (2) (2015) 199‐203 European Journal of Chemistry ISSN 2153‐2249 (Print) / ISSN 2153‐2257 (Online)  2015 Atlanta Publishing House LLC ‐ All rights reserved ‐ Printed in the USA http://dx.doi.org/10.5155/eurjchem.6.2.199‐203.1249 European Journal of Chemistry Journal webpage: www.eurjchem.com Non‐isothermal decomposition kinetics of theobromine in nitrogen atmosphere Laila Tosson Kamel Narcotic Department, National Center for Social and Criminal Research, Giza, 11561, Egypt * Corresponding author at: Narcotic Department, National Center for Social and Criminal Research, Giza, 11561, Egypt. Tel.: +2.02.33461440. Fax: +2.02.33036069. E‐mail address: lailatosson.1160@hotmail.com (L.T. Kamel). ARTICLE INFORMATION ABSTRACT DOI: 10.5155/eurjchem.6.2.199‐203.1249 Received: 21 January 2015 Received in revised form: 20 March 2015 Accepted: 22 March 2015 Published online: 30 June 2015 Printed: 30 June 2015 The non‐isothermal decomposition process of theobromine under nitrogen atmosphere was studied using the differential thermal analysis (DTA), from room temperature up to 500 °C, at heating rates, 5, 15 and 20 °C/min. The results showed that theobromine decomposes in two steps. The kinetic analysis of the first decomposition step was performed using Kissinger, Friedman, Flynn‐Wall‐Ozawa, and Kissinger‐Akahira‐Sunose isoconventional methods. The kinetic model was determined using Šatava‐Šesták method. Results showed that the non‐ isothermal decomposition mechanism of theobromine corresponds to nucleation and growth, following the Avrami‐Erofeev equation. The forms of the integral and differential equations for the mechanism function are g(α)=(‐ln(1‐α))2/3 and f(α)=(3/2)(1‐α)(‐ln(1‐α))1/3, respectively. Thermodynamic parameters of the non‐isothermal decomposition process, change of enthalpy (ΔH), change of entropy (ΔS), and change of Gibbs free energy (ΔG) values were calculated. KEYWORDS Theobromine Šatava‐Šesták method Thermal decomposition Thermodynamic parameters Linear isoconversional methods Non‐isothermal kinetic parameters Cite this: Eur. J. Chem. 2015, 6(2), 199‐203 1. Introduction Methylxanthines have important pharmacological properties and are commonly used as therapeutic agents. Stimulatory effects on the central nervous system as well as on the gastrointestinal, cardio‐vascular, renal and respiratory systems have been ascribed to these compounds [1]. Theobromine (TB), 3,7‐dimethylxanthine, is an alkaloid of the cacao plant and TB is a caffeine derivative and metabolite, Figure 1. TB is the second most important methylxanthine in the diet and TB has the same caffeine effects. Both TB and caffeine improve alertness without inducing irregular heartbeat or hypertension [2]. TB also has diuretic and bronchial muscle relaxing effects [1]. Figure 1. Structural formula of theobromine. The thermal decomposition of TB have been studied [3,4], using TG/DTG, DTA and DSC methods. To our knowledge, the thermodynamic and kinetic data of the thermal decomposition of TB have not been reported. In this paper, the kinetic parameters such as activation energy, E, and apparent pre‐ exponential factor, A, of the thermal decomposition of TB were calculated using Kissinger, Friedman, Flynn‐Wall‐Ozawa, Kissinger‐Akahira‐Sunose and Šatava‐Šesták methods. Šatava‐ Šesták method was used to establish the kinetic model of the thermal decomposition of TB. The thermodynamic data, such as enthalpy change (ΔH), entropy change (ΔS) and Gibbs free energy change (ΔG) for the non‐isothermal decomposition process were calculated. These data can play an important role to understand the physico‐ chemical interactions and thermodynamic properties for TB at high temperatures. 2. Experimental 2.1. Materials TB was supplied by Sigma (St. Louis, MO). It is used without any further purification. 2.2. Physical measurements The thermogravimetric measurements were carried out at three different heating rates (5, 15 and 20 °C/min), from room temperature up to 500 °C under dynamic nitrogen atmosphere 200 Kamel / European Journal of Chemistry 6 (2) (2015) 199‐203 Table 1. The algebraic expression of g(α) for the various kinetic reaction models. g(α)Nog(α) No ‐ln(1‐α)9α2 1 ln 1 α , n 2 3 , 1 2 , 1 3 , 4 , 1 4 , 2 , 3 10‐16 α+(1‐ α)ln(1‐ α) 2 1 1 α n, n 1 2 , 3, 2, 4 , 1 3 , 1 4 17‐22 1 2 3 α 1 α 2 3 3 αn, (n = 1, 3 2 , 1 2 , 1 3 , 1 4 ) 23‐27 1 1 α 1/3 n , (n = 2, ½) 4‐5 1 α 1 28 1 1 α 1/2 1/2 6 1 α 1 1 29 1 α 1 3 1 2 7 1 α 1 230 1/ 1 α 1 3 1 2 8 (20 mL/min), using about 2 mg of powdered samples contained in an alumina crucible. 2.3. Theoretical analysis The kinetic analysis of solid state thermal decomposition is usually described by the following Equation (1) [5]. k T (1) where , dα/dt is the rate of conversion, α is the conversion of the reaction which is defined as α = (m0‐mt)/(m0‐mf), where m0 and mf are the initial and final masses of the sample at each stage of decomposition, respectively, and mt is the mass of the sample at time t (or temperature T), f(α) is a mathematical model function of kinetics which depends on the reaction type and reaction mechanism, k(T) is the specific rate constant, whose temperature dependence is commonly described by the Arrhenius Equation (2). k T Ae (2) by combining Equation (1) and (2), taking into consideration the heating rate β = dT/dt (°C/min), under non‐isothermal condition, the kinetic analysis of solid state thermal decomposition is described by Equation (3). β Ae (3) Most of the methods that describe the kinetics of reactions in solids use Equation (3) as well as several approximation of its integral form. g α e dT (4) where g α dα (5) is the integral form of the model function that does not depend on the heating rate used. 2.3.1. Kissinger (K) method Kissinger method [6‐9] is expressed by Equation (6) ln ln (6) where i= 1, 2, 3 …….., by plotting ln versus , EK and AK can be calculated from slope (‐EK/R) and intercept ln(AKR/EK), respectively. 2.3.2. Friedman (FR) method FR method [10], a linear differential method based on Equation (7). ln ≡ ln β ln A α (7) 2.3.3. Flynn‐Wall‐Ozawa (FWO) method FWO method [6,7,11,12], a linear integral method based on Equation (8). lnβ ln 5.331 1.052 (8) 2.3.4. Kissinger‐Akahira‐Sunose (KAS) method KAS method [9,13], a linear integral method based on Equation (9). ln ln (9) For α = constant, the plot of ln(dα/dt) vs 1/T, or lnβ vs 1/T, or ln(β/T2) vs 1/T from the experimental thermogravimetric curves recorded for several constant heating rates, should be a straight line, the activation energy, E, being evaluated from these slopes, by means of FR, FWO, and KAS methods, respectively. 2.3.5. Šatava‐Šesták method The expression from Šatava‐Šesták method [14] is given by Equation (10). lng α ln 5.330 1.0516 (10) where g(α) comes from one of 30 forms of integral formula in the literature [15,16].These forms of integral formula are given in Table 1. For every fixed βi (i =1, 2, 3, 4, …), and each mechanism functions g(α), the values of activation energy (Es) and pre‐exponential factor (As), can be obtained using Equation (10), respectively. The model of the reaction can be identified as long as 0 < Es < 400 kJ/mol. It is necessary that Es values compared with the values of E0 where E0 is the average activation energy calculated by FR, KAS, and FWO methods. If Es meets with the condition of│(E0 ‐Es)/ E0│≤ 0.1 , the Es is acceptable. lnAs calculated need to be compared with lnAk calculated by Kissinger method, if lnAs meets with the condition │(lnAs‐lnAk)/lnAs│≤ 0.46, the lnAs is acceptable. If g(α) meets the above mentioned requirements, then it will be an integral form of the most probable mechanism function of reaction. 2.3.6. Thermodynamic parameters After E and A values are obtained using non‐isothermal method, the thermodynamic parameters can be calculated [17,18] using equations ∆S Rln (11) Kamel / European Journal of Chemistry 6 (2) (2015) 199‐203 201 Table 2. Values of Ti, Tp and Tf for the TB decomposition determined by thermogravimetric analysis at different heating rates. β, °C/min Ti, °C Tp, °C Tf, °C 5 206.1 280.4 303.5 15 206.1 307.6 332.3 20 206.1 315.8 337.9 Table 3. The activation energy calculated using FR, FWO and KAS. α FR method FWO method KAS method E (kJ/mol) r2 E (kJ/mol) r2 E (kJ/mol) r2 0.2 118.523 0.993 128.665 0.999 129.651 0.985 0.3 118.869 0.995 125.612 0.999 124.277 0.993 0.4 117.379 0.996 127.151 0.999 125.709 0.993 0.5 117.780 0.993 123.753 0.999 122.230 0.997 0.6 121.144 1.000 123.243 0.999 121.464 0.996 0.7 129.210 0.996 127.452 0.999 129.651 0.996 0.8 122.884 0.993 124.123 0.999 121.685 0.998 Mean 120.827 125.714 124.952 kB is the Boltzmann constant (1.3807×10‐23 ), and is the Planck constant (6.625×10‐34 J/s). ΔH = E – RTp (12) ΔG = ΔH – TpΔS (13) The change of enthalpy (ΔH), change of entropy (ΔS), and change of Gibbs free energy (ΔG), in the thermal decompo‐ sition process decomposition are calculated. In all of the above equations, α represents the fractional conversion, β is the heating rate (°C/min), T is the temperature (K), Tp is the temperature at the maximum rate of the weight loss (differential thermogravimetry (DTG)) peak temperature, E is the apparent activation energy (kJ/mol), A is the pre‐ exponential factor (1/min), R is the gas constant (8.314 J/mol·K) and g(α) is the integral conversion function. 3. Results and discussion 3.1. Thermal decomposition of TB TG/DTG and DTA curves of the thermal decomposition of TB under nitrogen atmosphere, from room temperature up to 500 °C, at the heating rates (5, 15, 20 °C/min) are shown in Figure 2 and 3, respectively. It is clear that the TG curves are shifted to higher temperatures as the heating rates increases from 5 to 20 °C/min. The shapes of the curves are quite similar, all curves showed two decomposition steps. There is no mass loss up to 240 °C, as temperature increases the TG curves of TB exhibit a sharp mass loss of about 90% in the temperature range 260‐330 °C, which corresponds to the endothermic peak as shown in the DTA curves, Figure 3, in the temperature range 289‐320 °C. This mass loss may be due to the loss of the xanthine group. In the second step, the TG curves show a mass loss of about 10%, in the temperature range 345‐400 °C, where an endothermic peak appears in the DTA curves, Figure 3, in the range 369‐403 °C. The first step was chosen as the main object of discussion. Values of initial temperature (Ti), inflection temperature (Tp) and final temperature (Tf) from thermogravimetric curves for the chosen step at various heating rates are presented in Table 2. 3.2. Non‐isothermal kinetic of TB The non‐isothermal decomposition of the first decomposition step of TB was investigated using Kissinger, FR, KAS, FWO and Šatava‐Šesták methods. The activation energy values were calculated in the conversion range 0.2 ≤ α ≤ 0.8. This range is strongly recommended because most reactions, especially solid‐state ones, are not stable at the beginning and ending periods [19]. The values of activation energy Ek and pre‐exponential factor ln Ak calculated by Kissinger method are 116.953 kJ/mol and 29.595/min, respectively. The linear correlation coeffi‐ cient (r2) is 0.985. Activation energy calculated by FR, KAS, and FWO methods are tabulated in Table 3. The relationship between activation energy, E, and conversion (α) are shown in Figure 4. Figure 2. TG/DTG curves of the thermal decomposition of TB in nitrogen atmosphere at different heating rates (5, 15, 20 °C/min). Figure 3. DTA curves for the thermal decomposition of TB in nitrogen atmosphere at different heating rates (5, 15, 20 °C/min). By comparing the activation energies calculated by the three isoconversional methods (FR, KAS, and FWO), it is clear, that the activation energy values calculated by FWO and KAS are in good agreement, while these determined by FR differential method is slightly lower. The average of the activation energy (E0) values calculated by the three methods (FR, KAS, and FWO) is 123.832 kJ/mol. The kinetic parameters calculated by Šatava‐Šesták method are listed in Table 4. The values of activation energy and pre‐exponential factor calculated by the Šatava‐Šesták method compare, respectively, with the average of activation 202 Kamel / European Journal of Chemistry 6 (2) (2015) 199‐203 Table 4. Activation energy and pre‐exponential factor calculated using Šatava‐Šesták method. No β = 5 °C/min β = 15 °C/min β = 20 °C/min Es (kJ/mol) ln As r2 Es (kJ/mol) ln As r2 Es (kJ/mol) ln As r2 1 264.668 62.230 0.996 255.711 59.279 0.997 256.101 58.936 0.999 2 295.255 68.611 0.998 285.552 66.771 0.999 285.347 66.989 0.999 3 307.478 69.931 0.999 297.521 66.419 0.999 296.135 65.685 0.999 4 88.222 24.161 0.996 85.236 23.933 0.997 85.367 23.720 0.999 5 22.055 10.859 0.996 21.309 11.652 0.997 21.548 11.913 0.999 6 33.083 12.902 0.996 31.963 13.524 0.997 32.012 13.732 0.999 7 332.202 75.646 0.999 321.744 71.827 0.999 320.706 70.993 0.998 8 209.641 47.189 0.991 202.443 45.064 0.993 203.332 44.975 0.996 9 185.627 45.701 0.999 180.026 44.119 0.998 179.049 43.697 0.995 10 123.751 32.151 0.999 120.017 31.473 0.998 119.366 31.289 0.995 11 92.813 25.460 0.999 90.013 25.234 0.998 89.524 25.169 0.995 12 61.875 18.888 0.999 60.008 19.113 0.998 59.683 19.168 0.995 13 742.509 169.920 0.999 720.107 160.204 0.998 716.197 157.640 0.995 14 46.406 15.687 0.999 45.006 16.138 0.998 44.542 16.328 0.995 15 371.254 86.877 0.999 360.053 82.583 0.998 356.34 82.015 0.995 16 556.882 128.340 0.999 540.081 121.335 0.998 534.511 120.330 0.995 17 66.167 19.553 0.996 63.927 18.898 0.997 64.645 19.755 0.999 18 397.002 91.201 0.996 383.565 86.208 0.997 384.152 86.222 0.999 19 264.668 62.230 0.996 255.711 59.279 0.997 256.101 59.384 0.999 20 529.336 120.289 0.996 511.420 113.254 0.997 512.203 113.180 0.999 21 44.111 15.062 0.996 42.618 15.515 0.997 42.683 15.696 0.999 22 33.083 12.902 0.996 31.963 13.524 0.997 32.012 13.732 0.999 23 132.334 33.547 0.996 127.855 32.639 0.997 128.050 32.610 0.999 24 199.172 47.960 0.996 193.606 46.240 0.997 193.937 46.041 0.999 25 66.390 19.594 0.996 64.535 19.772 0.997 64.645 19.896 0.999 26 44.260 15.088 0.996 43.023 15.583 0.997 43.097 15.761 0.999 27 33.195 12.921 0.996 32.267 13.573 0.997 32.322 13.778 0.999 28 120.947 32.563 0.923 116.298 31.693 0.913 111.534 30.649 0.896 29 253.729 61.287 0.988 245.369 58.514 0.985 240.826 57.122 0.978 30 60.473 19.106 0.923 58.149 19.239 0.913 55.767 18.882 0.896 Figure 4. The relationship between activation energy, E, and conversion, α. energy (E0) calculated using the above mentioned methods (FR, KAS, and FWO methods), and the value of the pre‐ exponential factor calculated by the Kissinger method. It is clear from the results that the decomposition reaction of TB for the chosen step (first decomposition step) is consistent with the mechanism of nucleation and growth, Avrami‐Erofeev equation, (that is serial‐number 10 in Table 1), as the values of Es and lnAs meet with the conditions of both │(E0 ‐Es)/E0│≤ 0.1 and │(lnAs–lnAk)/lnAs │≤ 0.46, respectively. The forms of the integral and differential equations for the mechanism function are g(α) = (‐ln(1‐α))2/3 and f(α) = (3/2)(1‐α)(‐ln(1‐α))1/3, respectively. The activation energy and pre‐exponential factor were 121.045 kJ/mol, 5.496×1013 1/min, respectively. 3.3. Thermodynamic parameters When the values of activation energy, E, and pre‐ exponential factor, A, have been obtained, thermodynamic parameters of the reaction can be calculated from the previous Equations (11‐13). The calculated values of the thermo‐ dynamic parameters, enthalpy change (ΔH), entropy change (ΔS) and Gibbs free energy change (ΔG) for the first decompo‐ sition step of TB are 116.076 kJ/mol, ‐45.087 J/mol·K, and 143.019 kJ/mol, respectively. The entropy of activation, ΔS, value for the decomposition of TB is negative, which indicates a highly ordered activated complex, and the degrees of freedom of rotation as well as of vibration are less than they are in the non‐activated complex. The positive value of the enthalpy, ΔH, is in good agreement with endothermic effects in DTA data. The positive values of the enthalpy, ΔH, and Gibbs free energy, ΔG, for the decompo‐ sition stage show that it is a non‐spontaneous process. These thermodynamic functions are consistent with kinetic parameters and thermal analysis data. 4. Conclusion Kinetic analysis of non‐isothermal decomposition process of TB under nitrogen atmosphere was performed using Kissinger, Friedman, Flynn‐Wall‐Ozawa, and Kissinger‐ Akahira‐Sunose. For the determination of kinetic model function of the considered process, the Šatava‐Šesták method was used. It was found that the decomposition kinetic model of TB corresponds to nucleation and growth, following the Avrami‐Erofeev equation. The activation energy and pre‐ exponential factor were 121.045 kJ/mol, 5.496×1013 1/min, respectively. Thermodynamic parameters, change of enthalpy (ΔH), change of entropy (ΔS) , and change of Gibbs free energy (ΔG),for the first decomposition step of TB are 116.076 kJ/mol, ‐45.087 J/mol·K, and 143.019 kJ/mol, respectively. References [1]. De Sena, A. R.; Aparecida, A. S.; Branco, A. Food Technol. Biotech. 2011, 49, 413‐423. [2]. Mitchell, E. 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