TITA B - Revista de Chimie

Kinetic Study of Decomposition of Ibuprofen under Isothermal Conditions BOGDAN TITA,1,2* ADRIANA FULIAS,1 MIRCEA STEFÃNESCU,2 ELEONORA MARIAN,3 DUMITRU TITA1 1 University of Medicine and Pharmacy “Victor Babeº”, Faculty of Pharmacy, 2 Eftimie Murgu Square, Timisoara, 300041, Romania 2 Politehnica University of Timiºoara, Industrial Chemistry and Environmental Engineering Faculty, 2 Victoriei Square , Timiºoara, 300006, Romania 3 Oradea University, Faculty of Medicine and Pharmacy, Speciality of Pharmacy, 29 Nicolae Jiga Str., 410028, Oradea, România

Thermal analysis is one of the most widely used methods for studying the solid state of pharmaceutical substances. The thermoanalytical curves provide important information regarding the physical properties of the pharmaceutical compounds (stability, compatibility, polymorphism, phase transition, kinetic analysis etc). The purpose of a kinetic investigation is to calculate the kinetic parameters and the kinetic model for the studied process. The results are further to predict the system behaviour in various circumstances. This paper is the third one of a systematic study regarding the thermal behaviour of ibuprofen and its compatibility with excipients. Simultaneous thermogravimetry/derivative thermogravimetry (TG/DTG) and differential thermal analysis (DTA) techniques were used for the characterization of the thermal decomposition of ibuprofen. Thermal curves revealed that the thermal decomposition occurs in one step, after melting, in the temperature range of 180–300°C and in a nitrogen atmosphere. A kinetic study regarding the ibuprofen thermal decomposition was performed under isothermal conditions for the temperature steps: 190; 195; 200; 205; 210°C. The TG/DTG data were processed by three methods for decomposition process following first order reaction: isothermal model-fitting, isothermal-isoconversional and Friedman’s isothermal-isoconversional. The obtained results are in accord with the data resulted in non-isothermal conditions from a previous work. The careful treatment of the kinetic parameters obtained in different thermal conditions is necessary, as well as the choice of the adequate calculation method. Keywords: ibuprofen, TG/DTG/DSC, isothermal, non-isothermal, thermal decomposition,kinetic study

Ibuprofen α–methyl–4–(2–methylpropyl)benzeneacetic acid figure 1, is one of the most potent of the clinically used non-steroidal anti-inflammatory drugs, NSAIDs, and interferes with prostaglandin synthesis by direct inhibition of the two cyclooxygenase enzyme systems, COX-1 and COX-2.

Fig.1. The chemical structure of the ibuprofen

Inhibition of the COX-2 system results in antiinflammatory action, while inhibition of the COX-1 enzyme system results in anti-inflammatory action as well as gastric irritation. Additional interest in NSAIDs lies in their possible therapeutic benefits in the prevention of various cancers including colorectal and lung cancers and even in the treatment of Alzheimer’s disease [1–4]. Thermal analysis is one of the most frequently used instrumental techniques in the pharmaceutical research, for the thermal characterization of different materials from solids to semi-solids, which have pharmaceutical relevance. The term of thermal characterization refers to the thermal stability and decomposition of the substances of pharmaceuticals interest. The evaluation of the thermal stability of a drug is realised especially by analyzing its decomposition in isothermal and non-isothermal conditions. Usually, this takes place by irreversible mass

loss. The drugs decomposition reactions have a theoretical, as well as a practical signification [5–8]. The thermoanalytical techniques, especially thermogravimetry/derivative thermogravimetry (TG/DTG) and differential scanning calorimetry (DSC) are used in solving some pharmaceutical problems, like for example the determination of purity level, the qualitative and quantitative analysis of drug formulations, the polymorphism, the thermal stability with the determination of the corresponding kinetic parameters etc [9–13]. Solid-state kinetic studies have increasing importance in thermal analysis, whose main purposes are to calculate the parameters of Arrhenius equation and to determine the mechanism of decomposition reaction. These data can provide valuable information about the time and conditions of storage. The knowledge of such parameters for pure drugs and for drugs-excipients mixtures is also meaningful in order to elucidate the miscibility/incompatibility and its effects on thermal stability [14–19]. In our previous papers [20–28] we provided the importance and utility of the kinetic analysis in estimation on the thermal behaviour of different pharmaceuticals. Thermogravimetry (TG) is a useful convenient method for the study of a variety of decomposition processes for pharmaceuticals. Often kinetic data are extracted from a plot of mass loss vs. time or temperature. Reliable information may be obtained for well-defined single processes in which the evolution of a well-characterized gaseous product or products reflects the rate of decomposition [10,11,13].

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REV. CHIM. (Bucharest) ♦ 62♦ No. 2 ♦ 2011

In many cases, the decomposition does not correspond to a single, well-defined event. Often many processes occur simultaneously. In these cases, the “kinetic data” obtained are characteristic of no fundamental process and are of limited value [29,30]. The most appropriate way to obtain reliable kinetic data is to monitor mass loss vs. time to obtain rate constants at several different temperatures [15,31,32]. Several repetitions at each temperature provide a good reflection of the uncertainty in the values for the rate constants obtained. This mode of work corresponds to the theoretical principles of the isothermal methods [15,29–32]. The methods proposed for the kinetic study of thermal decomposition are generally classified in model-fitting and model-free methods. In each case, data from isothermal and/or non-isothermal experiments can be used [33-35]. The model-fitting defines a single reaction step, while the model-free approach represented by isothermalisoconversional methods gave the dependence of the activation energy with the extent of conversion [7,8,36– 39]. The model-free isoconversional methods are considered as also being the most trusted, especially the Friedman method [7], because of its theoretical and experimental advantages. The kinetic parameters, the rate constant (k), the activation energy (E), the pre-exponential factor (A) and the reaction order (n) may be calculated using different methods according to the mentioned classification, under isothermal and/or non-isothermal conditions [25–32]. In a previous work, a kinetic study of the decomposition of ibuprofen was realised under non-isothermal conditions [25]. The purpose of the present paper is to determine kinetic parameters for thermal decomposition of ibuprofen under isothermal conditions and to establish the nature of the decomposition process (single or multi-step) on the base of the obtained values (especially n and E). Also, the values of the kinetic parameters are compared with the adequate values determined under non-isothermal conditions. Experimental part The ibuprofen was available as pure compound, able to be used for medical purpose. It was obtained from Terapia S.A./Ranbaxy, Cluj-Napoca, Roumania. The isothermal TG curves were measured at 190; 195; 200; 205 and 210°C with a heating rate of 10°C . min–1 until isothermal temperature, under a dynamic atmosphere of nitrogen at a flow of 20 mL . min–1 and utilizing platinum crucibles. The curves were recorded by stepwise isothermal heating. The stepwise isothermal approach consists of heating at a constant rate, until a mass change begins and then holding isothermally until the mass change is complete. This approach has significant advantages over the other techniques as the onset and complete reaction can be very carefully controlled. Results and discussions Experimental data processing strategy It is well-known that solid compounds submitted to heating treatment undergo simple or multi-step thermal decomposition processes in relation to the complexity of their structures. Kinetic analysis of decomposition process is traditionally expected to produce an adequate kinetic description of the process in terms of the reaction model and the Arrhenius parameters using a single-step kinetic equation: dα / dt=k(T) . f(α) REV. CHIM. (Bucharest) ♦ 62♦ No. 2 ♦ 2011

(1)

where t is the time, T is the temperature, α is the conversion degree and f(α) is the reaction model. The temperature dependence of the rate constant is introduced by replacing k(T) with Arrhenius equation, which gives: dα /dt=A . exp(–E/RT) . f(α)

(2)

where E (the activation energy) and A (the pre-exponential factor) are the Arrhenius parameters and R is the gas constant. For non-isothermal conditions dα/dt in eq. (2) is replaced with β . dα/dT where β is the heating rate giving: dα/dT=(A/β) . exp(–E/RT) . f(α)

(3)

The three components (f(α), E and A) called “kinetic triplet” define both in (2) and (3) a single-step reaction that disagrees with the multi-step nature of decomposition that usually occurs in solid state. For compounds having complex structures, it can be hypothesised that several steps with different energies will be involved. If a process involves several steps with different activation energies, the relative contributions of these steps to the overall reaction rate will var y with both the temperature and the extent of conversion. This means that the effective activation energy, determined from the analysis of the results, will also be a function of these two variables. The use of eqs. (2) and (3) determines reactions model that does not represent multi-step kinetics. For this reason one cannot justify the establishment of the reaction mechanism from f(α) alone. An alternative approach to kinetic analysis is to use model-free methods that allow for evaluating Arrhenius parameters without choosing the reaction model. The isoconversional methods make up the best representation of the model-free approach. These methods yield the variation of the effective activation energy as a function of the extent of conversion. The knowledge of the dependence E on α allows detecting multi-step processes and predicting some mechanistic conclusions on the reaction kinetics over a wide temperature range. The isoconversional methods could also yield similar dependencies of the activation energy on the extent of conversion for isothermal and non-isothermal experiments. Kinetic analysis The thermal curves of this substance obtained under non-isothermal conditions are presented in figure 2. From the thermal curves (fig. 2), it is observed that the ibuprofen presents a thermal stability relatively reduced, and at 79°C, this substance is melting. The melting process is followed by decomposition and evaporation of breakdown products. The decomposition takes place in the temperature range of 180–300°C with Tmax=282°C and a complete loss of mass. The thermal decomposition devolves in a single step by an unitary well defined process. The DTA curve confirms the thermal behaviour of the substance and presents two endothermical and nonsymmetrical peaks. The first corresponds to the melting with the maximum shifted to the left, while the second corresponds to the decomposition and the maximum is shifted to the right. According to mentioned temperature range, the following temperatures were chosen: 190; 195; 200; 205; and 210°C for the experiments which were effectuated in isothermal conditions. The rate constant (k), the reaction order (n); the activation energy (E) and the pre-exponential factor (A)


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Fig.2. The thermoanalytical curves TG/DTG/DTA obtained at β=10°C×min–1 for ibuprofen

were determined from TG curves, by using the following methods: isothermal model-fitting [36-38], isothermalisoconversional [36-38] and Friedman’s isothermalisoconversional [40]. Isothermal model fitting method It is well known that isothermal kinetics of solid-state reactions can be represented by the equation: g(α) = k·t

(4)

where k is the specific constant rate and g(α) is an integral mathematical expression related to a mechanism of solid phase reactions. The choice of the kinetic equation which describes the reaction mechanism is done after the verification of several possible kinetic equations, taking into account that in isothermal conditions, where the rate constant is independent of the reaction time, the graphical representation of g(α) vs. time gives a straight line for the correct chosen form of g(α). According to the squared correlation coefficient values r2 (table 1), which was calculated for various possible

kinetic functions, from plotting, it was revealed that the decomposition process is most likely a first order kinetic (r 2=0.963). The squared correlation coefficient was calculated according to the experimental values from figure 3, and the graphical representation of the verified functions vs. time is presented in figure 4. For decomposition processes following first order reaction g(α)=–ln(1–α); for n≠1 and the g(α)=–ln(1– α)n reaction rate is described by: dα/dt = k(T)·(1– α)n

(5)

where k(T) = the rate constant at temperature T and (1–α) n=f(α) the differential conversion function. By linearization, it became: ln(dα/dt) = lnk(T) + n·ln(1–α)

(6)

and by plotting ln(dα/dt) vs. ln(1–α) (fig.5), the values of lnk and n for each temperature can be obtained (table 2). Considering the temperature dependence of k to be of Arrhenius type, by plotting lnk(T) vs. 1/T (fig.6), the activation

Fig.3. The evolution of conversion degree in time at different isothermal temperatures for ibuprofen

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Table 1 THE r2 SQUARED VALUES FOR DIFFERENT POSSIBLE KINETIC FUNCTIONS

Fig.4. Graphical representation of the lng(α) with lnt

Fig.5. ln(dα/dt) vs. ln(1–α) plot for obtaining the rate constant and reaction order values

energy E and the pre-exponential factor A will be obtained (table 2). According to the values presented in table 2, it was not observed a significant variation of the reaction order vs. temperature of reaction and, according to [40], this denotes the presence of a process which takes place in a single step. The values of activation energy, pre-exponential factor and reaction order are in agreement with those obtained under non-isothermal conditions [25]. Isothermal-isoconversional method An alternative procedure, the isothermal-isoconversional method, was used to verify that activation energy value E related to decomposition process remains constant and a single mechanism occurs in the experimental temperature range. From isothermal TG curves, a set of temperature T and t values were obtained for fixed values of α. Substituting k=A·exp(–E/RT) in eq.4 one obtains: g(α) = A·exp(–E/RT)·t

(7)

where the obtained t and T are the time and temperature values which make constant the function g(α). By using the logarithmic form of eq.7 it can be written: lng(α) = lnA – E/RT + lnt

(8)

and rearranging it, one obtains: lnt = – lnA + lng(α) + E/RT

(9)

By plotting lnt vs. 1/T according to eq.9 the activation energies were found at any given α value from the slope of a regression straight line (fig.7). The activation energy’s values are presented in table 3. The variation in a small range of E with α does not reveal a multistage process. It must be taken into account that in the isothermal mode the reactions are ver y slow at the lowest temperatures, so that the experiments will be limited by long times to completion and by low detection limits, while for high temperatures the reaction will be too fast. These restrictions imply that the experimental isothermal domain of temperature available is limited;

Table 2 KINETIC PARAMETERS FOR IBUPROFEN, ACCORDING TO EQ.6



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Fig.6. lnk vs. 1/T plots drawn from isothermal experiments

Fig.7. The graphical representation of lnt vs. 1/T

Table 3 ACTIVATION ENERGY’S VALUES OBTAINED BY FRIEDMAN ISOCONVERSIONAL ISOTHERMAL METHOD (FR) AND BY ISOCONVERSIONAL ISOTHERMAL METHOD (IIS) FOR IBUPROFEN

hence the possible separation of several reactions with isothermal isoconversional method will depend on this. Furthermore, the complexity of the process could be concealed if different processes have similar activation energy. Friedman’s isothermal-isoconversional method This method is based on the relation: ln(dα/dt) = ln[A·f(α)] – E/RT

(10)

and for f(α)=(1–α)n, at a constant conversion and with temperature dependence according to Arrhenius equation, the reaction rate is: ln(dα/dt) = n·ln[A·(1–α)] – E/RT

(11)

By plotting the left member vs. 1/T the activation energy should be obtained at different conversion degrees (table 3) and from the variation of E with α, it was showed that the process takes place in a single decomposition stage. 220

The activation energy values are in good agreement between them, respectively with the values determined in non-isothermal conditions [25]. As shown in table 3, the activation energy values fluctuate around the average values presented. A weak variation of E vs. a is observed, indicating an unitary decomposition process. Conclusions There was performed a kinetic study for the thermal decomposition of ibuprofen active substance, in a nitrogen atmosphere and under isothermal conditions, comparatively with the study performed in non-isothermal conditions. In the literature, there are plenty of papers that show the superiority of the isothermal methods to those which are non-isothermal because of the way of experimental data processing. The study suggests that the decomposition of ibuprofen occurs after melting in a single step. The TG/DTG data obtained in mentioned conditions have been processed by three methods (characteristic to the isothermal study): the



one of isothermal model fitting, isothermal-isoconversional and Friedman isothermal-isoconversional. The model-free isoconversional method, especially Friedman isothermal-isoconversional method offers the best results. The large advantage of the model-free analysis is founded in its simplicity and the avoidance of the errors connected with the selection of a kinetic model. For the choice of the kinetic equation which describes the reaction mechanism, several equations were verified by plotting and the adequate correlation coefficient was calculated. Based on its values, it was chosen the reaction model which corresponds to a first-order kinetic. The kinetic parameter values determined under isothermal conditions by the mentioned methods are in good accord as well as with those determined in nonisothermal conditions by applying of the mentioned methods. The concordance of the values obtained for the kinetic parameters and the dependence mode of the activation energy on the conversion degree show the correctness of the applied methods and the fact that the thermal decomposition process of the ibuprofen is indeed a unitary process. The activation energy’s values and the pre-exponential factor, as well as the range of decomposition indicate a lower thermal stability of ibuprofen. The correlation between the kinetic parameter values determined under different thermal conditions confirms the need to use different methods for experimental data processing. The activation energy values can be used in the quality control of drug, with a view to the improvement of the final product and for the determination of drug quality via the technological parameters. Finally, kinetic study can be a fast alternative or a complementary method to estimate the self-life of medicines. References 1. DENDRINOU-SAMARA, C., TSOTSOU, G., EKATERINIADOU, L.V., KORTSARIS, A.H., RAPTOPOULOU, C.P., TERZIS, A, KYRIAKIDIS, D.A., KESSISSOGLOU, D.P., J. Inorg. Biochem., 71, 1998, p. 171 2. TESLYUK, O.I., BELTYUKOVA, S.V., YEGOROVA, A.V., YAGODKIN, B.N., J. Anal. Chem., 62, 2007, p.330 3. KOVALA-DEMERTZI, D., J. Organomet. Chem., 691, 2006, p. 1767 4. KAFARSKA, K., CZAKIS-SULIKOWSKA, D., WOLF, W.M., J. Therm. Anal. Cal., 96, 2009, p. 617 5. FELIX, F.S., DA SILVA, L.C.C., ANGNES, L., MATOS, J.R., J. Therm. Anal. Cal., 95, 2009, p. 877 6. YI, C., CHIN, J., Inorg. Chem., 22, 2006, p. 288 7. DICKINSON, C.F., HEAL, G.R., Thermochim Acta, 494, 2009, p. 1 8. DICKINSON, C.F., HEAL, G.R., Thermochim Acta, 494, 2009, p. 15 9. NETO, H.S., BARROS, F.A.P., DE SOUSA CARVALHO, F.M., MATOS, J.R., J. Therm. Anal. Cal. 2010;doi:10.1007/s10973-009-0419-3 10. MACÊDO, R.O., ARAGÃO, C.F.S., DO NASCIMENTO, T.G., MACÊDO, A.M.C., J. Therm. Anal. Cal., 56, 1999, p. 1323

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