- Email: [email protected]
Estimation of the fragility index of indomethacin by DSC using the heating and cooling rate dependency of the glass transition
Estimation of the Fragility Index of Indomethacin by DSC Using the Heating and Cooling Rate Dependency of the Glass Transition JOAQUIM J. MOURA RAMOS,1 RAQUEL TAVEIRA-MARQUES,1 HERMI´NIO P. DIOGO2 1
Centro de Quı´mica-Fı´sica Molecular, Complexo 1, IST, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
2
Centro de Quı´mica Estrutural, Complexo 1, IST, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
Received 14 October 2003; revised 22 December 2003; accepted 30 December 2003
ABSTRACT: In this study we have investigated the features of the glass transition relaxation of indomethacin using Differential Scanning Calorimetry (DSC). The purpose of this work is to provide an estimation of the activation energy at the glass transition temperature, as well as of the fragility index, of amorphous indomethacin from DSC data. To do so, the glass transition temperature region of amorphous indomethacin was characterized in both cooling and heating regimes. The activation energy for structural relaxation (directly related to glass fragility) was estimated from the heating and cooling rate dependence of the location of the DSC profile of the glass transition. The obtained results were similar in the heating and in the cooling modes. The results on the fragility index of indomethacin obtained in the present study, m ¼ 60 in the cooling mode and m ¼ 56 in the heating mode, are compared with other values previously published in the literature. ß 2004 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 93:1503–1507, 2004
Keywords: molecular mobility; indomethacin; glass transition; fragility; differential scanning calorimetry; DSC
INTRODUCTION The relevance of the amorphous state to the formulation of pharmaceuticals has been underlined.1,2 On the other hand, the knowledge of the time scales of molecular motions in amorphous systems, that is, the knowledge of the relaxation map that characterizes the molecular dynamics in a given material, is needed for profiting from the advantages of the amorphous state, and is an important requirement for a safe use of amorphous pharmaceutical solids.3,4 Indomethacin is a model pharmaceutical solid that has been commercialized since 1963, and was an important
Correspondence to: Joaquim Jose´ Moura Ramos (Telephone: 351 21 8419253; Fax: 351 21 8464455; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 93, 1503–1507 (2004) ß 2004 Wiley-Liss, Inc. and the American Pharmacists Association
milestone in the therapy of rheumatic diseases. It also served, for a long time, as a clinical standard, and has been a valuable tool in the study of the inflammatory process. The molecular mobility in indomethacin has been studied by several experimental techniques,5–7 which allowed the determination of the fragility index from the experimental data. The methods of thermal analysis allowing the determination of glassformer fragility have been recently reviewed.8 A value for the fragility m ¼ 77 is reported, which was obtained from the heating rate dependence of the calorimetric glass transition temperature.6 This value is, however, significantly different from the values m ¼ 63 and m ¼ 64 obtained from Thermally Stimulated Depolarization Currents (TSDC) data.9,10 To clarify this difference we performed a careful study of indomethacin by Differential Scanning Calorimetry (DSC), in the temperature region of the glass transition. An
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 93, NO. 6, JUNE 2004
1503
1504
MOURA RAMOS, TAVEIRA-MARQUES, AND DIOGO
important feature of this study is that it has been carried out in both heating and cooling modes, and it was concluded that the obtained results are similar in both modes. Moreover, as will be shown, these values are in good agreement with values recently reported in the literature9,10 obtained by other experimental techniques.
to the experimental values to correct the data for the effect of the heating rate on the temperature of the DSC signals. Similarly, the correction for each cooling rate, (DT)qc ¼ a0 qc3 þ b0 qc2 þ c0 qc, was added to the experimental values obtained on cooling. The enthalpy was also calibrated using indium (melting enthalpy DmH ¼ 28.71 J g1).
EXPERIMENTAL RESULTS AND DISCUSSION Indomethacin (1-[4-chlorobenzoyl]-5-methoxi-2methylindole-3-acetic acid) was a Sigma product (catalogue number I-7378, lot 77H18461), with a melting point at 1578C obtained by DSC, and it was used without further purification. Its calorimetric glass transition temperature is reported to be Tg ¼ 428C (315.2 K) for a heating rate of 1 K/min.11 The calorimetric measurements were performed with a 2920 MDSC system from TA Instruments Inc. Dry high purity He gas with a flow rate of 30 cm3/min was purged through the sample. Cooling was accomplished with the liquid nitrogen cooling accessory (LNCA), which provides automatic and continuous programmed sample cooling down to 1508C. The baseline was calibrated scanning the temperature domain of the experiments with an empty pan. The temperature calibration was performed taking the onset of the endothermic melting peak at an heating rate of q ¼ 10 K min1 of several calibration standards: n-decane (Tm ¼ 243.75 K), n-octadecane (Tm ¼ 301.77 K), hexatriacontane (Tm ¼ 347.30 K), indium (Tm ¼ 430.61 K), and tin (Tm ¼ 506.03 K). The organic standards were high purity Fluka products, while the metal standards were supplied by TA Instruments Inc. The correction of the temperature for different heating and cooling rates was performed on the basis of results obtained with indium. The onset temperature of the melting peak of indium, (Ton)m, was obtained at several heating rates, qh, and the obtained values were fitted to a third order polynomial, (Ton)m ¼ a qh3 þ b qh2 þ c qh þ d. On the other hand, the onset temperature of the exothermic crystallization peak of indium, (Ton)cr, was obtained at several cooling rates, qc, and the obtained results were also fitted to a third-order polynomial, (Ton)cr ¼ a0 qc3 þ b0 qc2 þ c0 qc þ d0 . The temperature correction for each heating or cooling rate allows the extrapolation to the melting of indium in infinitely slow rate conditions. In this context, the correction for each heating rate, (DT)qh ¼ a qh3 þ b qh2 þ c qh, was subtracted JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 93, NO. 6, JUNE 2004
The fragility index, m, of a substance was defined as the slope of the log10 t(T) versus Tg/T line at the glass transition temperature, that is, at T ¼ Tg.12,13 dlog10 tðTÞ m¼ ð1Þ dðTg =TÞ T¼Tg where t is the structural relaxation time which slows down to 100 s at Tg. Fragility of a glass forming system describes the temperature dependence of the molecular dynamics of the supercooled liquid. Equation 1 can be expressed in terms of the temperature dependent apparent activation energy, Ea, as Ea ðTg Þ 1 m¼ ð2Þ 2:303 RTg Any experimental technique that allows the determination of the activation energy of a motional process from the rough experimental data is thus useful for obtaining the fragility index of a glass-forming system. It was shown14 that the dependence of the glass transition temperature, Tg, on the heating or cooling rate, jqj, of a conventional DSC experiment is given by d lnjqj Dh ¼ d1=Tg R
ð3Þ
where Dh* is the activation enthalpy for the structural enthalpy relaxation. It is to be enhanced that a necessary constrain for applying eq. 3 on heating is that, prior to reheating, the glass must be cooled from above to well below the glass transition region at a rate equal or proportional to the reheating rate. The value of Dh* obtained from eq. 3 was set equal to Ea(Tg) in eq. 2 in the calculation of the fragility of indomethacin.6 The obtained value was m ¼ 77. It is to be noted that the experiments in the work previously referred were carried out in the heating mode.
ESTIMATION OF THE FRAGILITY INDEX OF INDOMETHACIN BY DSC
However, it is well known that the DSC results obtained on heating depend on the thermal treatments used to produce the glass (namely on the cooling rate), present the so-called overshoot peak in the heat capacity, and are influenced by aging effects.15 Nevertheless, most of the DSC studies of the glass transition are carried out on heating, which is due to the difficulty of obtaining reliable thermograms under cooling conditions. One of the reasons is probably that the accurate control of the temperature variation is more difficult on cooling than on heating. The calibration of the temperature-scale during cooling is also reported to be problematic. Despite these problems, we decided to calculate the fragility of indomethacin on the basis of DSC data obtained on cooling because, as noted, the results obtained in this regime are not influenced by the previous thermal treatments and/or aging effects. Experiments in the heating mode will also be done, and the results obtained in both modes will be compared. The DSC profile of the glass transition is a sigmoidal change in the heat flux, corresponding to a change in heat capacity, (DCP)Tg. The heat capacity jump is characterized by a set of temperatures, namely the onset and endset temperatures, respectively Ton and Tend, and the midpoint of the heat capacity jump, Tmid. The first problem to solve is to decide which of these temperatures must be identified with Tg. It is common to consider the midpoint of the heat capacity jump as Tg, given that it appears to be less sensitive to the noise in the baseline. However, the two other temperatures eventually have a most clear physical meaning. The onset temperature, Ton, represents the temperature at which the lost of the metastable equilibrium is becoming detectable. The endset temperature, Tend, on the other hand, is the temperature at which the nonequilibrium glassy state can be considered to be reached. In many cases, the DSC sigmoidal signal of the glass transition obtained on cooling shows some asymmetry, such that the onset temperature can be obtained with a higher accuracy, compared with the endset and midpoint temperatures (see Fig. 1a). This was observed in our work, so that we will analyze the influence of the cooling rate on the onset temperature, Ton, of the glass transition signal. The results of part of our experiments are shown in Figure 2, on the form of a plot of ln jqj versus 1/Ton. The experimental onset temperatures were corrected as previously explained in the experi-
1505
Figure 1. DSC profile of the glass transition of indomethacin; (a) cooling curve obtained with a sample of 3.3170 mg at a cooling rate of q ¼ 17 K min1; (b) heating curve obtained with a sample of 3.6420 mg at a heating rate of q ¼ þ17 K min1. The figure indicates the position of the characteristic temperatures: onset temperature, Ton, endset temperature, Tend, and midpoint temperature, Tmid.
mental part. Figure 2a shows data obtained on cooling, while Figure 2b shows data obtained on heating. From the observation of Figure 2a and from the linear regression analysis of the corresponding data, we can draw the following conclusions: 1. The data points show a significant scattering. In fact, the coefficient of determination, R2, is 0.93, which indicates that the evaluation of the onset temperature of the glass transition on cooling is subjected to some uncertainties. 2. The slope of the regression straight line is 44.0 (with a confidence interval of 2.1). From this slope, the value of 365.5 kJ mol1 JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 93, NO. 6, JUNE 2004
1506
MOURA RAMOS, TAVEIRA-MARQUES, AND DIOGO
Figure 2. ‘‘Arrhenius plot’’ (logarithm of the rate as a function of 1/Ton) for the glass transition of indomethacin; (a) data obtained on cooling with rates between 20 and 2 K min1; (b) data obtained on heating with rates between þ1 and þ22 K min1.
was obtained (using eq. 3) for the activation energy. Introducing this value in eq. 2 and considering Tg ¼ 47.68C ¼ 320.7 K (onset temperature of the glass transition signal measured on cooling at 10 K min1), leads to the value of m ¼ 60 for the fragility index of indomethacin. From the observation of Figure 2b, which presents data obtained on heating, and from the linear regression analysis of the corresponding data, we can draw the following conclusions: 1. The data points are not so scattered as those obtained on cooling (Fig. 2a). In fact, the coefficient of determination, R2, is 0.97. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 93, NO. 6, JUNE 2004
2. The slope of the regression straight line is 40.9 (with a confidence interval of 1.4). From this slope, the value of 340.0 kJ mol1 was obtained for the activation energy, and the corresponding value of the fragility index is m ¼ 56, in good agreement with the value obtained in the cooling mode. This is an interesting point to be underlined. As pointed out before, each one of the experimental regimes (heating or cooling) has its own advantages and/or drawbacks. However, if used properly, they should lead to similar results, and that is what we showed in this particular case of indomethacin. Moreover, the obtained values (60 and 56) are in very reasonable agreement with values recently reported, obtained from thermally stimulated depolarization currents data,9,10 and with the value m ¼ 63 obtained from the width of the glass transition.8 The fact that a value of m ¼ 77 obtained by DSC was previously reported6 is not surprising, because it is nothing but a preliminary result, using only four heating rates, with average of only three determinations for each rate. Let us briefly mention that it was shown16,17 that eq. 2 can be rewritten in the form of an empirical rule as Dh*/R(1/T1 1/Tu) ¼ C, where Tl and Tu are, respectively, the lower and upper end of the glass transition region, and C is a constant (equal to 5 for inorganic glasses). However, this empirical equation cannot be used to predict the activation enthalpy of the structural relaxation of indomethacin because it holds only for strong glasses. Finally, the heat capacity jump associated to the glass transition of indomethacin was found to be (DCP)Tg ¼ (0.388 0.005) J g1 K1 on cooling (18 independent experiments), and (DCP)Tg ¼ (0.414 0.006) J g1 K1 on heating (10 independent experiments), in good agreement with the value of 0.41 J g1 K1 reported in the literature.8
CONCLUSIONS When the experiment is carried out on heating, the shape of the Differential Scanning Calorimetry signal of the glass transition strongly depends on the thermal history of the sample. To avoid this drawback, we decided to analyse this signal in the cooling mode. Specifically, the variation of the
ESTIMATION OF THE FRAGILITY INDEX OF INDOMETHACIN BY DSC
onset temperature as a function of the cooling rate has been studied. Some difficulties were encountered, arising from the low accuracy and reliability of the thermograms obtained under these conditions, which lead to some scattering of the experimental results. The fragility index of indomethacin calculated from these results was m ¼ 60. In the heating mode, on the other hand, a value of m ¼ 56 was obtained for the fragility index of this pharmaceutical solid, in very good agreement with the value obtained on cooling. Furthermore, these values are in excellent agreement with those recently reported obtained by thermally stimulated depolarization currents and from the width of the glass transition.
8.
9.
10.
11.
REFERENCES 12. 1. Hancock BC, Zografi G. 1997. Characteristics and significance of the amorphous state in pharmaceutical systems. J Pharm Sci 86:1–12. 2. Craig DQM, Royal PG, Kett VL, Hopton ML. 1999. The relevance of amorphous state to pharmaceutical dosage forms: Glassy drugs and freeze dried systems. Int J Pharm 179:179–207. 3. Shambling SL, Tang X, Chang L. Hancock BC, Pikal MJ. 1999. Characterization of the time scales of molecular motion in pharmaceutically important glasses. J Phys Chem B 103:4113–4141. 4. Shambling SL, Hancock BC, Dupuis Y, Pikal MJ. 2000. Interpretation of relaxation time constants for amorphous pharmaceutical systems. J Pharm Sci 89:417–427. 5. Adronis V, Zografi G. 1997. Molecular mobility of supercooled amorphous indomethacin, determined by dynamical mechanical analysis. Pharm Res 14: 410–414. 6. Adronis V, Zografi G. 1998. The molecular mobility of supercooled amorphous indomethacin as a function of temperature and relative humidity. Pharm Res 15:835–842. 7. He R, Craig DQM. 2001. An investigation into the thermal behaviour of an amorphous drug using low frequency dielectric spectroscopy and modulated
13.
14.
15.
16.
17.
1507
temperature differential scanning calorimetry. J Pharm Pharmacol 53:41–48. Crowley KJ, Zograft G. 2001. The use of thermal methods for predicting glass-former fragility. Thermochim Acta 380:79–93. Correia NT, Moura Ramos JJ, Descamps M, Collins G. 2001. Molecular mobility and fragility in indomethacin: A Thermally Stimulated Depolarisation Currents study. Pharm Res 18:1767–1774. Moura Ramos JJ, Correia NT, Taveira-Marques R, Collins G. 2002. The activation energy at Tg and the fragility index of indomethacin, predicted from the influence of the heating rate on the temperature positron and on the intensity of the Thermally Stimulated Depolarisation Current peak. Pharm Res 19:1879–1884. Adronis V, Zografi G. 2000. Crystal nucleation and growth of indomethacin polymorphs from the amorphous state. J Non-Cryst Solids 271: 236–248. Bohmer R, Ngai KL, Angell CA, Plazek DJ. 1993. Nonexponential relaxation in strong and fragile glass formers. J Chem Phys 99:4201–4209. Bohmer R, Angell CA. 1994. Local and global relaxations in glass-forming materials. In: Richert R, Blumen A, editors. Disorder effects on relaxational processes. Berlin: Springer-Verlag, pp 11–54. Moynihan CT, Esteal AJ, Wilder J, Tucker J. 1974. Dependence of the glass transition temperature on heating and cooling rates. J Phys Chem 76:2673– 2677. Simatos D, Blond G, Roudaut G, Champion D, Perez J, Faivre AL. 1996. Influence of heating and cooling rates on the glass transition temperature and the fagility parameter of sorbitol and fructose as mesaured by DSC. J Thermal Anal 47:1419– 1436. Moynihan CT. 1993. Correlation between the width of the glass transition region and the temperature dependence of the viscotity of high-Tg glasses. J Am Ceram Soc 76:1081–1087. Moynihan CT, Lee SK, Tatsumisago M, Minami T. 1996. Estimation of activation energies for structural relaxation and viscous flow from DTA and DSC experiments. Thermochim Acta 280/281:153– 162.
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 93, NO. 6, JUNE 2004
Centro de Quı´mica-Fı´sica Molecular, Complexo 1, IST, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
2
Centro de Quı´mica Estrutural, Complexo 1, IST, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
Received 14 October 2003; revised 22 December 2003; accepted 30 December 2003
ABSTRACT: In this study we have investigated the features of the glass transition relaxation of indomethacin using Differential Scanning Calorimetry (DSC). The purpose of this work is to provide an estimation of the activation energy at the glass transition temperature, as well as of the fragility index, of amorphous indomethacin from DSC data. To do so, the glass transition temperature region of amorphous indomethacin was characterized in both cooling and heating regimes. The activation energy for structural relaxation (directly related to glass fragility) was estimated from the heating and cooling rate dependence of the location of the DSC profile of the glass transition. The obtained results were similar in the heating and in the cooling modes. The results on the fragility index of indomethacin obtained in the present study, m ¼ 60 in the cooling mode and m ¼ 56 in the heating mode, are compared with other values previously published in the literature. ß 2004 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 93:1503–1507, 2004
Keywords: molecular mobility; indomethacin; glass transition; fragility; differential scanning calorimetry; DSC
INTRODUCTION The relevance of the amorphous state to the formulation of pharmaceuticals has been underlined.1,2 On the other hand, the knowledge of the time scales of molecular motions in amorphous systems, that is, the knowledge of the relaxation map that characterizes the molecular dynamics in a given material, is needed for profiting from the advantages of the amorphous state, and is an important requirement for a safe use of amorphous pharmaceutical solids.3,4 Indomethacin is a model pharmaceutical solid that has been commercialized since 1963, and was an important
Correspondence to: Joaquim Jose´ Moura Ramos (Telephone: 351 21 8419253; Fax: 351 21 8464455; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 93, 1503–1507 (2004) ß 2004 Wiley-Liss, Inc. and the American Pharmacists Association
milestone in the therapy of rheumatic diseases. It also served, for a long time, as a clinical standard, and has been a valuable tool in the study of the inflammatory process. The molecular mobility in indomethacin has been studied by several experimental techniques,5–7 which allowed the determination of the fragility index from the experimental data. The methods of thermal analysis allowing the determination of glassformer fragility have been recently reviewed.8 A value for the fragility m ¼ 77 is reported, which was obtained from the heating rate dependence of the calorimetric glass transition temperature.6 This value is, however, significantly different from the values m ¼ 63 and m ¼ 64 obtained from Thermally Stimulated Depolarization Currents (TSDC) data.9,10 To clarify this difference we performed a careful study of indomethacin by Differential Scanning Calorimetry (DSC), in the temperature region of the glass transition. An
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 93, NO. 6, JUNE 2004
1503
1504
MOURA RAMOS, TAVEIRA-MARQUES, AND DIOGO
important feature of this study is that it has been carried out in both heating and cooling modes, and it was concluded that the obtained results are similar in both modes. Moreover, as will be shown, these values are in good agreement with values recently reported in the literature9,10 obtained by other experimental techniques.
to the experimental values to correct the data for the effect of the heating rate on the temperature of the DSC signals. Similarly, the correction for each cooling rate, (DT)qc ¼ a0 qc3 þ b0 qc2 þ c0 qc, was added to the experimental values obtained on cooling. The enthalpy was also calibrated using indium (melting enthalpy DmH ¼ 28.71 J g1).
EXPERIMENTAL RESULTS AND DISCUSSION Indomethacin (1-[4-chlorobenzoyl]-5-methoxi-2methylindole-3-acetic acid) was a Sigma product (catalogue number I-7378, lot 77H18461), with a melting point at 1578C obtained by DSC, and it was used without further purification. Its calorimetric glass transition temperature is reported to be Tg ¼ 428C (315.2 K) for a heating rate of 1 K/min.11 The calorimetric measurements were performed with a 2920 MDSC system from TA Instruments Inc. Dry high purity He gas with a flow rate of 30 cm3/min was purged through the sample. Cooling was accomplished with the liquid nitrogen cooling accessory (LNCA), which provides automatic and continuous programmed sample cooling down to 1508C. The baseline was calibrated scanning the temperature domain of the experiments with an empty pan. The temperature calibration was performed taking the onset of the endothermic melting peak at an heating rate of q ¼ 10 K min1 of several calibration standards: n-decane (Tm ¼ 243.75 K), n-octadecane (Tm ¼ 301.77 K), hexatriacontane (Tm ¼ 347.30 K), indium (Tm ¼ 430.61 K), and tin (Tm ¼ 506.03 K). The organic standards were high purity Fluka products, while the metal standards were supplied by TA Instruments Inc. The correction of the temperature for different heating and cooling rates was performed on the basis of results obtained with indium. The onset temperature of the melting peak of indium, (Ton)m, was obtained at several heating rates, qh, and the obtained values were fitted to a third order polynomial, (Ton)m ¼ a qh3 þ b qh2 þ c qh þ d. On the other hand, the onset temperature of the exothermic crystallization peak of indium, (Ton)cr, was obtained at several cooling rates, qc, and the obtained results were also fitted to a third-order polynomial, (Ton)cr ¼ a0 qc3 þ b0 qc2 þ c0 qc þ d0 . The temperature correction for each heating or cooling rate allows the extrapolation to the melting of indium in infinitely slow rate conditions. In this context, the correction for each heating rate, (DT)qh ¼ a qh3 þ b qh2 þ c qh, was subtracted JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 93, NO. 6, JUNE 2004
The fragility index, m, of a substance was defined as the slope of the log10 t(T) versus Tg/T line at the glass transition temperature, that is, at T ¼ Tg.12,13 dlog10 tðTÞ m¼ ð1Þ dðTg =TÞ T¼Tg where t is the structural relaxation time which slows down to 100 s at Tg. Fragility of a glass forming system describes the temperature dependence of the molecular dynamics of the supercooled liquid. Equation 1 can be expressed in terms of the temperature dependent apparent activation energy, Ea, as Ea ðTg Þ 1 m¼ ð2Þ 2:303 RTg Any experimental technique that allows the determination of the activation energy of a motional process from the rough experimental data is thus useful for obtaining the fragility index of a glass-forming system. It was shown14 that the dependence of the glass transition temperature, Tg, on the heating or cooling rate, jqj, of a conventional DSC experiment is given by d lnjqj Dh ¼ d1=Tg R
ð3Þ
where Dh* is the activation enthalpy for the structural enthalpy relaxation. It is to be enhanced that a necessary constrain for applying eq. 3 on heating is that, prior to reheating, the glass must be cooled from above to well below the glass transition region at a rate equal or proportional to the reheating rate. The value of Dh* obtained from eq. 3 was set equal to Ea(Tg) in eq. 2 in the calculation of the fragility of indomethacin.6 The obtained value was m ¼ 77. It is to be noted that the experiments in the work previously referred were carried out in the heating mode.
ESTIMATION OF THE FRAGILITY INDEX OF INDOMETHACIN BY DSC
However, it is well known that the DSC results obtained on heating depend on the thermal treatments used to produce the glass (namely on the cooling rate), present the so-called overshoot peak in the heat capacity, and are influenced by aging effects.15 Nevertheless, most of the DSC studies of the glass transition are carried out on heating, which is due to the difficulty of obtaining reliable thermograms under cooling conditions. One of the reasons is probably that the accurate control of the temperature variation is more difficult on cooling than on heating. The calibration of the temperature-scale during cooling is also reported to be problematic. Despite these problems, we decided to calculate the fragility of indomethacin on the basis of DSC data obtained on cooling because, as noted, the results obtained in this regime are not influenced by the previous thermal treatments and/or aging effects. Experiments in the heating mode will also be done, and the results obtained in both modes will be compared. The DSC profile of the glass transition is a sigmoidal change in the heat flux, corresponding to a change in heat capacity, (DCP)Tg. The heat capacity jump is characterized by a set of temperatures, namely the onset and endset temperatures, respectively Ton and Tend, and the midpoint of the heat capacity jump, Tmid. The first problem to solve is to decide which of these temperatures must be identified with Tg. It is common to consider the midpoint of the heat capacity jump as Tg, given that it appears to be less sensitive to the noise in the baseline. However, the two other temperatures eventually have a most clear physical meaning. The onset temperature, Ton, represents the temperature at which the lost of the metastable equilibrium is becoming detectable. The endset temperature, Tend, on the other hand, is the temperature at which the nonequilibrium glassy state can be considered to be reached. In many cases, the DSC sigmoidal signal of the glass transition obtained on cooling shows some asymmetry, such that the onset temperature can be obtained with a higher accuracy, compared with the endset and midpoint temperatures (see Fig. 1a). This was observed in our work, so that we will analyze the influence of the cooling rate on the onset temperature, Ton, of the glass transition signal. The results of part of our experiments are shown in Figure 2, on the form of a plot of ln jqj versus 1/Ton. The experimental onset temperatures were corrected as previously explained in the experi-
1505
Figure 1. DSC profile of the glass transition of indomethacin; (a) cooling curve obtained with a sample of 3.3170 mg at a cooling rate of q ¼ 17 K min1; (b) heating curve obtained with a sample of 3.6420 mg at a heating rate of q ¼ þ17 K min1. The figure indicates the position of the characteristic temperatures: onset temperature, Ton, endset temperature, Tend, and midpoint temperature, Tmid.
mental part. Figure 2a shows data obtained on cooling, while Figure 2b shows data obtained on heating. From the observation of Figure 2a and from the linear regression analysis of the corresponding data, we can draw the following conclusions: 1. The data points show a significant scattering. In fact, the coefficient of determination, R2, is 0.93, which indicates that the evaluation of the onset temperature of the glass transition on cooling is subjected to some uncertainties. 2. The slope of the regression straight line is 44.0 (with a confidence interval of 2.1). From this slope, the value of 365.5 kJ mol1 JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 93, NO. 6, JUNE 2004
1506
MOURA RAMOS, TAVEIRA-MARQUES, AND DIOGO
Figure 2. ‘‘Arrhenius plot’’ (logarithm of the rate as a function of 1/Ton) for the glass transition of indomethacin; (a) data obtained on cooling with rates between 20 and 2 K min1; (b) data obtained on heating with rates between þ1 and þ22 K min1.
was obtained (using eq. 3) for the activation energy. Introducing this value in eq. 2 and considering Tg ¼ 47.68C ¼ 320.7 K (onset temperature of the glass transition signal measured on cooling at 10 K min1), leads to the value of m ¼ 60 for the fragility index of indomethacin. From the observation of Figure 2b, which presents data obtained on heating, and from the linear regression analysis of the corresponding data, we can draw the following conclusions: 1. The data points are not so scattered as those obtained on cooling (Fig. 2a). In fact, the coefficient of determination, R2, is 0.97. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 93, NO. 6, JUNE 2004
2. The slope of the regression straight line is 40.9 (with a confidence interval of 1.4). From this slope, the value of 340.0 kJ mol1 was obtained for the activation energy, and the corresponding value of the fragility index is m ¼ 56, in good agreement with the value obtained in the cooling mode. This is an interesting point to be underlined. As pointed out before, each one of the experimental regimes (heating or cooling) has its own advantages and/or drawbacks. However, if used properly, they should lead to similar results, and that is what we showed in this particular case of indomethacin. Moreover, the obtained values (60 and 56) are in very reasonable agreement with values recently reported, obtained from thermally stimulated depolarization currents data,9,10 and with the value m ¼ 63 obtained from the width of the glass transition.8 The fact that a value of m ¼ 77 obtained by DSC was previously reported6 is not surprising, because it is nothing but a preliminary result, using only four heating rates, with average of only three determinations for each rate. Let us briefly mention that it was shown16,17 that eq. 2 can be rewritten in the form of an empirical rule as Dh*/R(1/T1 1/Tu) ¼ C, where Tl and Tu are, respectively, the lower and upper end of the glass transition region, and C is a constant (equal to 5 for inorganic glasses). However, this empirical equation cannot be used to predict the activation enthalpy of the structural relaxation of indomethacin because it holds only for strong glasses. Finally, the heat capacity jump associated to the glass transition of indomethacin was found to be (DCP)Tg ¼ (0.388 0.005) J g1 K1 on cooling (18 independent experiments), and (DCP)Tg ¼ (0.414 0.006) J g1 K1 on heating (10 independent experiments), in good agreement with the value of 0.41 J g1 K1 reported in the literature.8
CONCLUSIONS When the experiment is carried out on heating, the shape of the Differential Scanning Calorimetry signal of the glass transition strongly depends on the thermal history of the sample. To avoid this drawback, we decided to analyse this signal in the cooling mode. Specifically, the variation of the
ESTIMATION OF THE FRAGILITY INDEX OF INDOMETHACIN BY DSC
onset temperature as a function of the cooling rate has been studied. Some difficulties were encountered, arising from the low accuracy and reliability of the thermograms obtained under these conditions, which lead to some scattering of the experimental results. The fragility index of indomethacin calculated from these results was m ¼ 60. In the heating mode, on the other hand, a value of m ¼ 56 was obtained for the fragility index of this pharmaceutical solid, in very good agreement with the value obtained on cooling. Furthermore, these values are in excellent agreement with those recently reported obtained by thermally stimulated depolarization currents and from the width of the glass transition.
8.
9.
10.
11.
REFERENCES 12. 1. Hancock BC, Zografi G. 1997. Characteristics and significance of the amorphous state in pharmaceutical systems. J Pharm Sci 86:1–12. 2. Craig DQM, Royal PG, Kett VL, Hopton ML. 1999. The relevance of amorphous state to pharmaceutical dosage forms: Glassy drugs and freeze dried systems. Int J Pharm 179:179–207. 3. Shambling SL, Tang X, Chang L. Hancock BC, Pikal MJ. 1999. Characterization of the time scales of molecular motion in pharmaceutically important glasses. J Phys Chem B 103:4113–4141. 4. Shambling SL, Hancock BC, Dupuis Y, Pikal MJ. 2000. Interpretation of relaxation time constants for amorphous pharmaceutical systems. J Pharm Sci 89:417–427. 5. Adronis V, Zografi G. 1997. Molecular mobility of supercooled amorphous indomethacin, determined by dynamical mechanical analysis. Pharm Res 14: 410–414. 6. Adronis V, Zografi G. 1998. The molecular mobility of supercooled amorphous indomethacin as a function of temperature and relative humidity. Pharm Res 15:835–842. 7. He R, Craig DQM. 2001. An investigation into the thermal behaviour of an amorphous drug using low frequency dielectric spectroscopy and modulated
13.
14.
15.
16.
17.
1507
temperature differential scanning calorimetry. J Pharm Pharmacol 53:41–48. Crowley KJ, Zograft G. 2001. The use of thermal methods for predicting glass-former fragility. Thermochim Acta 380:79–93. Correia NT, Moura Ramos JJ, Descamps M, Collins G. 2001. Molecular mobility and fragility in indomethacin: A Thermally Stimulated Depolarisation Currents study. Pharm Res 18:1767–1774. Moura Ramos JJ, Correia NT, Taveira-Marques R, Collins G. 2002. The activation energy at Tg and the fragility index of indomethacin, predicted from the influence of the heating rate on the temperature positron and on the intensity of the Thermally Stimulated Depolarisation Current peak. Pharm Res 19:1879–1884. Adronis V, Zografi G. 2000. Crystal nucleation and growth of indomethacin polymorphs from the amorphous state. J Non-Cryst Solids 271: 236–248. Bohmer R, Ngai KL, Angell CA, Plazek DJ. 1993. Nonexponential relaxation in strong and fragile glass formers. J Chem Phys 99:4201–4209. Bohmer R, Angell CA. 1994. Local and global relaxations in glass-forming materials. In: Richert R, Blumen A, editors. Disorder effects on relaxational processes. Berlin: Springer-Verlag, pp 11–54. Moynihan CT, Esteal AJ, Wilder J, Tucker J. 1974. Dependence of the glass transition temperature on heating and cooling rates. J Phys Chem 76:2673– 2677. Simatos D, Blond G, Roudaut G, Champion D, Perez J, Faivre AL. 1996. Influence of heating and cooling rates on the glass transition temperature and the fagility parameter of sorbitol and fructose as mesaured by DSC. J Thermal Anal 47:1419– 1436. Moynihan CT. 1993. Correlation between the width of the glass transition region and the temperature dependence of the viscotity of high-Tg glasses. J Am Ceram Soc 76:1081–1087. Moynihan CT, Lee SK, Tatsumisago M, Minami T. 1996. Estimation of activation energies for structural relaxation and viscous flow from DTA and DSC experiments. Thermochim Acta 280/281:153– 162.
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 93, NO. 6, JUNE 2004