10806
J. Phys. Chem. B 2008, 112, 10806–10814
Calorimetric Relaxation in Pharmaceutical Molecular Glasses and Its Utility in Understanding Their Stability Against Crystallization E. Tombari,† C. Ferrari,† G. P. Johari,*,‡ and Ravi M. Shanker§ Istituto per i Processi Chimico-Fisici del CNR, Via G. Moruzzi 1, 56124 Pisa, Italy, Department of Materials Science and Engineering, McMaster UniVersity, Hamilton, Ontario L8S 4L7, Canada, and Groton Laboratories, Pfizer Inc., Groton, Connecticut 06340 ReceiVed: February 28, 2008; ReVised Manuscript ReceiVed: June 19, 2008
Glassy states of three pharmaceuticals, acetaminophen, griseofulvin, and nifedipine, and an acetaminophen-aspirin (1:1 mol) alloy were made by slow cooling of the melt and studied by calorimetry. Measurements were performed by cooling and heating at significantly slow rates of 20 K/h, which were comparable to the rate used in adiabatic calorimetry. The results were modeled in terms of a nonexponential, nonlinear structural relaxation. The calorimetric relaxation of all four pharmaceutical samples were less nonexponential than those of polymeric or inorganic glasses, and this finding was attributed to additional contributions to energy change that would arise from temperature and time dependent variation in the hydrogen bond population, the extent of isomerization, and/or the ionic equilibria that exist in these materials. Four calculated and relevant parameters for the pharmaceutical samples were, ln A ) -183, β ) 0.75, x ) 0.4, and ∆h* ) 457 kJ/mol for acetaminophen, ln A ) -170, β ) 0.75, x ) 0.45, and ∆h* ) 516 kJ/mol for griseofulvin, ln A ) -189, β ) 0.69, x ) 0.39, and ∆h* ) 503 kJ/mol for nifedipine, and ln A ) -160, β ) 0.70, x ) 0.50, and ∆h* ) 363 kJ/mol for the acetaminophen-aspirin alloy. The significance of these parameters and, in particular, their values are discussed in the context of the stability of the pharmaceuticals against crystallization and compared against the significance of the localized motions of the JG relaxation in the same context. Acetaminophen was found to be significantly more prone to crystallization on heating than the other two pharmaceuticals as well as the acetaminophen-aspirin alloy. 1. Introduction When a glass is heated from its fixed structure at temperature T, its enthalpy and entropy first increase very slowly and then decrease as its structure begins to relax irreversibly toward the equilibrium state. Upon further heating, the enthalpy and entropy of its ultraviscous melt increase relatively more rapidly and its structure changes reversibly. These effects are studied1-7 by measuring the time-, and temperature-dependent heat capacity, Cp,app, using differential scanning calorimetry (DSC), and analyzing the data in terms of a nonexponential nonlinear structural relaxation model. Such analyses1-3 yield the characteristic (calorimetric or structural) relaxation time τ, and a nonexponential relaxation parameter β. The parameter β is interpreted as the distribution of relaxation time and whose value is less than 1. The values of τ and β determined from calorimetry differ from the corresponding values determined from dielectric and mechanical relaxation measurements.5 It has been pointed out that this difference arises from the often overlooked nature of the structural fluctuations that occur in one type of relaxation and are absent or less active in the other type8 and which couple selectively to the stimulus used for making the relaxation measurements. The equilibrium properties of a liquid contain contributions from all physical and chemical processes as they involve changes in energy. Since these process occur at different time scales with different activation energies, their contributions to * Corresponding author. E-mail:
[email protected]. † Istituto per i Processi Chimico-Fisici del CNR. ‡ Department of Materials Science and Engineering, McMaster University. § Groton Laboratories, Pfizer Inc.
Cp,app would differ as T is varied. Also, the kinetic rates and equilibrium constants of the different processes vary differently with T. To elaborate, in most polymeric melts, on one extreme, a change in T causes changes in configurations resulting from angular displacement of segments of the macromolecules; in atomic liquids such as metals, on the other extreme, the changes involve only the position of atoms resulting from random diffusion. The Cp,app of both types of materials is determined by the temperature- and time-dependent changes of the R-relaxation process and from localized molecular motions of the Johari-Goldstein (JG) relaxation.9-14 In contrast to the polymers and ultraviscous metal, the majority of the organic molecular liquids contain inter- and intramolecular hydrogen bonds, isomeric states, and ions and ion-pairs in their condensed phase structure. Since the kinetic rate constant of hydrogen bond formation, isomeric transformation and ion-pair formation varies with T, it has been argued15-17 that Cp,app of such molecular liquids is determined additionally by the energy changes resulting from these interactions. When such molecular liquids are cooled, the population of hydrogen bonds, isomers and ions in their structure kinetically freezes at a temperature at which their characteristic transformation rates become comparable to the diffusion rate. On further cooling thereafter, the nonequilibrium population of the entities involved remains kinetically frozen in the glassy state. When the glass is heated, the properties measured during heating therefore contain contributions from three additional effects: (i) a decrease in the net energy as the hydrogen bond equilibrium shifts such as to decrease their population, (ii) an increase in the energy as change in the isomeric equilibrium increases the population of high energy isomers, and there is a gain or loss of metastable
10.1021/jp801794a CCC: $40.75 2008 American Chemical Society Published on Web 08/07/2008
Pharmaceutical Molecular Glasses rotational conformations of groups within a molecule, and (iii) an increase in the net energy as any ions T ion-pair equilibrium shifts such as to increase the ion population. Some of these processes may kinetically unfreeze during the heating of a glass before or after the structure unfreezes. (During the cooling of a melt the reverse would occur, i.e., these processes would kinetically freeze before or after the structure freezes.) Thus the relative contributions of the three effects to both Cp and enthalpy become heating-rate dependent. Consequently, τ and β obtained by analyzing the Cp,app data differ when different heating rates are used for the DSC study and/or when the thermal history of the glass is varied by annealing. Some of these effects have been discussed in relation to calorimetry of alcohols,15,16 proteins,17 contents of certain foods,18 and pharmaceuticals.19 As part of our studies of molecular motions in the glassy and ultraviscous states of organic, pharmaceutical molecules and of the role of these motions on the stability of a glass against crystallization, we have used calorimetry to determine the relaxation features of a variety of materials. In these studies we have purposely used cooling/heating rates that are 60-times slower than the rates used in conventional, commercially available DSC instruments. The rates used in these investigations are also comparable to those used in adiabatic calorimetry of glasses. Such studies yield τ and β that are closer to their true and equilibrium values. Here we report a detailed study of four molecular substances that are used as pharmaceuticals. The results show that their relaxation time distributions, β is much greater than that known for polymers and other liquids. We also consider how structural relaxation features determine the stability of a molecular glass and of its melt against crystallization, and argue that the effects observed would be common to structures containing hydrogen bonds, isomeric states and ions.
J. Phys. Chem. B, Vol. 112, No. 35, 2008 10807 as standards. The sample for both the calibration and the study was contained in a hermetically sealed 90 mm long glass capillary of 2.2 mm internal diameter and ∼0.3 mm wall thickness, which is referred to as the sample cell. The hermetically sealed capillary with the sample contained air whose molar volume was negligible in comparison with the moles of the sample. The powdered crystalline sample was melted inside the cell by placing it in a convection oven at the desired temperature for 5 min and then quenched in ∼ 6 s by immersing in an ethanol bath kept at a desirable temperature. The sample was then immediately placed inside the calorimeter that had been isothermally kept at the same temperature as the ethanol bath and it was then heated and cooled at 20 K/h rate. These rates are greatly slower than the usual DSC scan rate of 10 K/min (600 K/h), and are comparable with the ∼5-15 K/h heating rate used for measuring Cp by adiabatic calorimetry.29 Since Tg is defined for cooling and heating rates of 10 or 20 K/min, we do not use this term in analyzing our data. For convenience, the structural formula of the four pharmaceuticals studied here are given below. These indicate the hydrogen-bonding sites for the various atoms:
2. Experimental Methods Crystalline powder of acetaminophen (>99% purity) was purchased from Sigma-Aldrich Chemicals. Acetaminophen is also known as 4-acetamidophenol or 4′-dihydroxyacetanilide (C8H9NO2, mol wt 151.16 Da), Tylenol, and paracetamol. Micronized fine crystalline powder of griseofulvin of 99 + % purity also known as (2S,6′R)-7-chloro-2′,4,6-trimethoxy-6′methyl-3H, 4′H-spiro[1-benzofuran-2,1′-cyclohex[2]ene]-3,4′dione (C17H17ClO6, mol wt 352.77 Da) was also purchased from Fluka, and used as such. Nifedipine also known as dimethyl 2,6-dimethyl-4-(2-nitrophenyl-1,4 dihydropyridine-3,5-dicarboxylate)) (C17H18N2O6, mol wt 346.34 Da), of >98% purity and acetyl salicylic acid (aspirin) or 2-(acetyloxy)benzoic acid; (C9H8O4, mol wt 180.15 Da) of >99% purity was purchased from Sigma Aldrich Chemicals. These pharmaceuticals were studied in the as-received state. The melting points of the most frequently reported polymorph of acetaminophen is 441.7 K. Its Tg, as determined from the onset temperature of the endotherm obtained by heating at 10 K/min the samples that had been cooled at 10 K/min, is 296 K.20 For the same cooling and heating rates, Tg of griseofulvin is 362 K21 and of nifedipine is 322 K.22 The calorimeter used in this study was designed for temperature-modulation calorimetry. It has been described earlier23 and used in a variety of studies.24-28 It allows extremely slow cooling/heating of a sample, and thus has an advantage over the commercial equipment. For this study, the calorimeter was operated in a normal scanning mode. Its temperature calibration was performed by measuring the melting point of indium, and of ice, and finally by using a standard PT-100 thermometer. It was calibrated for Cp values by using glycerol and dodecanol
3. Results In the initial study of acetaminophen, the crystalline sample inside the cell was melted at 447 K and quenched to 250 K in ∼ 6 s. Its Cp,app was measured during heating at 20 K/h and its value is plotted against T in Figure 1A. It shows that Cp,app decreased in the range 270 to 280 K and then finally increased in the equilibrium state at 300 - 320 K, after showing a peak at 294.2 K. On heating from 320 K, a deep exotherm, which is only partly seen here on an enlarged scale, appeared. This indicates that the ultraviscous acetaminophen had begun to crystallize. On further heating, a shallow exotherm appeared at T in the 340-360 K range and finally Cp of the crystal phase is reached. Thus, there are two exotherms that partly overlap, one is sharp and deep and it indicates rapid crystallization. The second exotherm is small and appears as an inverted shoulder beginning at 340 K. It indicates relatively slow solid state transformation of the crystal phase. (The crystal phase formed on heating the glass is likely to be orthorhombic as found in a number of earlier studies.20,30-32 The significance of the second, small exotherm will be discussed in another report.) The crystallized sample was temperature-cycled between 373.2 and 253.2 K while measuring its Cp,app during both the cooling and heating, as shown by the dotted line in the lower part of Figure 1A. (The full line is for the crystal state and the dashed line on the top is the equilibrium liquid line, and its extrapolation.) To enable detailed analysis of acetaminophen’s structural relaxation features, which we would discuss later here, Cp,app is replotted in Figure 1B. In a subsequent experiment, a new sample of acetaminophen was melted, quenched to 298 K in water and then placed in the calorimeter maintained at 305.2 K. Cp,app of
10808 J. Phys. Chem. B, Vol. 112, No. 35, 2008
Figure 1. A. The heat capacity of acetaminophen measured during heating from 253.2 to 373.2 K at 20 K/h rate is shown by open circles. The Cp,app shows an overshoot at 294.2 K and thereafter a deep exotherm caused by crystallization of the supercooled melt acetaminophen. Also shown by dashed and dotted lines are the Cp values of crystallized acetaminophen measured during the cooling and thereafter on heating the sample. Open triangles show the Cp,app calculated by using the nonexponential, nonlinear structural relaxation using a fixed value for the distribution parameter, ln A ) -183, β ) 0.75, x ) 0.4, and ∆h* ) 457 kJ/mol and taking 2000 K/min for the cooling rate for vitrification of acetaminophen. Figure 1B. The same data as in panel A, but the Cp was calculated by assuming that the sample was vitrified by cooling at 10 K/min. See text for details. The upper dashed line extrapolated from high temperatures is for Cp,liquid and the lower dotted line is for Cp,glass. These were used for normalizing the data. The lower full line is for the crystal state.
its melt was measured during the cooling from 305.2 to 253.2 at 20 K/h rate and that of its glass was thereafter measured during the heating from 253.2 to 305.2 K at the same rate. The data are plotted against T in Figure 2. Griseofulvin sample was melted at 497 K and was quenched to 250 K. Its Cp,app was then measured during heating from 253.2 to 373.2 at 20 K/h rate. This data is plotted against T as open circles in Figure 3A. (Since this sample did not crystallize, Cp,app of griseofulvin’s crystal was not measured.) In a subsequent experiment, ultraviscous griseofulvin was cooled from 373.2 to 293.2 at 20 K/h rate and its Cp,app was measured during the cooling. It is plotted against T in Figure 3B. Its glassy state was thereafter heated from 293.2 to 373.2 at 20 K/h rate and its Cp,app measured during the heating is plotted against T also in Figure 3B. It shows an overshoot at 356.2 K before returning to the equilibrium melt value. Nifedipine sample was similarly melted and its melt was quenched from 452 to 298 K. It also showed no indication of crystallization. Its Cp,app was then measured first during cooling from 325 to 270 at 20 K/h rate and then during heating from 270 to 325 at 20 K/h rate. The values are plotted against T in Figure 4. Its Cp,app shows an overshoot at 313 K. The acetaminophen-aspirin alloy of 1:1 mol composition was prepared by accurate weighing. The mixture was powdered to fine particles, transferred to the sample cell, melted at 447 K and allowed to cool to ambient temperature. Unlike pure
Tombari et al.
Figure 2. Heat capacity of acetaminophen measured during first cooling from 305.2 to 253.2 K at 20 K/h and then heating from 253.2 to 305.2 K at 20 K/h rate. The Cp measured during the cooling are shown by open squares and those measured during heating by open circles. The Cp shows an overshoot at 294.2 K. The Cp of crystalline acetaminophen is plotted as a smooth line and is taken from Figure 1 A. Note the hysteresis between the Cp measured during cooling and during heating. Smooth lines show the value of Cp calculated by using the nonexponential, nonlinear structural relaxation with ln A ) -183, β ) 0.75, x ) 0.4, and ∆h* ) 457 kJ/mol both during cooling and successive heating. See text for details. The upper dashed straight line extrapolated from high temperatures is for Cp,liquid and the lower one for Cp,glass used for normalizing the data.
acetaminophen, the acetaminophen-aspirin alloy showed no signs of crystallization. Its Cp,app was measured during first cooling from 277.2 to 246.2 at the 20 K/h rate and then measured during heating from 246.2 to 277.2 K at the same rate. Its plot against T provided in Figure 5 shows an overshoot at 266 K. As for others in Figures, 2, 3B, and 4, it also shows a hysteresis between the Cp,app measured during the cooling and heating. We now analyze the Cp,app against T data for the four pharmaceuticals. It has been known that all models developed for fitting to the DSC heating scans through the glass softening or Tg range admit to the phenomenology of structural relaxation toward an equilibrium state. These have been based on the original observations of Winter-Klein33 and Tool34 and the formalisms introduced by Narayanaswamy.35 The Tool-Narayanaswamy model was combined with a distribution of relaxation time parameter, β, and the formalism was used originally by Moynihan and co-workers1 to fit the DSC scans of a variety of substances. Algorithms for such analysis and simulation of the data, developed by Hodge et al.,36 are now used for fitting to the DSC scans of mainly amorphous polymers and inorganic glasses. We fit the formalism of the nonexponential, nonlinear relaxation model developed by Tool-Narayanaswamy-Moynihan (TNM model) for fitting to the Cp,app against T plots. The basic equation for the nonlinearity of structural relaxation in terms of change in the relaxation time τ with change in the fictive temperature, Tf, is written as
[
τ ) A exp
x∆h* (1 - x)∆h* + RT RTf
]
(1)
where ∆h* is the activation energy, A is a parameter equal to τ when both T and Tf are formally infinite, and x is an empirical parameter referred to as the nonlinearity parameter, whose value is between zero and 1. (The fictive temperature Tf is the temperature at which the glass state is at equilibrium, i.e., its properties are the same as that of the equilibrium melt.1,34-36)
Pharmaceutical Molecular Glasses
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Figure 3. (A) Apparent Cp of griseofulvin measured during heating from 253.2 to 373.2 K at 20 K/h rate is shown by open circles. It shows an overshoot at 356 K. Full smooth line show the Cp calculated by using the nonexponential, nonlinear structural relaxation using a fixed value for the distribution parameter, ln A ) -170, β ) 0.75, x ) 0.45, and ∆h* ) 516 kJ/mol and taking 2440 K/min for the cooling rate at which griseofulvin had vitrified. (B). Apparent Cp of griseofulvin measured during first cooling from 373.2 to 253.2 K at 20 K/h and then heating from 253.2 to 373.2 K at 20 K/h rate. The Cp data measured during the cooling are shown by open squares and those measured during heating by open circles. The Cp shows an overshoot at 356.2 K. Note the hysteresis between the Cp measured during cooling and during heating. Smooth lines show the value of Cp calculated by using the nonexponential, nonlinear structural relaxation with ln A ) -170, β ) 0.75, x ) 0.45, and ∆h* ) 516 kJ/mol both during cooling and successive heating. See text for details. The upper dashed straight line extrapolated from high temperatures is for Cp,liquid and the lower one for Cp,glass used for normalizing the data.
The relaxation function is written as φ ) φ0 exp[-(t/τ)β]. The details of the equation and the manner of data fitting may be found in refs 1, 3, 15, 16, 20, and 22. Briefly, the data are transformed into a normalized heat capacity by using
Cp,app,norm )
[Cp,app(T) - Cp,glass(T)] [Cp,liquid(T) - Cp,glass(T)]
(2)
where Cp,app is the measured value, Cp,glass is the value measured at low temperatures and extrapolated linearly to high temperatures and Cp,liquid is Cp,0 of the melt measured at high temperatures and extrapolated linearly to low temperatures. Thus Cp,app,norm increases from zero value for the glass at low temperatures to unity in the equilibrium melt at high temperatures. It exceeds unity at the temperature of Cp,app-overshoot or the Cp,app peak. The fit to experimental data is obtained by a least-squares Marquardt algorithm by using temperature steps of 0.5 K. This step corresponds to 1.5 min time interval for heating and cooling rates of 20 K/h, during which the state of the ultraviscous melt and glass in this study reached closer to the chemical and structural equilibrium. (In contrast, in the usual DSC scan at 10 K/min, a period of only 0.1 min corresponds to the 1 K step.) The best-fit value of the parameters, ln A, β, x, and ∆h*, was obtained by searching the best overlap of the calculated and measured plots of Cp,app, norm against T. In contrast
Figure 4. Heat capacity of nifedipine measured during first cooling from 325 to 270 K at 20 K/h and then heating from 270 to 325 K at 20 K/h rate. The Cp measured during the cooling are shown by open squares and those measured during heating by open circles. The Cp shows an overshoot at 313 K. Note the hysteresis between the Cp measured during cooling and during heating. Smooth lines show the value of Cp calculated by using the nonexponential, nonlinear structural relaxation with ln A ) 189, β ) 0.69, x ) 0.39 and ∆h* ) 503 kJ/mol both during cooling and successive heating. See text for details. The upper dashed straight line extrapolated from high temperatures is for Cp,liquid and the lower one for Cp,glass used for normalizing the data.
Figure 5. Heat capacity of (1:1 mol) acetaminophen-aspirin mixture measured during first cooling from 277.3 to 253.2 K at 20 K/h and then heating from 253.2 to 373.2 K at 20 K/h rate. The Cp measured during the cooling are shown by open squares and those measured during heating by open circles. The Cp shows an overshoot at 356.2 K. Note the hysteresis between the Cp measured during cooling and during heating. Smooth lines show the value of Cp calculated by using the nonexponential, nonlinear structural relaxation with ln A ) -160, β ) 0.70, x ) 0.50 and ∆h* ) 363 kJ/mol both during cooling and successive heating. See text for details. The upper dashed straight line extrapolated from high temperatures is for Cp,liquid and the lower one for Cp,glass used for normalizing the data.
to the usual DSC scans obtained for 30 - 60 times faster heating rate, the fitting was done here for both the Cp,app measured during the cooling to form the glassy state and the Cp,app measured during the heating of the glassy state to T > Tg. Equation 2 was fitted to the Cp,app against T plots measured during the cooling of acetaminophen melt at 20 K/h and thereafter heating at the same rate. The best-fit parameters obtained are as follows: ln A ) -183, β ) 0.75, x ) 0.4, and ∆h* ) 457 kJ/mol. The calculated Cp,app is shown by a full line for both heating and cooling in Figure 2. The same procedure was used for obtaining the best fit parameters for
10810 J. Phys. Chem. B, Vol. 112, No. 35, 2008
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TABLE 1: Parameters for the Nonexponential Nonlinear Equation Used for Fitting the Cp,app against T Plots for the Glassy State of Four Pharmaceuticals pharmaceutical
ln A
∆h* [kJ/mol]
x
β
acetaminophen griseofulvin nifedipine acetaminophen-aspirin (1:1 mol)
-183 -170 -189 -160
457 516 503 363
0.40 0.45 0.39 0.50
0.75 0.75 0.69 0.70
Cp,app against T plots measured during both cooling and heating for griseofulvin, nifedipine and acetaminophen-aspirin alloy. For the four pharmaceuticals, these parameters are summarized in Table 1. The corresponding figures showing the goodness of fit of the calculated plots to experimental data for griseofulvin, nifedipine and acetaminophen-aspirin alloy are provided in Figures 3B, 4, and 5, respectively. For acetaminophen-aspirin alloy, the calculated Cp,app shows a good fit except in the temperature range of 4 K from 267-271 K. It should also be noted that there are two limitations of this analyses; (a) eq 1 becomes equal to τ ) Aexp(∆h*/RT) for equilibrium liquids for which T ) Tf, which is contrary to the characteristic non-Arrhenius dependence of τ of supercooled liquids on T, and, (b) extrapolation of the equation, τ ) A exp(∆h*/RT) to T f ∞, yields a ln A value of -189 to -160, which is significantly lower than ln A of -32.2 to -27.6 expected from the pre-exponential factor of 10-14 to 10-12 s observed from viscosity, dielectric, and mechanical relaxation studies. Because of these limitations, eq 1 would seem to be useful only over a relative small range of Cp,app over which Tf changes during the cooling and during the heating. 4. Discussion 4.1. General Features of Time- and Temperature-Dependent Heat Capacity. Pharmaceutical molecular glasses investigated in this study show several characteristics that have been reported for other materials. For example, in Figure 1A, Cp,app of the acetaminophen glass decreases on heating to a value that is below the Cp of the crystal phase. This is not an unusual occurrence because Cp,app is not the true heat capacity. It contains effect of the heat released on spontaneous decrease in the enthalpy during structural relaxation, which occurs more rapidly as T increases during the course of such measurements. This aspect has been discussed in detail in connection with the study of the usual Tg of water and metallic glasses.37 Similar observations for the appearance of a shallow minimum in the Cp,app against T plot for griseofulvin in Figure 3A is also likely to indicate decrease in Cp,app below the value of its crystal’s Cp . The plots in Figures 2, 3B, 4, and 5 for the various pharmaceuticals show that when measurements are made on cooling, Cp,app decreases in a sigmoidal manner. On heating the glassy state, Cp,app initially remains the same as on cooling the glassy state. Upon continued heating, Cp,app then becomes less than that observed on cooling, crosses the Cp,app plot obtained on cooling from below, shows a peak or an overshoot before finally reaching the Cp of the equilibrium liquid. Onset of the decrease in Cp,app during cooling indicates the beginning of the ergodicity loss and onset of the increase in Cp,app during heating shows the beginning of the ergodicity regain. In terms of the specific behavior of the pharmaceuticals, Cp,app of the vitrified and ultraviscous acetaminophen in Figure 2 remains above the Cp of the crystal phase, and the difference between the two is equal to the excess Cp of the glass and the ultraviscous liquid over the crystal phase value. Zhou et al.38
Figure 6. (A) Enthalpy difference between cooling and heating plotted against the temperature for acetaminophen, griseofulvin, nifedipine, and (1:1 mol) acetaminophen-aspirin alloy. (B) Corresponding entropy difference between cooling and heating plotted against the temperature.
have reported the excess Cp of acetaminophen melt. Its value read from their Figure 438 is ∼ 100 J/(mol K) at 313 K. From Figures 1 and 2 here, the excess Cp at 313 K is 93 J/(mol K), i.e., ∼ 7 J/mol K less than Zhou et al.’s.38 Since they used excess Cp instead of the configurational Cp to determine “configurational entropy” which was then related to τ, this difference of ∼7 J/(mol K) would lead to a revision in their estimates for τ.39 4.2. Relaxation and Thermal History. Two aspects of structural relaxation have been studied here: (i) the enthalpy and entropy change during both cooling and heating at the same rates of 20 K/h, and, (ii) the changes in the state of the sample on quenching the liquid and then on heating the quenched state. For investigating the first, Cp,app was plotted against T and the enthalpy difference between cooling and heating, δHcool-heat, was determined with respect to a reference temperature, Tref. Also, Cp,app was plotted against ln(T) and the corresponding entropy difference, δScool-heat, was determined. The relations used for determining the two quantities at T > Tref are:
δHcool-heat) [H(T)cool-H(T)heat] )
∫TT (Cp,app,cool - Cp,app,heat) dT ref
(3)
δScool-heat) [S(T)cool-S(T)heat] )
∫TT (Cp,app,cool - Cp,app,heat) d(ln T) ref
(4)
The plots of δHcool-heat and of δScool-heat against T for the four pharmaceuticals are shown in Figures 6A and 6B. The two quantities increase from zero in the glassy state to a peak value and finally decrease to zero in the equilibrium liquid state. (Note that in the temperature-modulated calorimetry studies, δHcoolheat and δScool-heat remain zero when the cooling and heating rates are extremely low, and the sample remains in the equilibrium state.) The peak appears when the rate of increase as a result of
Pharmaceutical Molecular Glasses structural relaxation to a lower energy equilibrium melt state becomes equal to the rate of decrease on structural recovery to the higher energy equilibrium melt state in a time-, and temperature-dependent manner. The position of such peaks would shift to higher T when higher cooling and heating rates are used and their height would vary with the annealing conditions. It may be possible to describe the increase in δHcoolheat and δScool-heat by using a suitable relaxation function with the parameters β and x, and then to describe the decrease also by using the same function and parameters. Since such an analysis of the δHcool-heat and δScool-heat plots is broadly applicable and may be useful for other studies, we will discuss it in the future in the context of new relaxation studies. We now consider the effect of quenching the melt on the observed structural relaxation. In Figure 1A, the Cp,app against T plot (circles) for acetaminophen are for a sample that had been made by quenching the melt from 447.2 to 250 K in ∼6 s, i.e., at a cooling rate of ∼2000 K/min. When we used this approximate cooling rate to determine the best-fit values of the four parameters for heating of the quenched glass, we obtained, ln A ) -183, β ) 0.75, x ) 0.4, and ∆h* ) 457 kJ/mol. These agree with the parameters listed in Table 1 that had been obtained by fitting to the Cp,app plot for the 20 K/h cooling and heating rates in Figure 2. However, the best-fit plot (triangles) obtained for heating the quenched state in Figure 1A shows significant deviations from the measured values (circles) in that there is a much deeper exothermic minimum due to structural relaxation between 250 and 285 K, and a smaller height of the Cp,app peak than that measured. To understand the reasons for such a large deviation, we examined if there were other effects that dominated the shape of the plot. For this purpose, we varied the cooling rate for which the best-fit was obtained for the measured Cp,app-T plot while keeping the same four parameters, ln A ) -183, β ) 0.75, x ) 0.4, and ∆h* ) 457 kJ/mol. This best-fit cooling rate was found to be 10 K/min. The calculated curve (triangles) for this deduced cooling rate is shown in Figure 1B. Now, both the depth of the exothermic minimum and the overshoot peak height match well. Since the sample was actually cooled at a rate much higher than 10 K/min, this means that either the approximations made in deducing eq 1 do not yield an appropriate fit to the Cp,app-T plot for the quenched sample or else the quenched sample inadvertently annealed when kept at 250 K and thus reached a state that would have been obtained by cooling at 10 K/min. It seems likely that the quenched sample had structurally relaxed probably to a state that would have been obtained by cooling the melt at 10 K/min rate. Nevertheless, this analysis also shows the internal consistency of the procedure used and its merit for determining the thermal history of a glass. It may be noted that a similar difficulty had appeared in fitting eq 1 to the DSC scans of rapidly cooled melt of tri-Rnaphthylbenzene.40 The Cp,app against T plot (circles) for griseofulvin’s quenched sample in Figure 3A was analyzed in a manner similar to that of acetaminophen in Figure 1A. Here we used the best-fit parameters, ln A ) -170, β ) 0.75, x ) 0.45, and ∆h* ) 516 kJ/mol determined from the 20 K/h cooling and heating rates in order to estimate the cooling rate of the quenched sample. By fitting only the endothermic rise in the 343 - 365 K range in Figure 3A, this rate was estimated as 2440 K/min, and the calculated Cp,app is plotted by a continuous line in Figure 3A. The calculated and measured Cp,app agree in this range, but not in the 280 - 343 K range, where the calculated Cp,app is initially higher and then lower than the measured Cp,app. Attempts to fit by using other cooling rates did not yield a better fit. This shows
J. Phys. Chem. B, Vol. 112, No. 35, 2008 10811 that, as for acetaminophen in Figure 1A, the sample may not only have annealed when kept at 250 K prior to the measurements done during heating, but also that other energetic changes may have become dominant. 4.3. Relaxation Parameters. It is significant to note that the nonexponentiality parameter β of 0.75 for acetaminophen obtained here is considerably higher than β of 0.65 obtained from the dynamic Cp data,41 and 0.67 from DSC using much higher cooling and heating rates.20 The discrepancy may arise partly from the fact that the shape of Cp,app against T plots is determined by both β and x, and that different set of β and x pairs can produce nearly the same shape of such plots. Also, in analyzing Cp,app, as in analyzing the dynamic Cp, it has been assumed that β does not vary with T. In the dielectric relaxation studies of acetaminophen melt,42 β was found to be 0.79 and in those measurements it did not vary with T. But since the longest dielectric relaxation time measured in that study was 1 s, it is not known whether β, if measured at lower T and longer τ, would be lesser than 0.79, or would it remain at 0.79. Nevertheless, the value of β obtained in this study using significantly lower heating and cooling rates than commercial DSC equipment is closer to the value obtained by dielectric relaxation time. For intercomparison of the structural relaxation of pharmaceuticals, we note that β is 0.75 for acetaminophen and griseofulvin, and slightly less, 0.69 for nifedipine and 0.70 for the acetaminophen-aspirin alloy. If β were to be a reflection of the distribution of relaxation time in a dynamic heterogeneity view, the faster modes of motions alone may determine the nucleation and crystallization rates. In that case, one would expect that nifedipine and the acetaminophen-aspirin alloy, whose β values are smaller than those of acetaminophen and griseofulvin, are likely to crystallize relatively more rapidly on heating to T above their usual Tg (measured for 10 or 20 K/min DSC scans). However, acetaminophen crystallized more readily and griseofulvin did not. This indicates that other type of mobility, such as localized motions, may also have a role in crystal nucleation in glasses and ultraviscous melts. Also there is a need to consider decoupling of diffusion from relaxation for crystal nucleation as well as the strengths and limitations of applying classical nucleation theory for crystal nucleation and growth in glass forming melts. This subject has been recently reviewed by Schmelzer.43 We now consider the significance of the nonlinearity parameter x. In Table 1, it is lowest, 0.39, for nifedipine and highest, 0.50, for acetaminophen-aspirin. Its magnitude is a measure of the rate of increase in τ on structural relaxation during storage and/or heating rate of a glass. When x ) 1 in eq 1, τ does not change with time and it increases with time progressively more rapidly as x is decreased. In relative terms, x of 0.39 for nifedipine and 0.50 for the acetaminophen-aspirin alloy means that there is a greater increase in τ on structural relaxation of nifedipine than on that of the acetaminophen-aspirin alloy. As has been shown by constructing the normalized Cp,app against T plots with different sets of these parameters,44 the parameter x, like ∆h* and β, has an effect on the width of the glasssoftening endotherm. Also, for a given set of x, ∆h* and β, this width is greater if its Tg measured in a usual DSC scan is higher, which is related to the fact that the change in T needed to cause the same change in a kinetic property is large when T itself is high and is relatively small when T is low. In Table 1, ∆h* represents the average activation energy for calorimetric relaxation. Its value for the equilibrium melt is highest for nifedipine, 503 kJ/mol, and lowest for acetaminophen-
10812 J. Phys. Chem. B, Vol. 112, No. 35, 2008 aspirin mixture, 363 kJ/mol. The values are also much higher than those found from dielectric and mechanical relaxation of most liquids and polymers, and they exceed even the energy, 340 kJ/mol, required to break a covalent C-C bond. Though physically less meaningful, such large ∆h* and -ln A values are useful for intercomparison of materials behavior. We now consider the effect of heating rate on the relaxation parameters. It is now known that the parameters β, x, and ∆h* obtained by fitting to the DSC scan obtained for one heating rate do not fit the DSC scan obtained for another heating rate.20,40,44,45 For example, for heating rate of 10 K/min, β is found to be 0.67 for acetaminophen20 and 0.73 for nifedipine.22 Also, from dynamic heat capacity studies,41 in which contribution to Cp from irreversible structural relaxation is absent, β has been found to be 0.65 for acetaminophen and 0.67 for griseofulvin.28 These are much greater than the β values of 0.35 to 0.58 obtained for organic polymers, and inorganic and metallic glasses.1-3,5,6,44,46 Variation of a melt’s τ, and of β, x and ∆h* with the heating rate are attributable to the heating rate dependence of the various contribution to energy. Most of these contributions would come to their respective equilibrium values if slow-heating rate were used, thereby yielding a closer to true value of β and x. Alternatively, isothermal structural relaxation studies may be performed which would show that the fitting parameters obtained differ from those determined from the DSC scans made at high heating rates. In physical terms, structural relaxation decreases the potential energy associated with the geometrical arrangement of molecules. It also decreases the kinetic, or vibrational energy. These are physical effects, which may be described also in measurable chemical thermodynamic terms. In the intermolecular network structure of a monocomponent melt, there are three further processes that are truly chemical in nature,45 (i) decrease in the energy as the hydrogen-bond population increases, (ii) decrease in the energy when the low energy isomer is favored in an isomeric equilibrium, and/or loss of metastable rotational conformations of groups within a molecule, and (iii) decrease in the net energy as ions T ion-pair equilibrium shifts toward more ion-pair population. In mixtures of materials, there is a further effect from the relative change in the topological and chemical short-range orders. All these processes have their characteristic rate constants and they would not all kinetically freeze at the same T at which the structure freezes on cooling a melt, or kinetically unfreeze at the same T at which the structure unfreezes on heating a glass. Thus their relative contribution to enthalpy and Cp are expected to become dependent on the cooling and/or heating-rate. Some of these effects have been discussed already in a study of alcohols, water, proteins and food materials.15-18 Pharmaceutical molecules usually contain hydrogen-bond acceptor and donor sites and some of these also exist in isomeric states. Moreover, their melt and glass may contain ionic impurities. Briefly, an acetaminophen molecule contains one -NH2 and one -OH group, a griseofulvin molecule has several hydrogen bond donor and acceptor sites, and a nifedipine molecule contains one N-H group and two dO groups (of the carboxylates). Aspirin also contains acceptor and donor groups that are capable of forming intermolecular hydrogen bonds. FTIR47 and Raman spectra48 of crystalline, liquid and glassy states of acetaminophen have shown the presence of intermolecular hydrogen bonds. However, FTIR and Raman spectra of nifedipine in its glassy and three crystalline states have shown no features attributable to hydrogen bonds.49 The importance and role of intermolecular hydrogen bonds in molecular
Tombari et al.
Figure 7. Plots of the calculated log(τ) against the reciprocal temperature for acetaminophen, griseofulvin, nifedipine and (1:1 mol) acetaminophen-aspirin alloy. The data were calculated from the parameters listed in Table 1. The plots are shown for both the heating and cooling experiments performed at 20 K/h. The horizontal dashed line refers to a relaxation time of 100 s, which is normally taken to be the value at Tg.
recognition and prediction of formation of specific crystals or polymorphs of organic compounds has been the matter of extensive research50,51 and these concepts have a considerable significancefortheformationandstabilityofglassypharmaceuticals. Finally, we use the parameters, ln A, β, x, and ∆h* to calculate τ for the four pharmaceuticals. Its value measured for both the heating and cooling at 20 K/h rate is plotted logarithmically against 1000/T in Figure 7, where the horizontal dashed line is drawn to show τ of 100 s, a value normally taken to be the structural relaxation time at Tg measured in a DSC scan. The “knee-shape” of the plots in Figure 7 shows that the extrapolated τ of the equilibrium melt, which may be reached after full structural relaxation at T below this Tg, would be higher than the calculated τ in the nonequilibrium glass of a fixed structure.52-55 This higher value would be achieved asymptotically during storage of the glassy state. It is also worth noting that when Tf of a glass formally remains constant with its changing T, the term A exp[(1 - x)∆h*/RTf)] in eq 1 becomes constant and hence τ varies as exp[(∆h*/RT) + constant]. The slope of the consequent linear plot of log10τcal against 1/T for a glass is much smaller than the slope of the plot for the ultraviscous melt. This slope for a glass varies with its x value, which is 0.39 for nifedipine and 0.50 for the acetaminophen-aspirin alloy. For a given glass or for a fixed value of x, it varies with its Tf or its thermal history. 4.4. Stability against Crystallization and Relaxation. Currently, there is much interest in controlling the nucleation and crystal-growth processes in an amorphous pharmaceutical so that its higher bioavailability over the crystal phase may be maintained during storage at a given temperature. To discuss this aspect, we recall that crystal nuclei formation results from the localized, faster mobility of molecules. This mobility may be seen in terms of the so-called dynamic heterogeneity, which postulates that there are dynamically distinct domains in a liquid and glass with a time constant given by the sum of single relaxation times ranging from very short to very long,56,57 and which is seen as a reason for β < 1. A lower β value indicates a greater dynamic heterogeneity than a higher β. Since faster modes of molecular motions within a given distribution of times remain kinetically unfrozen in a glass,58 it would seem that in the absence of other effects, a glass of lower β would be more susceptible to nucleation than a glass of higher β. One would expect that small molecular liquids with propensity of intermolecular hydrogen bonds, such as glycols and glycerol, should
Pharmaceutical Molecular Glasses show a similar behavior. However, the fit of the TNM equation to the calorimetric data obtained by such slow cooling/heating rates are not yet available for such liquids. Also, as mentioned earlier here, different stimuli used for measuring molecular relaxation couple differently with structural fluctuations. (For example, translational motion of a molecule without rotation does not appear in dielectric but does so in calorimetric relaxation, and rotation of a dipole about its 2-fold symmetry axis does not contribute to dielectric but does to calorimetric relaxation.) Therefore, the known dielectric relaxation features for such liquids may not be directly comparable with those of the calorimetric relaxation. Nucleation may also result from molecular motions within localized regions in the structure of a glass, a process known as the β-process,8-11 or the JG relaxation, which has also been observed in the Cp measurements.12-14 In this context, it has been argued that this relaxation is the precursor of the longrange molecular mobility or the R-relaxation.11,49,59,60 Studies of organic molecular glasses have shown that these localized motions, and not the long-range diffusion of the R-relaxation process, determine the nucleation and crystallization rates in the glassy state.62-65 The effect of physical aging on the nucleation of amorphous pharmaceutical, indomethacin controlled by the region of the β or the JG relaxation has been reported.61 Moreover, the broad relaxation times distribution of the localized motions of the JG relaxation partially overlaps the distribution due to the dynamic heterogeneity. In cases where the strength of the JG relaxation is small, the unfrozen faster modes of motion in the distribution of relaxation times may have a predominant role in crystal nucleation. Thus, a greater dynamic heterogeneity in such cases would appear to raise the possibility of crystal nucleation. In this respect, dynamics of supercooled liquids and glassy solids of organic small molecules has been the subject of extensive experimental investigations especially using solid state NMR techniques.66 Dielectric relaxation and DSC techniques have been utilized to study the influence of R- and β- relaxation dynamics on the crystallization of acetaminophen near its glass transition temperature.67 Evidently, there is a considerable interest in the subject with a focus on a need to gain better understanding of the physical basis for stabilization of glassy pharmaceuticals. This understanding would be advantageous in improving the bioavailability and retaining it over the shelf life of a product. In particular, it would be desirable to determine experimentally how (a) an increase in the distribution of relaxation times, or dynamic heterogeneity, (i.e., decrease in the parameter β), and (b) decrease in the strength of the JG relaxation control the stability of their glassy state against crystallization. A further effect also needs to be considered. Structural relaxation by long-range molecular diffusion densifies a glass, which in turn (i) increases the diffusion time and (ii) reduces the number of molecules participating in the JG relaxation.68-72 Were faster motions to control nuclei formation in the glassy state, process ii would decrease the nucleation sites and stabilize a glass against random nucleation. Crystal-growth requires longrange diffusion and would likely be determined by the structural relaxation rate,62-65 which decreases on densification as the equilibrium state is approached,68-72 and therefore structural relaxation would slow the crystal-growth. Thus nucleation and crystallization in a glass is expected to become slower or less probable with time. When structural relaxation is faster than the crystal-growth, a glass would relax to a lower energy structure sooner than it would crystallize and, as molecular diffusion consequently becomes slower with time, crystallization
J. Phys. Chem. B, Vol. 112, No. 35, 2008 10813 would become controlled by this diffusion time. Judging from the pharmaceutical alloys’ observed stability against crystallization,22 and of acetaminophen-aspirin alloy here, their structural relaxation seems to be faster than crystal growth. The requirement that their crystal-nuclei should contain a different population of hydrogen bonds and isomeric states would become a further constrain on crystallization of pharmaceuticals. 5. Conclusions The nonexponentiality of the structural relaxation of pharmaceuticals is much less than that observed for polymers and inorganic glasses, and the nonlinearity parameter is greater. When compared with the earlier data, their values appear to depend upon the rate of cooling of the ultraviscous liquid and then the rate of heating of the glass. This dependence is attributed to additional thermal effects from the temperature and time-dependent changes in the chemical equilibria of hydrogen bonds, isomeric states, and ion-association, which do not directly determine the molecular mobility. Consequently, data on relaxation time alone may be insufficient for determining the thermodynamic changes needed to estimate the nucleation and crystal-growth rates in an amorphous pharmaceutical during storage. Glassy states obtained by slow cooling of griseofulvin, nifedipine and equimolar acetaminophen-aspirin alloy are more stable against crystallization on heating than that of pure acetaminophen. In the current discussion of the potential energy landscape paradigm,73-75 the state of a glass is described by a deep minimum in configurational space. When a glass is heated, structural relaxation brings the state to a deeper minimum and both the potential and the kinetic energies change. When a liquid is heated, its structure explores an increasing number of higher potential energy minima with differing force constants. The energy change due to the variation in hydrogen-bond and ionpair populations and isomeric states with time and temperature would add to this description. Understanding and predicting the stability of small molecular weight, organic glasses of pharmaceutical interest necessitate not only the use of established and emerging physical chemistry of glassy materials but also inclusion of an understanding of intermolecular interactions mediated through hydrogen bond, isomeric states, ionic impurities and the influence of additives incorporated into multicomponent glasses. Acknowledgment. This research was supported in part by Pfizer Inc. References and Notes (1) Moynihan, C. T.; Macedo, P. B.; Montrose, C. J.; Gupta, P. K.; Debolt, M. A.; Dill, J. F.; Dom, B. E.; Drake, P. W.; Easteal, A. J.; Eltermann, P. B.; Moeller, R. A.; Sasabe, H.; Wilder, J. A. Ann. N.Y. Acad. Sci. 1976, 279, 15. (2) O’Reilly, J. M. CRC Crit. ReV. Solid State Mater. Sci. 1987, 13, 227. (3) Hodge, I. M. J. Non-Cryst. Solids 1994, 169, 211. (4) Moynihan, C. T.; Easteal, A. J.; BeBolt, M. A.; Tucker, J. J. Am. Ceram. Soc. 1976, 59, 12. (5) McKenna, G. B. Glass formation and glassy behaviour. In ComprehensiVe Polymer Science; Booth, C.; Price, C., Eds.; Pergamon: Oxford, U.K., 1989; Vol. 2, Chapter 10, p 311. (6) Scherer, G. W. Relaxation in Glass and Composites; Wiley: New York, 1986. (7) Simon, S. L. Physical Aging. In Encyclopedia of Polymer Science and Technology; Kroschwitz, J., Ed.; John Wiley & Sons: New York, 2002. (8) Johari, G. P. J. Non-Cryst. Solids 2002, 387, 307–310. (9) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1970, 53, 2372. (10) Johari, G. P. J. Chem. Phys. 1973, 58, 1766. (11) Ngai, K. L.; Paluch, M. J. Chem. Phys. 2004, 120, 857.
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