Article pubs.acs.org/IECR
Influence of Polymorphs on the Transformation Water Activity of Theophylline Chongjun Liu, Leping Dang,* Yao Tong, and Hongyuan Wei School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P. R. China ABSTRACT: In this paper, the influence of polymorphs on the transformation water activity that corresponds to the transformation between hydrate and anhydrate of theophylline was investigated. Theophylline is known to exist either as anhydrates or a monohydrate. The transformation water activities of theophylline form II and IV were determined respectively, and the solubility data of these two forms in methanol, ethanol, acetonitrile, and acetone was also determined. The following thermodynamic derivation indicates that the transformation water activity ratio of theophylline forms II to IV can be correlated with the solubility ratio. According to the above study, the stability and intercoversion of theophylline polymorphs is discussed. This work will be useful in understanding the transformation process and benificial for industrial process control.
1. INTRODUCTION Anhydrates and hydrates may exhibit different properties such as density, solubility, and physical/chemical stability;1 therefore, it is vital to understand and control the solid phase that crystallizes during the pharmaceutical development and manufacturing processes. Previous studies on hydrates and anhydrates of organic molecules have demonstrated the importance of the water activity in controlling whether hydrates or anhydrates are the stable phase.2,3 It has been proved that hydrate is the more stable form when the water activity is higher than the transformation water activity or vice versa.4−7 At transformation water activity, the two forms have identical solubility, and thus identical stability. However, little attention has been devoted to the difference of formation hydrate between polymorphs. Considering that different polymorphs exhibit significantly different thermodynamic properties, it is necessary to study the influence of polymorphs on the transformation water activity. Theophylline was isolated from tea leaves in 1888,8 and is widely used to prevent and treat wheezing, shortness of breath, chest tightness caused by asthma, chronic bronchitis, emphysema, and other lung diseases. Theophylline has four polymorphs which exit as anhydrates and a monohydrate. The anhydrate form II is used as an active pharmaceutical ingredient and the anhydrate form IV is the stable phase at room temperature.9 This is the reason why theophylline is a good example to discuss the influence of polymorphs on the transformation water activity. In the present work, the difference of transformation water activity between theophylline forms II and IV and the solubility data of these two forms were investigated. The relationship between the transformation water activities and solubility ratios was then discussed, which indicates that the transformation water activity ratio of theophylline forms II to IV is equal to the solubility ratio of forms IV to II. Finally, stability and intercoversion of different forms of theophylline were analyzed in order to offer the whole information of the transformation process. © 2013 American Chemical Society
2. EXPERIMENT 2.1. Material. Theophylline (Form II, 99% in mass fraction) was purchased from Shanghai Aladdin-reagent Technology Co. Ltd. (China). Form IV was prepared using a slurry experiment at 298.15 K in organic solvent lasting 1 month. The methanol, ethanol, acetonitrile, and acetone (purchased from the Tianjin Kewei Chemical Reagent Co.,China) used for experiments were of analytical grade (99+% purity). The distilled deionized water was used in all experiments. 2.2. Apparatus. 2.2.1. Determination of the Transformation Water Activity. The solution mediated transformation ofathe anhydrate form to the hydrate was investigated to determine the value of water activity, aw, at which anhydrate converts to the hydrate. A range of mole fractions of water/methanol were prepared (e.g., aw = 0.1, 0.2, 0.3, ..., 0.9), and aw was assigned for each composition using the Wilson equation and the related parameters which can be obtained from vapor−liquid equilibrium data collection.10 Excessive anhydrate was equilibrated using methanol and water mixtures (10 mL) at varying temperatures from 293.15 to 313.15 K. Samples were seeded with hydrate after 16 h slurring to ensure an excessive solid of both the anhydrous and monohydrate forms. The mixtures were constantly stirred for up to 3 days, using a magnetic stirrer, in order to attain equilibrium. The excessive solid phases were analyzed by PXRD.11 2.2.2. Determination of Solubility. The solubility was measured by a gravimetric method.12,13 Solubility data was determined by equilibrating the solute with solvent in a waterjacketed vessel with electromagnetic stirring in a constant temperature water bath (±0.05 K) for 72 h. The water temperature was controlled by a PT100 sensor with ±0.05 K accuracy. The upper solution was extracted by injector (membrane filtration, and 0.45 μm), and the sample was Received: Revised: Accepted: Published: 14979
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diffraction analyses (PXRD) were performed using a Rigaku D/max-2500 X-ray powder diffractometer using Cu KR radiation (λ = 1.54 Å) and a tube voltage of 40 kV, and a tube current of 100 mA was used to collect XRPD patterns of solid phases. Data was collected from 5 to 50 at a continuous scan rate of 1.2 deg min−1.
weighed after drying using an analytical balance (type FA2004, China) with an accuracy of ±0.1 mg. When the mass was unchanged, the data can be used to calculate the solubility. Excessive solids equilibrated with saturated solutions were collected by filtration and then characterized by PXRD. 2.2.3. PXRD. These three forms can be identified by using Xray powder diffraction pattern (Figure 1). X-ray powder
3. RESULTS AND DISCUSSION 3.1. Solubilities of Theophylline Forms II and IV. The solubilities of polymorphs are important thermodynamic data. From solubility data, the relative stability and the relationship between different polymorphs can also be determined. In the present study, the solubility of theophylline was determined from 293.15 to 313.15 K in methanol, ethanol, acetone, and acetonitrile. The results are shown in Figure 2. The van’t Hoff equation was used to correlate the experimental solubility data in these four solvents. ln x =
−ΔHsol ΔSsol + RT R
(1)
where x is the solubility in mole fraction, ΔHsol and ΔSsol are the dissolution enthalpy and entropy of theophylline present in the temperature range, R is the ideal gas constant, and T is the saturation temperature corresponding to x and the form of interest. The dissolution enthalpy and entropy are given in the Table 1. The determined solubility data of the two polymorphs shows that form IV is thermodynamically stable at the experimental temperature. Table 2 summarizes the solubility ratios and error
Figure 1. XRD patterns of the anhydrates and monohydrate of theophylline crystals.
Figure 2. Experimentally measured solubility data of theophylline forms II (black) and IV (red) are shown for (a) methanol, (b) ethanol, (c) acetone, and (d) acetonitrile. 14980
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Table 1. Dissolution Enthalpy and Entropy of Theophylline in Four Solvents ΔHsol (kJ/mol)
ΔSsol (J/mol)
theophylline form II methanol ethanol acetone acetonitrile
2.82 2.15 1.69 2.05
methanol ethanol acetone acetonitrile
3.34 2.77 2.42 2.84
2.91 0.46 −1.13 −0.79 theophylline form IV 4.66 1.77 1.05 1.59
Table 2. Solubility Ratio and Standard Deviation of Theophylline Forms II to IV in Different Solvents T/K
methanol
ethanol
acetone
acetonitrile
SD
293.15 298.15 303.15 308.15 313.15
1.228 1.187 1.149 1.115 1.083
1.318 1.158 1.128 1.100 1.073
1.307 1.268 1.210 1.164 1.122
1.419 1.336 1.302 1.247 1.184
0.0784 0.0806 0.0780 0.0662 0.0503
Figure 3. Phase diagram after 3 days for theophylline form IV in water and methanol at 298.15K.
The transformation water activity of theophylline form IV increases from 0.71 to 0.79, when the temperature is increased from 293.15 to 313.15 K. The result implies that the transformation water activity is clearly dependent on temperature, as increasing the temperature results in an obvious increase of the transformation activity to be exhibited. The transformation water activity of form II was determined by the same way. It is shown in Table 3 that the transformation
analysis of the two polymorphs under various temperatures. The standard deviation (SD) was used to test the correlation accuracy, which is defined as N
SD =
∑ (xi − x ̅ )2 /(N − 1) i=1
Table 3. Transformation Water Activity of Theophylline Forms II and IV at Different Temperatures
(2)
where N is the number of data point and xi and x̅ are the experimental and mean solubility ratio in four solvents. For these solvents, the solubility ratios are quite similar. It can also be seen that the solubility ratio of forms II to IV reduces with increasing temperature, and the solubility of form II is almost 1.3 times that of form IV at 293.15 K. However, the solubility of form IV is nearly equal to the solubility of form II at higher temperature such as 313.15 K. 3.2. Transformation Water Activities of Theophylline Polymorphs. According to previous reports, the transformation water activity was commonly screened by phase transformation experiments.14 Use of this method is limited by the long time period required to complete the phase transformation, especially near the transformation point.11 It may take as long as several weeks to reach phase equilibrium. Since seeding the stable form can reduce the time of nucleation,15 the monohydrate was seeded into the solution to accelerate the transformation process. Here we use the phase transformation experiments in a mixture of water and methanol to measure the water activity at which the anhydrate−hydrate transition occurs. Figure 3 shows example results of phase equilibrium experiments at 298.15 K. For theophylline form IV, if the water activity of solution is lower than 0.72, no monohydrate forms in the solid after 3 days. On the contrary, theophylline monohydrate is the only form in the solid when the water activity is higher than 0.73. Consequently, the transformation water activity is defined as 0.73. It is obvious that the precision of the water activity value is due to the water activities tested. The more experiments which are carried out, the more accurate the value of transformation water activity can be obtained.15
T/K
transformation water activity of form II
transformation water activity of form IV
aT[H2O]IV/aT[H2O]II
293.15 298.15 303.15 308.15 313.15
0.56 0.59 0.62 0.66 0.71
0.71 0.73 0.74 0.76 0.79
1.27 1.24 1.19 1.15 1.11
water activity of theophylline form II is lower than that of theophylline form IV. The difference reduces from 0.15 at 293.15 K to 0.08 at 313.15 K. Compared with the solubility ratios, it exhibits an opposite trend with increase of temperature. 3.3. Thermodynamic Derivation Based on Equilibrium Constants. In previous reports,16 the transformation from theophylline form II to theophylline monohydrate at transformation water activity can be represented by the following equilibrium: K1
K2
THE II(solid) + H 2O ⇔ [THE] + H 2O ⇔ THE ·H 2O(solid)
(3)
The thermodynamics equilibrium constants for the two sequential reactions are
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K1 =
a[THE]II a[THE(solid)]II
(4)
K2 =
a[THE· H 2O(solid)] a[THE]II a T[H 2O]II
(5)
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where a[THE·mH2O(solid)] and a[THE(solid)]II are the activity of theophylline monohydrate, theophylline form II. The aT[H2O]II is the transformation water activity of theophylline form II, and the a[THE]II is the activity of theophylline in the solution, which is saturated with theophylline form II. If the reference states of the solids are assumed to be their pure phases and therefore exhibit an activity of 1, eq 5 simplifies to a T[H 2O]II =
1 a[THE]II K 2
of any anhydrous form was observed when stored in a desiccator. When water activity is higher than the transformation water activity, the monohydrate is the stable form. The chart shown in Figure 4 summarizes the conversions between forms observed during the study. The theophylline
(6)
For theophylline form IV, the transformation water activity can also be calculated by the same way. a T[H 2O]IV =
1 a[THE]IV K 2
Figure 4. Intercoversion of theophylline solid forms at 298.15 K. (7)
Combing these two equations: a[THE]IV γ[THE]IV x[THE]IV a T[H 2O]II = = a T[H 2O]IV a[THE]II γ[THE]II x[THE]II x[THE]IV = x[THE]II
form II can transform into form IV, if allowed enough time in organic solvent. The theophylline form II can be formed by heating monohydrate.14 The hydrate profile of theophylline form II and form IV have been determined. The transformation water activity of theophylline form II is 0.59 at 298.15 K, in agreement with the study by Ticehurst et al,11 and the transformation water activity of theophylline form II is 0.73 at this temperature. Without seeding form IV, there is no transformation from theophylline monohydrate to from IV, when the water activity is lower than 0.73.
(8)
Here we assume that thnpe solute obeys Henry’s law for dilute solutes and thus γ[THE]II = γ[THE]IV. Therefore, the transformation water activity ratio of theophylline forms II to IV is equal to the solubility ratio of forms IV to II. The above derivation describes the situation at which three forms of the solute are in equilibrium: as a constituent of the liquid solution, as the anhydrate, and as the hydrate. The transformation point is the point at which the solubility of theophylline form II(or form IV) and that of theophylline monohydrate is identical. Both transformation points are located on the solubility curve of the theophylline monohydrate. Therefore, the thermodynamics equilibrium constants K2 can be applied both to theophylline form II (eq 6) and theophylline form IV (eq 7). Equation 6 shows that the transformation water activity is depended on the activity of theophylline and thermodynamics equilibrium constants K2. Since both of them are only influenced by temperature, the transformation water activity is only dependent on temperature. In addition, since there is a difference of activity between the theophylline polymorphs, this equation indicates that there is not only one transformation water activity in a polymorph system. Further, eq 8 shows the relationship between the transformation water activity ratio and solubility ratio. The polymorph, which has a high solubility, has a low transformation water activity. However, since this derivation is based on the hypothesis of “a dilute solution” and activity coefficient of solute is assumed to be a constant, a deviation may not be able to be avoided when eq 8 is applied for some real solution systems. 3.4. Stability and Interconversion of Theophylline Forms. Based on the investigation above, we can summarize the stability state and interconversion of different forms of theophylline. From Figure 2, it is clear that the solubility order of anhydrous theophylline was observed to be form II > form IV, indicating that form IV is more stable than form II at experimental temperature. Both of them were found to be kinetically stable at room temperature. No solid state transition
4. CONCLUSION In this paper, the influence of polymorphs on transformation water activity of theophylline was investigated. The solubility data of theophylline forms II and IV was determined in methanol, ethanol, acetone, and acetonitrile from 293.15 to 313.15 K. The dissolution enthalpy and entropy of both forms were calculated by correlating the solubility and temperature using the van’t Hoff equation. The solubilities of both forms increase with increasing temperature. The solubility ratio of forms II to IV decreases with increasing temperature. The transformation water activities of theophylline forms II and IV were determined. The transformation water activities of both forms depended on temperature, and the water activities ratio of forms IV to I also decreases with increasing temperature. Furthermore, it was found that the polymorph which has a higher solubility has a lower transformation water activity. The relationship between transformation water activity and solubility ratio was then derived by thermodynamics equilibrium. The result indicates that the transformation water activity ratio of theophylline forms II to IV is inversely proportional to their solubility ratio at certain temperature. At last, the stability and intercoversion of different forms of theophylline was obtained. The transformation chart can be used under the guidance of the process design and control.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel: +86-22-27405754. Fax: +86-22-27400287. Notes
The authors declare no competing financial interest. 14982
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ACKNOWLEDGMENTS We acknowledge the Doctoral Fund of Ministry of Education of China (20110032110022) and Tianjin Municipal Natural Science Foundation (11JCYBJC 04600, 13JCQNJC05200).
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REFERENCES
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