Article pubs.acs.org/jced
Amoxicillin Solubility and Supercritical Carbon Dioxide Mehdi Ahmadi Sabegh,† Hamid Rajaei,‡ Ali Zeinolabedini Hezave,‡ and Feridun Esmaeilzadeh*,‡ †
Department of Chemistry, Ahar Branch, Islamic Azad University-Ahar, Iran Chemical and Petroleum Engineering Department, School of Engineering, Shiraz University, Iran
‡
ABSTRACT: During the past 20 years, an increase through measuring, correlating, and calculating solid solubilities especially pharmaceuticals in supercritical fluids for processes such as purification, extraction, and size reduction processes have been observed. In this direction, the solubility of amoxicillin with the International Union of Pure and Applied Chemistry (IUPAC) name of (2S,5R,6R)-6-{[(2R)-2-amino-2-(4hydroxyphenyl)-acetyl]amino}-3,3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0] heptane2-carboxylic acid in the pressure and temperature ranges of 16 MPa to 40 MPa and 308.15 K to 338.15 K, respectively, has been measured. For this purpose, a simple gravimetric-based method was utilized to obtain the amoxicillin solubility in supercritical carbon dioxide. During the measurements it was found that the amoxicillin solubility was in the range of 1.08·10−5 and 7.23·10−3 based on the mole fraction. Besides, due to a vast number of efforts have been performed on the solubility correlation by several researchers, four semiempirical density-based correlations including Mendez-Santiago and Teja (MST), Bartle et al., Chrastil, and Kumar and Johnston (K-J) models were used to correlate the measured solubility data. The obtained results revealed the capability of the used correlation through the solubility correlation with an acceptable level of accuracy.
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INTRODUCTION Supercritical-based technologies have widely used in the past 20 years in particular for particle engineering, treatment, and purification of pharmaceuticals.1−5 The greatest benefits of using supercritical fluids instead of traditional processes are a few environmental related problems and a low level of product contamination and that easy recovery of the solvent leads to a small amount of solvent losses. Among the different candidates for supercritical solvents, carbon dioxide is the most favorable one due its mild critical conditions and other beneficial features especially being environmentally friendly.1,2,6 Among the many possible applications of the supercritical fluid-based technologies, the particle size reduction of active pharmaceutical ingredients (APIs) is the most interesting one.7−9 The supercritical fluid method involving the recrystallization process was adopted by pharmaceutical industry since the mid-1980s.10 The point is crucial to develop the suitable processes for the pharmaceuticals, especially APIs, is their solubilities in supercritical fluids, in particular in supercritical carbon dioxide. In this direction, numbers of researchers and scientific groups around the world have examined the solubility of several pharmaceuticals in supercritical fluids especially in carbon dioxide.11−13 But, unfortunately, it is crucially necessary to measure more experimental data for APIs for the proper selection of the suitable supercritical-based processes.14 It should be mentioned that, due to the large number of pharmaceutics, it is not always possible to measure the solubility experimentally. In this direction, besides the experimentally measuring the solid solubility in supercritical carbon dioxide, correlating, predicting, and estimating using © XXXX American Chemical Society
different approaches such as equation of state (EoS), semiempirical correlation, and solution models have been examined during the past few decades.15−19 Generally, EoS's are the first option to predict the solubility of compounds in supercritical fluids. Unfortunately, the application of the EoS's is not commonly proposed since the availability of necessary parameters through them is limited especially for pharmaceuticals. In other words, if the EoS approach is applied, the sublimation pressure and the critical properties of the solute, which are not experimentally available in many cases especially for a complex solid which must be estimated through different prediction tools such as group contribution methods, are required.20 So, for most of the pharmaceutical compounds, EoS-based modeling is usually limited due to these uncertain data. With respect to this, more recently density-based semiempirical correlations such as Mendez-Santiago and Teja (MST),16 Bartle et al.,17 Chrastil,18 and Kumar and Johnston (K-J)19 models have been considered as candidates for a replacement of EoS-based solubility modeling. The obtained results through the different published works have been reported rather successful for these correlations to well-correlate the solubilities. What makes these correlations interesting is that the supercritical density and the system temperature and pressure are the only necessary parameters to find a fitting parameter of those correlations. In other words, they do not require physical properties such as critical properties, acentric factors, and so forth. Received: June 6, 2012 Accepted: August 30, 2012
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Based on the aforementioned facts, the solubility of amoxicillin in supercritical carbon dioxide under the temperature and pressure ranges of 308.15 K to 338.15 K and 16 MPa to 40 MPa, respectively, was experimentally measured, which can be considered the novelty of the present study. Amoxicillin is a member of a group of antibiotic drugs called penicillins. Amoxicillin is used to cure a wide range of bacterial infections. Its mechanism of action stops the growth of bacteria. In other words, amoxicillin does not kill bacteria, but it surrounds the bacteria by producing a wall and preventing their multiplication. To the best of our knowledge, there are no reported experimentally measured solubility data for this compound in supercritical carbon dioxide through previously published literature. Finally, the measured solubilities were used to find the fitting parameters of the four density-based correlations.17−19 These obtained fitting parameters which were reported in this study correlate the solubility of amoxicillin in the temperature and pressure ranges of 308.15 K to 338.15 K and 16 MPa to 40 MPa, respectively. The successful performed self-consistency tests for the amoxicillin solubilities revealed that the model parameters can be used to even extrapolate the solubilities.
The point must be mentioned is that the temperature of cell was controlled by a feedback controller connected to the PT100 controller with precision of ± 1 K. Also, the pressure of equilibrium cell was monitored by a digital pressure gauge (WIKA) ranged up to 45 MPa with the division of 0.01 MPa. The system pressure of each experiment was maintained to within ± 0.5 % of the desired pressure. Finally, it must be considered that the weight of the used carbon dioxide in each experiment was obtained using the density of carbon dioxide at the specific temperature and pressure which were reported by Yamini et al.,6 while the used volume of carbon dioxide for all of the experiments was kept constant.
EXPERIMENTAL SECTION Materials. The amoxicillin was supplied from Hejrat Company (Iran) and was further purified by passing supercritical carbon dioxide at 308.15 K and 40 MPa for two hours. In addition, carbon dioxide was supplied from Abughadareh Industrial Gas Company (Iran; see Table 1).
Table 2. Solubility Data of the Amoxicillin at Different Pressures and Temperatures Based on Mole Fractiona
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RESULTS AND DISCUSSION In this study, the amoxicillin solubility at temperatures of 308.15 K, 318.15 K, 328.15 K, 338.15 K, and 348.15 K over a pressure range from 16 MPa to 40 MPa was measured and reported in Table 2. The solubility of the amoxicillin was measured based on the mole fraction, y, of the solute in supercritical CO2. To measure the reliable solubility of amoxicillin, each measurement at each specific pressure and temperature was performed at least three times, and the average
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P/MPa
solubility of amoxicillin
16 20 24 28 32 36 40
1.10·10−5 2.46·10−5 4.25·10−5 6.96·10−5 1.04·10−4 1.51·10−4 2.04·10−4
16 20 24 28 32 36 40
1.52·10−5 4.95·10−5 1.12·10−4 2.04·10−4 3.51·10−4 5.21·10−4 8.27·10−4
16 20 24 28 32 36 40
1.47·10−5 8.24·10−5 2.51·10−4 5.24·10−4 1.00·10−3 1.62·10−3 2.50·10−3
16 20 24 28 32 36 40
1.08·10−5 1.09·10−4 4.47·10−4 1.19·10−3 2.47·10−3 4.43·10−3 7.23·10−3
Table 1. Physiochemical Properties of the Amoxicillin name
source
mass fraction purity
melting point/K 467.15
amoxicillin
Hejrat Company
0.968
carbon dioxide
Abughadareh Industrial Gas Company
0.998a
a
analysis method gas−liquid chromatography
Mole fraction.
Laboratory Apparatus. A complete description of the used solubility measurement apparatus has been reported in previously published research.21−23 Briefly, 1 g of the compacted drug was loaded in the equilibrium cell, and then, the pressurized carbon via a reciprocating water-drive oil-free pump and displacer was entered into the equilibrium cell to be contacted to the loaded drug. The equilibrium cell was rated for pressures of 600 bar at 673.15 K. It was made of stainless steel 316 with an internal volume of 50 cm3 equipped with a sapphire window. All of the process tubing used in this apparatus was 1/8-in. O.D. tubing made of stainless steel 316. After that, using a circulating hot water system, the temperature of the system was varied in the range of 308.15 K to 338.15 K. The drug and supercritical carbon dioxide was left for two hours to ensure equilibrium has been reached. Finally, the equilibrium cell was suddenly depressurized to the ambient conditions, and the remained drug was weighted to 0.1 mg using a Sartorius BA110S Basic series balance. The typical mass of solute for each experiment was greater than 5 mg, giving a potential error due to weighing of 2 wt %.
standard deviation T = 308.15 K 9.35·10−7 2.02·10−6 3.45·10−6 4.21·10−6 5.62·10−6 7.12·10−6 9.30·10−6 T = 318.15 K 1.22·10−6 2.98·10−6 4.65·10−6 8.23·10−6 2.21·10−5 3.35·10−5 4.01·10−5 T = 328.15 K 1.25·10−6 3.62·10−6 9.87·10−6 2.98·10−5 3.67·10−5 7.63·10−5 9.46·10−5 T = 338.15 K 9.18·10−7 6.20·10−6 1.12·10−5 5.24·10−5 8.67·10−5 2.01·10−4 3.01·10−4
relative standard deviation (%) ±8.50 ±8.21 ±8.12 ±6.05 ±5.40 ±4.72 ±4.56 ±8.03 ±6.02 ±4.15 ±4.03 ±6.30 ±6.43 ±4.85 ±8.50 ±4.39 ±3.93 ±5.69 ±3.67 ±4.71 ±3.78 ±8.50 ±5.69 ±2.51 ±4.40 ±3.51 ±4.54 ±4.16
a
Maximum relative standard deviation % = 8.5 %, maximum pressure uncertainty = 2 bar, and temperature uncertainty = 1 K.
B
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been reported by Foster et al.33 that the consistency and reliability of experimental solubility data can be examined considering the existence of a crossover pressure in solidsupercritical systems. Correlation of Experimental Solubility Data. Finally, the measured solubilities were used to find the fitting parameters of the four widely used density based correlations, namely, Mendez-Santiago and Teja (MST),16 Bartle et al.,17 Chrastil,18 and Kumar and Johnston (K-J)19 models since using those fitting parameters one can not only correlate the amoxicillin solubility in a wide range of temperatures and pressures but also even extrapolate the solubility of amoxicillin. In this regards, the simple data fitting and mean square error approaches were applied to find the fitting parameters for the used semiempirical correlations (Table 3). As aforementioned, due to the several existing limitations on thermophysical properties availability especially critical properties and acentric factors of the complex compounds, for example, pharmaceuticals, the application of semiempirical correlations such as density-based equations has been widely proposed. In other words, since there is no need to estimate and use thermophysical properties for the majority of the empirical correlations, they are considered the most widely applicable simple predictive tools. Among the correlations, Chrastil’s model18 (see Table 3) which correlates the solubility of a solute in a supercritical solvent to the density and temperature is one of the most widely used correlations. The basis of this method is the association of the solute molecules with c molecules of a supercritical solvent to form a solvate complex, which is in equilibrium with the system. In the Chrastil correlation, S is the solubility of the compound in SC−CO2, and ρ is the density of the pure CO2 at the experimental absolute temperature T and pressure p. The constant c expresses an average equilibrium association number, which is a characteristic constant for a given gas−solute system. The point makes the Chrastil model interesting is the ability of the Chrastil model to predict the enthalpies of vaporization and solvation using the parameter a defines as ΔHSub/R, where R is the universal ideal gas constant. In this study, the fitting parameters were obtained using simple data fitting lead to find the values of a (−19347), b (70.52), and c (19.43). The correlated solubilities using these obtained fitting parameters leads to AARD % of 7.53 % (see Figure 2). The point must be mentioned is that the AARD % was calculated using the following formula:
of those measurements was reported as the solubility. The error analysis of the mole fraction of the solutes which was the average of the three dependent measurements revealed that the obtained data points were reproducible within the maximum ± 8.5 %. From the data given in Table 2, it is completely obvious that an increase in the pressure leads to an increase in the solubility of amoxicillin at each isotherm. This can be related to the effect of the temperature and pressure on the supercritical carbon dioxide density. In other words, the density of CO2 increases as an increase in the pressure introduces if the temperature kept constant. This density enhancement leads to a lower intermolecular distance which leads to a higher solubility strength. So, the solubility of amoxicillin increases as the pressure increases. In addition, the effect of pressure on the solubilities was more significant at higher temperatures. For example, the results revealed that it is possible to enhance the amoxicillin solubility in the supercritical carbon dioxide better just 19 times if increasing the pressure from 16 MPa to 40 MPa at a constant temperature of 308.15 K, while the solubility enhances more than a factor of 74.3 at 338.15 K. Obviously, this is in contrast to conventional evidence stating that the supercritical fluid’s density must increase to increase the solubility and extraction efficiency.24,25 A similar trend was reported by Asghari-Khiavi and Yamini26 when measuring the bisacodyl solubility in supercritical carbon dioxide at the different pressures and temperatures. Besides, by investigating the effect of the temperature on the solubility data (Table 2 and Figure 1), it can be observed that a crossover region exista at about 16 MPa to 18 MPa for amoxicillin.
Figure 1. Solubility of amoxicillin in a wide range of pressure and temperature (y is the amoxicillin solubility in supercritical carbon dioxide). Isotherms at: ○, 308.15 K; □, 318.15 K; ×, 328.15 K; and ●, 338.15 K.
AARD(%) =
1 N
N
⎛ solubility exp − solubility cal solubility exp ⎝
∑ ⎜⎜ i=1
⎞ ⎟⎟ ⎠
(1)
cal
where solubility is the calculated solubility at specific pressure and temperature and solubilityexp is the experimental one at the same pressure and temperature. In the second stage, the Bartle et al.17 model was used as a potential correlation to model the amoxicillin solubility. In this correlation (see Table 3), y is the mole fraction solubility, p is the pressure, Pref is a reference pressure of 0.1 MPa, ρ is the density of pure CO2, and ρref is a reference density for which a value of 700 kg·m−3 was used.24 In brief, the following procedure has been utilized to find the adjustable parameters of the Bartle et al.17 model. At first, ln(y·p/Pref) values were plotted versus density, and the values were fit with a straight line by least-squares regression to obtain
Such a retrograde (crossover versus pressure effect) behavior has already been reported for different organic compounds.27−32 Briefly, the observed trend can be described in this way that, if the pressures are less than the crossover region, solvent densities decrease by small increases in temperature, because the density significantly influenced in this region leads to the solubility reduction with temperature elevation. At higher pressures, the solvent density is less dependent on temperature, so that the increase in solubility is primarily due to the higher vapor pressure of the solid leads to higher solubility of the amoxicillin in the supercritical carbon dioxide. Generally, it has C
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Table 3. Obtained Fitting Constants for Four Density-Based Correlations constants model
a
semiempirical correlation
Bartle (5.26 %)
⎛ y·p ⎞ ln⎜ ⎟ = a + b/(T /K) + c(ρ − ρref ) ⎝ Pref ⎠
Mendez-Santiago−Teja (6.26 %)
⎛ y·p ⎞ T ln⎜ ⎟ = a + b·(T /K) + c·ρ /kg·m−3 ⎝ Pref ⎠
Kumar and Johnston (7.05 %)
ln y = a + b/(T /K) + c·ρ /kmol ·m−3
Chrastil (7.53 %)
ln S /kg·m
−3
= a + b/(T /K) + c ln ρ /kg·m
59.83 −29112
32.27 −3
−19347
b −21501
64.19 −19288 70.52
c 0.027
8.820
0.991 19.430
correlative capability of this model for the amoxicillin solubility correlation. The general form of the MST model needs sublimation pressure at a specific temperature. But, since measuring the experimental value of sublimation pressures are not often possible, the general form of the MST model was changed to a correlation with three fitting parameters with the assist of a Clausius−Clapeyron expression for the sublimation pressure (see Table 3) where Pref is a standard pressure of 0.1 MPa, y is the equilibrium solubility, and a, b, and c are fitting parameters. Finally, the Kumar and Johnston model19 was used to correlate the solubility of the amoxicillin. Similar to the previous sections a simple data fitting was applied to find the three fitting parameters. The obtained fitting parameters for MST and K-J models are given in Table 3. In addition, the obtained fitting parameters were used to calculate the solubility of amoxicillin which leads us to obtain the AARD % for K-J and MST models of 7.05 % and 6.26 %, respectively. Furthermore, it should be mentioned that the selfconsistency tests (see Figure 4) were performed for the experimental data using the MST, K-J, Bartle et al., and Chrastil models. In this direction, the experimental results were plotted in a way that a linear trend appears for the solubility data using each empirical correlation. Then, the solubility data were fitted using a line passes through all of the experimental data. The correlation coefficients (R2) obtained for all of the used four semiempirical methods including MST (0.999), Bartle et al., KJ (0.9983,) and Chrastil (0.9889) were considered as an indication of which method has the highest capability for the extrapolation. As it is completely clear, the Bartle et al. method interestingly revealed the best extrapolation capability considering the highest correlation coefficient (R2) value of 1. In other words, the linear behavior of Bartle et al. model shown in Figure 4 confirms that the measured solid solubility data are consistent at all experimental conditions. So, the correlated parameters of the Bartle et al. model are applicable to extrapolate the experimental solubility of amoxicillin. In addition, considering the error analysis and plotted data in Figure 4 with respect to the obtained correlation coefficient (R2) values, it seems that the lower AARD % leads to the closer R2 value to 1. As can be seen, the Bartle et al. model which introduced an AARD % of 5.6 % leads to the R2 value of 1, while the Chrastil model leads to an AARD % of 7.53 % demonstrated the lowest R2 value among the other models. Based on these findings, one can conclude that a direct relation exists between the higher self-consistency capability of model and its lower AARD %.
Figure 2. Correlated solubility of amoxicillin using the Chrastil model versus the experimental ones. Isotherms at: ○, 308.15 K; □, 318.15 K; ×, 328.15 K; ●, 338.15 K. The dashed line is the correlated solubility by the Chrastil method.
the c parameter. After that, values of a and b parameters were obtained by a simple data fitting, while the average value of the found c in the previous stage was used. Finally, by holding c at its average value (0.027) and a and b at the found values of 59.83 and −21501, respectively, the experimental solubility data were calculated, and the AARD % (5.26 %) was obtained (see Figure 3). Besides the two previous correlations, the Mendez-Santiago and Teja (MST) model16 have been utilized to check the
Figure 3. Correlated solubility of amoxicillin versus experimental ones using the Bartle et al. model. Isotherms at: ○, 308.15 K; □, 318.15 K; ×, 328.15 K; ●, 338.15 K. The dashed line is the correlated solubility by the Bartle et al. method. D
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Figure 4. Self-consistency tests using four different models: (a) MST model self-consistency test, (b) Bartle et al. self-consistency test, (c) K-J model self-consistency test, and (d) Chrastil model self-consistency test. Isotherms at: ○, 308.15 K; □, 318.15 K; ×, 328.15 K; ●, 338.15 K. The dashed lines reveal the linearity of the used models.
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CONCLUSION In this investigation, the equilibrium solubility of the amoxicillin in the supercritical carbon dioxide in the temperature and pressure range of 308.15 K to 338.15 K and 16 MPa to 40 MPa, respectively, was experimentally obtained using a gravimetricbased method. Totally, the experiments revealed that the amoxicillin can be solubilized in supercritical carbon dioxide in the range of 1.08·10−5 and 7.23·10−3 based on the mole fraction under different temperatures and pressures. The measured solubilities completely revealed that an increase in the pressure leads to an increase in the solubilities with a higher impact of pressure on the solubility enhancement at the higher temperatures. Besides, the obtained results demonstrated a crossover pressure of 16 MPa to 18 MPa for this system. In addition, possible mechanisms of action were discussed in detail for a more reliable conclusion. Finally, the fitting parameters of the four density-based correlations, namely, MST, Bartle et al., Chrastil, and K-J models, were obtained using those experimentally measured solubility data. Using the fitting parameters of those correlations which were obtained using a simple data fitting revealed that the correlations are able to calculate the solubilities with AARD % of 5.26 %, 6.26 %, 7.05 %, and 7.53 % for Bartle et al., MST, K-J, and Chrastil models, respectively. Also, the self-consistency test which was performed using four different semiempirical models revealed the capability of Bartle et al. model to well-extrapolate the solubility of the amoxicillin.
AUTHOR INFORMATION
Corresponding Author
*Address: Shiraz University, School of Chemical and Petroleum Engineering, P.O. Box 7134851154, Namazi Square, Shiraz, Iran. Tel.: +98 711 2303071; fax: +98 711 6287294. E-mail:
[email protected] (F. Esmaeilzadeh). Notes
The authors declare no competing financial interest.
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