Determining the Solubility of Nifedipine and Quinine in Supercritical

Article pubs.acs.org/jced

Determining the Solubility of Nifedipine and Quinine in Supercritical Fluid Carbon Dioxide Using Continuously Stirred Static Solubility Apparatus Interfaced with Online Supercritical Fluid Chromatography Ben Li, Wei Guo, and Edward D. Ramsey* Sustainable Technology Research Centre, University of Science and Technology Liaoning, Anshan 114051, China ABSTRACT: A high pressure vessel equipped with continuous magnetic stirring has been interfaced directly online with supercritical fluid chromatography (SFC). The interface consists of an oven housing a recirculation pump that maintains a constant flow of supercritical fluid solution from the vessel through a sample injection valve for online SFC analysis. The method involves increasing the vessel pressure in controlled steps to produce a series of progressively more saturated supercritical fluid carbon dioxide solutions for online SFC solubility measurements. The integrated static solubility system provides a convenient means to ensure equilibrium is established prior to performing online SFC solubility measurements and also facilitates a self-validation accuracy check procedure. For nifedipine, solubility data was obtained at 333.15 and 353.15 K through the pressure range from 12.5 to 27.5 MPa using 2.5 MPa steps. For quinine, solubility data was obtained at 323.15 and 343.15 K through the pressure range from 12.5 to 27.5 MPa using 3 MPa steps. All sets of experimental solubility data for each compound were correlated using the Mendéz-Santiago and Teja model. flow of SF-CO2 through a saturation cell filled with an excess of compound and rely on the assumption that a saturated SF-CO2 solution is quickly formed. Thereafter, the quantity of compound dissolved in a known volume of SF-CO2 is determined. This involves a trapping procedure at a point of decompression built into the dynamic system to collect a sample for off-line analysis. In contrast, static methods involve dissolving the compound in a fixed volume of SF-CO2 before usually withdrawing a small sample for off-line analysis. In order to eliminate errors associated with sample collection and sample preparation stages required for off-line analysis, several reports have described the use of static SF-CO2 solubility apparatus coupled online with spectroscopy or chromatography. To perform online spectroscopic measurements, the supercritical solubility vessel (SSV) is equipped with high pressure inspection windows that facilitate UV/vis, IR, or fluorescence analysis.16,17 Several reports have described the use of a SSV directly coupled online with HPLC to perform static solubility measurements.18−20 The development of these techniques involves using a mobile phase with high organic modifier content to prevent gas bubbles derived from decompressed injections of SF-CO2 samples interfering with the stability of the HPLC detector.21 We have previously

1. INTRODUCTION It is well established that carbon dioxide in its supercritical fluid state can be manipulated via density control to imitate a range of nonpolar organic solvents.1,2 Industrial processes for which environmentally benign supercritical fluid carbon dioxide (SFCO2) demonstrates potential to replace environmentally damaging organic solvents include extraction, purification, fractionation, impregnation, cleaning, dyeing, catalysis, reactions, advanced material manufacture, particle engineering, and tissue engineering.3−5 The design of such processes is greatly facilitated by the availability of SF-CO2 solubility data. Consequently, efforts have been directed toward compiling experimental SF-CO2 solubility data for a wide range of organic compounds.6,7 This includes the application of various models to help rationalize and predict the solubility of compounds in SF-CO2.8,9 Within the pharmaceutical industry, SF-CO2 solubility data for drug compounds is becoming increasingly relevant. This is largely due to the development of a diverse range of supercritical based particle engineering processes for micronization and control of the morphology of resultant drug nanoparticles.10−12 Such processes are showing potential to improve the bioavailability of drugs including those that exhibit low solubility in water.13 Equipment used to perform SF-CO2 solubility measurements falls into one of two categories that facilitate either dynamic or static methods.14,15 Dynamic methods involve the continuous © XXXX American Chemical Society

Received: January 4, 2017 Accepted: March 14, 2017

A

DOI: 10.1021/acs.jced.7b00012 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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reported the development of a two-valve interface to monitor the progress of an esterification reaction conducted in SF-CO2 using online HPLC.22 However, the development of online SSV−SFC seems more logical due to the direct compatibility of injected aliquots of SF-CO2 solution with the SFC mobile phase.23 Accordingly, the two-valve interface has also been used to perform online static SSV−SFC solubility measurements24,25 for two neutral compounds, caffeine and analogues of monensin sodium salts in pure SF-CO2 with the results being successfully correlated using the model proposed by MendézSantiago and Teja (MST).26 Despite the two-valve interface demonstrating considerable potential, its operation requires a relatively complex valve switching procedure. This report describes the further development of SSV−SFC instrumentation that now utilizes a more robust and simplified interface. The new interface design consists of a recirculation pump incorporated into a flow circuit that connects a magnetically stirred SSV with a single SFC sample injection valve. In this study, we report the use of the integrated SSV− SFC system to measure the solubility of the pharmaceutical compounds nifedipine and quinine in pure SF-CO2. These compounds were selected to further test the capability of the SSV−SFC method to establish whether it can be applied to examples of basic drugs. The sets of experimental results obtained for both compounds were used to further evaluate the applicability of the MST model to correlate solubility data obtained using the SSV−SFC method.

Figure 1. Molecular structures of (a) nifedipine and (b) quinine.

(Middleton, WI, USA) whose pump head was cooled to 253.15 K using an Anachem pump head refrigeration unit (Luton, Bedfordshire, U.K.) was used to supply liquid carbon dioxide to the SSV for all SF-CO2 solubility studies. A PTX 500 series pressure transmitter (Druck, Leicester, U.K.) was used to calibrate the pump pressure transducer. Estimated accuracy for the SSV pressure was ±0.1 MPa. A cylinder containing high purity liquid carbon dioxide equipped with a liquid draw-off tube was connected to the pump. After a complete series of nifedipine and quinine SSV−SFC solubility studies were completed, the SSV and interface were vented via a solvent wash exhaust system.22 2.3. SSV−SFC Interface. The interface used to connect the SSV directly online to SFC was constructed using a Rheodyne 7010 valve (Cotati, CA, USA) fitted with a 10 μL sample loop. This sample injection valve was mounted inside a Gilson 831 oven that had been modified to house a Micropump model GAH-X21 (Micropump Inc., WA, USA) recirculation pump. As shown in Figure 2, the recirculation pump provided a continuous flow of SF-CO2 solution drawn from the SSV through the SFC sample injection valve. For SSV−SFC, linked carbon dioxide pump programs provided an initial flow of liquid carbon dioxide to the SSV at 20 mL·min−1 until a prepressure of 11.0 MPa was obtained. Thereafter, following a thermal equilibration period of 30 min, the second linked pump program delivered liquid carbon dioxide at 8 mL·min−1 until the first SSV target pressure for solubility studies was attained. After this, the SSV was continuously stirred for a fixed period before the first set of online SSV−SFC injections were made. For both nifedipine and quinine, samples of the SF-CO2 solutions produced at each target pressure were analyzed at appropriate time intervals for each compound to ascertain that dissolution equilibrium had been established before solubility measurements were performed. Once sets of nifedipine or quinine solubility measurements were completed at the first target pressure, the pressure of the SSV was incremented in steps to produce a series of progressively more saturated compound solutions for further online SSV−SFC solubility measurements. Throughout the solubility studies, the performance of the recirculation pump was checked during system cleaning with ethanol and then n-heptane. This involved disconnecting the SSV from the interface, thereafter using a stopwatch and measuring cylinder to check pump performance. After the pump was primed with ethanol it was determined that at a speed of 2000 rpm the recirculation pump delivered a flow of approximately 20 mL·min−1 ethanol through the interface. In order to achieve this flow rate of ethanol, the SFC sample injection valve was set at the inject position to bypass the resistance to flow caused by the very fine bore 10.0 μL sample loop.

2. EXPERIMENTAL SECTION 2.1. Materials and Reagents. The purity of nifedipine and quinine and all reagents used in these studies is provided in Table 1. Table 1. Information Concerning Compounds and Reagents chemical name

CAS no.

source

nifedipine

21829-25-4

quinine methanol ethanol

130-95-0 67-56-1 64-17-5

acetonitrile carbon dioxide

75-05-8 124-38-9

Tokyo Chemical Industry J & K Chemical Sigma-Aldrich Beijing Chemical Works Sigma-Aldrich Airichem

a

mole fraction purity

analysis method

≥0.98

HPLCa

≥0.99 ≥0.999 ≥0.999

HPLCa GCb GCb

≥0.999 ≥0.999

GCb GCb

HPLC is high performance liquid chromatography. chromatography.

b

GC is gas

The molecular structures of nifedipine and quinine are shown in Figure 1. 2.2. Solubility Apparatus. A Jasco EV-3 50 mL high pressure vessel (Hachioji, Japan) with a magnet stir bar served as the SSV and was used to prepare saturated solutions of nifedipine and quinine dissolved in SF-CO2. The SSV was housed within a Jasco SCF-Sro oven whose design includes an integral variable speed magnetic stir bar drive. The specification of this oven is ±0.3 K. Saturated SF-CO2 solutions of both nifedipine and quinine were prepared using a stir bar speed of 600 rpm at various oven temperatures. For each series of solubility measurements performed at a fixed temperature, the SSV was loaded one time with either 50 mg of nifedipine powder or 200 mg quinine powder. A Gilson 307 pump B



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Figure 2. Diagram of the SSV−SFC system, where DAD is diode-array detector and BPR is back pressure regulator.

Standards and Technology (NIST) Web site.27 The uncertainty values for the NIST density values are specified as 0.03−0.05% for the experimental temperature and pressure ranges used in these studies. For quinine five calibration standards whose concentrations ranged from 2.5 to 40 mg of quinine dissolved in 100 mL of ethanol were analyzed. By use of the quinine SFC peak integral values obtained for the calibration standards at 235 nm and considering the origin to be a data point, a linear calibration graph was obtained for quinine that provided a correlation coefficient of 0.9998. Thereafter, the SF-CO2 solubility concentrations for quinine measured using SSV− SFC were determined and these values were converted into mole fractions using SF-CO2 density values obtained from NIST. 2.6. Determination of SSV−SFC Experimental Accuracy. This was achieved using a self-check validation procedure and was performed once SSV−SFC solubility data had been obtained. The method involves using the actual experimental SSV−SFC solubility results obtained for a compound to derive a quantity of the compound whose mass when loaded into the SSV is below yet close to that which should be fully soluble according to the SSV−SFC method. Typically the SSV is loaded with 90−95% of the mass of compound at its SSV−SFC experimental solubility limit in SF-CO2 at a specific temperature and pressure. Thereafter, the concentration of the compound in the subsaturated solution is experimentally determined and the level of accuracy is assessed by comparison with the correct dissolution value if the compound was completely dissolved. For nifedipine and quinine, self-check accuracy tests were performed at each experimental temperature using two different pressures at each temperature. By use of this procedure, the experimental accuracy of the SSV−SFC method for nifedipine was determined as 96.1 ± 2.6%, whereas for quinine the SSV−SFC experimental accuracy was 92.4 ± 2.9%. 2.7. Determination of the Solubility of Quinine in nHeptane. A Jasco EV-3 100 mL high pressure vessel with a magnet stir bar housed within a Jasco SCF-Sro oven was used as solubility apparatus. With this system, the solubility of quinine in 50 mL of n-heptane was measured at approximately 13.8 mg at 323.15 K and 25.0 mg at 343.15 K. Complete dissolution of these masses of quinine required several hours of continuous stirring at 600 rpm.

2.4. Supercritical Fluid Chromatography. SFC was performed using a Jasco PU-2080-CO2 Plus pump linked to a Jasco PU-2080 Plus HPLC pump. Solvent mixing was performed using a Jasco HG-1580-32 dynamic mixer. Detection was performed using a Jasco MD-2018 Plus diode-array detector set to operate through the range from 200 to 300 nm for both nifedipine and quinine analyses. The SFC operating pressure was regulated using a Jasco BP-2080 Plus back pressure regulator and for each compound was set at 17.5 MPa with a temperature of 333.15 K. The SFC system was controlled using Jasco ChromNAV software. All SFC analyses for nifedipine were performed using a 150 mm × 4.6 mm i.d. cyano column obtained from Phenomenex (Macclesfield, Cheshire, U.K.) packed with Luna 5 μm stationary phase. For quinine, SFC was performed using a 250 × 4.6 mm i.d. amino column obtained from Phenomenex packed with Luna 5 μm stationary phase. The columns were housed within an AutoScience AT-950 oven (Tianjin, China) operated 328.15 K, with accuracy ±0.5 K. For nifedipine the mobile phase was carbon dioxide/methanol (90:10 v/v) with flow rate at 4.5 mL·min−1, whereas for quinine the mobile phase was carbon dioxide/ methanol (87:13 v/v) with flow rate at 4.5 mL·min−1. 2.5. Quantitation. The concentration of nifedipine and quinine in a saturated SF-CO2 solution was determined via the construction of external SFC calibration graphs. In order to construct the calibration graphs, the plumbing to the sample injection valve in the SSV−SFC interface was modified to enable manual injections of standard ethanolic solutions of nifedipine and quinine. This involved substituting the line between the recirculation pump and sample injection valve with a line that provided a port to accommodate a manual sample injection syringe. The same 10 μL sample loop used to perform the online SSV−SFC solubility measurements was manually loaded with calibration standard solutions. Excess calibration standard solution was discharged from the loaded sample injection valve via the transfer line that was disconnected from the SSV during the SFC analyses of calibration standards. For nifedipine six calibration standards whose concentrations ranged from 3 to 100 mg nifedipine dissolved in 250 mL of ethanol were analyzed. By use of the nifedipine SFC peak integral values obtained for the calibration standards at 235 nm and with the origin considered a data point, a linear calibration graph was obtained that provided a correlation coefficient of 0.9999. The concentrations of nifedipine in saturated SF-CO2 solutions were then calculated. These values were then converted into nifedipine mole fraction values using SF-CO2 density values obtained from the National Institute of

3. RESULTS AND DISCUSSION 3.1. Nifedipine SF-CO2 Solubility Studies. The SF-CO2 solubility of nifedipine was measured at 333.15 and 353.15 K C



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chamber wall. Also nondissolved nifedipine powder whose morphology had not changed remained in the base of the SSV chamber. These observations confirmed that sufficient nifedipine had been loaded into the SSV at the outset of each SSV−SFC solubility study to produce a full series of saturated nifedipine SF-CO2 solutions at both experimental temperatures and all pressures used to perform solubility measurements. The mole fraction (y) solubility results obtained for nifedipine are summarized in Table 2 that also includes the

through the pressure range from 12.5 to 27.5 MPa with sets of SSV−SFC solubility data being acquired using incremental 2.5 MPa steps of SF-CO2 pressure. An intrinsic advantage of static solubility apparatus equipped with online analysis capability is that for any selected pressure and temperature values, sets of data can be very conveniently acquired at controlled time intervals to ensure that equilibrium conditions have been established. This is a vital experimental procedure to help obtain accurate solubility data. For nifedipine, the SSV was stirred for 1 h intervals before a set of SSV−SFC analyses (n = 5 for each set) were performed. Four equilibrium checks were performed throughout a 4 h continuous stir period. Comparison of the sets of peak integration values obtained for nifedipine established that equilibrium was reached within 1 h, since this was sufficient time to produce a set of SSV−SFC peaks with constant integration values that remained stable and did not increase at longer check times. This was the case for all pressures and temperatures used to perform the SSV−SFC solubility measurements. This finding agrees with that previously reported by Knez et al.28 who reported 1 h was sufficient to reach equilibrium conditions for nifedipine dissolved in SF-CO2. The static solubility method employed by Knez et al. involved mounting a loaded high pressure vessel in a frame that was shaken using a motor coupled to the frame via an extenuator. Figure 3 shows a typical chromatogram obtained for a nifedipine data set whose reproducible chromatographic peak

Table 2. Meana Solubility Values of Nifedipine in SF-CO2 (y, Mole Fraction of Nifedipine) with Concentration Values (C) at Temperatures (T), Pressures (P), and Densitiesb (ρ) T, K

P, MPa

ρ, kg·m−3

solubility, y × 106

C, mg·50 mL−1

333.15

12.5 15.0 17.5 20.0 22.5 25.0 27.5 12.5 15.0 17.5 20.0 22.5 25.0 27.5

473.43 605.6 677.53 724.63 759.51 787.28 810.43 318.3 428.15 524.06 594.85 646.89 686.98 719.29

9.7 13.1 17.9 23.2 26.2 31.0 36.6 7.9 11.1 19.9 26.0 35.2 43.7 53.6

1.8 3.1 4.7 6.6 7.8 9.6 11.6 1.0 1.9 3.6 6.1 8.9 11.1 15.1

353.15

Average of three sets of five replicate injections. bDensity values for SF-CO2 and uncertainty values for the densities obtained from the NIST Web site.27 Standard uncertainties u are u(T) = 0.3 K; u(P) = 0.1 MPa; relative standard uncertainties ur are ur(ρ) = 0.05; ur(y) = 0.06; ur(C) = 0.06. a

concentration values for nifedipine dissolved in SF-CO2. Solubility results are presented as the mean values of three sets of five replicate injections. The RSD values for the nifedipine peak integration values used for all quantitations using the external calibration graph fell within 2.2%. To the best of our knowledge only two other reports have previously provided SF-CO2 solubility data for nifedipine.28,29 The static method used by Knez et al.28 involved trapping an aliquot of SF-CO2 nifedipine solution in ethanol prior to quantitation using off-line UV spectroscopy. In contrast, Wang et al.29 have described the use of dynamic solubility apparatus that involved collecting the nifedipine dissolved in a volume of SF-CO2 that generated about 4−6 L of gaseous carbon dioxide during the decompression stage. After decompression, Wang et al. used a 5 mL aliquot of methanol through which the 4−6 L of decompressed carbon dioxide was percolated to trap the nifedipine, and this was then combined with further methanol used to wash the dynamic system transfer lines. Thereafter, Wang et al. used a quantitative off-line UV spectroscopy method to finally determine nifedipine solubility in SF-CO2. A comparison of the solubility results obtained at the same experimental temperature values is shown in Figure 4 for the three studies. At 333.15 and 353.15 K the static SSV−SFC solubility results were higher than those obtained using the static method employed by Knez et al. Despite using a dynamic method, at 333.15 K Wang et al. obtained higher nifedipine SFCO2 solubility results than those obtained using either of the

Figure 3. Chromatogram obtained for a set of five online SSV−SFC injections of a saturated SF-CO2 nifedipine solution prepared at 22.5 MPa and 353.15 K. Injections made at 0, 3, 6, 9, 12 min giving rise to nifedipine peaks 1−5. Detection at 235 nm with peak integration baseline is shown.

heights confirmed stable performance of the SSV−SFC system. Once online SSV−SFC analyses were completed at the first SFCO2 target pressure, the pressure in the SSV was increased by 2.5 MPa and the solubility of nifedipine was measured at the next target pressure. Although nifedipine is very light and also air sensitive particularly when dissolved in organic solvents, there was no chromatographic indication of any decomposition occurring in SF-CO2 throughout all conditions used in these studies. After a complete series of nifedipine SF-CO2 solubility studies were completed at 333.15 and 353.15 K, the SSV was opened for inspection. For both experimental temperatures a thin layer of needle-like nifedipine crystals formed by rapid expansion of supercritical solution was deposited on the vessel D



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additional 12 h overnight stir periods resulting in some samples being stirred for 24 h. Figure 5 shows a typical series of chromatograms obtained for a data set (n = 5 for each set) used to determine the

Figure 4. Comparison of SF-CO2 solubility results obtained for nifedipine using the static SSV−SFC method with those obtained using the static method used by Knez et al.28 and the dynamic method of Wang et al.29

Figure 5. Chromatogram obtained for a set of five online SSV−SFC injections of a saturated SF-CO2 quinine solution prepared at 12.5 MPa and 323.15 K. Injections were made at 0, 4, 8, 12, 16 min giving rise to quinine peaks 1−5. Detection at 235 nm with peak integration baseline is shown.

two static solubility methods. This is somewhat surprising, since it has been reported that dynamic methods can produce low solubility values due to the failure to establish and/or maintain equilibrium.15,23 Presumably in this instance, the rapid rate of nifedipine dissolution in SF-CO2 was sufficiently favorable to facilitate the dynamic method used by Wang et al. for this specific compound. Although the comparative data shown in Figure 4 is not an ideal outcome, it is known that relatively large differences in experimentally determined SF-CO2 solubility values for the same compound may occur.15,23−25 In response we have previously reported24,25 the introduction of an experimental self-check procedure to measure the accuracy of the solubility results obtained for compounds using the SSV−SFC method. The procedure is described in the Experimental Section, and for nifedipine the accuracy of the SF-CO2 solubility results obtained using the SSV−SFC method were determined to be 96.1 ± 2.1%. As far as we are aware, no other method for obtaining SF-CO2 solubility data described in the literature thus far involves using a self-check procedure to measure the accuracy of the experimental SF-CO2 solubility results. The SSV−SFC method has been previously validated using caffeine as a test compound for which it generally provided mid-range solubility values when compared to several different sets of published caffeine SF-CO2 solubility values.25 The comparative results shown in Figure 4 are within a range that might be reasonably expected given the different experimental apparatus, sample preparation, and analysis techniques used. 3.2. Quinine SF-CO2 Solubility Studies. The SF-CO2 solubility of quinine was measured at 323.15 and 343.15 K through the pressure range 12.5−27.5 MPa using 3 MPa steps. As with nifedipine a series of analyses were made at both experimental temperatures and each SF-CO2 pressure to ensure that equilibrium had been reached before solubility measurements were performed. It was rapidly realized that unlike nifedipine, quinine dissolved in SF-CO2 at a very slow rate despite the SSV−SFC system being equipped with very efficient continuous magnetic stirring. The results of six sets of SSV−SFC analyses performed at 2 h intervals confirmed that initial 10 h periods of continuous stirring would be required to establish equilibrium for quinine dissolution in SF-CO2 at both experimental temperatures and all pressure values. This was confirmed by some further confirmatory checks involving

solubility of quinine in SF-CO2. After SSV−SFC solubility measurements were completed at the first SF-CO2 target pressure, the pressure in the SSV was increased by 3 MPa. The process of using 3 MPa pressure steps, then measuring that equilibrium was established before performing solubility measurements was repeated until a full series of quinine SFCO2 solubility measurements were obtained at 323.15 and 343.15 K. As described previously for nifedipine, visual checks of the vented SSV following a complete series of solubility measurements confirmed that sufficient quinine was used to produce saturated SF-CO2 solutions at all experimental pressures and temperatures used to perform solubility measurements. The mole fraction (y) solubility results obtained for quinine are summarized in Table 3. Solubility results are presented as the mean values determined from one set of five replicate injections obtained at dissolution equilibrium. The RSD values for the quinine peak integration values used for all quantifications using the external calibration graph were all within 2.2%. As shown in Figure 6, the SSV−SFC solubility results do not compare favorably with those reported by Zabihi et al.30 who have apparently produced the only report in the literature concerning the solubility of quinine in SF-CO2. Their method used a static solubility system consisting of a relatively large volume unstirred saturation cell through which a recycled flow of SF-CO2 was maintained using a recirculation pump. With this system it was reported that quinine reached equilibrium in 2 h after which a sample tube was disconnected from the recirculation line by means of isolation valves. Following transfer, the pressurized contents of the sample tube were depressurized into a solvent trap and a sample was prepared for off-line UV analysis. Taking into careful consideration the results reported by Zabihi et al. for quinine, especially those at 328.15 K, an auxiliary experiment was performed. This experiment involved determining whether it was possible to fully dissolve a mass of quinine greater than that which the SSV−SFC method had determined to be soluble in E



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Table 3. Meana Solubility Values of Quinine in SF-CO2 (y, Mole Fraction of Quinine) with Concentration Values (C) at Temperatures (T), Pressures (P), and Densitiesb (ρ) T, K

P, MPa

ρ, kg·m−3

solubility, y × 106

C, mg·50 mL−1

323.15

12.5 15.5 18.5 21.5 24.5 27.5 12.5 15.5 18.5 21.5 24.5 27.5

615.1 712.7 765.45 802.19 830.69 854.14 374.68 529.08 626.35 687.75 731.48 765.29

15.3 17.4 22.7 23.6 28.6 29.8 12.0 17.9 23.5 32.2 39.8 50.4

4.0 4.5 6.4 7.0 8.7 9.4 1.7 3.5 5.4 8.1 10.7 14.2

343.15

although the carbon dioxide pump would pulse to maintain set target pressure. The results obtained for the accuracy test and also the nheptane dissolution experiment serve to support the validity of the SSV−SFC solubility results shown for quinine in Table 3. 3.3. Density Based Correlation. The density based semiempirical model proposed by Mendéz-Santiago and Teja26 in a form simplified by Hansen et al.31 was used to correlate the experimental results for nifedipine and quinine. The simplified equation is T ln(yP /P0) = A + Bρ + CT

(1)

where P is the experimental pressure of the system in MPa, P0 = 1.0 MPa, y is the mole fraction solubility of the solute, ρ is the density of carbon dioxide, and T is temperature in K. In this model, the solubility of the solid is calculated using multiple linear regression to optimize the parameters A, B, and C which are independent of temperature. These calculations were performed using Athena Visual Studio version 14.0 software applied to the experimental data shown in Tables 2 and 3. The values given in Table 4 provide the best fits for the model for each compound.

Average of three sets of five replicate injections. bDensity values for SF-CO2 and uncertainty values for the densities obtained from the NIST Web site.27 Standard uncertainties u are u(T) = 0.3 K; u(P) = 0.1 MPa; relative standard uncertainties, ur are ur(ρ) = 0.05; ur(y) = 0.06; ur(C) = 0.06. a

Table 4. Values of Constants A, B, and C Used in the MST Model Derived from Number of Samples (N) at Temperatures (T) and Pressures (P)a parameter

nifedepine

quinine

N T, K P, MPa A, K B, K·m3·kg−1 C R2

14 333.15, 353.15 12.5−27.5 −72454.03 2.2652 9.2282 0.978

12 323.15, 343.15 12.5−27.5 −6902.9 1.956 9.044 0.968

a

Standard uncertainty values u for nifedipine are u(A) = 523.51 K; u(B) = 0.103 K·m3·kg−1; u(C) = 1.43. Standard uncertainty values u for quinine are u(A) = 576.21 K; u(B) = 0.121 K·m3·kg−1; u(C) = 1.58. Figure 6. Comparison of SF-CO2 solubility results obtained for quinine using the static SSV−SFC method with those obtained using the static method performed by Zabihi et al.30

The results shown in Figure 7 illustrate that the MST model provides a good fit for all experimental solubility results obtained for both nifedipine and quinine, respectively. The absolute average relative standard deviation AARD (%) for the correlated solubility results is calculated as follows:

SF-CO2 at 323.15 and 343.15 K at 27.5 MPa in n-heptane. The rationale for this auxiliary experiment is that it is generally accepted that the solvating strength of SF-CO2 equates to that of nonpolar organic solvents such as alkanes.1,2 The results of the n-heptane dissolution experiments are provided in the Experimental Section. The results serve to establish that if the solvating strength of SF-CO2 does approximate that of n-heptane, it would be feasible to dissolve 9.4 and 14.2 mg of quinine in 50 mL of SFCO2 at 323.15 and 343.15 K, respectively, at a pressure of 27.5 MPa. As shown in Table 3, these were the highest masses of quinine determined using the SSV−SFC method to be soluble in SF-CO2 using the experimental conditions. By use of the selfvalidation accuracy check, the SSV−SFC method was found to be 92.4 ± 2.9% accurate for quinine. This value is less than that obtained for nifedipine and also lower than that previously obtained for three other compounds using the SSV−SFC accuracy self-check method.24,25 This might be explained by the subsaturation loaded SSV−SFC system not being absolutely leak tight through the prolonged 10 h equilibration periods

AARD (%) =

100 N

N

∑ i=1

y exp − y calcd y exp

(2)

where N is the number of data points. The experimental mole fraction and calculated mole fraction solubility data calculated according to the simplified MST solubility model are denoted with the superscripts exp and calcd, respectively. For nifedipine the AARD was 9.63%, whereas for quinine the AARD was 11.36%. These AARD values are in the range we have previously obtained using the MST model applied to correlate the SSV−SFC solubility values determined for benzoin and 3,3′,4,4′-benzophenonetetracarboxylic dianhydride.24 The AARD values obtained for nifedipine and quinine also compare favorably with those reported for a wide range of organic compounds including drugs using several different correlation models.8,9 F



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particularly well suited in some instances for obtaining solubility data for compounds that exhibit low solubility in SF-CO2. In general we consider variations in published SF-CO2 solubility data values for the same compound to be attributable to the use of a wide range of methodologies, failure to establish equilibrium, the use of different off-line and online analysis techniques, scale, accuracy, and calibration of the experimental equipment used.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Edward D. Ramsey: 0000-0002-8217-0905 Funding

E.D.R. expresses his sincere gratitude to the 1000 Plan for Foreign Experts Program sponsored by the Chinese Central Government, Project WQ20122100062, who provided funding to help facilitate these studies. B.L. acknowledges financial support provided by Liaoning Provincial Government Project L2015258 and USTL Talent Project 601009816-12 to purchase chemicals. Notes

The authors declare no competing financial interest.

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REFERENCES

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Figure 7. Correlation of the experimental solubility data for (a) nifedipine and (b) quinine in SF-CO2 using the MST model. Experimental: (a) ◇, 333.15 K; △, 353.15 K; (b) ◇, 323.15 K; △, 343.15 K. Model: −, best fit line for experimental data in (a) and (b).

4. CONCLUSIONS The results provided in this report serve to demonstrate the ability of the static SSV−SFC method to obtain SF-CO2 solubility for two basic drugs. The online system effectively eliminates errors associated with sample collection including trapping, subsequent sample preparation, and manipulation stages prior to using off-line analysis methods. The design of the SSV−SFC interface has now been simplified and is easier to operate compared with the previous two-valve interface used in other studies.22,24,25 The results of this study demonstrate that very significant differences in dissolution rates exist for different compounds and that this must be carefully factored into the experimental design to obtain accurate solubility results. The integrated SSV−SFC system provides a convenient online experimental method to ensure equilibrium dissolution conditions are achieved prior to performing solubility measurements and also facilitates a self-validation procedure to determine the accuracy of SF-CO2 solubility results. The use of online SFC rather than HPLC to perform SF-CO2 solubility measurements is relatively straightforward and eliminates any compatibility issues associated with chromatographic mobile phase composition. The ability to perform online SFC solubility measurements is particularly applicable when dealing with compounds that are moisture and/or light sensitive. In addition SFC often provides narrower chromatographic peak widths compared with those obtained using conventional HPLC, and this can lead to improved detection limits. Therefore, online SFC using UV/vis detection may be G



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Determining the Solubility of Nifedipine and Quinine in Supercritical

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