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Ind. Eng. Chem. Res. 2001, 40, 1732-1739
Solubility Analysis of Drug Compounds in Supercritical Carbon Dioxide Using Static and Dynamic Extraction Systems Simon Bristow,† Boris Y. Shekunov,*,‡ and Peter York†,‡ Bradford Particle Design plc, 69 Listerhills Science Park, Campus Road Bradford, Bradford BD7 1HR, U.K., and Drug Delivery Group, Postgraduate Studies in Pharmaceutical Technology, School of Pharmacy, University of Bradford, 59 Listerhills Science Park, Campus Road, Bradford BD7 1HR, U.K.
The equilibrium solution concentration (solubility) is the most important thermodynamic parameter which defines both extraction and precipitation processes. The most demanding applications, for example, those in conjunction with the particle formation technology, require reliable and fast determination of solubilities within the low range 10-9-10-4 mole fraction. The present work aimed to develop and evaluate two experimental systems based on static recirculation and dynamic through-flow extraction methods combined with high-performance liquid chromatographic off-line and spectroscopic on-line analytical modes. The model compounds included paracetamol (acetaminophen), ortho, meta, and para isomers of hydroxybenzoic acid and isomers of methoxybenzamide. The dynamic on-line method proved to be the most effective, rapid, accurate, and reproducible technique applicable to small amounts of sample (ca. 25 mg). It has been shown that the solubility measurements are a prerequisite in optimization of particle formation technology as well as in the design of separation and purification processes with supercritical fluids. 1. Introduction In recent years there has been an increasing level of interest in utilizing supercritical fluid (SF) technology for processing pharmaceutical and nutraceutical materials. The unique feature of the supercritical state is that the solvating power strongly depends on the fluid density and can be adjusted, without changing chemical composition, by controlling the pressure and temperature. This property opens up a wide range of possibilities for selective extraction, purification, and precipitation processes. Carbon dioxide is by far the most important processing medium because of its relatively low critical temperature and pressure (31.3 °C and 72.9 bar, respectively), low toxicity, and low cost (quoted about $0.05/lb). In the compressed state, SF-CO2 can be described as a hydrophobic solvent with a polarity comparable to that of hexane or pentane. SF-CO2 is miscible (or partly miscible below the critical mixture point) with most organic solvents, forming homogeneous binary and ternary solvent-CO2 systems. The ability to form such mixtures greatly increases the solvating power and polarity range of SF-CO2. The single most important and common criterion affecting the efficacy of all SF processing technologies is the equilibrium solubility of the test material in the chosen SF. In general, the rate, yield, and economy of any process are greatly defined by solute solubility. Depending upon the adopted technique, either a very high solubility or an extremely low solubility in the SF is typically required. The biggest commercial application of SF technology has traditionally been in the field of SF extraction, where the high solubility power of SFCO2 has been exploited for the removal of lipophilic materials such as caffeine and hop oils.1 In contrast, low * Corresponding author. Tel.: +44 (1274) 305540. Fax: +44 (1274) 305570. E-mail:
[email protected]. † Bradford Particle Design plc. ‡ University of Bradford.
solubilities are required for modified CO2-organic solvent mixtures used in SF antisolvent precipitation, where the solubility function not only defines the yield and the cost but also strongly affects the particulate and solid-state properties of the products. The emphasis on extraction processes has meant that most research into solute solubility has focused upon highly soluble lipophilic materials. The solute-SF system most widely studied is that of naphthaleneCO2,2 which is now regarded as standard calibration data for any SF solubility apparatus, with typical solubility levels being on the order of 10-3-10-2 mole fraction at 308 K. A variety of lipophilic solutes3 and more polar substances4 have typical solubilities on the order of 10-4-10-3. With such high solubility, measurement can be undertaken relatively simply and accurately using gravimetric techniques. However, it has been demonstrated that, even in this case, the interpolation of solubility data is unreliable; discrepancies of up to 50% for the naphthalene-CO2 system near the critical point have been observed.5 In addition, a lack of fundamental design data has been recognized as the major obstacle for the reliable scaling up of the extraction projects.6 In comparison, relatively little data are available for the materials demonstrating solubilities below 10-5. Analytical determination at these concentrations becomes more challenging, requiring more accurate, validated high-performance liquid chromatographic (HPLC) and/or spectroscopic quantification. SF extraction strategies involve static, dynamic, or coupled static/dynamic modes. A static extraction refers to that with a fixed amount of fluid in contact with the analyte. This technique is relatively slow and prone to technical problems with extracting and measuring small amounts of the gaseous phase. A dynamic extraction employs supercritical flow which is continuously pumped through a bed of sample and is therefore simpler and faster than the static method. However, one of the main factors affecting dynamic extraction, in addition to the
10.1021/ie0002834 CCC: $20.00 © 2001 American Chemical Society Published on Web 03/09/2001
Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1733
Figure 1. Experimental system for solubility measurements using a static extraction method.
solubility, is the mass-transfer rate between the fluid and analyte matrix. There is always a possibility that the solute concentration has not reached its equilibrium value and this factor should always be taken into account. In the present work, we compare static and dynamic analytical systems designed for measurements at the low end of the solubility scale (e.g., minimal equilibrium concentrations of ca. 10-9), adopted for modified SFsolvent mixtures. The main aim is to provide a validated, fast, and reliable data acquisition technique for emerging SF particle formation technologies. 2. Experimental Methods 2.1. Static Extraction System. A schematic diagram of the static solubility apparatus is shown in Figure 1. Pressures in the range of 80-300 bar and temperatures between 308 and 363 K were investigated with this apparatus. A pressure transducer rated to 350 bar (Sensotec model GM, Columbus, OH) was used to monitor the overall pressure of the closed system. Calibration of this apparatus was performed elsewhere7 and compared to literature values. The kit operated in a recirculating mode. Initially the system was evacuated via valve V5 for about 1 h using a single-stage “Speedivac” high vacuum pump (Edwards, Runcorn, U.K.). All of the system valves (V1V5) were then closed. Liquid CO2 was charged into the system using a PU880 reciprocating HPLC pump modified with a cooling head unit (Jasco, Tokyo, Japan) and by opening valves V4 and V1. When the required pressure was achieved, valve V4 was closed. V2 was opened and the magnetic recirculation pump (DB Robinson Associates, Edmonton, Canada) started. This gently and continuously drew CO2 from the base of the packed bed through V2 and then pushed it back into the top end; circulating fluid also passes through a stainless steel sample loop located at switching valve SW1 (Rheodyne, Cotati, CA). An additional PU880 cosolvent pump with calibrated flow delivery was used to pump the modifier solvent
together with CO2 at the requisite flow rates. The solvent and CO2 streams converged in a mixing chamber; two heat exchangers were used to facilitate mixing and to generate a homogeneous SF-solvent mixture. Initially the modified SF-CO2 passed through an in-line manual back-pressure regulator (Tescom, Elk River, MN) to maintain the mixture above its critical pressure. To ensure that an equilibrated SF-CO2-solvent mixture was obtained, SW3 was switched initially to the vent position for 30 min before finally diverting the flow into the equilibrium apparatus via valve V1. The CO2solvent mixture was then recirculated as described before. The sampling procedure was as follows. During equilibration SW1 and SW2 were set in the bypass mode. The mobile phase was pumped to SW2, bypassing the sample loop to return to the reservoir. An in-line valve, V3, was partially closed to keep the mobile phase above atmospheric pressure (∼100 bar). A PU980 HPLC pump (Jasco, Tokyo, Japan) was used to deliver the mobile phase and monitor back pressure. To sample, SW2 was switched, diverting the mobile phase through the sample loop and dissolving any solute present. The mobile phase solution containing dissolved solute was collected into a volumetric flask under atmospheric pressure for off-line quantification by HPLC or UV analysis (section 2.5). SW2 was returned to the bypass mode and the loop flushed with pure or modified CO2 by opening V4 and venting at SW2. Finally, SW1 was switched to the sample mode and the system allowed to reequilibrate; a duplicate sample was taken after 4-6 h. After sampling at a given pressure, additional CO2 or modified CO2 was charged into the system to the next required pressure. Back-flushing of the equilibrated solute-SF-CO2 out of the apparatus was avoided by ensuring that the charging medium was held at a higher pressure than that within the apparatus (indicated by the HPLC pump pressure transducer display). The system was then left to reequilibrate at the new pressure and sampled again. It was critical to quantify the volume (and therefore mass) of fluid sampled. An HP1050 series HPLC autosampler (Hewlett-Packard, Waldbronn, Germany) employing a calibrated metering device was used to inject a sample six times onto an HPLC system. The mean peak areas and standard deviation for the six injections were calculated. Similarly, the same sample solution was injected through the SW1 sample loop of unknown volume using a manual switching valve (Rheodyne, Cotati, CA) and the mean peak area determined. The volume of the loop was then calculated from the ratio of these peak areas. For a given temperature, CO2 density data8 were plotted against pressure and a line was fitted using TableCurve software. The exact SFCO2 density at the employed experimental pressures was determined by interpolation from this line. The mole fraction solubility of solute material (Y) was calculated from the following equations:
Y ) n2X2/(n1X1 + n2X2)
(1)
n1X1 ) dV/Mr
(2)
n2X2 ) M/Mr
(3)
where n1X1 is the total moles of CO2 sampled, n2X2 is the total moles of drug material sampled, d is the CO2
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Figure 2. Experimental system for the determination of solubility using a dynamic extraction technique.
density, V is the volume of the sample loop (typically 5-100 µL), M is mass of solute in the loop (obtained from the off-line HPLC or UV measurements; see section 2.6), and Mr is the CO2 molar mass. In addition to the off-line measurements described, on-line measurements with the HPLC system continuously connected to the sample loop were also carried out. However, the presence of gaseous CO2 in the mobile phase complicated the measurements. The reduction of measurement time using the on-line sampling was not significant when compared to the total time for equilibrating the system; therefore, this on-line mode was not applied during experiments. 2.2. Dynamic Solubility System. A schematic diagram of the apparatus is shown in Figure 2. Determination of the solubility is based on a through-flow arrangement of the CO2 flow and was performed in both on-line and off-line analytical modes. Starting at the lowest pressure to be investigated, SF-CO2 or organic solvent modified SF-CO2 was pumped at a defined flow rate (Jasco PU980 reciprocating pumps). Initially, two Rheodyne valves were switched to direct the CO2 flow along a bypass line and through a high-pressure UV flow cell (Jasco UV-975). The effluent fluid then passed through a solvent trap, which was also used for possible off-line quantification. A back-pressure regulator (BPR; Jasco 880-81) controlled the overall system pressure, and a computer was used to capture and process UV data using Borwin version 1.21 software (JMBS Developments, Le Fontanil, France). In the bypass mode the detector response was set to zero to establish a baseline response from the pure or modified SF-CO2. When the baseline stabilized, the Rheodyne valves were switched to sample mode, diverting the SF through the extraction vessel. As solute was extracted into the fluid, a characteristic UV response was observed. The BPR pressure was then raised and the procedure repeated. Typically, up to 10 different pressures between 80 and 300 bar were investigated in a single isothermal run of duration of about 1 h. Both pure or solvent-modified SF solubility were investigated, the level of solvent modification was simply adjusted by altering the CO2 and/or solvent flow rate. A T-piece low-volume mixing chamber combined with three coiled heat exchangers ensured that a homogeneous single fluid-solvent phase was maintained prior to the extraction and analysis.
Calibration of the on-line UV detector response was carried out by pumping standard solutions of solute material prepared in an appropriate solvent. Initially, blank solvent was pumped directly through the flow cell at the ambient pressure and temperature to establish a zero baseline response. Starting with the lowest concentration, a minimum of six calibration standards were successively pumped through the flow cell, ensuring that the range of standards adequately brackets the sample response. Using a cursor function in the Borwin software, a typical response for each calibrant was manually taken and then plotted against concentration to produce a calibration curve using TableCurve 2D V3 software (Jandel Scientific, San Rafael, CA). Sample response data were interpolated from the standard curve to quantify the concentration of solute present in the SF. The density of SF was taken into account when calculating the molar fraction of the solute according to eq 1. 2.3. Effluent Concentration Measurements. A detailed analysis of the effluent concentration (residual solution concentration during precipitation) is given elsewhere.9 A brief reference to this method is necessary here because these measurements played an important role for clarification of acetaminophen solubility data obtained using the static and dynamic solubility methods. Effluent analysis is similar to the dynamic solubility measurement except that the extraction vessel is replaced by a precipitation vessel (Figure 2) where a drug solution and CO2 are mixed and drug material precipitates. The UV detector (section 2.2) was placed in-line between the precipitation vessel and the BPR. The effluent concentration depends on the mixing conditions; however, it has to be somewhat higher than the equilibrium value because precipitation always occurs from the supersaturated state. 2.4. Pressure and Temperature Calibration. The BPR in the dynamic kit and the pressure transducer in the static kit were adjusted to within (2 bar or 2% (whichever the greater) at 100, 200, and 300 bar using a certified and calibrated transducer, model ADW15DT-240-FC (Applied Measurements Ltd., Aldermaston, U.K.). The oven temperature was calibrated at 35 and 80 °C ((1 °C) using a NS-932 thermocouple (Hanna Instruments, Leighton Buzzard, U.K., certified by RS Components, Corby, U.K.). 2.5. Materials. Both on-line dynamic mode and offline (HPLC) dynamic and static modes were used to study the solubility of paracetamol (acetaminophen). This material was selected as a representative aromatic organic drug sparingly soluble in pure SF-CO2 (∼10-6 mole fraction). In addition, solubilities of ortho, meta, and para isomers of hydroxybenzoic acid (HBA) and 3- and 4-methoxybenzamide (3- and 4-MBA) were investigated using dynamic on-line analysis. o-HBA was used for comparison of the developed static and dynamic experimental systems. This compound has a solubility on the order of 10-4 mole fraction in pure SF-CO2 and, importantly, the solubility data can be referred to those in the literature.10,11 Other compounds indicated solubilities between 10-6 and 10-4 mole fraction in pure SF-CO2 and were investigated using the dynamic apparatus. Some literature data on the solubility of m-HBA are also available.12 The test material was coated onto 220-310 µm glass beads in a 20:1 ratio of beads/solute; a homogeneous
Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1735 Table 1. Solubility Determination of o- and m-HBA in Pure and Solvent-Modifieda CO2 Using Static and Dynamic Extraction Systems 104y T (K)
P (bar)
308
80 90 100 110 120 130 140 150 85 90 95 100 105 110 112 115 125 130 135 145 150 161 170 175 200 202 80 90 100 125 135 150 165
318
328
a
o-HBA in pure CO2 dynamic static 0.07 0.79 1.44 1.82 2.11 2.24 2.54 2.72 0.30 0.46 0.98
m-HBA in modifieda CO2 (dynamic)
0.74 (0.76, 0.82) 3.00 2.93 (3.61)
1.69 1.91
Figure 3. Comparison of solubility profiles for o-HBA in pure CO2 at 318 K obtained using both static and dynamic extraction systems and in comparison with data.10
2.08 2.09 2.42
3.01 3.36 3.26
2.68 2.95
3.44 3.27 4.48 3.54 3.55 3.41 (3.66) 5.59
0.16 0.27 0.35 (0.46) 1.96 2.64 (2.68) 3.33 (3.54) 3.90
Figure 4. Solubility profile of o-HBA in pure CO2 at 308 K obtained using the dynamic system in comparison with data.10,11
3.5 mol % methanol-modified CO2.
mixture was prepared by vortex mixing (Autovortex SA6, Stuart Scientific, Redhill, U.K.). This mixture is packed into a stainless steel vessel and sandwiched between filter paper circles to prevent entrainment of coated solute. The vessel was mounted into the static or dynamic solubility kit (Figures 1 and 2). Solid materials were obtained from Sigma Chemicals, Poole, U.K. All solvents used were of either AnalaR or HPLC grade and were obtained from BDH (Leicester, U.K.). Industrial-grade CO2 (>99.95% v/v purity) was supplied by Air Products (Manchester, U.K.). 2.6. UV and HPLC Analysis. The description of the on-line UV calibration and measurement procedures is given in section 2.2. A suitable wavelength for UV determination was selected by scanning the UV spectrum for each of the compounds investigated: 235 or 298 nm for o-HBA, 254 nm for m-HBA, and 242 nm for acetaminophen. Samples, diluted as necessary, and standards were analyzed using a Pharmacia UV and Swift software. Methanol was used as the vehicle solvent. Solubility determination off-line for acetaminophen was performed using a fully validated HPLC analysis. Aliquots of prepared sample solutions, diluted if necessary, were interspersed with calibration solutions. The mobile phase was a mixture of acetonitrile (15%) and 0.05 M sodium dihydrogen phosphate (anhydrous) buffer, pH 3.0 (85%).
Figure 5. Solubility profile of o-HBA in pure CO2 at 328 K obtained using the dynamic system in comparison with data.10
3. Results 3.1. Solubility of HBA and MBA Isomers. o-HBA (Table 1) was used as the principal compound to validate the present experimental methods, because data obtained in pure CO2 can be referred to those reported in the literature. Figure 3 demonstrates a good agreement of the static and dynamic solubility results obtained in the present work with data published by Gurdial and Foster,10 who used a static, equilibrium solubility method. In addition, the dynamic measurements at both 308 and 328 K are in close agreement with the data obtained elsewhere10,11 (Figures 4 and 5). Further confirmation that equilibrium solubility was reached in
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Figure 6. Solubility of m-HBA in modified (3.5 mol % methanol) CO2 at 318 K obtained using the dynamic system in comparison with data.13
Figure 7. Solubility profile of 3-MBA and 4-MBA in pure CO2 at 343 and 363 K obtained using the dynamic system.
the dynamic mode was provided by the fact that variation of the CO2 flow rate had no influence on the analyte concentration. Under the experimental conditions applied, o-HBA solubility was relatively high, typically on the order of 10-4 mole fraction. The flow-through apparatus was also validated for solubility determinations made in methanol-modified CO2 using m-HBA (Figure 6 and Table 1). The dynamic data obtained showed close agreement with the equilibrium data reported.12 During these experiments it was noticed that increasing the operating temperature from 328 to 338 K as well as prolonged experimental runs caused the packed bed to compact, reducing the total surface area and the solute dissolution rate into the modified SF-CO2. This result demonstrated that it was imperative to coat the glass beads with the minimum of solute material. The high level of methanol cosolvent used in the validation (3.5 mol %) may have mobilized the solute and facilitated fusion, especially when pure CO2 is used to purge cosolvent from the vessel at the end of each run. Under the experimental conditions applied, m-HBA solubility was also high, typically on the order of 10-4 mole fraction, and therefore comparable with o-HBA in pure CO2. The solubility of p-HBA was investigated using pure CO2 at 343 K and found to be in the micromole fraction region (10-6) when pressure was varied between 90 and 120 bar. This solubility agrees with the data,13 which indicated that p-HBA was the least soluble HBA isomer in pure CO2 studies conducted at 373 K for pressures between 200 and 400 bar.
Figure 8. Solubility of acetaminophen in pure and 0.85 mol % ethanol-modified CO2 obtained using the dynamic system with offline analysis.
Figure 9. Solubility of acetaminophen in pure and 0.85 mol % ethanol-modified CO2 obtained using the dynamic system with online analysis. Table 2. Solubility Determination of 3- and 4-MBA in Pure CO2 at 343 and 363 K Using the Dynamic Extraction System 104y 3-MBA
4-MBA
P (bar)
343 K
363 K
343 K
363 K
90 100 120 140
5.60 (6.43) 9.02 (9.85) 20.21
12.10 18.00 34.50
2.00 3.23 6.73 10.28
3.99 6.30
Figure 7 and Table 2 show how the dynamic solubility method has been applied to another group of disubstituted aromatic isomers, 3- and 4-MBA. The results demonstrate that the meta isomer (3-MBA) form is far more soluble than the para isomer (4-MBA) form. This solubility difference was enhanced with temperature and pressure, with the difference in solubility at 120 bar and 343 K reaching an order of magnitude. This difference in solubility is associated with more symmetrical molecular packing and greater lattice energy of 4-MBA than those of 3-MBA. The different crystal structure results in the fact that the melting point of 4-MBA (ca. 437 K) is greater than that of 3-MBA (ca. 407 K). 3.2. Solubility of Acetaminophen. Solubility data obtained for acetaminophen using the dynamic technique with on-line (UV) and the more time-consuming off-line (HPLC) analysis (Figures 8 and 9 and Table 3)
Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1737 Table 3. Solubility Determination of Acetaminophen in Pure and Modifieda CO2 at 313 and 353 K Using Static, Dynamic, and Effluent Systems 106y off-line dynamic P (bar)
pure CO2
modified CO2
on-line dynamic pure CO2
modified CO2
modifieda CO2 static effluent
(a) 313 K 80 100 105.6 124.7 125 150 150.9 175 182.5 200 210 211.8 225 248.7 250 300 80 100 106.3 125 127.4 146 150 167.3 175 185.2 200 202.1 224.7 225 246.4 250 a
0.37
1.31
0.41
1.01 1.21
1.16 6.78 8.59
0.65
1.77
0.61
1.49 2.68 8.17
1.08
2.84
0.10
2.25 9.01 2.94
1.37
3.33
1.22
2.63
Figure 10. Solubility profile of acetaminophen in modified (with 0.85 mol % ethanol) CO2 obtained using the static system.
8.54 8.43 1.78
4.32
1.40
3.13
0.072 0.18
0.022 0.098
(b) 353 K 0.64 0.22 0.52 0.17
3.15 3.26 1.02 2.55 2.73
0.76
1.54 5.98 7.78
1.36
2.91
1.62
3.65
2.83 8.50 9.24
4.07
4.21
6.79 10.70 16.10
8.89
7.75 (8.12) 17.20
8.14
7.74
10.05
0.85 mol % ethanol-modified CO2.
closely agree. On-line measurement can therefore be considered as an effective and rapid quantification technique. The addition of the polar modifier ethanol enhanced the acetaminophen solubility (Figure 9). This phenomenon is anticipated because acetaminophen is also polar. The region of lowest solubility is found at 353 K and pressures below 120 bar. However, the 353 K isotherm for pure CO2 intersects the 313 K ethanolmodified isotherm: increasing pressure at high temperature produces a dramatic increase in the acetaminophen solubility. At 353 K and between 80 and 250 bar, the solubility of acetaminophen is seen to increase by 2 orders of magnitude. The acetaminophen static solubility was also determined in ethanol-modified CO2; the data obtained are shown in Figure 10 and Table 3. The static solubility was found to be significantly (by a factor of 2 or 10) higher than the dynamic solubility determinations. Interestingly, the profiles of the static and dynamic solubility in modified CO2 (Figures 8-10) were comparable with the distinctive intersection of the 313 and 353 K isotherms at 120-150 bar despite differences in absolute values. Although, generally, both techniques demonstrated that acetaminophen has a relatively low (micromole fraction) solubility of several orders of magnitude below that of o-HBA, the principal problem arose as to whether the dynamic kit provided equilibrium solubility values for acetaminophen. To examine this possibility, several experiments were undertaken.
Figure 11. SEDS (Solution Enhanced Dispersion by Supercritical Fluid)18 effluent concentration of acetaminophen in 0.85 mol % ethanol-modified CO2.
First, variation of the extraction vessel length and cross section would be expected to change the acetaminophen concentration. The vessel length was changed between 7 and 70 cm, and the internal vessel diameter was changed between 0.22 and 1.4 cm. No change in the dynamic solubility profile was detected. Similarly, variation of the CO2 flow or the effect of packing integrity did not produce any noticeable changes in the solubility profile. The final confirmation came from the effluent studies (see section 2.3). Figure 11 and Table 3 show that the effluent concentrations are somewhat higher but very similar to the observed solubility obtained with the dynamic apparatus (Figures 8 and 9). Because the effluent concentration cannot be lower than the equilibrium solubility, the dynamic method provided accurate equilibrium data, for example, in the case of o-HBA (section 3.1). One of the most important analytical functions is the relationship between the solubility and the solvent-CO2 composition. Such dependence for acetaminophen in an ethanol-CO2 solution is shown in Figure 12 and Table 4. The linear increase (r2 ) 0.95) in the acetaminophen concentration (logarithmic scale) with the ethanol concentration suggests an exponential-type enhancement in solubility. At concentrations above ca. 2% mole fraction of ethanol, the modified CO2 could be effectively considered as a solvent rather than an antisolvent. This fact, therefore, imposes limitations on the maximum solution flow rate during any antisolvent precipitation process.
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specific, and it is important to distinguish conditions under which the equilibrium is reached at the extractor exit. Assuming extraction is steady, the radial dispersion is negligible, and the mass-transfer coefficient, k, is independent of the solute concentration, c, the differential mass-balance equation gives the following wellknown relationship:
c/c0 ) 1 - exp(-kSl/u)
(4)
where c0 is the equilibrium concentrations and S is the specific surface area of the dissolving particles. The mass-transfer coefficient can be subdivided into diffusion, kd, and surface kinetic, ks, parts defined by the following equations:14,15 Figure 12. Acetaminophen solubility as a function of the ethanol concentration in modified CO2 at 313 K and 250 bar. Table 4. Acetaminophen Solubility as a Function of the Ethanol Concentration in Modified CO2 at 313 K and 250 bar [ethanol] in CO2 (mol %)
[acetaminophen] (mol × 106)
[ethanol] in CO2 (mol %)
[acetaminophen] (mol × 106)
0.00 0.42 0.84 1.66
0.079 0.28 0.54 1.12
2.47 3.26 4.03 4.78
1.33 1.52 2.55 3.35
3.3. Precision and Accuracy. The precision of the on-line dynamic system was tested using acetaminophen in pure CO2 at 313 K. Measurements were made using different analysts and packed vessels, and the experiments were performed over a period of 2 years. The relative standard deviation (RSD) values obtained were 14.6%, 13.0%, and 11.6% at 100 bar (n ) 5), 175 bar (n ) 8), and 210 bar (n ) 7), indicating that the technique is robust. In pure CO2, dynamic measurements were accurate to within 10% of the literature values (Figures 3-5). For determinations in solventCO2 mixtures (Figure 6), the precision is estimated at between 5 and 15% RSD; the maximum deviation in accuracy is 15%. Data precision for the static system was not calculated. In terms of accuracy, positive deviations from literature values of up to 27% (Figure 3) were observed. The acetaminophen solubility was typically between 3 and 12.5 times greater on the static apparatus (Figure 10) compared to the on-line dynamic determinations (Figure 9). The major error contribution to the static system is from the multiple analytical steps required for quantification at a given sampling point. Furthermore, the large number of valves, unions, and other connections used frequently introduced system leaks. Inaccuracy was greater at high temperature; this is possibly due to the inefficiency of the recirculating pump at low, gaseous-like CO2 densities. 4. Discussion The major criterion in validation of the dynamic solubility method was that this technique had to provide equilibrium solubility data. Establishment of a saturation plateau was achieved for all of the materials investigated in the way that the concentration at the exit of the extractor was independent of the extractor column length, l, and the flow velocity, u (or Reynolds number, Re). In general, this phenomenon is material-
1/k ) 1/kd + 1/ks
(5)
kd ) D/δ
(6)
where the diffusion component is expressed through the effective thickness of the diffusion boundary layer, δ, and diffusion coefficient, D. The coefficient ks is defined by the properties of the solid state, surface dissolution mechanism, and solution thermodynamics and has yet to be measured in supercritical solutions. However, this coefficient was determined for single crystals of acetaminophen in aqueous solutions by measuring the growth and dissolution rates of the crystal faces.16 Because the properties of the solid phase and the surface largely remain the same in different solutions, we assume that ks is the same order in SF-CO2. The diffusion mass transfer for each individual solid particle can be approximated as
Sh ) d/δ ) 2 + C(Re1/2)Sc1/3
(7)
in which the number 2 is the correction factor for the mass transfer in a static solution, d is the particle diameter, and constant C depends on the particle shape and equals 0.72 for spherical particles.14,15 The dimensionless parameters are the Sherwood number, Sh, the Reynolds number, Re ) ud/ν, and the Schmidt number, Sc ) ν/D, where ν is the solution kinematic viscosity. It has been shown elsewhere that the complex fluid dynamics inside the extractor bed may result in a somewhat different order of Re in eq 7 between 0.5 and 0.8;17 however, eq 7 is a good estimate at low Reynolds numbers. For a standard column used in the present experiments, acetaminophen was packed with the typical bulk density of 0.1 g cm-3 and the flow velocity was u = 0.1 cm s-1. The following parameters were measured using Sympatec particle size analysis: d (volume mean diameter) = 50 µm, S = 600 cm-1, and u = 0.1 cm s-1. Taking the surface kinetic coefficient ks ∼ 5 × 10-3 cm s-1 from work16 and typical SF-CO2 parameters ν = 10-3 cm2 s-1 and D = 10-4 cm2 s-1 from eq 7, Sh = 3.1. Equations 5 and 6 show that the mass-transfer coefficient is mostly defined by its surface contribution (the diffusion transfer is relatively fast as compared to the surface dissolution). Equation 4 gives c/c0 = 0.95 at the column length of 0.1 cm. The above results show that, even at this short column length and the small amount of material loaded (e.g., 25 mg), the concentration attains equilibrium. This prediction is in agreement with the experimental observations. As seen from eq 4, there is no direct relationship between the compound
Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1739
solubility, c0, and its extraction rate (the time in which the equilibrium is attained). An indirect relationship, however, is contained in the different values of ks for different materials. For example, for most materials both ks and c0 increase with temperature. In addition, for chemically similar entities, such as isomers, the material with lower melting point is expected to have both increased solubility and mass-transfer coefficient as compared to the higher melting compound. Thus, the solubility and kinetic data obtained by the dynamic method can be used to develop operating conditions for enhanced separation of isomers using SF precipitation. The solubility analysis is also crucial for the development of the precipitation process. This process is governed by the strong dependence of the nucleation rate N ∼ exp(s-2) on supersaturation, where s ) ln(c/ c0). This high sensitivity of the nucleation rate on the equilibrium concentration has a remarkable effect on the precipitation kinetics, for example, those of acetaminophen.18 At 80 bar and 358 K, the solubility level is on the order of 10-8 mole fraction resulting in extremely high supersaturation, high nucleation, and fast crystal growth, producing a large number of agglomerated 1-3 µm particles. At another extreme condition, 250 bar and 353 K, high solubility (>10-5) results in low supersaturation and produces a small number of acicular crystals as large as several millimeters. The latter conditions consequently result in a low yield (ca. 4%) of the precipitated material. The intermittent solubility during mixing between the drug solution and the SF antisolvent is defined by changing the composition of the solvent-antisolvent mixture similar to that shown in Figure 12. These measurements enable calculation of the supersaturation profile developed during mixing between the drug solution and CO2.19 In this respect, on-line data produced from the dynamic solubility measurements provide a rapid analytical probe for predicting and optimizing the precipitation processes. 5. Conclusions Two experimental techniques, dynamic and static, have been developed to measure the solubility of sparingly soluble drug substances in pure and modified SFCO2. The dynamic method with on-line UV detection can be applied to analyze small quantities (ca. 25 mg or less) of drug compounds in order to obtain the equilibrium solubility with a resolution of 10-9 mole fraction. It has proved to be an effective, reliable, and rapid quantification technique. Off-line measurements are more time-consuming and require at least one additional processing step such as dilution/concentration or change of vehicle solvent prior to analysis, introducing additional errors into the quantification. The static measurements also showed large errors for measurement of solubilities below ca. 10-6 mole fraction. Solubility measurements become a necessary step for the successful design of precipitation and extraction processes with SF-CO2. This point has been illustrated for
a range of applications including optimization of the particle size distribution in precipitation, improvement of the product yield, and separation and purification of isomers. Literature Cited (1) McHugh, M.; Krukonis, V. J. Supercritical Fluid Extraction, 2nd ed.; Butterworth-Heinemann: Boston, 1994. (2) Tsekhanskaya, Y. V.; Iomtev, M. B.; Mushinka, E. V. Solubility of Naphthalene in Ethylene and Carbon Dioxide under Pressure. Russ. J. Phys. Chem. 1964, 38, 1173. (3) Schmitt, W. J.; Reid, R. C. Solubility of Monofunctional Organic Solids in Chemically Diverse Supercritical Fluids. J. Chem. Eng. Data 1986, 31, 204. (4) Hutchenson, K. W.; Foster, N. R. In Innovations in Supercritical Fluids: Science and Technology; Hutchenson, K. W., Foster, N. R., Eds.; ACS Symposium Series 608; American Chemical Society: Washington, DC, 1995; p 1. (5) Richards, M.; Campbell, R. M. Comparison of Supercritical Fluid Extraction, Soxhlet and Sonication Methods for the Determination of Priority Pollutants in Soil. LC-GC 1991, 4 (7), 33. (6) Hedrick, J. L.; Mulcahey, L. J.; Taylor, L. T. Supercritical Fluid Extraction. Microchim. Acta 1992, 108, 115. (7) Palakodaty, S.; Hanna, M.; York, P.; Humphreys, G. An Experimental Method for the Determination of Solid Solubility in Pure and Modified Supercritical Carbon Dioxide. Proc. 16th Pharm. Technol. Conf. 1997, 3, 22. (8) Angus, S.; Armstrong, B.; De Reuck, K. Carbon Dioxide International Thermodynamic Tables of the Fluid State, 3rd ed.; Pergamon Press: New York, 1976. (9) Bristow, S. C.; Shekunov, B. Yu.; York, P. Analysis of the Supersaturation and Precipitation Process with Supercritical CO2. J. Supercrit. Fluids 2001, submitted for publication. (10) Gurdial, S.; Foster, N. R. Solubility of o-Hydroxybenzoic Acid in Supercritical Carbon Dioxide. Ind. Eng. Chem. Res. 1991, 30, 575. (11) Ke, J.; Mao, C.; Zhong, M.; Han, B.; Yan, H. Solubilities of Salicylic Acid in Supercritical Carbon Dioxide with Ethanol Cosolvent. J. Supercrit. Fluids 1996, 9, 82. (12) Gurdial, G. S.; Macnaughton, S. J.; Tomasko, D. L.; Foster, N. R. Influence of Chemical Modifiers on the Solubility of o- and m-Hydroxybenzoic Acid in Supercritical CO2. Ind. Eng. Chem. Res. 1993, 32, 1488. (13) Krukonis, V. J.; Kurnik, R. T. Solubility of Solid Aromatic Isomers in Carbon Dioxide. J. Chem. Eng. Data 1985, 30, 247. (14) Chernov, A. A. Modern Crystallography III, Crystal Growth; Springer Series in Solid State Physics; Springer: Berlin, 1984. (15) Mullin, J. W. Crystallization; Butterworth-Heinemann: Oxford, U.K., 1993. (16) Shekunov, B. Yu.; Grant, D. J. W. In Situ Optical Interferometric Studies of the Growth and Dissolution behaviour of Paracetamol (Acetaminophen) Growth Kinetics. J. Phys. Chem. 1998, 101, 33973. (17) Tan, C.-S.; Liang S.-K.; Liou, D.-C. Fluid-Solid Mass Transfer in Supercritical Fluid Extractor. Chem. Eng. J. 1988, 38, 17. (18) Shekunov, B. Yu.; Hanna, M.; York, P. Crystallization Process in Turbulent Supercritical Flows. J. Cryst. Growth 1999, 198/199, 1345. (19) Shekunov, B. Yu.; Baldyga, J.; York, P. Particle Formation by Mixing with Supercritical Antisolvent at High Reynolds Numbers. Chem. Eng. Sci. 2000, in press.
Received for review March 2, 2000 Accepted January 24, 2001 IE0002834
