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Ind. Eng. Chem. Res. 1997, 36, 3954-3959
Phase Behavior of Mixtures Containing Antibiotics. Chloramphenicol Partitioning Ram B. Gupta* Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849-5127
Rajesh Kumar and Guru V. Betageri Department of Pharmacal Sciences, Auburn University, Auburn, Alabama 36849-5503
Phase equilibrium behavior of antibiotics is important in drug design and for optimization of the recovery processes in manufacturing. Antibiotics are high-cost fine chemicals, mostly manufactured by fermentation using inexpensive substrates. The major cost of manufacturing is involved in the separation processes. The aqueous/organic partitioning behavior of a clinically important antibiotic, chloramphenicol, is measured. The organic phase includes the pure solvents n-hexane, chloroform, diethyl ether, and ethyl acetate. In addition, measurements are also made for a mixed organic phase composed of n-hexane + ethyl acetate. Partitioning increases with the hydrogen bonding tendency of the solvent in the order n-hexane < chloroform < diethyl ether < ethyl acetate. Based on UNIQUAC and lattice-fluid hydrogen-bonding theories, an activity coefficient model (UNIQUAC-HB) is developed that includes hydrogen-bonding interaction. Single-solvent organic-phase data are correlated with the model, and free energy of hydrogen bonding parameters are obtained. Predictions made for mixed-solvent organic-phase systems agree well with the experimental data without using any adjustable parameter. Introduction Investigation of the phase equilibrium behavior of antibiotics is important both in understanding the partition mechanism and in the design and optimization of downstream recovery processes (Strong, 1986; Evans, 1988; Zhu et al., 1990; Gupta and Heidemann, 1990). The thermodynamic behavior of antibiotics also plays a key role in drug design in pharmaceutical science (Davis et al., 1974). The concepts of thermodynamics can be applied to biological systems because these processes are essentially physical and chemical changes involving the exchange of energy. These concepts provide the basis for determining important parameters for rational drug design. Almost all antibiotics of commercial importance are manufactured by large-scale aerobic fermentation. Although the companies producing antibiotics have been reluctant to publish process details, general outlines of the processes are well-known. The fermentation media are designed to give maximum production. Carbohydrate sources such as glucose, sucrose, lactose, and/or starch and nitrogen sources such as urea, ammonium sulfate, soybean meal, cornsteep liquor, and/or whey are used. Sometimes chemical compounds are added to the fermentation broth so that it can react with the naturally produced antibiotic and make a desired product. After the production cycle, the fermentation broth is taken for harvesting. Microorganisms are removed by filtration or centrifugation. Antibiotic is recovered by solvent extraction, ion-exchange chromatography, precipitation, crystallization, or a combination of these methods. In most cases, solvent extraction is used (Belter et al., 1988; Chaubal et al., 1995). However, some highly water-soluble antibiotics (e.g., streptomycin) require ion-exchange separation (Bartels et al., 1958). In addition, a new extraction process based on * To whom all the correspondence should be addressed. E-mail:
[email protected]. Phone: (334) 844-2013. Fax: (334) 844-2063. S0888-5885(97)00160-7 CCC: $14.00
reverse micelles was recently proposed by Hu and Gulari (1996) for neomycin and gentamycin. Due to a very low concentration of antibiotic in the final fermentation broth, recovery constitutes a major portion of the total manufacturing cost. Unfortunately, this area of research has not been given adequate attention, and bioseparation units are designed empirically rather than on the basis of rational information. In general, bioseparation processes are governed by thermodynamics and kinetics. The most important of these two is thermodynamics, which has received the least attention. Although there are empirical equations (Gupta and Heidemann, 1990; Taft et al., 1996; Tsuji et al., 1977, 1978, 1979; Bogardus and Palepu, 1979; Orella and Kirwan, 1987; Chen et al., 1989) used for correlating some experimental data (Salvatore and Katz, 1993; Andrew and Weiss, 1959; Tomlinson and Ragosz, 1985), comprehensive and predictive models for antibiotic solutions that can be used to scale up and optimize manufacturing processes do not exist (Zhu et al., 1990). Development of a predictive model for representing the phase equilibrium behavior of antibiotics has been difficult due to the lack of adequate experimental data (Zhu et al., 1990). Hence, there is clearly a need for a comprehensive study of antibiotic thermodynamics. This work focuses on the phase behavior of a clinically important antibiotic, chloramphenicol. Chloramphenicol, the first “broad-spectrum” antibiotic discovered, was originally isolated from Streptomyces venezuelae. Chloramphenicol is a potent inhibitor of bacterial protein synthesis. Chloramphenicol remains the drug of choice for the treatment of salmonella infections such as typhoid and paratyphoid fever and in severe systemic Arizona infections. Chloramphenicol, because of its high intraocular penetration properties, is used in various bacterial eye infections such as Bacillus cereus panophthalmitis, which occurs particularly in drug abusers. Chloramphenicol is used as a “back-up” drug for various venereal diseases such as © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3955
chancroid, Lymphogranuloma venereum, and Granuloma inguinale. Chloramphenicol is also used in the treatment of plague, tularemia, and louse-brone relapsing fever (Kucers and Bennett, 1987) and in the falciparum infections (Yeo and Reickmann, 1994). Chloramphenicol also has applications in biotechnology; for example, Zhou and Traxler (1992) reported that an enhanced butanol production is possible by reducing the autolysin activity of Clostridium acetobutylicum after treatment with chloramphenicol during the production of butanol by fermentation. Chloramphenicol is obtained by fermentation from S. venezuelae or by organic synthesis. The antibiotic is readily extracted from clarified culture fluid at slightly alkaline pH with a solvent such as ethyl acetate (Vining and Westlake, 1984). The residue after removing the solvent is freed from lipid by leaching with petroleum ether (naphtha). The product is crystallized from water, ethylene dichloride, or a mixture of petroleum ether and diethyl ether. The first objective of this study is to determine the phase behavior of chloramphenicol in single-component and multicomponent mixtures of industrially important solvents such as n-hexane, chloroform, diethyl ether, and ethyl acetate. The second objective is to develop an activity coefficient model based on molecular thermodynamics that can be used to extrapolate the experimental data to conditions where data are not available so that, in addition to bioseparation, the understanding of molecular interactions obtained here can be extended to drug design.
Table 1. Partitioning of Chloramphenicol between n-Hexane and Water Phases at 30 °C
Materials and Method
Table 4. Partitioning of Chloramphenicol between Ethyl Acetate and Water Phases at 30 °C
Chemicals. Chloramphenicol was purchased from Sigma Chemical Co. (St. Louis, MO). Chloroform, n-hexane, and diethyl ether from Fisher Scientific Co. (Fairlawn, NJ) were reagent grade, and ethyl acetate (Fisher Scientific Co.) was sequencing grade. Determination of the Partition Coefficient. Chloramphenicol is dissolved in distilled water (pH, 7.0 ( 0.2) to give a concentration of 2 mg/mL. From this, serial dilution was made to achieve concentrations of 0.5, 1.0, and 1.5 mg/mL. Convenient volumes of the antibiotic solution (5 mL) and the appropriate solvent or solvent mixture are added to 20-mL scintillation vials that have Teflon stoppers. The organic and aqueous phases are equilibrated for 2 h at 30 ( 0.1 °C in a shaking water bath (Dubnoff metabolic shaker). The concentration of chloramphenicol in the aqueous phase is determined by a UV spectrophotometer (Beckman DU-65) at 278 nm. The concentration of chloramphenicol in the organic phase is estimated by a mass balance. In separate experiments, it was confirmed that the 2-h phase contacting is enough to achieve equilibrium. New Experimental Data Experimental data for chloramphenicol partitioning in the aqueous phase in equilibrium with pure solvents, n-hexane (Table 1), chloroform (Table 2), diethyl ether (Table 3), and ethyl acetate (Table 4), are presented. Partitioning of the antibiotic increases with increasing polarity and hydrogen-bonding (H-bonding) tendency of the sovent in the order n-hexane < chloroform < diethyl ether < ethyl acetate. It appears that ethyl acetate is the best solvent for extraction and n-hexane is the best antisolvent for precipitation of the antibiotic. Data for the mixed organic phase, ethyl acetate + n-hexane, with varying ethyl acetate content are presented in Tables
chloramphenicol in org phase
chloramphenicol in aq phase partition coeff
Corg, mg/mL
xorg, µmol/mol
Caq, mg/mL
xaq, µmol/mol
Corg/Caq
xorg/xaq
0.000 0.000 0.000 0.017
0.0 0.0 0.0 6.8
0.501 1.090 1.600 1.983
26.9 59.3 88.1 110.5
0.00 0.00 0.00 0.009
0.00 0.00 0.00 0.062
Table 2. Partitioning of Chloramphenicol between Chloroform and Water Phases at 30 °C chloramphenicol in org phase
chloramphenicol in aq phase partition coeff
Corg, mg/mL
xorg, µmol/mol
Caq, mg/mL
xaq, µmol/mol
Corg/Caq
xorg/xaq
0.097 0.167 0.430 0.500
24.1 41.8 107.0 155.0
0.403 0.833 1.070 1.500
22.5 46.4 59.6 83.5
0.241 0.20 0.40 0.33
1.07 0.901 1.80 1.86
Table 3. Partitioning of Chloramphenicol between Diethyl Ether and Water Phases at 30 °C chloramphenicol in org phase
chloramphenicol in aq phase partition coeff
Corg, mg/mL
xorg, µmol/mol
Caq, mg/mL
xaq, µmol/mol
Corg/Caq
xorg/xaq
0.365 0.759 1.140 1.590
116 243 369 517
0.135 0.241 0.364 0.407
07.1 12.5 19.7 21.5
2.70 3.14 3.12 3.90
16.3 19.4 18.7 24.1
chloramphenicol in org phase
chloramphenicol in aq phase partition coeff
Corg, mg/mL
xorg, µmol/mol
Caq, mg/mL
xaq, µmol/mol
Corg/Caq
xorg/xaq
0.481 0.962 1.444 1.932
137 285 432 579
0.019 0.038 0.056 0.068
1.0 1.8 3.1 3.5
25.60 25.32 25.78 28.40
137 158 139 165
Table 5. Partitioning of Chloramphenicol between n-Hexane + Ethyl Acetate (47 mol % Ethyl Acetate) and Water Phases at 30 °C chloramphenicol in org phase
chloramphenicol in aq phase partition coeff
Corg, mg/mL
xorg, µmol/mol
Caq, mg/mL
xaq, µmol/mol
Corg/Caq
xorg/xaq
0.221 0.361 0.577 0.940
079 129 206 335
0.279 0.639 0.923 1.006
15.5 35.6 51.4 59.0
0.79 0.56 0.63 0.89
5.10 3.62 4.00 5.68
5-7. As the n-hexane content is increased, the antibiotic partitioning decreases due to a decrease in solventantibiotic H-bonding. The pH value of the chloramphenicol + water solution is observed to be the same as that of the pure water used in this study. The pKa value for chloraphenicol is 5.5 (McEvoy, 1997). For simplicity in the theoretical work, the dissociation of the antibiotic is assumed to be negligible, similar to the approach of Gupta and Heidemann (1990). Theory Liquid-liquid (organic-aqueous) phase equilibrium is determined by equating the activity (a) in the organic
3956 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 6. Partitioning of Chloramphenicol between n-Hexane + Ethyl Acetate (57.1 mol % Ethyl Acetate) and Water Phases at 30 °C chloramphenicol in org phase
and qi are the volume and surface area parameters for compound i, and θi and φi are the area and volume fractions, respectively
chloramphenicol in aq phase partition coeff
Corg, mg/mL
xorg, µmol/mol
Caq, mg/mL
xaq, µmol/mol
Corg/Caq
xorg/xaq
0.288 0.569 0.917 1.320
99.8 197.2 317.7 457.4
0.211 0.431 0.583 0.683
11.8 24.0 32.5 38.0
1.36 1.32 1.57 1.92
8.46 8.22 9.78 12.04
θi )
xiri
partition coeff
xorg, µmol/mol
Caq, mg/mL
xaq, µmol/mol
Corg/Caq
xorg/xaq
0.476 0.948 1.427 1.899
148 294 444 591
0.024 0.052 0.073 0.101
1.37 2.88 4.05 5.60
10.90 13.29 14.70 15.10
108.03 102.08 109.63 105.54
(org) and aqueous (aq) phases for all components in the solution
aorg ) aaq i i
for all i
(1)
The activity of component i is written in terms of the activity coefficient (γi) based on the mole fraction (xi) as
ai ) γixi
(2)
The activity coefficient is a function of the solution composition, temperature, and pressure. Following the concept proposed by Fu et al. (1995), we propose an activity coefficient model that includes hydrogen bonding, UNIQUAC-HB. Here the activity coefficient for a compound is expressed as the sum of combinatorial hb (γcomb ), residual (γres i i ), and H-bonding (γi ) contributions. Contribution by the combinatorial term is due to differences in the molecular size and shape, the residual term is due to weak energetic interactions, and the H-bonding term is due to the strong attactive force between proton donor and acceptor sites on the molecules. hb ln γi ) ln γcomb + ln γres i i + ln γi
(3)
The combinatorial and residual terms are from the original UNIQUAC (Universal Quasi-Chemical) activity coefficient model (Abrams and Prausnitz, 1975). These are given as
θi
φi
z z + qi ln + (ri - qi) - (ri - 1) xi 2 φi 2 φi z xj (rj - qj) - (rj - 1) (4) xi j 2
(
∑
and
φi )
chloramphenicol in aq phase
Corg, mg/mL
ln γcomb ) ln i
∑j
[
)
θjτij
∑j θjτji) - ∑j θ τ
ln γres i ) qi 1 - ln(
k kj
]
(5)
where z is the coordination number (taken to be 10), ri
(6)
xjqj
and
Table 7. Partitioning of Chloramphenicol between n-Hexane + Ethyl Acetate (92.3 mol % Ethyl Acetate) and Water Phases at 30 °C chloramphenicol in org phase
xiqi
∑j
(7)
xjrj
τij is equal to
( )
τij ) exp -
uij RT
(8)
where uij is an UNIQUAC parameter representing the weak energetic interaction between components i and j. For the contribution due to hydrogen bonding, Fu et al. (1995) have used Wertheim’s theory (Wertheim, 1984; Chapman et al., 1990). In this work, a latticefluid hydrogen-bonding theory (Gupta and Prausnitz, 1996; Gupta and Johnston, 1994; Panayiotou and Sanchez, 1991; Vetysman, 1990; Veytsman and Gupta, 1996) is used because this theory has well-defined H-bonding parameters with a clear physical meaning and which can be measured spectroscopically. In addition, lattice-fluid hydrogen-bonding theory can easily account for complex H-bonding equilibria such as in the antibiotic mixtures presented here.
ln
γhb i
hb µhb i - µpure-i ) RT
(9)
hb where µhb i and µpure-i are the chemical potential contributions due to H bonding in mixture and in pure form, respectively. In the liquid-liquid equilibria calculahb tions, the pure form part (µpure-i ) appears on both sides of eq 1 and cancels out; hence, this term is of no computational significance here, and it is dropped. The contribution from H bonding in the mixture is
ln
γhb i
) ri
∑k ∑l νkl - ∑k
dik
ln
νkd νk0
∑l
ail
νld
ln ν0l
(10)
where k is the type of proton-donor group, l is the type of proton-acceptor group (free electron pairs), dik is the number of k-type proton-donor groups on molecule i, ail is the number of l-type proton-acceptor groups on molecule i, and
νkl ) Nkl/rN νk0 ) Nk0/rN νkd ) Nkd/rN etc. (11) where Nkl is the number of kl H bonds, Nk0 is the number of free (non-H-bonded) donor sites of k type, N0l is the number of free (non-H-bonded) acceptor sites of l type, N is the total number of molecules, Nkd is the total number of k-donor groups in the solution, and r is the average size parameter for the mixture given as
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3957 Table 8. Molecular Parameters and H-Bonding Sites component
molecular structure
chloramphenicol
H H O2N H H
chloroform diethyl ether ethyl acetate n-hexane water
H
NHCOCHCl2
C
C
surface-area parameter (q)
donor sites
acceptor sites
9.9022
7.704
4
7
2.870 3.395 3.479 4.500 0.920
2.410 3.016 3.116 3.856 1.400
1 0 0 0 2
0 2 4 0 2
CH2OH
OH H
CHCl3 (C2H5)2O CH3COOC2H5 CH3(CH2)4CH3 H2O
r)
∑i rixi
(12)
The number of kl H bonds are calculated from the H-bonding equilibrium equations
νkl/νk0ν0l ) F˜ exp(-G°kl/RT) for all (k,l)
(13)
where F˜ is the reduced density of the mixture, and G°kl is the standard free energy of H bonding between donor k and acceptor l sites. Calculations The molecular size and shape parameters r and q are obtained from UNIFAC, a group contribution approach (Fredenslund et al., 1977). These parameters are given in Table 8. The numbers of H-bonding donor and acceptor sites on each molecule are also listed in Table 8. In this work, for simplicity, the values of the uij parameters are set equal to zero, assuming that the residual contribution is negligible as compared to the H-bonding contribution. For chloramphenicol molecule, all H-bond donor sites are assumed to be identical. The same is assumed for the acceptor sites. The assumption is needed in order to reduce the number of H-bonding parameters needed. The chloramphenicol-chloramphenicol H bonding, i.e., self-association, is negligible due to the low concentration. Equations 10 and 13 are rewritten here for the binary and ternary systems. Chloramphenicol + Water Mixture. The number of H bonds between various donor and acceptor sitess water-chloramphenicol (w-cm), water-water (w-w), and chloramphenicol-water (cm-w)sare calculated from the following three simultaneous equations:
rνw-w ) (2xw - rνw-w - rνw-cm) ×
(
)
ln γhb cm ) rcm(νw-w + νcm-w + νw-cm) 4xcm 7xcm 4 ln - 7 ln (17) 4xcm - rνcm-w 7xcm - rνw-cm Chloramphenicol + Chloroform Mixture. There is only one kind of H bonding in the system, chloroformchloramphenicol (c-cm), because the chloroform molecule has only a proton donor site. For this case,
(
rνw-cm ) (2xw - rνw-w - rνw-cm) ×
)
-G°c-cm F˜ rνc-cm ) (xc - rνc-cm)(7xcm - rνc-cm) exp r RT (18) and
ln γhb cm ) rcmνc-cm - 7 ln
7xcm 7xcm - rνc-cm
(19)
Chloramphenicol + Diethyl Ether Mixture. In this case also there is only one kind of hydrogen bonding present, i.e., chloramphenicol-diethyl ether (cm-e), since diethyl ether has only proton-acceptor sites:
(
)
-G°cm-e F˜ rνcm-e ) (4xcm - rνcm-e)(2xe - rνcm-e) exp r RT (20) and
ln γhb cm ) rcmνcm-e - 4 ln
4xcm 4xcm - rνcm-e
(21)
Chloramphenicol + Ethyl Acetate Mixture. Similar to the diethyl ether case, here also only one kind of H bonding is present, i.e., chloramphenicol-ethyl acetate (cm-ea). For this case,
rνcm-ea ) (4xcm - rνcm-ea) ×
(
)
-G°cm-ea F˜ (4xea - rνcm-ea) exp (22) r RT
-G°w-w F˜ (2xw - rνw-w - rνcm-w) exp (14) r RT and
(
)
-G°w-cm F˜ (7xcm - rνw-cm) exp (15) r RT rνcm-w ) (4xcm - rνcm-w) ×
no. of H-bond
vol parameter (r)
(
)
-G°cm-w F˜ (2xw - rνw-w - rνcm-w) exp (16) r RT The H-bonding contribution to the activity coefficient of chloramphenicol is
ln γhb cm ) rcmνcm-ea - 4 ln
4xcm 4xcm - rνcm-ea
(23)
The chloramphenicol + n-hexane mixture does not have any H bonds due to the absence of H-bonding sites on n-hexane. Values of G° are obtained by fitting the UNIQUACHB model to the experimental data in Tables 1-4 with the assumption that G°cm-i ) G°i-cm. For water-water H bonding, a literature value of -10.467 kJ/mol at 30
3958 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 9. Free Energy of Hydrogen Bonding type of H bonding (donor-acceptor or acceptor-donor)
free energy of H bonding (G°) at 30 °C, kJ/mol
water-water chloramphenicol-water chloroform-chloramphenicol chloramphenicol-diethyl ether chloramphenicol-ethyl acetate
-10.467 -14.542 -3.023 -6.445 -6.244
Figure 1. Chloramphenicol partitioning between aqueous and organic phases at 30 °C.
Figure 2. Chloramphenicol partitioning between mixed ethyl acetate + n-hexane phase and aqueous phase at 30 °C. Points are new data, and lines are UNIQUAC-HB calculations. For mixedsolvent cases, lines are theoretical predictions without any adjustable parameter.
°C is used (Gupta et al., 1992). The obtained H-bonding free-energy parameters are listed in Table 9. A fixed reduced density (F˜ ) of 0.9 is used for all calculations here because of low temperature. Calculations are in a good agreement with the experiential data, as shown in Figure 1. Using the parameters obtained from Figure 1, predictions are made for the liquid-liquid phase equilibria for the chloramphenicol + water/ chloramphenicol + ethyl acetate + nhexane system. The predicted phase equilibria are compared with the ternary data in Figure 2. A good overall agreement is obtained between the predictions and experiment, given that there are no adjustable parameters used. The predictions in the middle range of ethyl acetate concentrations show some deviation
from the data. A possible explanation for the deviation may be the residual interactions among hexane, ethyl acetate, and chloramphenicol molecules, which are neglected here in comparison to hydrogen-bonding interactions. Conclusion New experimental data are obtained for chloramphenicol partitioning between organic and aqueous phases, for both pure organic solvent and mixed-organicsolvent cases. It appears that the H bonding plays an important role in the phase behavior of chloramphenicol. Partitioning increases with the increasing H-bonding tendency of the organic solvent in the order n-hexane < chloroform < diethyl ether < ethyl acetate. A new activity coefficient model, UNIQUAC-HB, is proposed that includes H-bonding interaction. The model can accurately represent the observed phase behavior. The predicted phase equilibria for the mixed-organic-phase system is in a good agreement with the experimental data, without any adjustable parameters. The free energy of H-bonding parameters are obtained. The model can be used in the design of a bioseparation unit and in drug design to predict the drug activity. Literature Cited Abrams, D. S.; Prausnitz, J. M. Statitical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partially or completely Miscible Systems. AIChE J. 1975, 21, 116-128. Andrew, P. J.; Weiss, P. J. Solubility of Antibiotics in TwentyFour Solvents. Antibiot. Chemotherapy 1959, 9, 277-279. Bartels, C. R.; Kleiman, G.; Korzun, J. N.; Irish, D. B. A Novel Ion Exchange Method for Isolation of Streptomycin. Chem. Eng. Prog. 1958, 54, 49-51. Belter, P. A.; Cussler, E. L.; Hu, W.-S. Bioseparations. Downstream Processing for Biotechnology; Wiley-Interscience: New York, 1988. Bogardus, J. B.; Palepu, N. R. Int. J. Pharm. 1979, 4, 159-170. Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. New Reference Equation of State for Associating Liquids. Ind. Eng. Chem. Res. 1990, 29, 1709. Chaubal, M. V.; Pyne, G. F.; Reynolds, C. H.; Albright, R. L. Equilibria for the Adsorption of Antibiotics onto Neutral Polymeric Sorbents: Experimental and Modeling Studies. Biotechnol. Bioeng. 1995, 47, 215-226. Chen, C. C.; Zhu, Y.; Evans, L. B. Phase Partitioning of Biomolecules of Amino Acids. Biotechnol. Prog. 1989, 5, 111-118. Davis, S. S.; Higuchi, T.; Rytting, J. H. In Advances in Pharmaceutical Sciences; Bean, H. S., Beckett, A. H., Carless, J. E., Eds.; Academic: London, 1974. Evans, L. B. Bioprocess Simulation: A New tool for Process Development. Bio/Technology 1988, 6, 200-203. Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria using UNIFAC; Elsevier: New York, 1977; pp 3942. Fu, Y.-H.; Sandler, S. I.; Orbey, H. Modified UNIQUAC Model That Includes Hydrogen Bonding. Ind. Eng. Chem. Res. 1995, 34, 4351-4363. Gupta, R. B.; Heidemann, R. A., Solubility Models for Amino-Acids and Antibiotics. AIChE J. 1990, 36, 333-341. Gupta, R. B.; Johnston, K. P. Hydrogen Bonding Lattice Fluid Model with a Local Segment Density. Fluid Phase Equilib. 1994, 99, 135-151. Gupta, R. B.; Prausnitz, J. M. Vapor-Liquid Equilibria for Solvent-Polymer Systems from a Perturbed Hard-SphereChain Equation of State. Ind. Eng. Chem. Res. 1996, 35, 12251230. Gupta, R. B.; Panayiotou, C. G.; Sanchez, I. C.; Johnston, K. P. Theory of Hydrogen Bonding in Supercritical Fluids. AIChE J. 1992, 38, 1243-1253. Hu, Z.; Gulari, E. Extraction of Aminoglycoside Antibiotics with Reverse Micelles. J. Chem. Tech. Biotechnol. 1996, 65, 45-48.
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Received for review February 19, 1997 Revised manuscript received May 16, 1997 Accepted May 22, 1997X IE970160S
X Abstract published in Advance ACS Abstracts, August 1, 1997.
