Solubilities and Partition Coefficients of Semi-Synthetic Antibiotics in

398

Ind. Eng. Chem. Res. 2001, 40, 398-406

Solubilities and Partition Coefficients of Semi-Synthetic Antibiotics in Water + 1-Butanol Systems E. S. J. Rudolph, M. Zomerdijk, M. Ottens, and L. A. M. van der Wielen* Kluyver Laboratory for Biotechnology, Julianalaan 67, 2628 BC Delft, The Netherlands

In this contribution, experimental data are presented on the solubilities and partition coefficients of two semi-synthetic antibiotics (amoxicillin, ampicillin) and their precursors (D-phenylglycine, D-(p-hydroxy)phenylglycine, 6-aminopenicillanic acid) in water + 1-butanol mixtures at a constant temperature of 298 K. In the aqueous phase, the solubility of amoxicillin and ampicillin increases with increasing butanol concentration. For the other components, the solubility decreases. In the organic phase, the solubility of all components is less than that in the aqueous phase. The partition coefficients are approximately constant for all components and less than unity, indicating the higher solubility in the aqueous phase. No influence of the solutes on the phase behavior of the solvent system is detected. The phase behavior is described with the gex model, as suggested by Gude et al. (Gude, M. T.; Meeuwissen, H. H. J.; Van der Wielen, L. A. M.; Luyben, K. Ch. A. M. Ind. Eng. Chem. Res. 1996, 35, 4700. Gude, M. T.; Van der Wielen, L. A. M.; Luyben, K. Ch. A. M. Fluid Phase Equilib. 1996, 116, 110), in its original and in a modified version. This model, based on an excess solubility approach, contains a single adjustable interaction parameter that correlates with the hydrophobicity of the solute. The description by the original model is reasonable but cannot reproduce the phase behavior in the aqueous phase of the systems containing amoxicillin and ampicillin. The modified version of the model gives a better representation of the experimentally found phase behavior. Unfortunately, neither model describes solubilities and partitioning simultaneously in a quantitatively correct fashion. Introduction The development of novel processes for the production of semi-synthetic β-lactam antibiotics in aqueous environments requires a sound knowledge of the phase behavior of these systems. Thermodynamic models should support this optimization procedure. However, both the complexity of biomolecules because of their multiple functional groups and the crucial role of water make the standard available thermodynamic models unattractive for the computation of phase behavior. Therefore, new thermodynamic models for the description of the phase behavior of systems containing biomolecules are required. To verify a thermodynamic model, reliable experimental phase equilibrium data are necessary, such as solubilities in mixed- and singlesolvent systems as well as partition coefficients. For the former, n-alcohols are commonly used as antisolvents. In recent years, several research groups investigated the phase behavior of systems containing amino acids or proteins. Amino acids have especially been used because the influence of the increasing complexity of the biomolecule is easily investigated by varying the functional side-chains of the amino acids.1,2 However, the phase behavior in mixed-solvent systems has hardly been studied.1-4 In this work, the solubilities and partition coefficients of semi-synthetic antibiotics and their precursors in mixed-solvent systems have been investigated. Semisynthetic β-lactam antibiotics are more complex than amino acids because of their β-lactam nucleus, whereas * Author to whom correspondence should be addressed. E-mail: [email protected]. Fax: +31 (0)15 278 2355.

their functional side chains are comparable to the functional side chains of the amino acids. It is expected that the phase behavior of systems containing a homologous series of these antibiotics can be correlated with the phase behavior of systems containing amino acids. Therefore, the thermodynamic models describing the phase behavior of amino acid systems might be applied and possibly extended to the description of systems containing semi-synthetic antibiotics. Theory Thermodynamic models developed for the description of the phase behavior of amino acids5-8 give good results when applied to single-solvent systems. The solvent is predominantly water. However, for the description of the phase behavior in mixed-solvent systems, a Born correction term has to be added. Still, the phase equilibrium computation results are unsatisfying.2,9 Orella and Kirwan,2 as well as Gude et al.,3,4 used an excess solubility approach instead of a Born correction term, resulting in an improved representation of the experimentally observed phase behavior. The excess solubility takes the effect of the mixing of the solvent components on the solubility of the solute in the mixture into account. A similar approach was applied for the correlation of the Henry coefficients of hydrocarbon gases in water + alcohol mixed-solvent systems.10,11 The application of this approach for systems containing amino acids is reasonable because the excess solubility of amino acids in mixed alcohol + water systems shows behavior similar to that of the hydrocarbon gases in the same solvent systems.2 The excess solubility xEi in an N-component solvent mixture is defined as follows:10,11

10.1021/ie000089h CCC: $20.00 © 2001 American Chemical Society Published on Web 12/06/2000

Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001 399 N

ln

xEi

≡ ln

xsat i

-

(x′j ln ∑ j)1

sat xi,j )

Therefore, ln xEi in the aqueous phase is approximately zero, and one obtains for the partition coefficient N

sat where xsat is the solubility in the solvent mixture, xi,j i the solubility in the pure solvent j, and x′j is the solutefree solvent composition. Incorporating the standard thermodynamic equilibrium conditions between a solid and a liquid phase, the expression for the excess solubility becomes

ln xEi ) -ln γ∞i +

N

N

∞ /,sat (x′j ln γi,j ) - ln γ/,sat + ∑(x′j ln γi,j ) ∑ i j)1 j)1

∞ are the symmetric activity coefficients at γ∞i and γi,j infinite dilution of the solute in the solvent mixture and /,sat and γi,j are in the pure solvent j respectively. γ/,sat i the unsymmetrically defined activity coefficients of the solute in the solvent mixture and in the pure solvent j, respectively. For amino acids, activity coefficients and solubilities in water have been investigated experimentally. The solubilities are low, and the activity coefficients are commonly close to their values at infinite dilution.12 However, the activity coefficients in organic solvents and mixed-solvent systems containing organic solvents are not known. Because the solubilities in organic solvents and also in mixed-solvent systems are lower than those in pure water, the activity coefficients of the solutes in these solvent systems are approximated by unity.3,4 Consequently, the expression for the excess solubility simplifies to

ln

xEi

≈ -ln

γ∞i

N

+

(x′j ln ∑ j)1

ln Ki ) ln

xai

N

)

sat [(x′j ,o - x′j ,a) ln xi,j ]+ ∑ j)1

γ/,sat γ/,sat i i a + ln | - ln |o ln / / E,a xi γi γi xE,o i

The superscript o denotes the organic phase, the superscript a the aqueous phase, and the superscript sat the saturated state. It can further be assumed that the solubility in the aqueous phase is approximately the same as the solubility in pure water as only small amounts of alcohol are dissolved in the aqueous phase.13

sat [(x′j,o - x′j ,a) ln xi,j ] + ln xE,o ∑ i j)1

For the computation of the solubility as well as for that of the partition coefficient, the solubility of the solutes in the pure solvents and the activity coefficients are needed. With the assumptions made above, the latter can be computed with gex models; the first is obtained from experiments. The incorporation of most models does not give satisfying results even though the number of adjustable parameters commonly exceeds three. Gude et al. defined a gex model,3,4 which, when the excess solubility approach is applied, has only one adjustable parameter. It represents the phase behavior of amino acids in mixed-solvent systems quite well. Therefore, this model was chosen for the description of the water + 1-butanol solvent system containing semisynthetic β-lactam antibiotics and their precursors. The original model of Gude et al. consists of two terms, a combinatorial term taking the volume differences of the molecules into account, and a “residual” term considering the interactions between the molecules.

( )

gE gE ) RT RT

comb

+

( ) gE RT

res

The combinatorial term is identical to the UNIQUAC combinatorial term with the surface parameters therein set equal to zero.

( ) gE

∞ γi,j )

For the β-lactam antibiotics and their precursors studied here, the activity coefficients in water, organic solvents, and mixed-solvent systems are not known. However, their solubilities are generally lower than those of amino acids. Therefore, the same assumptions as for amino acids were made, namely, that because of the low solubility, the activity coefficients approach their infinite dilution values. This means that the activity coefficients /,sat and γi,j approach unity. γ/,sat i Additionally, the excess solubility can be used for the computation of partition coefficients. The excess solubilities in the aqueous and the organic phases must be computed along the binodal of the investigated system. The expression for the partition coefficient Ki is

xoi

ln Ki )

comb

Φk

∑k xk ln x

)

RT

k

The residual term contains binary interaction parameters Aij and ternary interaction parameters Cjli.

( ) gE

res

N

)

RT

N

∑ ∑ j)1 l>j

N

[Ajlxjxl(1 - Cjlixi)] +

Ajixjxi ∑ j)1

where j and l are the indices describing the solvent components and i stands for the solute, while the index k represents the solute as well as the solvent. Φk ) xkrk/ ∑xkrk is the effective volume fraction of component k k computed with the help of UNIQUAC volume parameters.14 Applying the excess solubility approach, only the binary solvent-solvent interaction parameters Ajl and the ternary interaction parameter Cjli remain.

∑j

ln xEi ) ln (

ri

(

N

x′jrj) 1

∑j x′jrj

x′j ln rj + ∑ j)1 N

-

)

x′j

∑ j)1 r

j

N

+

N

∑ ∑[Ajlx′jx′l(1 + Cjli)] j)1 l>j

The binary interaction parameters Ajl are obtained from fits of the model to experimental phase equilibrium data of the binary solvent systems. Therefore, if experimental phase equilibrium data of the solvent systems exist, the only remaining adjustable parameters of the ternary or

400

Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001

Table 1. Supplier and Purity of Components component D-phenylglycine D-(p-hydroxy)phenylglycine

6-APA ampicillin amoxicillin n-butanol water, double-distilled

supplier

purity

DSM DSM DSM DSM DSM Bakker

>98% >99% >98.5% ∼99% 98.9% >99% electrical conductivity less than 10-6 S cm-1

multicomponent system in the Gude model are the ternary interaction parameters Cjli. For amino acids in a binary-solvent system, it was found that the ternary interaction parameter Cjli can be correlated quite well with the hydrophobicity of the amino acid.3,4 The model of Gude et al. was modified by incorporating a surface contribution into the combinatorial term. This contribution takes the active surface of the molecules into account, so that the shape and the size differences of the molecules are also considered, which becomes more and more important with increasing size and complexity of the molecule. Consequently, the combinatorial term is the same as the combinatorial term of the UNIQUAC model

( ) gE

comb

RT

N

)

Φk

∑ xk ln x k)1

k

+

z

N

Θk

∑ qkxk ln Φ 2 k)1

k

where z is the coordination number, which is commonly set equal to 10, and Θk ) xkqk/∑xkqk is the effective k surface fraction of component k, which is computed using UNIQUAC surface parameters.14 Experiments The solubilities and partition coefficients of D-phenylglycine (PG), D-(p-hydroxy)phenylglycine (HPG), 6-aminopenicillanic acid (APA), amoxicillin (amox), and ampicillin (ampi) in water + 1-butanol mixtures were determined at a constant temperature of 298 K. The stated purity and the suppliers of the chemicals are listed in Table 1. The pH was adjusted by addition of either 0.1 M KOH or 0.5 M H2SO4 during the solubility experiments of the systems containing APA, amoxicillin, and ampicillin. However, the pH was not further adjusted during the partition coefficient determinations. Consequently, each solution had a pH close to the isoelectrical point of the studied component, and therefore, this component was mainly present as zwitterion.1 For the solubility as well as for the partition coefficient measurements, the samples were prepared gravimetrically using a Mettler-Toledo balance. Glass flasks with screw caps were immersed in a thermostated water bath controlled by a Julabo U3 Thermostate. The bath temperature was determined by a Unisystem U1410 Pt100 temperature meter. The samples were stirred with the help of plastic-covered magnetic stirrers agitated by magnetic coupling. All samples were stirred for at least 4 h. After equilibration, the mixtures were allowed to settle before sampling was performed. The samples were withdrawn with the help of syringes with attached 0.2-µm filters to avoid entrainment of the solids. The concentrations of the solutes in the sample were analyzed with the help of HPLC. The concentrations of the butanol in the organic and aqueous phase were determined with the help of gas chromatography.

Additionally, the densities of the samples were determined with a Paar density meter DMA 48. For the solubility experiments, various homogeneous mixtures of 1-butanol and water were prepared gravimetrically to cover the entire range of miscibility of the solvent system. The solute was added in excess to ensure the determination of the solubility. For the determination of the partition coefficients, 80mL glass flasks with screw caps and two additional side ports with septa were used. Mixtures of water and 1-butanol in the region of immiscibility were prepared in such a way that the volumes of the two coexisting phases allowed for sampling through the two side ports. Various weighed amounts of solute were added to the samples not exceeding the solubility. For the analysis of the solute concentration by HPLC, a Waters system consisting of a Zorbax SB-C18 4.6 mm × 7.5 cm 3.5-µm column thermostated at a temperature of 33 °C, a Waters 484 variable UV detector set at 230 nm, a 712 Wisp 10-µL injector, and a Waters 510 pump with a flow of 1 mL min-1 were used. Prior to the analysis, the samples were diluted with buffer. For PG, HPG, and APA the buffer was composed of 8 mM tetrabutylammoniumbromide, 10 mM Na2HPO4, and 5% v/v acetonitril. For amoxicillin and ampicillin, it consisted of 10 or 20% v/v methanol, respectively, and 70 mM Na2HPO4. With H3PO4, it was brought to a pH of 3. The reproducibility of the concentrations of the solvent was within 2%. Because of the very low solubilities of the solutes in the organic phase and in pure 1-butanol, the samples of well-known weight were freeze-dried prior to analysis with HPLC. Because of this more complicated preparation of the sample for the analysis, the reproducibility lies within 5%. The amounts of 1-butanol in the aqueous and organic phases were determined by gas chromatography. A Chrompack CP 9001 (Chrompack, Netherlands) gas chromatograph with an HP-Innowax (Hewlett-Packard) column in combination with a flame ionization detector was used. 3-methyl-1-butanol served as the internal standard. The amounts of water were calculated from mass balance. The accuracy of the solvent composition determination is estimated to be 0.3 mol %. Results and Discussion In Tables 2 and 3, the results of the solubility and partition coefficient experiments are listed. In Figure 1, the relative solubility, i.e., the ratio of the solubility in the mixed-solvent system to the solubility in pure water at the same temperature and pressure, as a function of the solvent composition is depicted. For all investigated systems, a comparable phase behavior could be observed. However, for amoxicillin and ampicillin in the water-rich solvent composition range, the relative solubility increases with increasing butanol concentration in the solvent mixture. For HPG, the relative solubility stays approximately constant at unity before it decreases in the butanol-rich solvent mixture. For the other components (PG, APA), the relative solubility is less than unity over the entire solvent mixture composition range. Additionally, the solubility in 1-butanol increases from PG to HPG to APA to ampicillin to amoxicillin. Computing the hydrophobicity of the solutes according to Nozaki et al.,15 it can be concluded that the relative solubility changes with the

Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001 401 Table 2. Solubilities of PG, HPG, 6-APA, Amoxicillin, and Ampicillin (i) in Miscible Water (1) + 1-Butanol (2) Mixtures at 298 K (a) PG and HPG phase

x′1

F [g/L]

xi

ci [mol/L]

phase

x′1

D-phenylglycine

organic

aqueous

0 0.16372 0.2907 0.3931 0.4497 0.4857 0.4680 0.1630 0.2885 0.3960 0.4727 0.5340 0.5348 0.9813 0.9802 0.9814 0.9859 0.9911 0.9954 0.9826 0.9827 0.9819 0.9862 0.9910 0.9952 1

1.84e-6 1.75e-5 6.03e-5 1.13e-4 1.50e-4 2.10e-4 2.07e-4 1.51e-5 6.39e-5 1.13e-4 1.77e-4 2.02e-4 2.00e-4 4.88e-4 5.02e-4 4.91e-4 4.99e-4 5.14e-4 5.09e-4 4.81e-4 4.86e-4 4.95e-4 5.09e-4 5.22e-4 5.31e-4 5.49e-4

F [g/L]

xi

ci [mol/L]

D-(hydroxy)phenylglycine

805.8 815.1 823.7 831.7 837.6 844.6 844.7 815.0 823.4 831.7 840.1 844.5 844.5 987.4 987.3 987.3 990.0 993.0 995.5 987.4 987.3 987.9 990.2 992.9 995.3 998.4

2.00e-5 2.20e-4 8.60e-4 1.81e-3 2.58e-3 3.79e-3 3.66e-3 1.90e-4 9.10e-4 1.81e-3 3.13e-3 3.86e-3 3.83e-3 2.519e-2 2.583e-2 2.540e-2 2.619e-2 2.749e-2 2.768e-2 2.497e-2 2.522e-2 2.562e-2 2.675e-2 2.788e-2 2.883e-2 3.034e-2

organic

aqueous

0 0.1509 0.2907 0.3895 0.4740 0.1636 0.2897 0.3912 0.4740 0.9817 0.9866 0.9911 0.9953 0.9808 0.9860 0.9906 0.9956 1

1.43e-5 3.79e-5 1.07e-4 2.04e-4 3.38e-4 4.54e-5 1.36e-4 2.47e-4 3.34e-4 2.034e-3 2.022e-3 2.096e-3 2.096e-3 1.982e-3 1.971e-3 2.062e-3 2.004e-3 2.115e-3

806.0 814.2 823.4 831.5 840.0 815.2 823.7 830.9 840.5 992.7 995.4 998.1 1000.9 992.8 995.2 998.1 1001.2 1003.9

1.56e-4 4.71e-4 1.52e-3 3.25e-3 5.98e-3 5.71e-4 1.935e-3 3.945e-3 5.910e-3 0.1045 0.1056 0.112 0.1129 0.1016 0.1028 0.1093 0.1082 0.1159

(b) 6-APA, amoxicillin, and ampicillin at different pHs phase aqueous

organic aqueous

pH

x′1

3.4 4.74 5.37 5.99 6.69 7.12 3.48 4.74 5.38 5.99 6.65 7.11 3.72 3.88 4.06 4.29 5.55 3.46 3.59 4.7 4.91 5.41 5.54 5.98 6.12 6.51 6.76 7.06 7.15 IEP

1 1 1 1 1 1 0.9949 0.9948 0.9949 0.9950 0.9949 0.9948 0.9905 0.9905 0.9896 0.9896 0.9897 0.9817 0.9810 0.9816 0.9812 0.9818 0.9811 0.9812 0.9816 0.9821 0.9819 0.9832 0.9821 0

3.51 4.53 4.75 5.28 5.97 6.56 7.13 3.59 4.63 4.81 5.27 5.93 6.47 7.04

1 1 1 1 1 1 1 0.9870 0.9872 0.9872 0.9872 0.9871 0.9870 0.9874

xi 6-APA 1.970e-4 3.590e-4 6.980e-4 1.477e-3 3.6584e-3 6.878e-3 1.840e-4 3.290e-4 7.080e-4 1.568e-3 3.720e-3 7.790e-3 1.840e-4 2.000e-4 2.130e-4 2.780e-4 9.810e-4 1.66e-4 1.18e-4 2.94e-4 3.28e-4 7.34e-4 6.93e-4 1.659e-3 1.698e-3 3.250e-3 4.110e-3 7.263e-3 8.841e-3 1.11e-5 ampicillin 2.93e-4 2.68e-4 2.71e-4 2.70e-4 2.89e-4 3.11e-4 4.42e-4 3.09e-4 3.00e-4 2.98e-4 3.01e-4 3.02e-4 3.36e-4 4.80e-4

F [g/l]

ci [mol/l]

998.0 998.8 1001.1 1006.4 1018.8 1040.8 994.7 995.7 997.8 1002.7 1015.3 1038.9 992.1 992.2 1000.6 1001.0 1005.1 987.4 986.9 988.4 988.0 990.6 990.4 995.4 996.1 1004.0 1010.2 1034.6 1032.5 806.1

1.086e-2 1.98e-2 3.855e-2 8.18e-2 1.988e-1 3.848e-1 9.94e-3 1.776e-2 3.825e-2 8.48e-2 2.016e-1 4.24e-1 9.75e-3 1.059e-2 1.147e-2 1.493e-2 5.282e-2 8.48e-3 9.218e-3 1.504e-2 1.676e-2 3.76e-2 3.54e-2 8.48e-2 8.70e-2 1.668e-1 2.116e-1 3.816e-1 4.544e-1 1.209e-4

998.9 998.6 998.6 998.7 998.7 999.0 1001.0 991.4 991.2 991.1 991.2 991.2 991.4 999.28

1.616e-2 1.482e-2 1.496e-2 1.491e-2 1.594e-2 1.714e-2 2.436e-2 1.626e-2 1.583e-2 1.569e-2 1.583e-2 1.589e-2 1.770e-2 2.525e-2

phase aqueous

organic aqueous

organic

pH 3.82 4.68 4.90 5.38 5.89 6.44 7.06 3.90 4.79 4.96 5.34 5.81 6.92 6.35 IEP 3.42 4.65 5.06 6.09 6.50 7.26 7.46 3.43 4.70 4.92 6.38 6.04 7.10 7.55 3.31 4.78 5.27 6.04 6.52 7.12 7.68 3.40 4.77 5.14 6.01 6.50 7.04 7.59 IEP

x′1

xi

ampicillin (cont.) 0.9946 2.93e-4 0.9946 2.97e-4 0.9946 2.85e-4 0.9946 2.82e-4 0.9947 2.88e-4 0.9947 3.15e-4 0.9947 4.57e-4 0.9803 3.29e-4 0.9806 3.12e-4 0.9806 3.11e-4 0.09806 3.00e-4 0.9805 3.10e-4 0.9807 4.54e-4 0.9807 3.41e-4 0 1.72e-5 amoxicillin 1 1.26e-4 1 1.09e-4 1 1.07e-4 1 1.10e-4 1 1.17e-4 1 1.74e-4 1 2.23e-4 0.9871 1.51e-4 0.9872 1.29e-4 0.9872 1.27e-4 0.9872 1.38e-4 0.9878 1.29e-4 0.9875 1.92e-4 0.9874 3.13e-4 0.9949 1.39e-4 0.9949 1.17e-4 0.9950 1.13e-4 0.9950 1.14e-4 0.9949 1.23e-4 0.9949 1.61e-4 0.9951 2.88e-4 0.9815 1.74e-3 0.9818 1.36e-4 0.9816 1.35e-4 0.9817 1.36e-4 0.9819 1.46e-4 0.9813 1.86e-4 0.9821 3.335e-4 0 1.21e-5

F [g/l]

ci [mol/l]

995.1 995.3 995.4 995.5 995.5 995.8 996.9 988.7 988.5 988.3 988.5 998.5 989.9 988.8 815.9

1.585e-2 1.605e-2 1.541e-2 1.527e-2 1.559e-2 1.704e-2 2.468e-2 1.694e-2 1.609e-2 1.603e-2 1.545e-2 1.598e-2 2.339e-2 1.755e-2 1.901e-4

997.9 997.8 997.8 997.8 997.9 998.4 998.8 990.6 990.3 990.4 990.5 990.5 990.9 992.1 994.9 994.7 994.7 994.8 994.8 995.0 996.3 987.8 987.6 987.5 987.6 987.8 988.2 989.4 815.2

6.965e-3 6.043e-3 5.923e-4 6.063e-4 6.464e-4 9.595e-4 1.231e-2 7.955e-3 6.786e-3 6.714e-3 7.269e-3 6.845e-3 1.011e-2 1.649e-2 7.518e-3 6.354e-3 6.112e-3 6.212e-3 6.675e-3 8.724e-3 1.564e-2 8.99e-3 7.058e-3 6.987e-3 7.027e-3 7.562e-3 9.613e-2 1.731e-2 1.329e-4

402


Table 3. Partitioning of Solutes Investigated in This Work (i) in Water (1) + 1-Butanol (2) Mixtures at 298 K aqueous phase x′1

xi

F [g/l]

organic phase ci [mol/l]

x′1

xi

partition coefficients

F [g/l]

ci [mol/l]

Kci

Ki

844.6 844.5 844.4 844.7 844.5 844.5 844.5 844.5 844.5 844.6

2.23e-3 2.45e-3 2.56e-3 3.14e-3 3.07e-3 3.64e-3 3.70e-3 3.72e-3 3.59e-3 3.79e-3

0.1527 0.1522 0.1561 0.1602 0.1498 0.1597 0.1581 0.1537 0.1465 0.1504

0.4326 0.4295 0.4385 0.4538 0.4161 0.4469 0.4437 0.4286 0.4135 0.4303

D-phenylglycine

0.9811 0.9812 0.9809 0.9810 0.9809 0.9810 0.9812 0.9810 0.9812 0.9812

2.82e-4 3.12e-4 3.17e-4 3.79e-4 3.98e-4 4.43e-4 4.53e-4 4.69e-4 4.74e-4 4.88e-4

986.6 986.9 986.9 987.0 986.9 986.9 987.3 987.0 987.2 987.4

1.46e-2 1.61e-2 1.64e-2 1.96e-2 2.05e-2 2.28e-2 2.34e-2 2.42e-2 2.45e-2 2.52e-2

0.4961 0.5007 0.4995 0.4932 0.5060 0.5031 0.5025 0.5056 0.5003 0.4848

1.22e-4 1.34e-4 1.39e-4 1.72e-4 1.66e-4 1.98e-4 2.01e-4 2.01e-4 1.96e-4 2.10e-4

0.9810 0.9810 0.9808 0.9811 0.9812 0.9809 0.9812 0.9810 0.9811 0.9810

5.49e-4 5.58e-4 7.70e-4 9.17e-4 1.28e-3 1.32e-3 1.50e-3 1.67e-3 1.73e-3 1.93e-3

987.1 987.5 988.1 988.7 989.8 989.7 990.5 990.4 991.1 992.1

2.83e-2 2.88e-2 3.97e-2 4.73e-2 6.60e-2 6.79e-2 7.70e-2 8.55e-2 8.85e-2 9.88e-2

0.5049 0.4930 0.5065 0.4995 0.4946 0.5052 0.4970 0.5047 0.5025 0.5089

1.18e-4 1.17e-4 1.71e-4 1.97e-4 2.60e-4 2.69e-4 2.91e-4 3.50e-4 3.51e-4 3.91e-4

844.3 844.4 845.9 844.4 844.5 844.5 844.6 844.5 845.0 844.5

2.19e-3 2.13e-3 3.17e-3 3.61e-3 4.74e-3 4.96e-3 5.33e-3 6.46e-3 6.46e-3 7.25e-3

0.0774 0.074 0.0799 0.0763 0.0718 0.0731 0.0692 0.0756 0.0730 0.0734

0.2149 0.2097 0.2221 0.2148 0.2031 0.2038 0.1940 0.2096 0.2029 0.2026

0.9825 0.9814 0.9824 0.9822 0.9814 0.9813 0.9822 0.9824 0.9824 0.9822 0.9823 0.9814 0.9814 0.9822 0.9823


986.2 986.2 986.4 986.4 986.5 986.5 986.5 986.6 986.6 986.7 986.7 986.7 987.0 987.0 987.0


0.4965 0.5168 0.5003 0.5089 0.5172 0.5202 0.5081 0.5050 0.4985 0.5019 0.5100 0.5250 0.5207 0.5111 0.5072

6-APA 1.03e-5 1.44e-5 1.36e-5 1.86e-5 1.82e-5 2.48e-5 2.44e-5 2.49e-5 2.82e-5 3.30e-5 3.54e-5 3.71e-5 4.37e-5 5.05e-5 5.14e-5

843.5 843.8 843.3 843.3 843.8 843.8 843.6 843.4 843.5 843.4 843.6 843.8 843.8 843.7 843.7


0.1199 0.1281 0.1074 0.1154 0.1039 0.1240 0.1184 0.1165 0.1189 0.1192 0.1246 0.1299 0.1086 0.1193 0.1192

0.2917 0.3038 0.2599 0.2763 0.2456 0.2914 0.2836 0.2804 0.2884 0.2876 0.2982 0.3041 0.2556 0.2845 0.2855

0.9807 0.9808 0.9812 0.9807 0.9805 0.9805 0.9806 0.9808

3.17e-5 5.40e-5 5.95e-5 8.16e-5 1.29e-4 1.30e-4 1.73e-4 2.01e-4

986.4 986.5 986.7 986.5 986.7 986.4 987.1 987.2

1.64e-3 2.79e-3 3.08e-3 4.21e-3 6.65e-3 6.71e-3 8.91e-3 1.04e-2

0.4636 0.4618 0.4579 0.4711 0.4663 0.4637 0.4688 0.4712

ampicillin 1.18e-5 2.24e-5 2.58e-5 3.17e-5 4.95e-5 5.16e-5 7.06e-5 7.87e-5

844.2 844.2 844.3 843.8 844.4 844.2 844.5 844.5

2.08e-4 3.93e-4 4.50e-4 5.61e-4 8.73e-4 9.07e-4 1.25e-3 1.40e-3

0.1268 0.1409 0.1461 0.1333 0.1313 0.1352 0.1403 0.1346

0.3722 0.4148 0.4336 0.3885 0.3837 0.3969 0.4081 0.3915

0.9812 0.9803 0.9807 0.9804 0.9805 0.9799 0.9806 0.9812

4.18e-5 5.26e-5 5.74e-5 7.94e-5 7.97e-5 8.64e-5 8.68e-5 1.35e-4

986.4 986.4 986.4 986.6 986.7 986.7 986.7 987.0

2.16e-3 2.71e-3 2.97e-3 4.10e-3 4.11e-3 4.45e-3 4.48e-3 6.95e-3

0.4253 0.4253 0.3494 0.3984 0.3644 0.4304 0.4830 0.4549

amoxicillin 7.75e-6 1.27e-5 1.34e-5 2.02e-5 1.96e-5 2.01e-5 1.62e-5 2.91e-5

844.5 844.2 844.3 844.2 844.2 844.3 844.2 844.2

1.30e-4 2.14e-4 2.08e-4 3.29e-4 3.08e-4 3.41e-4 2.90e-4 5.06e-4

0.0602 0.0789 0.0700 0.0802 0.749 0.0766 0.0647 0.0728

0.1854 0.2414 0.2334 0.2544 0.2459 0.2326 0.1866 0.2156

D-(p-hydroxy)phenylglycine

hydrophobicity of the solute. With exception of APA, this is also valid in the water-rich solvent mixture composition range. The pH has a strong influence on the solubilities of amoxicillin, ampicillin, and APA in water. Therefore, the influence of the “pH” on the solubility in the mixedsolvent systems has been investigated experimentally. The results are depicted in Figure 2. The pH has the same influence on the solubility in the mixed-solvent system as in pure water. The pH influence on the phase behavior of aqueous systems containing PG or HPG is negligible and was therefore not investigated further. In Figure 3, the partition coefficients of the solutes as a function of the reduced concentration of the solute

in the aqueous phase, i.e., the ratio of the concentration of the dissolved solute in the aqueous phase to its solubility in the aqueous phase, are depicted. In the investigated composition range, the partition coefficients are approximately constant. The solutes predominantly dissolve in the aqueous phase, resulting in partition coefficients smaller than one. According to Gude et al.,3 the partition coefficient is a measure for the saltingout effect of the solute. Amino acids having a decreasing partition coefficient with increasing solute concentration in the system were found to “widen” the miscibility gap of the solvent system (salting-out). An increasing partition coefficient is characteristic for a solute that “closes” the miscibility gap (salting-in). The systems investigated

Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001 403

Figure 1. Experimental relative solubility at 298 K in miscible water + 1-butanol mixtures at the iso-electric points of the solutes. (a) Entire solvent-composition range. (b) Aqueous phase: 9, PG; [, HPG; 2, APA; f, ampicillin; and b, amoxicillin. Lines are drawn to guide the eye. The dashed area displays the region of demixing of the solvent system.

in this work have a partition coefficients that are approximately independent of the solute concentration. This implies that the investigated solutes do not show any salting-in or salting-out effects on the solvent system. From experiments, it can be concluded that the amount of 1-butanol dissolved in the aqueous phase and the amount of water dissolved in the organic phase are constant within the experimental error. Thus, the investigated solutes do not influence the phase behavior of the solvent system. The phase behavior found experimentally at pH values close to the iso-electrical point of the solute was described with the help of the model suggested by Gude et al.3,4 and a modified version of this model. The fact that the phase behavior changes according to the hydrophobicity of the solute, with the exception of APA, supports the idea that the phase behavior can be described with the help of the model of Gude et al. For both models, the binary interaction parameter Aji has been adjusted to experimental binary water-butanol data from the literature;13 the ternary parameters Cjli have been adjusted directly to the experimental data of the ternary systems presented here. In Figure 4, the performance of the original Gude model is documented. The input parameters and adjusted parameters are listed in Table 4. The butanol-rich composition range is described reasonably well (Figure 4a). It should be mentioned that the fits of the systems containing amox,

Figure 2. Experimental solubility at 298 K as a function of pH at different solute-free solvent compositions of 1-butanol (mole fractions): 9, 0; [, 0.05; 2, 0.1; b, 0.18; and ×, 1. (a) APA, (b) ampicillin, and (c) amoxicillin.

Figure 3. Partition coefficients in the partially miscible solvent system at 298 K as a function of the ratio of the concentration of dissolved solute in the aqueous phase to the solubility in the aqueous phase. Lines are drawn to guide the eye. 9, PG; [, HPG; 2, APA; f, ampicillin; and b, amoxicillin.

ampi, and APA can only be compared to two experimental solubility data points, namely, the solubilities in pure butanol and in the organic phase with the highest water content. The water-rich composition range is described poorly. Here, for all components, a relative solubility less than one is computed. Only for PG and APA is the phase behavior nicely reproduced. However, the resulting curves show an influence on the hydro-

404


Figure 4. Representation of the phase behavior with the help of the original Gude model.3,4 (a) Relative solubility, entire solventcomposition range; (b) relative solubility, aqueous phase; (c) partition coefficient; (d) adjusted ternary interaction parameters as a function of the hydrophobicity.15 The symbols display the experimental values, the lines the fit. 9, s, PG; [, - -, HPG; 2, - ‚‚ -, APA; f, - - -, ampicillin; and b, - - ‚, amoxicillin. Table 4. Parameters Used in the Original Model of Gude et al. UNIQUAC parameter solute D-phenylglycine

(PG)

D-(hydroxy)phenylglycine

(HPG) 6-aminopenicillanicacid (6-APA) ampicillin (ampi) amoxicillin (amox)

volume ri

ternary interaction parameter C

hydrophobicity (Tanford)

5.4647 5.8286

2.993 1.368

0.3421 0.3967

5.8121

0.394

0.6376

10.5866 10.9505

2.152 1.784

0.6780 0.7194

solvent

UNIQUAC parameter volume

binary solvent interaction parameter A12

water 1-butanol

0.92 3.9243

3.15

phobicity that is the opposite of what was found experimentally. The hydrophobicity in the organic-rich composition range shows the same influence on the hydrophobicity as was found experimentally. Also, the partition coefficient of the solute in the water-butanol system is only qualitatively correct (Figure 4c). The ternary parameters Cjli resulting from the fits, however, correlate quite well with the hydrophobicities of the solutes investigated in this work and of the amino acids from previous studies3,4 (Figure 4d). In Figure 5, the results of the fits with the modified Gude model are shown. In Table 5, the input parameters and the parameters resulting from the fit are listed. Again, the relative solubility in the organic-rich phase is described well, whereas the relative solubility in the aqueous phase is not as well described (Figure 5a). However, the application of the modified version reproduces the increasing relative solubility in the water-rich

Table 5. Parameters Used in the Modified Model of Gude et al. UNIQUAC parameter

ternary interaction hydrovolume surface parameter phobicity C (Tanford) ri qi

solute

D-phenylglycine (PG) 5.4647 4.268 d-(hydroxy)phenylglycine 5.8286 4.548 (HPG) 6-aminopenicillanicacid 5.8121 4.504 (6-APA) ampicillin (ampi) 10.5866 7.888 amoxicillin (amox) 10.9505 8.168

UNIQUAC parameter

-0.639 -1.038

0.3421 0.3967

-2.306

0.6376

-3.221 -3.6

0.6780 0.7194

solvent

volume ri

surface qi

binary solvent interaction parameter A12

water 1-butanol

0.92 3.9243

1.4 3.668

2.87

range (Figure 5b). Nevertheless, relative solubilities less than one in the aqueous phase, as found for APA and PG, could not be described. Unlike the case of the original Gude model, the fitted curves behave qualitatively in the same way as was observed experimentally. The experimental sequence of the relative solubilities of the different solutes in both phases is reproduced correctly. The representation of the partition coefficient with the ternary interaction parameter fitted to relative solubilities is very poor (Figure 5c). Again, the data could be reproduced qualitatively. The ternary interaction parameters Cjli do not correlate in the same straightforward manner as for the original Gude model (Figure 5d). However, it is striking that, for components that are similar in their configurations, the Cjli values lie on a straight line. These groups are amino acids with an aromatic ring attached (PG, HPG, tyrosine, phenyl-

Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001 405

Figure 5. Representation of the phase behavior with the help of the modified Gude model. (a) Relative solubility, entire solvent-composition range; (b) relative solubility, aqueous phase; (c) partition coefficient; (d) adjusted ternary interaction parameters as function of the hydrophobicity.15 The symbols display the experimental values, the lines the fit. 9, s, PG; [, - -, HPG; 2, - ‚‚ -, APA; f, - - -, ampicillin; and b, - - ‚, amoxicillin

alanine, tryptophane) and solutes containing a β-lactam nucleus. The latter conclusion is quite rough because of the limited amount of data. The ternary interaction parameters in the original Gude model as well as those in the modified version of the model can be adjusted to the experimental partition coefficients, resulting in a good reproduction of the experimental findings. The values of these parameters differ quite strongly from the values obtained from the adjustment to the solubility data only. However, the use of these parameters for the representation of the solubility data does not yield satisfying results. This might imply that the solubility behaviors and the partition coefficients of the systems containing the given solutes are more complicated than those of the systems containing amino acids and, therefore, cannot completely be reproduced as described by Gude et al. However, it remains striking how well the phase behavior of such rather complicated systems could be described with such a simple model. At this point, it should be mentioned that small changes in the values of the interaction parameters Cjli do not have a large impact on the description of the phase behavior. An improved representation of the experimentally observed solubilities might be obtained by adjusting the volumes and the surface parameters of the functional groups. So far, for some of the functional groups that are not listed in the UNIQUAC tables, these parameters have been estimated based on van der Waals volumes.16 This might imply that some deficiency in the model is introduced by the definition of the functional groups. For a better representation of the phase behavior, it might be necessary to redefine the functional groups for these complex molecules. However, this requires a huge amount of experimental data that is not yet available. The improved representation of the phase behavior of

Figure 6. Comparison of the representation of the phase behavior of the system amox + water + 1-butanol applying different gex models. 9, experiments; s Gude, - ‚ - ‚, modified Gude; ‚‚‚ ‚‚‚, UNIQUAC; ‚‚ - ‚‚ -, NRTL.

systems containing bigger molecules by incorporation of surface and volume parameters further supports this idea. Finally, the performance of the applied models was benchmarked versus well-established models such as NRTL and UNIQUAC. For the systems containing amox, ampi or APA, these latter models are such less accurate than the models used in this work. This

406


comparison is depicted in Figure 6 in which the fits describing the phase behavior of the amox system applying the Gude model, the modified Gude model, NRTL, and UNIQUAC are compared. Similar results were obtained for the description of the phase behavior of systems containing ampi or APA.

Literature Cited

Conclusions

(4) Gude, M. T.; Van der Wielen, L. A. M.; Luyben, K. Ch. A. M. Fluid Phase Equilib. 1996, 116, 110.

The work reported here extends the knowledge of the phase behavior of aqueous systems containing biomolecules from systems containing amino acids toward systems containing similarly sized, more complex components, namely, β-lactam antibiotics and their precursors. The phase behavior found experimentally for these systems roughly corresponds to that found for aminoacid-containing systems. However, the evolution of the relative solubilities in the aqueous phase changes with increasing hydrophobicity such that the effect of the dissolved organic solvent is inverted. The hydrophobicity seems to be a good property for correlation purposes or for the crude estimation of the expected phase behavior for systems containing solutes that contain functional side chains similar to those found in natural amino acids. However, for systems containing molecules such as APA, the correlation by just hydrophobicity fails. It was found that a simple thermodynamic model such as the model of Gude et al. or its modified version with only one adjustable parameter can describe the phase behavior of the systems considered here reasonably well. Acknowledgment The authors thank DSM, The Netherlands, for the chemicals and Chemferm and the Dutch Ministry for Economical Affairs for the financial support. E.S.J.R. thanks Cor Ras for the HPLC analysis.

(1) Orella, Ch. J.; Kirwan, D. J. Ind. Eng. Chem. Res. 1991, 30, 1040. (2) Orella, Ch. J.; Kirwan, D. J. Biotechnol. Prog. 1989, 5, 89. (3) Gude, M. T.; Meeuwissen, H. H. J.; Van der Wielen, L. A. M.; Luyben, K. Ch. A. M. Ind. Eng. Chem. Res. 1996, 35, 4700.

(5) Gupta, R. B.; Heidemann, R. A. AIChE J. 1990, 36, 333. (6) Pinho, S. P.; Silva, C. M.; Macedo, E. A. Ind. Eng. Chem. Res. 1994, 33, 1341. (7) Chen, C. C.; Zhu, Y.; Evans, L. B. Biotechnol. Prog. 1989, 5, 1736. (8) Khoshkbarchi, M. K.; Vera, J. H. Ind. Eng. Chem. Res. 1996, 35, 4319. (9) Zerres, H.; Prausnitz, J. M. AIChE J. 1994, 40, 676. (10) O’Connell, J. P.; Prausnitz, J. M. Ind. Eng. Chem. Fundam. 1964, 3, 347. (11) O’Connell, J. P. AIChE J. 1971, 17, 658. (12) Cohn, E. J.; Edsall, J.T. Proteins, Amino Acids and Peptides as Ions and Dipolar Ions; Reinhold Publishing Corp.: New York, 1943. (13) Sørensen, J. M.; Arlt, W. Liquid-Liquid Equilibrium Data Collection; Chemistry Data Series; Dechema: Frankfurt/Main, 1979; Vol. 5. (14) Prausnitz, J. M.; Lichtenthaler, R. N.; De Azevedo, E.G. Molecular Thermodynamics of Fluid Phase Equilibria, 2nd ed.; Prentice Hall Inc.: New York, 1986. (15) Nozaki, Y; Tanford, C. J. Biol. Chem. 1971, 246, 2211. (16) Bondi, A. Physical Properties of Molecular Crystals, Liquids and Glasses; John Wiley & Sons: New York, 1968.

Received for review January 21, 2000 Accepted September 27, 2000 IE000089H

Solubilities and Partition Coefficients of Semi-Synthetic Antibiotics in

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