Ind. Eng. Chem. Res. 2007, 46, 6501-6509
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PROCESS DESIGN AND CONTROL COSMO-RS and UNIFAC in Prediction of Micelle/Water Partition Coefficients Liudmila Mokrushina,*,† Matthias Buggert,†,‡ Irina Smirnova,† Wolfgang Arlt,† and Reinhard Schoma1 cker‡ Chair of Separation Science & Technology, Friedrich-Alexander UniVersity of ErlangensNuremberg, Egerlandstrasse 3, 91058 Erlangen, Germany, and Technische UniVersita¨t Berlin, Fachgruppe Technische Chemie, Strasse des 17. Juni 135, 10623 Berlin, Germany
Partitioning of active agents between polar and nonpolar phases has a key role in the early stage of drug and drug-carrier design in the pharmaceuticals industry, as well as for separation of products in biosynthesis. In the present paper, the group-contribution Universal Quasi-Chemical Functional-Group Activity Coefficient (UNIFAC) and the a priori Conductor-like Screening Model for Real Solvents (COSMO-RS) models are applied to predict micelle/water partition coefficients. The models allow predictions based only on the molecular structure. The practical implementation of the models is examined by studying several homologous series of organic solutes in aqueous solutions of non-ionic (polyethoxy alcohols) and ionic surfactants (sodium dodecyl sulfate (SDS)). Good quantitative agreement with experimental data from the literature has been achieved. Factors that seem to be important in the calculation and to influence the prediction results are discussed. Among these are interfacial contribution and conformation analysis. Compared to UNIFAC, the COSMO-RS method opens up new perspectives, because ionic components, steric isomers, and inorganics can be modeled. Introduction Solubilization of chemicals in micellar solutions is a process that has a wide range of applications. Some examples include detergency, enhancement of the aqueous solubility of hydrophobic drugs, and separation of products in biosynthesis. Partition coefficients of a solute between the micellar and aqueous phases are used to be a measure of solubilization. In the pharmaceuticals industry, knowledge of the partitioning of drug candidates in different media of the human body (often approximated by the n-octanol/water (Kοw) or the micelle/water (Kmw) partition coefficients) is important at the early stage of the drug design process and should be known from measurements or calculations. In the case of biosynthesis, the separation of products from the reaction media is often made by adding surfactants to the system, followed by the separation of the product-containing micellar phase by filtration.1 In this case, proper information on Kmw is essential for choosing the surfactant with the highest selectivity. Thus, the possibility to predict the partitioning of the substance of interest (drugs or reaction products) in solutions that contain different surfactants would be especially valuable. Presently, a few model approaches give the possibility to predict Kmw. The most popular group of methods is based on linear correlations between certain partition coefficients and some properties of the substance. In the case of the property-property relationships (PPR),2 the partition coefficient is represented as a function of some macroscopic property of the substance (e.g., solubility). Linear solvation energy relations (LSERs)3 and quantitative structure-activity * To whom correspondence should be addressed. Tel.: +49 9131 8527447. Fax: +49 9131 8527441. E-mail address: liudmila.
[email protected]. † Friedrich-Alexander University of Erlangen-Nuremberg. ‡ Technische Universita ¨ t Berlin.
relationships (QSARs)4 correlate the partitioning with the structural or property descriptors of compounds. These physicochemical descriptors include parameters to account for hydrophobicity, topology, electronic properties, and steric effects, and can be determined mainly empirically or, more recently, using computational methods. However, different relations are used to evaluate the solubilities,5,6 n-octanol/water partition coefficients,4,7 critical micelle concentration,8-10 micelle/water partition coefficients,11 and other properties, as well as altered value sets of descriptors and/or equations are often used for unlike classes of substances.6 If micelles are treated as a macroscopic phase in equilibrium with the aqueous surrounding (the pseudo-phase approach), the partitioning of an active agent between these coexisting phases is determined by the thermodynamic equilibrium. Therefore, thermodynamic models based on estimation of chemical potentials or equivalently of activity coefficients can be principally applied to predict the partitioning of active agents between polar (water) and nonpolar (micelle) phases. Because such models account for the concentration of each ingredient and temperature, they can be also utilized to predict how the solute partitioning changes when these conditions are varied. In this work, thermodynamically based models (in particular, those that provide predictions based solely on the molecular structure) are discussed with regard to their potential in predicting the micelle/ water partitioning. Recently, it has been shown that the nonidealities of the coexisting pseudo-phases in colloid systems can be evaluated in the frame of gE models. Hiller et al.12 considered partitioning of volatile compounds (monomers and solvents) in latex systems. The Flory-Huggins model extended with an interfacial term to account for the small size of the polymer particles and the NRTL model to account for the nonideality of the aqueous phase were used. Tse et al.13 studied the distribution of a solute
10.1021/ie0704849 CCC: $37.00 © 2007 American Chemical Society Published on Web 08/31/2007
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in a polymer microemulsion. The systems considered were treated as containing three pseudo-phases: polymer microparticles, micelles, and the aqueous surrounding. The nonidealities in all pseudo-phases were treated in terms of a groupcontribution model (Universal Quasi-Chemical FunctionalGroup Activity Coefficient (UNIFAC) and UNIFAC-FV for the micellar and polymeric phases correspondingly). The distribution coefficients of two model active agents have been predicted qualitatively. In our recent publication,14 the UNIFAC and Conductor-like Screening Model for Real Solvents (COSMORS) models were first used to calculate partitioning of organic solutes in micellar systems, containing nonpolar surfactants. The interfacial contribution to the solute activity coefficient was introduced to take into account the small size of micelles. Several solutes and surfactants were considered to demonstrate the principal feasibility of these two approaches. In the present study, we demonstrate the potential of the UNIFAC and COSMO-RS models to predict the partitioning in micellar systems. To do so, the log(Kmw) calculations are performed for a variety of nonpolar and polar organic solutes of different homologous series; nonionic and ionic surfactants are considered. The results obtained are compared with experimental data from literature and the factors which may affect the quality of prediction (interfacial contribution and conformational analysis) are explored. Modeling Model calculations are based on the pseudo-phase approach. The micellar pseudo-phase is considered to contain molecules of a surfactant and solute i, with no water being allowed to penetrate inside. The aqueous pseudo-phase contains all three components: water, surfactant, and solute. The partition coefficient of a solute (Kmw) is calculated based on the thermodynamic equilibrium conditions as follows:
Kmw )
ximicellar phase xi
) aqueous phase
γiaqueous phase ; xi f 0 γimicellar phase
(1)
where ximicellar phase and xiaqueous phase are the mole fractions of solute i in the surfactant and aqueous phases, respectively, and γimicellar phase and γiaqueous phase are the activity coefficients of solute i in the surfactant and aqueous phases, respectively. Two models are examined here: the structure-interpolating UNIFAC model15 and the a-priori COSMO-RS model.16 (1) UNIFAC. The UNIFAC model15 is a group-contribution tool that allows calculations based on functional-group parameters, giving additive contributions to the properties of the system. Although several modifications of the original UNIFAC model that provides different physicochemical properties (vaporliquid equilibria, liquid-liquid equilibria, limiting activity coefficients, Kow values, heats of mixing, etc.) are known, only the original one has been reported to be quantitatively applicable to the surfactant-containing systems.13,17-19 Cheng et al.19 used the model to calculate critical micelle concentrations (CMCs) of homologous series of alkyl polyethoxy alcohols. The ethoxy group of the polar head group was defined as a separate main group; the interaction parameters were fitted to the experimental data on CMC of selected alkyl polyethoxy alcohols. The results showed that the model can be applied to the water-polyethoxy alcohol systems. Recently, we reported the principal applicability of the model to predict the solute partitioning in micellar solutions.14 The extramicellar fraction (the ratio of the solute concentration in the aqueous phase to that in the feed solution)
was calculated for two nonpolar solutes (toluene, p-xylene) in aqueous solutions of nonpolar surfactants (Triton X100, Lutensol FS10). In the framework of the UNIFAC approach, the logarithm of activity coefficient of a substance in a bulky phase is calculated as a sum of two contributions: combinatorial (to account for the molecule size and shape) and residual (to regard the group-group interactions) terms. To take into account the small size of micellar aggregates, we have introduced the interfacial contribution to the activity coefficient in terms of the Gibbs-Thompson theory (UNIFAC-IF).14 In the present study, the proposed UNIFAC-IF model is extended to a variety of organic solutes of different homologous classes in many nonpolar surfactants. The data necessary in calculations are the internal UNIFAC parameters (geometry and interaction parameters), the molar volumes of solutes and surfactants, the interfacial tension at the micelle/water interface, and the hydrodynamic radii of micelles. The matrix of the interaction parameters of the original UNIFAC covers more than 50 main groups and is available free in the literature.19,20 The molar volumes of solutes were obtained from the literature or, if unavailable, were estimated based on the solute critical parameters by the Yen-Woods method.21 The molar volumes of surfactants were calculated based on the group-contribution approach proposed by Durchschlag and Zipper.22 Because the interfacial tension on the micelle/water boundary is not known from measurements, the calculations were made based on the experimental data on surface tension, to avoid any adjustable parameters. Hydrodynamic radii of unloaded micelles were also provided from literature data (dynamic light scattering measurements) and, if no data were available, the values were estimated based on group contributions.23,24 (2) COSMO-RS. The COSMO-RS model16 is based on quantum mechanics and allows an a priori prediction of thermodynamic properties, such as activity coefficients based on the molecular structure only. In the COSMO model,25 the solute molecule is considered to be embedded in a cavity that is surrounded by a virtual conductor. The COSMO-RS concept,16 which is based on statistical thermodynamics, provides the transfer from the state of the molecule embedded in a virtual conductor to a real solvent. The only information needed in calculations is the molecular structure. Of special value is that steric isomers, as well as ionic substances (solutes, surfactants, additives), can be modeled. As known,26,27 conformations of a substance have a remarkable influence on the quality of the prediction of physicochemical properties. In the present study, the conformational analysis of all solutes was performed via the semiempirical PM3 method, using the HyperChem program (the details are reported below). The commercially available Turbomole program was used to perform the DFT/COSMO geometry optimization (on the BP-TZVP level) and generation of the COSMO-RS input data. The activity coefficients of the solutes were calculated using the COSMOtherm program. The calculations were made for the solutes from different homologous series in non-ionic polyethoxy alcohols as well as ionic surfactants (sodium dodecyl sulfate (SDS)). Results and Discussion To demonstrate the potential of the UNIFAC and COSMORS models in regard to predicting the micelle/water partition coefficients of solutes in aqueous solutions of non-ionic and ionic surfactants, we have organized the discussions as follows. In the first two sections, we summarize the prediction results obtained using the predefined procedures, to show what principally can be done. The next two sections involve the details
Ind. Eng. Chem. Res., Vol. 46, No. 20, 2007 6503
Figure 1. Comparison of experimental32,33 and predicted partition coefficients of solutes of different homologous series in aqueous Triton X100 solutions at 298 K using COSMO-RS.
of the chosen procedures and the factors that influence the prediction results, such as the interfacial contribution and conformational analysis. (1) Partition Coefficients in the Aqueous Solutions of Nonionic Surfactants. A well-studied polyethoxy alcohol, Triton X100, has been chosen as a model non-ionic surfactant. Nonpolar and polar organic solutes that belong to different homologous series are considered. For the calculations, the UNIFAC-IF model that has been extended with the interfacial contribution has been applied, whereas the COSMO-RS model has been used in its usual format. In the frame of the UNIFAC-IF approach, the following pure substance parameters are utilized: the molar volumes of solutes are taken from the DIPPR database,28 whereas that of the surfactant is calculated based on group contributions;22 the radius of the unloaded Triton X100 micelle is assumed to be equal to 4.4 nm, based on the DLS measurements;29,30 an experimental surface tension value of 30 mN/m is used.31 The COSMO-RS calculations have been performed for the linear conformer of Triton X100, whereas a mixture of conformations is considered for each single solute. Figure 1 shows the predicted micelle/water partition coefficients (COSMO-RS) plotted versus the experimental values taken from the literature.32,33 The two dotted lines in the figure (above and below the diagonal) indicate the experimental error corridor, which is supposed to be on the order of 0.3 in the log(Kmw) scale.34 Table 1 represents the numerical results and errors obtained in calculations by means of both the UNIFACIF and COSMO-RS models. Both models demonstrate a quantitative agreement with the experimental data for the most of solute classes. The percentage relative errors averaged for all solutes studied are 11% and 17% for the COSMO-RS and UNIFAC-IF models, correspondingly. Note that an inadequate prediction of partitioning of chlorine derivatives has been obtained in the framework of the UNIFAC model. The interaction parameters for the chlorine-containing groups are based on limited experimental data. That might be a reason for the failure of the UNIFAC model in predicting this class of solutes. (2) Partition Coefficients in the Aqueous Solutions of Ionic Surfactants. One of the advantages of the COSMO-RS model is that ionic substances can be treated in its framework. Figure 2 illustrates the potentiality of the COSMO-RS model to predict Kmw in aqueous solutions of ionic surfactants. An anionic surfactantssodium dodecyl sulfate (SDS)swas chosen at the
Figure 2. Comparison of experimental11 and predicted partition coefficients of solutes of different homologous series in aqueous SDS solutions at 298 K.
first step, for several reasons. First, SDS is a well-studied surfactant and can be considered as a model substance. Experimental log(Kmw) data for a series of substances are available in the literature.11,35 Second, the conformational analysis could be completed within a reasonable time range, giving a reasonable number of conformations (see below for explanations). Thus, the weighted mixture of the SDS conformers could be used in the calculations. Micelle/water partition coefficients have been evaluated for many homologous series of organics. In Figure 2, the predicted log(Kmw) values are plotted versus the experimental values.11,35 The percentage relative errors are collected in Table 2. The results are in rather good agreement with the experimental data. The average error for all substances under consideration is ∼13%. As a next step, we are extending the calculations for other systems that contain ionic species (e.g., cationic and zwitterionic surfactants, as well as saline and buffer solutions). This would be of special value in the field of biosynthesis and pharmaceutical applications, because most of the pharmaceutical formulations are prepared based on buffer solutions and many of biosurfactants are of the zwitterionic type. The results reported above demonstrate a high potential of both UNIFAC-IF and COSMO-RS in predicting the Kmw values. In the following sections, the calculation procedure and the factors that may affect the quality of prediction (interfacial contribution and conformational analysis) are explored. Two of the aspects seemed to be of main value: the small size of the micellar aggregates and the conformational structure of molecules. (3) Implementation of the Interfacial Term. It is thermodynamically obvious that the chemical potential of a molecule in a particle of radius r differs from that in the bulk. In the frame of a gE-model, the activity coefficient of a solute in a bulk phase is generally calculated as a sum of two contributions: combinatorial (ln γicombinatorial) and residual (ln γiresidual) parts. When a small micellar aggregate is considered, the additional interfacial contribution ln γiinterfacial should be introduced: A commonly used approach for estimating the depen-
dence of the particle energy on size is the Gibbs-Thompson relation:36
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Table 1. Micelle/Water Partition Coefficients in Aqueous Solutions of Triton X100 at 298 K
δ ) 100 × Experiment log Kmw
solute
mw ) - log(Kmw |log(KCalc Exp)|
log(Kmw Exp)
UNIFAC-IF (σ ) 30 mN/m; r ) 4.4 nm) log Kmw
UNIFAC log Kmw
δ (%)
δ (%)
COSMO-RS log Kmw
δ (%)
n-Alkanes32 pentane hexane heptane octane nonane decane undecane dodecane average (number of points)
4.72 5.23 5.84 6.50 7.20 7.70 8.60 8.50
3.70 4.12 4.54 4.97 5.40 5.84 6.23 6.66
propanol butanol pentanol hexanol octanol average (number of points)
1.52 2.15 2.84 3.29 4.14
1.61 2.03 2.46 2.89 3.75
butanone hexanone octanone decanone average (number of points)
1.49 2.56 3.60 4.67
1.74 2.59 3.42
22 21 22 24 25 24 28 22 23 (8)
3.96 4.43 4.90 5.37 5.83 6.30 6.77 7.24
16 15 16 17 19 18 21 15 17 (8)
4.34 4.86 5.41 5.94 6.47 6.99 7.53 8.06
8.2 7.1 7.4 8.7 10 9.2 12 5.2 8.6 (8)
1.79 2.26 2.73 3.19 4.13
18 5.0 4.0 3.0 0.31 6.0 (5)
1.36 1.91 2.39 2.88 4.02
10 11 16 12 2.9 11 (5)
1.95 2.89 3.82
31 13 6.2
1.53 2.67 3.65 4.74
2.6 4.2 1.3 1.5 2.4 (4) 7.5 7.0 2.8 5.8 (3)
n-Alkan-1-ols32 6.1 5.4 13 12 9.5 9.3 (5) n-Ket-2-ones32 17 1.0 5.1 7.6 (3)
17 (3)
Esters32 ethyl acetate propyl acetate butyl acetate average (number of points)
1.95 2.37 3.02
2.27 2.70 3.14
acetonitrile propionitrile butyronitrile valeronitrile average (number of points)
1.19 1.63 2.09 2.56
1.46 2.07 2.50 2.93
chlorobenzene m-dichlorobenzene o-dichlorobenzene p-dichlorobenzene average (number of points)
4.17 4.96 4.86 4.88
2.60 1.82 1.82 1.82
naphthalene phenanthrene pyrene average (number of points)
4.64 5.70 6.03
16 14 4.1 11 (3)
2.51 2.97 3.44
29 25 14 23 (3)
2.10 2.54 3.10
n-Alkane Nitriles32 23 27 20 15 21 (4)
1.60 2.25 2.72 3.19
35 38 30 25 32 (4)
0.58 1.22 1.76 2.29
Chlorobenzenes32 38 63 63 63 57 (4)
2.84 2.08 2.08 2.08
32 58 57 57 51 (4)
3.97 4.52 4.42 4.47
4.9 8.9 9.0 8.3 7.8 (4)
4.97 6.35 7.00
7.2 11 16 12 (3)
4.52 5.52 5.84
2.6 3.2 3.2 3.0 (3)
Poly(aromatic) Hydrocarbons, PAHs33 4.65 0.23 5.95 4.4 6.55 8.7 4.4 (3)
oVerall aVeragea (31 points) a
17/88
The percentage relative errors in log
ln γiinterfacial )
Kmw
is given as the first value, and those in
2σVi(1 - φi)1/3 RTr
(3)
where σ is the interfacial tension on the particle/water interface and is generally assumed to be independent of the particle radius r; Vi is the molar volume of solute i, and φi is the volume fraction of solute i. In eq 3, it is taken into consideration that the micelle radius alters by the addition of a solute, whereas the possible change in the aggregate size with the growing concentration of surfactant is not considered. As a first approximation, all micelles are treated as spheres having the same size. It is obvious that the interfacial term gives a positive contribution to the logarithm of the activity coefficient. In case of the macroscopic phases (infinitely large radius), this term is approximately zero
Kmw
20/160
51 25 16 11 26 (4)
11/49
are given as the second value.
and can be neglected, whereas its value rapidly increases with the decreasing radius of the aggregate. The effect of interfacial contribution has been analyzed in the framework of both the UNIFAC and COSMO-RS models. The partition coefficients were calculated using the original models and those extended by the interfacial contribution; the results were compared to the experimental data. Table 3 presents the partitioning of polyaromatic hydrocarbons (PAHs) in systems of many polyethoxy alcohols. In Figure 3, the calculated values of the micelle/water partition coefficients are plotted versus selected experimental values. For visual convenience, two dotted lines represent the error corridor of 0.3 in the log(Kmw) values (according to Table 3, the scattering in the experimental data seems to be even higher). In the case of PAHs, the log(Kmw) values decrease by ∼6%-10% if the interfacial contribution is
Ind. Eng. Chem. Res., Vol. 46, No. 20, 2007 6505 Table 2. Micelle/Water Partition Coefficients in Aqueous Solutions of Sodium Dodecyl Sulfate at 298 Ka Experiment log Kmw
solute pentane hexane average (number of points) methanol ethanol propanol butanol pentanol hexanol heptanol octanol decanol average (number of points) butanone pentanone hexanone heptanone nonanone average (number of points)
δ (%)
n-Alkanes 4.22 4.38
3.669 4.084
13 7 10 (2)
n-Alkan-1-ols 1.27 1.71 2.04 2.44 2.91 3.39 3.74 4.22 4.41
0.77 1.24 1.73 2.12 2.57 2.96 3.33 3.75 4.43
39 28 15 13 12 13 11 11 0.48 16 (9)
n-Ket-2-ones 2.11 2.43 3.11b 3.46 4.47b
1.53 1.98 2.32 2.73 3.61
28 19 25 21 19 22 (5)
Alkyl Benzenes 2.95 4.17 3.45 3.91b 4.34b 4.76b
3.15 3.93 3.54 3.91 4.32 4.69
n-Alkane Nitriles 2.38
1.83
benzene p-xylene toluene ethyl benzene n-propyl benzene n-butyl benzene average (number of points) valeronitrile chlorobenzenes o-dichlorobenzol
COSMO-RS log Kmw
3.89
4.00
6.8 5.8 2.6 0.026 0.53 1.5 2.9 (6) 23 2.9
Poly(aromatic) Hydrocarbons, PAHs naphthalene 3.81 4.09 phenanthrene 5.6 5.00 pyrene 6.2 5.26 average (number of points)
7.4 11 15 11 (3)
oVerall aVeragec (26 points)
13/55
a
Experimental data from Abraham et al.11 and Vitha et al.35 b The value is taken from ref 35. c The percentage relative errors in log Kmw is given as the first value, and those in Kmw are given as the second value.
included (see Figure 3). In the frame of the UNIFAC model, the quality of prediction increases with the addition of the interfacial term. The same effect (up to 12%) is observed for ketones, esters, and alkane nitriles in the aqueous solutions of Triton X100 but not for n-alkanes, alkanols, and chlorobenzenes (see Table 1). On average, the consideration of the interfacial term improves the predictive ability of the UNIFAC model by 3%. When the COSMO-RS is utilized for the Kmw prediction (see Figure 3b and Table 3), the values obtained without the interfacial term coincide better with the experimental data. The reason for this could be that, in the COSMO-RS calculations, the peculiarity of the micellar aggregates is already taken into account through the structure (surface charge density distribution) of surfactant molecules. To summarize this section, we would recommend considering the interfacial contribution in the framework of the UNIFAC model, whereas the COSMO-RS model should be utilized as is. (4) Effect of Conformations in the Calculations by the COSMO-RS Model. Recently, it has been shown that the values of the thermodynamic properties, calculated with the help of
the COSMO-RS model, are strongly dependent on the molecule conformation used in the calculations.26,27 Conformers are equivalent structures that arise as a result of the rotation of C atoms about a single (sigma) bond and are often rapidly interconverting. Thus, the “real” molecule is represented as a mixture of energetically preferred conformations. If the energy of different conformers is known, it is possible to calculate their relative abundance via Boltzmann weighting. In COSMORS, the probability of conformation i to occur is given by the formula
wi )
wci exp{-(TFEi - TFEmin)/RT}
∑j
(4) wcj exp{-(TFEj - TFEmin)/RT}
The symmetry factors wci represent the number of different possibilities of building the same structure. The term TFEi signifies the total free energy of conformer i and is calculated as
TFEi ) Ei,COSMO + ∆Ei + µi
(5)
where Ei,COSMO is the total quantum chemical energy of conformer i in the ideal conductor, FEi the correction of the screening charge energy, and µi the residual chemical potential of conformer i. The subscript “min” indicates the minimumenergy conformer. The weighting is made by the iterative procedure until the self-consistency is achieved. In the present study, the following procedure has been adopted to calculate the Kmw values. First, an initial molecular structure is generated and visualized with the help of HyperChem Release 7.51 for Windows. The obtained molecule or ion placed under vacuum then is subjected to a conformation analysis, where the potential energies are calculated by the semiempirical PM3 method (HyperChem). Furthermore, the geometry of each conformation obtained is optimized using DFT/COSMO by means of the Turbomole 5.7 program. The structures gained as a result of the conformational analysis and DFT/COSMO optimization (BP-TZVP) are used to calculate activity coefficients with the help of the COSMOtherm program (Ver.2.1 Rev.01.04). Finally, the micelle/water partition coefficients are estimated according to eq 1. Because the log(Kmw) values calculated by COSMO-RS can be affected by the conformations of both solutes and surfactants, the influence of both is discussed below. (a) Effect of Solute Conformations. To study the influence of conformations of a solute, two aspects are regarded: the influence of each conformation of a given solute, and the effect of different sets of conformers obtained using various conditions (initial structure and parameters) of the conformational search. Figure 4 shows the log(Kmw) values calculated using different conformations of 2-octanone as an example. Each point represents the log(Kmw) value obtained for a single conformation. As observed, the calculated partition coefficients cover a broad range of values. The numbers (even for the minimum-energy conformer) can be rather different from the measured one (continuous line). However, good agreement can be achieved (dotted line) if a mixture of conformers is considered. The results of the conformational search are known to be dependent on the initial molecular structure (it is hardly possible to be certain that a global minimum has been found) and on the parameters chosen for the search (energy within, root mean sqaure (rms) error, etc.). To verify the effects, we performed the calculation using different sets of conformers (each set is
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Table 3. Micelle/Water Partition Coefficients of PAHs in Aqueous Solutions of Polyethoxy Alcohols experiment solute
log
Kmw
UNIFAC-IF log
Kmw
UNIFAC
δ (%)
log
Kmw
COSMO-RS-IF δ (%)
4.64 5.24 4.61
4.65
0.23 11 0.88
4.97
7.2 5.1 7.9
4.21
9.2 20 8.6
5.70 5.90 5.57 5.72
5.95
4.4 0.88 6.9 4.1
6.35
11 7.6 14 11
5.13
10 8.0 13 10
6.03 5.90 6.58
6.55
8.7 11 0.42
7.00
16 19 6.3
5.45
9.7 7.7 17
4.63 5.68 6.01
4.66 5.95 6.54
0.63 4.7 8.8
5.02 6.39 7.03
8.4 12 17
4.57 5.72 6.41
4.69 6.00 6.60
2.7 4.8 2.9
Brij 30, naphthalenea phenanthrenea pyrenea
4.59 5.57 6.53
4.24 5.48 6.04
4.59
5.0 6.37 7.02
7.7 1.6 7.5
4.75 6.10 6.74
3.4 10 3.2
4.51
4.85
oVerall aVerage (23 or 20 points) a
3.2 6.5 1.0 3.5 5.84
3.2 1.1 11
4.20 5.20 5.51
9.4 8.5 8.2
4.54 5.54 5.86
2.0 2.5 2.5
2.4
5.13
4.02 4.97 5.29
12 11 19
4.31 5.27 5.59
6.1 5.5 14
(σ ) 40 mN/m;45 r ) 4.4 nm46) 12
4.18
8.9
4.59
0.022
(σ ) 50 mN/m;47 r ) 5.7 nm42)
Triton X305, naphthaleneb
2.6 14 2.0
(σ ) 28 mN/m;44 r ) 2.6 nm42)
C12H25(OCH2CH2)23OH 4.70
4.52
9.4 11 9.6
C12H25(OCH2CH2)4OH
Brij 35, naphthaleneb
δ (%)
(σ ) 30 mN/m;43 r ) 4.6 nm42)
Tergitol NP-10, naphthalenea phenanthrenea pyrenea
log Kmw
(σ ) 35 mN/m;41 r ) 4.6 nm42)
Igepal CA-720, naphthalenea phenanthrenea pyrenea
δ (%)
COSMO-RS
(σ ) 30 mN/m;31 r ) 4.4 nm29,20)
Triton X100, naphthalene data from ref 33 data from refs 32, 37 data from ref 38 phenanthrene data from ref 33 data from ref 37 data from ref 38 data from ref 39 pyrene data from ref 33 data from ref 38 data from ref 40
log
Kmw
7.5 5.1
5.26
17 10
4.25
5.7 11
4.65
3.1 5.2
Data taken from ref 33. b Data taken from ref 37.
obtained based on the fixed parameters that have been mentioned). The selected results are presented in Figure 5, where the values calculated using one of the sets are plotted versus the results based on another one. As observed, almost the same numbers are obtained, independent of which set of conformers is utilized, if the mixture of conformers is used in the calculations. (b) Effect of Surfactant Conformations. The effect of surfactant conformations is examined for both the ionic (SDS) and non-ionic (Triton X100) surfactants. The head group of SDS is rather small and builds no conformers; thus, the tail conformations only affect the calculations. Because the alkyl tail of SDS is sufficiently short, the molecule was subjected to conformational analysis, using the aforementioned procedure. Twenty eight conformers have been found. The COSMO-RS calculations were made for each single conformer, as well as for a weighted mixture of those conformers. Almost no influence on the calculated Kmw values has been detected. The head group of nonpolar Triton X100 represents a chain of 10 ethoxy groups (more than 60 atoms only in the head
group). The conformational analysis for such substances is rather tedious and time-consuming, because a great variety of conformers exist. To analyze the effect of surfactant conformations on the log(Kmw), we made the calculations for the linear and for the arbitrarily perturbed polyethoxy chain of the Triton X100 molecule (it seemed too time-consuming to converge the semiempirical procedure as well as the DFT/COSMO geometry optimization for such a large molecule). Solutes belonging to different homologous series were treated. For each solute, the mixture of conformations was used. As observed from Figure 6, the effect of the surfactant conformations changes from one series to another. Almost no influence has been observed for ketones, whereas the results differ significantly when log(Kmw) for all other classes are modeled. Figure 7 gives an example for n-alkanols in both the linear and arbitrary perturbed Triton X100. As evident from the figure, the calculated values are similar to the experimental values; however, it is difficult to say which of the Triton X100 conformers should be accepted. To summarize this section, it is worth noting that conformational analysis has special value in the COSMO-RS calculations
Ind. Eng. Chem. Res., Vol. 46, No. 20, 2007 6507
Figure 3. Micelle/water partition coefficients of polyaromatic hydrocarbons in aqueous solutions of polyethoxy alcohols calculated using the (a) UNIFAC and (b) COSMO-RS models, versus the experimental data. Solutes: naphthalene (0,9); phenanthrene (4,2); and pyrene (O, b).
Figure 4. Effect of conformer energy on the values of the micelle/water partition coefficient of 2-octanone in the aqueous solution of Triton X100 at 298 K (∆ECOSMO ) Ei - Emin, where Ei and Emin are the COSMO energies of conformer i and the minimum-energy conformer, respectively).
Figure 6. Effect of surfactant structure on the log(Kmw) values in the aqueous solutions of Triton X100: (0) linear conformer and (9) arbitrary perturbed conformer.
The conformational analysis based on the molecular dynamics simulation is known to be applicable and successful for large molecules. Moreover, the conformational search can be done for a molecule placed in a “real” solvent. This approach is the focus of our ongoing work in cooperation with Prof. Maginn’s group at the University of Notre Dame. Conclusions
Figure 5. Comparison of the log(Kmw) values of solutes in the aqueous Triton X100 solutions calculated based on different sets of conformers.
of micelle/water partitioning. The best approximation would be to use the weighted mixture of conformations for both the solute and the surfactant. However, an appropriate method to realize the conformational search for large surfactant molecules is still missing.
The predictive capability of the COSMO-RS and UNIFACIF models to describe the micelle/water partition coefficients has been demonstrated. Both models show a high potential in regard to predicting solute partitioning in micellar solutions. The theoretically predicted partition coefficients are determined to be in reasonable quantitative agreement with the experiments. Different classes of organic solutes (both nonpolar and polar) in non-ionic surfactant solutions can be treated. The interfacial contribution to the solute activity coefficient should be taken into account using the UNIFAC model, whereas COSMO-RS can make the quantitative predictions in the format provided. Note that the UNIFAC calculations can be conducted rather fast, but it is hardly possible to consider steric isomers as well as ionic substances. Compared to UNIFAC, the COSMO-RS
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Figure 7. Calculated micelle/water partition coefficients of n-alkanols in the aqueous solutions of linear and arbitrary perturbed Triton X100 versus the experimental data.32
model can be successfully applied to calculate the micelle/water partition coefficients in aqueous micellar solutions that contain ionic surfactants. A weighted mixture of solute conformations should be used in COSMO-RS calculations. The conformational analysis also is important for large surfactant molecules. However, the proper way for making the conformational search for large surfactant molecules should be found; the potential of molecular dynamics for this purpose is proven in our current research (publication in progress). It is obvious that both theoretical approaches can be easily extended and applied to multicomponent systems (mixtures of solutes and/or mixtures of surfactants). The effects of temperature and concentration also can be examined. The results of the modeling can be used for the prediction of the enhanced drug solubilization, as well as for the optimization of separation and purification processes in the biotechnology and pharmaceuticals industries. Fast UNIFAC calculations can be made first, to screen roughly the solutes (drugs) and/or surfactants; the selected compounds then can be subjected to the detailed conformational analysis and the Kmw values can be calculated quantitatively by COSMORS. Acknowledgment The authors appreciate the financial support of DFG (SM 82/4-1) and the helpful discussions of Dr. A. Klamt. Literature Cited (1) Ahuja, S., Ed. Handbook of Bioseparation; Academic Press: San Diego, CA, 2000. (2) Treiner, C.; Chattopadhyay, A. K. Correlation of Partition Coefficients for Polar Aromatic and Aliphatic Molecules between Trimethyldodecylammonium Bromide Micelles + Water and Octanol + Water Systems at 298.15 K. J. Colloid Interface Sci. 1986, 109, 101-108. (3) Taft, R. W.; Abboud, J.-L. M.; Kamlet, M. J.; Abraham, M. H. Linear Solvation Energy Relations. J. Solution Chem. 1985, 14, 153-186. (4) Hansch, C.; Leo, A. Exploring QSAR Fundamentals and Applications in Chemistry and Biology; ACS Professional Reference Book; American Chemical Society (ACS): Washington, DC, 1995. (5) Khadikar, P. V.; Mandloi, D.; Bajajc, A. V.; Joshi, S. QSAR Study on Solubility of Alkanes in Water and Their Partition Coefficients in Different Solvent Systems Using PI Index. Bioorg. Med. Chem. Lett. 2003, 13, 419-422. (6) Katritzky, A. R.; Oliferenko, A. A.; Oliferenko, P. V.; Petrukhin, R.; Tatham, D. B.; Maran, U.; Lomaka, A.; Acree, W. E. A General Treatment of Solubility. 1. The QSPR Correlation of Solvation Free Energies of Single Solutes in Series of Solvents. J. Chem. Inf. Comput. Sci. 2003, 43, 1794-1805. (7) Meyer, P.; Maurer, G. Correlation of Partition Coefficients of Organic Solutes between Water and an Organic Solvent. An Application of the Linear Solvation Energy Relationship. Ind. Eng. Chem. Res. 1993, 32, 2105-2110.
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Ind. Eng. Chem. Res., Vol. 46, No. 20, 2007 6509 (33) Edwards, D. A.; Luthy, R. G.; Lui, Z. Solubilization of Polycyclic Aromatic Hydrocarbons in Micellar Nonionic Surfactant Solutions. EnViron. Sci. Technol. 1991, 25, 127-133. (34) Marangoni, D. G.; Kwak, J. T. Comparison of Experimental Methods for the Determination of the Partition Coefficients of n-Alcohols in SDS and DTAB Micelles. In Solubilization in Surfactant Aggregates; Christian, S. D., Scamehorn, J. F., Eds.; Surfactant Science Series No. 55; Marcel Dekker: New York, 1995; pp 455-490. (35) Vitha, M. F.; Dallas, A. J.; Carr, P. W. Study of Water-Sodium Dodecyl Sulfate Micellar Solubilization Thermodynamics for Several Solute Homolog Series by Headspace Gas Chromatography. J. Phys. Chem. 1996, 100, 5050-5062. (36) Lewis, G. N. L.; Randall, M. Thermodynamik; Springer, Wien, 1927. (37) Kim, S.; Park, J. S.; Kim, K. W. Enhanced Biodegradation of Polycyclic Aromatic Hydrocarbons Using Nonionic Surfactants in Soil Slurry. Appl. Geochem. 2001, 16, 1419-1428. (38) Zhu, L.; Feng, S. Synergistic Solubilization of Polycyclic Aromatic Hydrocarbons by Mixed Anionic-Nonionic Surfactants. Chemosphere 2003, 53, 459-467. (39) Li, J.-L.; Chen, B.-H. Solubilization of Model Polycyclic Aromatic Hydrocarbons by Nonionic Surfactants. Chem. Eng. Sci. 2002, 57, 28252835. (40) Zhou, W.; Zhu, L. Solubilization of Pyrene by Anionic-Nonionic Mixed Surfactants. J. Hazard. Mater. B 2004, 109, 213-220. (41) The value is interpolated from the surface tension data from: Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physicochemical Properties of Selected Anionic, Cationic, and Nonionic Surfactants; Elsevier: Amsterdam, 1993.
(42) The value is calculated based on group contributions.23 (43) DOW TERGITOL NPE Surfactants Reference Chart: http:// www.dow.com/PublishedLiterature/dh_01b9/ 09002f13801b962a.pdf?filepath)surfactants/pdfs/noreg/11901494.pdf&fromPage)GetDoc. (44) Lin, S. Y.; Lin, Y. Y.; Chen, E. M.; Hsu, C. T.; Kwan, C. C. A Study of the Equilibrium Surface Tension and the Critical Micelle Concentration of Mixed Surfactant Solutions. Langmuir 1999, 15, 43704376. (45) Hoshino, E.; Tanaka, A. Enhancement of Enzymatic Catalysis of Bacillus amyloliquefaciens R-Amylase by Nonionic Surfactant Micelles. J. Surfactants Deterg. 2003, 6, 299-303. (46) Phillies, G. D. J.; Hunt, R. H.; Strang, K.; Sushkin, N. Aggregation Number and Hydrodynamic Hydration Levels of Brij-35 Micelles from Optical Probe Studies. Langmuir 1995, 11, 3408-3416. (47) Manglik, R. M.; Wasekar, V. M.; Zhang, J. Dynamic and Equilibrium Surface Tension of Aqueous Surfactant and Polymeric Solutions. Exp. Thermal Fluid Sci. 2001, 25, 55-54.
ReceiVed for reView April 3, 2007 ReVised manuscript receiVed July 3, 2007 Accepted July 9, 2007 IE0704849
