Prediction of Micelle Formation for Aqueous Polyoxyethylene Alcohol

merely correlative value. Moreover, they do not take ... from the correlation of binary water-poly(ethylene ... The objective of this study is to comb...
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Ind. Eng. Chem. Res. 2002, 41, 892-898

Prediction of Micelle Formation for Aqueous Polyoxyethylene Alcohol Solutions with the UNIFAC Model Hongyuan Cheng, Georgios M. Kontogeorgis, and Erling H. Stenby* Centre for Phase Equilibria and Separation Processes (IVC-SEP), Department of Chemical Engineering, Building 229, Technical University of Denmark DK-2800 Lyngby Denmark

Micelle formation, expressed often via the critical micelle concentration (cmc), is one of the most important properties for aqueous surfactant solutions. In this work, five different versions of the UNIFAC method have been systematically investigated for nonionic surfactants of the water + polyoxyethylene alcohol type. The results show that these five UNIFAC methods qualitatively predict the observed trend of the hydrophobic chain but not that of the hydrophilic chain. It has been established that by introducing a new oxyethylene group (CH2CH2O) and estimating its interaction parameters from vapor-liquid equilibrium data, the original UNIFAC VLE method can provide good prediction for the critical micelle concentration of water + polyoxyethylene alcohol systems, both with respect to varying hydrophobic and hydrophilic parts. Further improvement could be anticipated if the new parameters were refined based on additional ether + water vapor-liquid equilibrium data. Introduction Surface-active materials (surfactants) are often used in both industrial applications, e.g., enhanced oil recovery, pharmaceutical industry and biotechnology, and in daily life, e.g., as components of washing powders, shampoos, and creams. Understanding the chemical and physical properties of surfactants is very important for choosing suitable such chemicals for specific industrial applications. It is essential to have tools that can describe the physical properties and phase behavior of surfactants in both hydrophilic and hydrophobic environments. Such tools should predict some important properties of surfactants, such as the critical micelle concentration (cmc), the aggregate number, and various partition coefficients, all of which depend on the structure of surfactants. Blandamer et al.,1 Blankschtein et al.,2 Nagarajan,3 and Zana4 recently reviewed thermodynamic theories of surfactant solutions. The micelle formation is often treated as a pseudo-phase formation or via a massaction process. Through this assumption, a relation between surfactant concentration and cmc values can be set up. Blankschtein,5 Nagarajan, and Ruckenstein6 proposed molecular thermodynamic methods concerning the micelle formation and used these methods to determine critical micelle concentration, micelle aggregate number, micelle compositions, and other properties for surfactant systems.7-8 Such works are of merely correlative value. Moreover, they do not take advantage of the vast amount of molecule thermodynamic modeling work carried out in the past few decades for many different solutions. Various empirical and semiempirical methods were also proposed for determining cmc.9-12 However, only the relevant investigations with our work will be shortly reviewed below. Chen13 proposed a thermodynamic treatment using a segment-based NRTL (nonrandom two-liquid) model to represent the cmc for polyoxyethylene alcohol + water * Corresponding author: [email protected]

Fax:

+45-45882258 E-mail:

systems. In his work, the temperature-dependent interaction parameters of the NRTL model are obtained from the correlation of binary water-poly(ethylene glycol) system vapor-liquid equilibrium (VLE) data and water + hydrocarbon liquid-liquid equilibrium (LLE) data. The cmc values of some aqueous polyoxyethylene alcohol solutions are successfully predicted by this method. Li et al.14,15 took advantage of Chen’s13 thermodynamic treatment and employed the segment-based universal quasi-chemical model (UNIQUAC) and the statistical associating fluid theory (SAFT) to obtain the activity coefficient of aqueous nonionic and ionic surfactant solutions. In their work,14 the ethylene oxide group (C2H4O) and the ethylene group (C2H4) for hydrophilic and hydrophobic part of a molecule, respectively, are considered as single segment. This results when the carbon number is an odd number within hydrocarbon chain of a surfactant molecule, it is not clear how the segment number of the ethylene group in a surfactant molecule can be determined. From an industrial application viewpoint, it would be convenient to develop structure activity models possibly based on group contributions, which can predict the important properties of surfactants, such as the critical micelle concentration and the partition coefficients. The universal functional activity coefficient model (UNIFAC) is such a group contribution method for the estimation of activity coefficients. Comprehensive studies of UNIFAC have been presented by several researchers, but not for surfactant solutions. Several versions of UNIFAC with different group interaction parameters are readily available in the literature. Because of the extensive use of UNIFAC in the chemical industry and its large amount of group parameters, it appears very interesting to explore its applicability to surfactant systems. The objective of this study is to combine the UNIFAC model and the thermodynamic treatment proposed by Chen13 to investigate the prediction of cmc values for nonionic surfactant solutions. First, we compare existing UNIFAC models in the prediction of cmc values. Second,

10.1021/ie010072e CCC: $22.00 © 2002 American Chemical Society Published on Web 09/12/2001

Ind. Eng. Chem. Res., Vol. 41, No. 5, 2002 893 Table 1. Overview of the Five UNIFAC Models Considered in This Work models

ref

temp dependency

data useda

original UNIFAC VLE 1 UNIFAC LLE 1 original UNIFAC VLE 2 modified UNIFAC VLE 3 water-UNIFAC

18 19 20 21 22

a * f(T) a * f(T) aji ) aji,1 + aji,2(T - T0) aji ) aji,1 + aji,2(T - T0) + aji,3(T ln(T0/T) + T - T0) a * f(T)

VLE LLE VLE VLE & HE VLE & γ∞,aq

a Key: VLE, vapor-liquid equilibrium; LLE, liquid-liquid equilibrium; HE, excess enthalpy; γ∞,aq, activity coefficient at infinite dilute for aqueous solutions.

we estimate interaction parameters of selected UNIFAC group from direct fitting the critical micelle concentration (cmc) data. Then we use vapor-liquid equilibrium (VLE) data to regress the interaction parameters for these selected groups. Finally, by using these parameters from VLE data, cmc values of different polyethylene alcohol solutions are predicted with the UNIFAC model. Aqueous Surfactant Solutions Surfactants consist of molecules containing both polar and nonpolar parts (amphiphiles). The nonpolar (hydrocarbon) part of the molecule is responsible for its solubility in oil, while the polar groups such as -COOH, -OH, or ionic groups, have sufficient affinity to water to drag a nonpolar hydrocarbon chain into aqueous solutions. Because of the amphiphile characteristics of surfactant molecules in aqueous solutions, at fairly welldefined concentrations, abrupt changes in several physical properties, such as osmotic pressure, electrical conductance and surface tension, occur. McBain and Swain16 suggested that this seemingly anomalous behavior could be explained in terms of the formation of organized aggregates of the surfactant molecules (the micelles) in which the hydrophobic hydrocarbon chains are orientated toward the interior of the micelle, leaving the hydrophilic groups in contact with the aqueous medium. The concentration above where micelle formation becomes appreciable is termed the critical micelle concentration (cmc). cmc is one of the most important properties for surfactant systems. In this study, we focus on the cmc of nonionic surfactant systems. Following Chen’s13 treatment for micelle formation, the phase-separation method is used for establishing the thermodynamic expression for surfactant solutions when micelles are formed. After the micelles’ formation, the aggregated surfactant molecules (micelles) represent a pseudophase that is considered to be a pure liquid surfactant excluding solvent from their interiors. Thus, the standard-state chemical potential of the monomer in the micelle equals zero. At the concentration of micelles formation (critical micelle concentration), the activities of the two conformations of monomers, inside the micelles (am) and in solvent (as), should be the same and their activities should be unity

ascmc ) am ) 1.0

(1)

where cmc

as

) xs

cmc

γs

cmc

(2)

The composition of amphiphiles at cmc can be obtained from eq 1 and 2. We will employ this thermodynamic framework and use the UNIFAC model to obtain the

activity coefficient of surfactant molecules in aqueous surfactant solutions. Calculation of Cmc for Nonionic Surfactant Solutions with Existing UNIFAC Models Since the UNIFAC model has been introduced,17 several different versions (group interaction parameter tables) have been proposed. Among these, five popular versions that have been developed for different cases are as follows: the original UNIFAC VLE 1,18 UNIFAC LLE 1,19 UNIFAC VLE 2,20 modified UNIFAC VLE 321 and water-UNIFAC.22 Recently, the predictive SoaveRedlich-Kwong group contribution equation of state has been extended to epoxides, HF, HI, and COS groups.41 This method has its potential to predict phase equilibrium for the system including polyethylene alcohols because it includes the oxyethylene group. Table 1 lists the specific characteristics of these five UNIFAC models. All these models have been used to describe vapor-liquid and liquid-liquid phase equilibrium as well as water-hydrocarbon phase equilibrium. Chen13 used the original UNIFAC VLE 1 to predict the cmc for polyoxyethylene alcohol surfactant solutions. According to Chen, the predicted cmc values using UNIFAC follow qualitatively the observed trend as the hydrophobic alkyl chain part of surfactants increase. However, UNIFAC cannot (not even qualitatively) yield the observed trend with respect to the hydrophilic chain. In this work, we have first evaluated various existing UNIFAC models for several water + nonionic surfactant systems. The nonionic surfactants having a polyoxyethylene chain are among the most extensively investigated systems. These polyoxyethylene alcohol surfactants are often abbreviated as CiEj, where i is the number of alkyl carbon and j is the number of oxyethylene group (OCH2CH2). Extensive cmc investigations have been reported in the literature.23-25 Due to the fact that existing UNIFAC parameter tables do not contain a separate oxyethylene group, we first investigated, to a first approximation, how well the combination of an ether group (CH2O) and an alkyl group (CH2) can represent the oxyethylene group (CH2CH2O) for surfactant system. The values of group parameters Q and R are estimated as follows:

QCH2CH2O ) QCH2O + QCH2 ) 1.320 RCH2CH2O ) RCH2O + RCH2 ) 1.5927 The ether main group (CH2O) interaction parameters are used in these calculations. Using eqs 1 and 2, the cmc values of different aqueous nonionic surfactant solutions have been predicted with the five different versions of UNIFAC. The prediction results are shown graphically in Figures 1-4. Figures 1-4 indicate that all the five UNIFAC models have

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Figure 1. Predicted cmc values at 25 °C for surfactants with different hydrophobic alkyl chains.

Figure 2. Predicted cmc values at 25 °C for surfactants with different hydrophobic alkyl chains.

qualitatively similar behavior in aqueous surfactant solutions. The predicted trends for both the hydrophobic chain and the hydrophilic chains are in agreement to Chen’s13 results. However, these figures also show that the UNIFAC model may qualitatively be in position to describe phase equilibria for surfactant systems and that it may have potential for describing the micelle formation of aqueous surfactant solutions if appropriate improvements are introduced. Toward a UNIFAC Model for Surfactant Solutions As shown in the calculations in the previous section, the UNIFAC model has the correct cmc tendency with varying alkyl number in surfactant molecules, but not with varying oxyethylene number. We pursued therefore a further investigation of the applicability of the UNIFAC model to surfactant systems. We first evaluated the selection and need for a special new oxyethylene group (CH2CH2O). The new interaction parameters for this group are first directly correlated from experimental cmc values. Provided that the results from this step are satisfactory, the CH2CH2O interaction parameters would be then estimated solely from vapor-liquid phase equilibrium data. These interaction parameters from the second step will give the possibility for direct cmc prediction through UNIFAC. The New Oxyethylene Group for UNIFAC. Surfactants molecules cover a wide range of structural

Figure 3. Predicted cmc values at 25 °C for surfactants with different hydrophilic alkyl chains.

Figure 4. Predicted cmc values at 25 °C for surfactants with different hydrophilic alkyl chains.

features. For nonionic surfactants, there are seven typical structure families: branched alkyl ethoxylates, linear alkyl ethoxylates, octylphenol ethoxylates, alkanediols, alkyl mono- and disaccharides ethers and esters, ethoxylated alkylamines and amides, fluorinated linear ethoxylates, and amides.24 Most of these nonionic surfactants contain the oxyethylene group (ethylene oxide oligomers) in the hydrophilic domain of the molecule. These surfactants often contain a distribution of poly(ethylene oxide) chain lengths rather than a constant number of units. In this work, we are mainly concerned with two families, the branched alkyl ethoxylates and the linear alkyl ethoxylates, which are widely used in the chemical industry; they are among the most extensively investigated nonionic surfactants. Also, they are considered to be environmental friendly chemicals.30 These two classes can be represented as the sum of oxyethylene groups, CH2CH2O, and alkyl groups along with one alcohol group, OH. Thus, only one new main UNIFAC group, CH2CH2O, needs to be introduced in order to describe these two classes of surfactants. In their study of phase equilibrium of aqueous polymer solutions, Rasmussen and Rasmussen31 have introduced a special CH2CH2O (poly(ethylene oxide)) group in the UNIFAC model and successfully predicted the phase behavior of aqueous polymer solutions with its group interaction parameters. We have also used these group interaction parameters (shown in Table 2)

Ind. Eng. Chem. Res., Vol. 41, No. 5, 2002 895 Table 2. UNIFAC Interaction Parameters (in K) CH2(1)CH2CH2O(2)

CH2CH2O(1)H2O(2)

a1-2

a1-2

a2-1

a2-1

Rasmussen and Rasmussen31 106.60 63.55 705.9 -28.53 correlation from CMC (this work) 22.24 -66.99 25.14 -18.24 estimation from VLE (this work) -31.87 84.75 134.95 -67.77

for investigating the applicability of UNIFAC model for predicting cmc values of surfactant solutions. Some prediction results are shown in Figure 5. It can be seen that these parameters cannot satisfactorily provide both trends of nonionic surfactants (increasing hydrophobic and hydrophilic chains). Another group selection for surfactant solutions could be the special glycol ether group, which has been published by Hansen et al.18 However, the glycol etherether interaction parameters are not available in the current UNIFAC model; thus, this special selection was not tested further. This discussion and the previous calculations demonstrate that the possible way for applying UNIFAC to surfactant systems would be to estimate special group interaction parameters. In Figure 5, the prediction results of UNIFAC from Rasmussen31 show, as a first indication, that the UNIFAC model with oxyethylene group has the capability for predicting satisfactorily the cmc values for different hydrocarbon chain length in aqueous surfactant solutions. It is thus very valuable to further investigate the potential of the oxyethylene group. To predict the cmc of surfactant solutions, the experimental information from vapor-liquid phase equilibrium data (nonsurfactant solutions) will be used to estimate CH2CH2O group interaction parameters for UNIFAC model. However, we first needed to verify that the UNIFAC model has indeed the potential (functional ability) of getting “both trends” for surfactant solutions (i.e., increasing hydrophobic or hydrophilic chains). One of the ways to do so is via an estimation of CH2CH2O parameter values directly based on the actual cmc data. Correlation of Cmc Using UNIFAC The interaction parameters of CH2CH2O group are obtained by directly regressing cmc data. To obtain the UNIFAC interaction parameter values of the oxyethylene group, the thermodynamic condition, eq 1, is used for converting the experimental cmc values to activity coefficients. The logarithm of activity coefficients is used as the objective function (F).

F)

∑i ∑j (ln γi,Exp - ln γi,UNIFAC)j2

(3)

The cmc data used in this regression are listed in Appendix A. The oxyethylene group volume and surface area parameters are based on van der Waals volumes and surface areas and have the following values: R ) 1.5927; Q ) 1.320. The UNIFAC interaction parameters between the oxyethylene group CH2CH2O and CH2 and H2O groups are regressed using the cmc data by minimizing this objective function.17 The details of regression method can be found in refs 17, 18, 20, 35, and 36. The existing interaction parameters18 are maintained for the remaining groups. Typical regression results are shown in Figure 5. The obtained parameter values are shown in Table 2. For comparison the

Figure 5. Prediction and correlation results of cmc at 25 °C with different methods.

prediction results from the NRTL model are also presented in Figure 5. These results indicate that the UNIFAC model has the potential of representing the cmc values of different types of aqueous surfactant solutions. Other local composition models, e.g., NRTL and UNIQUAC, may behave in a similar way. Prediction of Cmc Using UNIFAC The interaction parameters of CH2CH2O group are obtained from VLE data. In parameter estimation from VLE phase equilibrium data, the selected UNIFAC interaction parameter pairs are the same as in the correlation procedure described in the previous section. Two interaction parameter pairs, CH2CH2O-CH2 and CH2CH2O-H2O, have been estimated here from VLE data. The existing interaction parameters for CH2OOH pair18 are used for CH2CH2O-OH pair parameters. Because of the fact that CH2CH2O group can be treated as the combination of group CH2O and CH2, the CH2CH2O main group should include several subgroups, such as CH3CH2O, CH3CHO, CH2CH2O, CH2CHO, CHCHO, CH2CO, and CH3CO. Moreover, we should consider that proximity effects are quite important between alkyl groups adjacent to O atom for CH2CH2O group. The agreement between UNIFAC and phase equilibrium data is not very satisfactory for mixtures containing glycol ethers, 1,4-dioxane, 1,3-dioxolane, etc.32,33 However, for nonionic surfactants, only the linear oxyethylene group is involved in branched alkyl ethoxylates and linear alkyl ethoxylates. Thus, only those systems including linear ether components are selected for the parameter estimation to avoid further complexities in the parameter estimation. The existing VLE phase equilibrium data of important ethers with nonpolar solvents have been reviewed and published by IUPAC.34 However, VLE data for ether + water systems are scarce. Most of existing data sets for water-ether systems seem to be thermodynamically inconsistent and thus cannot be used for reliable parameter estimation. Considering previous investigations for ether-water interaction parameters,35-36 we have only selected the water + 1,4-dioxane system37 for regressing the CH2CH2O-H2O interaction parameters. The following experimental VLE data have been used for the parameter estimation of CH2CH2O-CH2: nhexane + dibutyl ether38 and butylmethyl ether + heptane.39 No LLE data have been used. The estimation

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Figure 6. Predicted cmc values at 25 °C for surfactants with different hydrophobic alkyl chains.

Figure 7. Predicted cmc values at 25 °C for surfactants with different hydrophobic alkyl chains.

Figure 8. Predicted cmc values at 25 °C for surfactants with different hydrophobic alkyl chains or hydrophilic headgroups.

Figure 9. Predicted cmc values at 25 °C for surfactants with different hydrophilic headgroups.

is based on the objective function F which is similar to that used previously (eq 4):

F)

∑i ∑j (γi,Exp - γi,UNIFAC)j2

(4)

The details of regression method can be found in refs 17, 18, 20, 35, and 36. The interaction parameters from VLE data are listed in Table 2. Using the UNIFAC interaction parameters from vapor-liquid equilibrium data (Table 2), cmc has been predicted using eqs 1 and 2. The predicted results are shown in Figures 6-10 and are also compared with the correlation results. From these results, we conclude that the UNIFAC model, with the interaction parameter from VLE data, can quantitatively represent cmc for different aqueous nonionic surfactant solutions. Specifically, the UNIFAC model predicts well the observed effects of hydrophobic alkyl and hydrophilic chain for these nonionic surfactant solutions. Slight deviations in the hydrophilic tendencies could be attributed to the fact that interaction parameters are estimated only from water + 1,4-dioxane VLE data. The values of oxyethylene group interaction parameters could be different in the linear or cyclical states. On the other hand, the obtained cmc data are from different data sources; only part of them are from the compilation of Mukerjee and Mysels.23 Experimental cmc data may be subject to errors, which can be difficult to assess due to lack of a method for testing the consistency of the cmc data.

Figure 10. Predicted cmc values at 25 °C for surfactants with different hydrophilic headgroups.

Conclusions In this work different UNIFAC methods have been systematically investigated for water + polyoxyethylene alcohol systems. The results show that the original UNIFAC VLE, modified UNIFAC VLE, UNIFAC LLE, the linear temperature dependent UNIFAC VLE, and water-UNIFAC methods predict qualitatively correct the observed trend of the hydrophobic chain for aqueous nonionic surfactant solutions but fail to predict the trend of the hydrophilic chain. By introduction of a new group, the oxyethylene group (CH2CH2O), and estimation of

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its interaction parameters from vapor-liquid equilibrium data, the original UNIFAC VLE method can provide good prediction for micelle formation for water + polyoxyethylene alcohol systems for both the hydrophobic and hydrophilic trends. Because of the large amount of UNIFAC interaction parameters that are readily available in the literature (Hansen et al.18), the UNIFAC model should be in principle applicable to other nonionic surfactant solutions if (when required) new functional group parameters are introduced and estimated from available phase equilibrium data. Acknowledgment The authors thank Professor Peter Rasmussen and Dr. Chau-Chyun Chen for valuable discussions. This research is supported by “The Centre for Environment and Respiratory System” under the Danish Environmental Research Program, to whom the authors express their gratitude. Appendix A Table 3 lists the cmc data of aqueous nonionic surfactant solutions (Mukerjee and Mysels23) used in regressing UNIFAC interaction parameters. Table 3. Cmc Data (Mukerjee and Mysels23) name

temp°C

cmc mole fraction

C6E3 C6E3 C6E3 C8E3 C8E3 C8E6 C8E6 C8E6 C8E9 C8E9 C8E9 C10E3 C10E3 C10E3 C10E6 C10E6 C10E6 C10E9 C10E9 C10E9 C12E6 C12E6 C12E6 C16E7 C16E9 C16E12 C16E15 C16E21 C6E4 C6E5 C4E6 C4E6 C8E1

15 25 35 15 25 15 25 35 15 25 35 15 25 35 15 25 35 15 25 35 15 25 35 25 25 25 25 25 25 25 20 30 25

1.92596E-05 1.79677E-03 1.40203E-03 1.67372E-04 1.34982E-04 2.14154E-04 1.78168E-04 1.38581E-04 2.87917E-04 2.33945E-04 1.97961E-04 1.31398E-05 1.07999E-05 1.00799E-05 2.05196E-05 1.61997E-05 1.18799E-05 2.51994E-05 2.33995E-05 1.97996E-05 1.94400E-06 1.56600E-06 1.29600E-06 3.13200E-08 3.76200E-08 4.21200E-08 5.56200E-08 7.00200E-08 1.61738E-03 1.66223E-03 1.41256E-02 1.34954E-02 8.81922E-05

Literature Cited (1) Blandamer, M. J.; Cullis, P. M.; Soldi, L. G.; Engberts, J. B. F. N.; Kacperska, A.; van Os, N. M.; Subha, M. C. S. Thermodynamics of Micellar Systems: Comparison of Mass Action and Phase Equilibrium Models for the Calculation of Standard Gibbs Energies of Micelle Formation. Adv. Colloid Interface Sci. 1995, 58, 171. (2) Blankschtein, D.; Shiloach, A.; Zoeller, N. Thermodynamic Theories of Micelle and Vesicular Systems. Curr. Opin. Colloid Interface Sci. 1997, 2, 294.

(3) Nagarajan, R. Solubilization by Amphiphilar Aggregates. Curr. Opin. Colloid Interface Sci. 1997, 2, 282. (4) Zana, R. Aqueous Surfactan-Alcohol Systems: A Review. Adv. Colloid Interface Sci. 1995, 57, 1. (5) Blankschtein, D.; Thurston, G. M.; Benedek, G. B. Phenomenological Theroy of Equilibrium Thermodynamic Properties and Phase Separation of Micellar Solutions. J. Chem. Phys. 1986, 85, 7268. (6) Nagarajan, R.; Ruckenstein, E. Theory of Surfactant Selfassembly: A Predictive Molecular Thermodynamic Approach. Langmuir 1991, 7, 2934. (7) Nagarajan, R. Theory of Micelle Formation: Quantitative Approach to Predicting Micellar Propereties from Surfactant Molecular Structure. In Structure-Performance Relationships in Surfactants; Esumi, K., Ueno, M., Eds.; Marcel Dekker: New York, 1997. (8) Shiloach, A.; Blankschtein, D. Predicting Micellar Solution Properties of Binary Surfactant Mixtures. Langmuir 1998, 14, 1618. (9) Huibers, P. D. T.; Lobanov, V. S.; Katritzky, A. R.; Shah, D. O.; Karelson, M. Prediction of Critical Micelle Concentration Using a Quantitative Structure Property Relationship Approach. 1. Nonionic Surfactants. Langmuir 1996, 12, 1462. (10) Huibers, P. D. T.; Lobanov, V. S.; Katritzky, A. R.; Shah, D. O.; Karelson, M. Prediction of Critical Micelle Concentration Using a Quantitative Structure Property Relationship Approach. 2. Anionic Surfactants. J. Colloid Interface Sci. 1997, 187, 113. (11) Cox, K. R.; Benson, H. L. The Pseudo-phase Analogy: Application of Vapor-Liquid Equilibria Techniques to Micelle Solution. Fluid Phase Equilib. 1986, 30, 173. (12) Rosen, M. J. Surfactants and Interfacial Phenomena, 2nd ed., Wiely: NewYork, 1989. (13) Chen, C.-C. Molecular Thermodynamic Model Based on the Polymer NRTL Model for Nonionic Surfactant Solutions. J. AIChE 1996, 42, 3231. (14) Li, S. X.; Lu, L. F.; Li, Y. G.; Liu, J. C. Studies on UNIQUAC and SAFT Equations for Nonionic Surfactant Solutions. Fluid Phase Equilib. 1998, 153, 215. (15) Li, S. X.; Lu, L. F.; Li, Y. G. Study on Ionic Surfactant Solutions by SAFT Equation Incorporated with MSA. Fluid Phase Equilib. 2000, 168, 107. (16) McBain, J. W.; Swain, R. C. Measurements of Adsorption at the Air-Water Interface by the Microtome Methodology. Proc. R. Soc. (London) 1936, A154, 608. (17) Fredenslund, A.; Gmehling, J.; Rasmussen, P. VaporLiquid Equilibria using UNIFAC-a group-contribution method; Elsevier: Amsterdam, 1977. (18) Hansen, H. K.; Rasmussen, P.; Fredenslund, A.; Schiller, M.; Gmehling, J. Vapor-Liquid Equilibria by UNIFAC Group Contribution. 5. Revision and Extension. Ind. Eng. Chem. Res. 1991, 30, 2352. (19) Magnussen, T.; Rasmussen, P.; Fredenslund, A. UNIFAC Parameter Table for Prediction of Liquid-Liquid Equilibria. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 331. (20) Hansen, H. K.; Coto, B.; Kuhlmann, B. UNIFAC with Linearly Temperature-Dependent Group-Interaction Parameters. Internal Report SEP 9212, Department of Chemical Engineering, Technical University of Denmark, 1992. (21) Larsen, B. L.; Rasmussen, P.; Fredenslund, A. A Modified UNIFAC Group-Contribution Model for Prediction of Phase Equilibria and Heats of Mixing. Ind. Eng. Chem. Res. 1987, 26, 2274. (22) Chen, F.; Andersen, J. H.; Tyle, H. New Developments of the UNIFAC Model for Environmental Application. Chemosphere 1993, 26, 1325. (23) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; Natl. Stand. Ref. Data Ser. Nat. Bur. Stand.: Washington, DC, 1971; p 36. (24) Hinz, H.-J., Ed. Thermodynamic Data for Biochemistry and Biotechnology; Springer-Verlag: Berlin, 1986. (25) van Os, N. M.; Haak, J. R.; Rupert, L. A. M. PhysicalChemical Properties of Selected Anionic, Cationic and Nonionic Surfactants; Elsevier: Amsterdam, 1993. (26) Oishi, T.; Prausnitz, J. M. Estimation of Solvent Activities in Polymer Solutins Using a Group-Contribution Methodology. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 333.

898

Ind. Eng. Chem. Res., Vol. 41, No. 5, 2002

(27) Elbro, H. S.; Fredenslund, A.; Rasmussen, P. A New Simple Equation for the Prediction of Solvent Activities in Polymer Solutions. Macromolecules 1990, 23, 4707. (28) Kontogeorgis, G. M.; Fredenslund, A.; Tassios, D. P. A Simple Activity Coefficient Model for the Prediction of Solvent Activities in Polymer Solutions. Ind. Eng. Chem. Res. 1993, 32, 362. (29) Kontogeorgis, G. M.; Fredenslund, A.; Economou, I. G.; Tassios, D. P. Equations of State and Activity Coefficient Models for Vapor-Liquid Equilibria of Polymer Solutions. J. AIChE 1994, 40, 1711. (30) Review of the Knowledge Basis of Risk Evaluation of Air Pollutions in Relation to Lung Cancer and Respiratory System Allergy; Center for Environmental and Respiratory System, National Institute of Occupational Health: Copenhagen, Denmark, 2000 (in Danish). (31) Rasmussen, D.; Rasmussen, P. Phase Equilibria in Aqueous Polymer Solutions. Chem. Eng. Prog. 1989, 85, 50. (32) Kehiaian, H. V.; Tine, M. R. Thermodynamics of Binary Mixtures Containing Oxaalkanes Parts. Monoethers, Plolyethers, Acetals, Ortho esters and Cyclic Monoethers + n-Alkanes or Cyclohexane. Fluid Phase Equilib. 1989, 46, 131. (33) Wu, H. S.; Sandler, S. I. Proximity Effects on the Predictions of UNIFAC Model: I. Ethers. J. AIChE 1989, 35, 168. (34) Marsh, K. N.; Niamskul, P.; Gmehling, J.; Bo¨lts, R. Review of Thermophysical Property Measurements on Mixtures Conaining MTBE, TAME, and Other Ethers with Nonpolar Solvents. Fluid Phase Equilib. 1999, 156, 207.

(35) Skjold-Jørgensen, S. On the UNIFAC and UNIQUAC Models. Ph.D. Thesis, Department of Chemical Engineering, Technical University of Denmark, Lyngby, Denmark, 1980. (36) Larsen, B. L. Predictions of Phase Equilibria and Heat effects of Mixing with a modified UNIFAC Model. Ph.D. Thesis, Department of Chemical Engineering, Technical University of Denmark, Lyngby, Denmark, 1986. (37) Kortuem, G.; Valent, V. Thermodynamic Mixing Effect in the Water(1)-1,4-dioxane(2) and Methanol(1)-1,4-dioxane(2) Systems; A Comparison. Ber. Bunsen-Ges. Phys. Chem. 1977, 81, 752. (38) Marsh, K. N.; Ott, J. B.; Costigan, M. J. Excess Enthalpies, Excess Volumes, and Excess Gibbs Free Energies for n-Hexane + Di-n-Butyl Ether at 298.15 and 308.15 K. J. Chem. Thermodyn. 1980, 12, 857. (39) Treszczanowicz, T.; Lu, B. C.-Y. Isothermal Vapor-Liquid Equilibria for an Example of an Ether + a Hydrocarbon. J. Chem. Thermodyn. 1986, 18, 213. (40) Schick, M. J. Nonionic Surfactants-Physical Chemistry; Marcel Dekker: New York, 1987; pp 126-127. (41) Horstmann, S.; Fischer, K.; Gmehling, J. PSRK Group Contribution Equation of State: Revision and Extension III. Fluid Phase Equilib. 2000, 167, 173.

Received for review January 23, 2001 Revised manuscript received June 27, 2001 Accepted June 28, 2001 IE010072E