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Microstructures in the System Water/D2EHPA/Span-80/ n-Dodecane I. Abou-Nemeh†,‡ and H. J. Bart*,§ Christian-Doppler-Laboratorium fu¨ r Modellierung Reaktiver Systeme in der Verfahrenstechnik, Technical University of Graz, Inffeldgasse 25, A-8010 Graz, Austria, and Lehrstuhl fu¨ r Thermische Verfahrenstechnik, University of Kaiserslautern, P.O. Box 3049, D-67653 Kaiserslautern, Germany Received September 23, 1997. In Final Form: May 15, 1998 The solubilization of water by the single ionic amphiphile bis(2-ethyhexyl)phosphoric acid (D2EHPA) and the single nonionic surfactant Span 80 in a nonpolar medium has been investigated. The hydrodynamic, optical, and other various analytical techniques were extensively employed to study the physicochemical nature of the microstructures formed in D2EHPA/n-dodecane/water and Span 80/n-dodecane/water solutions. An analytical model based on geometrical assumptions of the spherical shape of the reversed micelles has been developed. The proposed model correlates, among several others, the aggregation number, and, thus, the size of microstructures with parameters such as the hydrocarbon chain length of the surfactant molecule, its concentration and volume fraction occupied by the reversed micelles, etc., the latter is being estimated from the Einstein viscosity equation and its two modified versions reported by Guth and Simha and Vand. Assuming the spherical shape of the aggregates, the Einstein equation was found to fit the experimental data of the D2EHPA solutions very well; however, Vand’s equation was found to be more suitable to fit those of Span 80 solutions. The molecular associates formed by D2EHPA were mostly dimers; however, relatively larger microstructures were formed by Span 80, the higher the concentration the smaller the size with a tendency to leveling off and the shape is nonspherical. The basic structural parameters, that is, the aggregation number, reversed micelle, and water pool radii were derived, and a good agreement between the experimental and the predicted data from the model was found.
Introduction The liquid surfactant membrane (LSM) process has been hailed to have the potential to solve numerous separation problems, particularly for the treatment of dilute solutions in various branches of industries, for example, chemical (phenol and ammonia separation from wastewater1), metallurgical (copper;2 cobalt, manganese, iron, nickel, and chromium;3 and zinc4 separation and recovery from mining and industrial waters), and biotechnological origin (enzyme-catalyzed L-amino acid preparation5 and lactic acid recovery from broth solutions and downstream effluents6). The main principle of the LSM process relies on adding a well-designed water-in-oil (W/O) emulsion to the contaminated aqueous feed. The organic phase (membrane) of the emulsion contains the surfactant, e.g., Span 80, ECA 4360, and the carrier, e.g., D2EHPA, both are dissolved in the membrane matrix, e.g., kerosene. The internal aqueous phase of the emulsion contains the * To whom all correspondence should be addressed. † Technical University of Graz. ‡ Present address: Department of Chemical Engineering, Chemistry and Environmental Science, New Jersey Institute of Technology, University Heights, Newark, NJ 07102. § University of Kaiserslautern. (1) Kitagawa, T.; Nishikawa, Y.; Frankfeld, J. W.; Li, N. N. Environ. Sci. Technol. 1977, 11, 602. (2) Bart, H. J.; Wachter, R.; Marr, R. In Separation Processes in Hydrometallurgy; Davies, G.A., Ed.; Ellis Horwood Ltd.: Chichester, 1987; p 347. (3) Abou-Nemeh, I.; Van Peteghem, A. P. Hydrometallurgy 1992, 31, 149. (4) Draxler, J.; Marr, R.; Pro¨tsch, M. Sep. Sci. Technol. 1988, 15, 204. (5) Scheper, T.; Makryaleas, K.; Likidis, Z.; Nowottny, C.; Meyer, E. R.; Schu¨gerl, K. Proc. Int. Conf. Solv. Extn. ISEC’86, vol. 2, 695, Dechema 1986 Frankfurt. (6) Chaudhuri, J. B.; Pyle, D. L. Chem. Eng. Sci. 1992, 1, 41.
stripping reagent, e.g., sulfuric acid, sodium hydroxide, etc. One of the major nonidealities encountered with the emulsion application in LSM is water transport during the solute permeation, which results in dilution of the concentrated recovered species. Consequently, an additional undesired preevaporation stage is required before the recovered solute can be recycled. Furthermore, the internal phase volume increase due to swelling and affects the emulsion performance, and thus, its stability, the breakage of the emulsion, and leaking of the internal phase reagent metallic species is of appreciable concern in LSM.7 The phenomenon of water transport can be attributed to osmosis, which is caused by the difference in the chemical potential of the phases, i.e., the feed (external phase) and internal phase of the emulsion across the membrane. From the quantitative point of view, osmosis is influenced by a number of factors and parameters8 such as, the surfactant, the carrier, the difference in ionic strength between the internal and external phases, the globule parameters, the residence time, the hydrodynamic conditions, and temperature. It has been reported by many authors8-12 that the absolute volume of the internal aqueous phase was doubled in several minutes of emulsion residence time. The incorporation of the carrier D2EHPA in the membrane is to facilitate mass transport of the solute by forming intermediate oil-soluble complexes (7) Abou-Nemeh, I.; Van Peteghem, A. P. J. Membr. Sci. 1992, 70, 65. (8) Bart, H. J., Draxler, J.; Marr, R. Hydrometallurgy 1988, 19, 351. (9) Abou-Nemeh, I.; Van Peteghem, A. P. Sep. Sci. Technol. 1994, 29 (6), 727. (10) Teramoto, M.; Sakuramoto, T.; Koyoma, T.; Matsuyama, H.; Miyake, Y. Sep. Sci. Technol. 1986, 21 (3), 229. (11) Matsumuto, S.; Inoue, T.; Kohda, M.; Ikura, K. J. Colloid Interface Sci. 1980, 77, 555. (12) Bart, H. J.; Ramasaeder, C.; Haselgru¨bler, T.; Marr. R. Hydrometallurgy 1992, 28, 253.
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D2EHPA-metal via an interfacial chemical reaction that takes place at the feed/membrane interface. However, this kind of enhancement is accompanied with water binding to the matrix of the complex formed, which can be represented by the following reaction:13
Mn+ + nNO3- + (w - ax)H2O + a[E(H2O)x] T M(NO3)n(H2O)w(E)a (1) The factors in eq 1 from left to right are as follows: the metallic ion; the anion; the aqueous phase water transferred from the aqueous to the organic phase; hydrated extractant molecule, e.g., D2EHPA, and extracted metal complex or ion-pair. However, the most important factor of all is water transport via the surfactant, and particularly nonionic surfactants of the ester type such as Span 80 and 85, Arlacel 83, etc. Many authors8,14-19 reported that some surfactants, S, undergo the reaction with themselves and water molecules to form different hydrates, SN(H2O)w(o), and/or aggregates, SN(o), micelles according to eqs 2, 3, and 4, respectively.
NS(o) + wH2O T SN(H2O)w(o)
(2)
SN-1 + S T SN
(3)
NS(o) T SN(o)
(4)
The huge amount of water that can be transferred during metal, phenol, and lactic acid permeation in LSM within few minutes is exceedingly difficult to explain by means of classical views such as carrier-solute hydrates or even surfactant hydrates permeation. In our view, there should be a large number of small “buckets” carrying the water and shuttling from the feed/membrane interface to the membrane/internal aqueous phase interface. Therefore, the main objective of the present paper is to obtain quantitative and qualitative data on the mechanism of water solubilization and to identify the association microstructures which form in the organic phase of D2EHPA/n-dodecane/water and Span 80/n-dodecane/ water systems. The latter one and the combination of both are being standard systems used in the LSM process for phenol and metals extraction, respectively.
Methods. Equal volumes of the organic phase containing various concentrations of D2EHPA or Span 80 in n-dodecane and ultrapure water were equilibrated in a thermostated bath at 20 °C. To ensure equilibrium is reached, the samples were contacted for 24 h by means of continuous agitation supplied by a mechanical rocking device at a frequency 100 min-1. After equilibration, the samples were centrifuged to break down the macroemulsion formed during mixing and to obtain a clear transparent solution of the organic phase. If reversed micelles are formed, then they are unlikely to be affected by the relatively low gravitational field 1600g at the meniscus and about 2000g at the base. A trial-and-error procedure was adopted to determine the optimal time required for phase disengagement. In different parts of this study, the equilibrium D2EHPA concentration in the membrane phase is the modified value obtained by subtracting the equilibrium aqueous phase D2EHPA concentration from its initial concentration in the membrane phase. The determination of D2EHPA concentration in the aqueous phase was carried out by high-performance liquid chromatography (HPLC) using a mixture of 85% 2-propanol and 15% water as a mobile phase and RP-18 reversed column as a stationary phase. An analogous procedure was applied for Span 80. However, it should be remarked that D2EHPA distribution between both phases is favored by the organic phase, and a maximum concentration of several parts per million in water was found. As far as Span 80 is concerned, only trace amounts of sorbitol and sorbitol derivatives were found in the aqueous phase. Viscosity. The organic phase, thus obtained, was subject to extensive investigations, where the kinematic viscosity was measured by means of viscometer Lauda Viscoboy 2, interfaced to a thermostat, at 20 ( 0.1 °C. Density. The density was measured by using the densimeter Paar DM 35 at 20 °C. A special precaution was taken to clean thoroughly both instruments with pure metanol and later dry it with clean, oil free, prefiltered air. Refractive Index. The refractive index was measured by means of thermostated Abbe´ refractometer, Atago 1T type, interfaced to a thermostat, at 20 °C. Water Content. The water content of the solutions was determined by employing the Karl-Fisher titration technique using a Mettler Toledo DL35 model titrator. Particle Size Determination. The ultrafine particle analyzer (UPA) Grimm model 3.150, was employed to measure the particle size. The dynamic light scattering technique was used to determine the linear dimension of the reversed micelles. The resolution range of the instrument varies from 1 nm to 0.005 mm. Therefore, particular care should be taken in sample handling before it can be measured by the instrument.
2. Experimental Section Materials. D2EHPA of AnalaR grade purity was purchased from Merck, its quality was checked by titration and yielded more than 98% purity. Span 80 (lot no. V-3106) was kindly supplied by ICI Essen-Germany. Another sample of Span 80 was purchased from Sigma and did not show any significant difference as far as the physical properties (viscosity, density, refractive index, etc.) surface tension, water solubilization, or physical appearance are concerned. All were used without further purification. n-Dodecane (99% Fluka) was used as received. The water employed in this study was purified by LP reverse-osmosis and NANOpure systems. The measured resistivity of water was 18 MΩ. cm and its pH was 6.73. (13) De, A. K.; Khopkar, S. M.; Chalmers, R. A. In Solvent Extraction of Metals; Van Nostrand Reinhold Co.: London, 1970; p 15. (14) Collinart, P. S.; Delephine, S.; Trouve, G.; Renon, H. J. Membr. Sci. 1984, 20, 167. (15) Florence, A. T.; Whitehill, D. J. Colloid Interface Sci. 1981, 79 (1), 351. (16) Matsumaoto, S.; Kohda, M. J. Colloid Interface Sci. 1980, 73, 13. (17) Zulauf, M.; Eicke, H. F. J. Phys. Chem. 1979, 83 (4), 480. (18) Ruckenstein, E.; Nagarajan, R. J. Phys. Chem. 1980, 84, 1349. (19) Abou-Nemeh, I., Solubilization and Microstructure of SPAN80/ D2EHPA-Systems. Paper presented at Kaiserslautern University, 1996
3. Theory The Viscosity Law and Related Equations. In an ideal solution of noninteracting dispersed spheres and ideal flow conditions, the molecules dispersed in the medium are large relative to the molecules making up the medium, so that the medium can be considered a continuum relative to the particles.20 The volume fraction of the solution taken up by the solute, φ1, is related to the specific viscosity, ηsp, by the Einstein equation
ηsp ) (η - η0)/η0 ) 2.5φ1
(5)
where η and η0 are the dynamic viscosity of the solution and solvent, respectively. Guth and Simha21 and later Vand22 proposed two modified extended relationships for (20) Einstein, A. Ann. Phys. 1911, 34, 591. (21) Guth, E.; Simha, R. Kolloid Z. 1936, 71, 266. (22) Vand, V. J. Phys. Colloid Chem. 1948, 52, 277.
Water Transport in the LSM Process
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moderate concentrations of the solute, eqs 6 and 7, respectively
ηsp ) 2.5φ3 + 14.1φ32
(6)
ηsp ) 2.5φ2 + 7.35φ22
(7)
Cheng and Schachman23 found the Einstein equation to hold for values in the region of low concentration (below 2% (v/v)), while those of Guth and Simha and Vand for φ3 had values up to ∼0.10 (10% (v/v)), i.e., for dispersions of relatively moderate concentration. On the other hand, Eirich et al.24 verified Einstein’s equation and concluded that the equation was valid for φ1 values higher than 0.10 regardless of the sphere size used as long as the major assumptions are met, in other words, the particles are solid spheres and their concentration is small. Current Views of Surfactant Films and Hydrodynamic Interactions. The Einstein theory is based on a model of dilute unsolvated spheres. Any deviation from the model can be a result of the following factors: (1) undilute concentrations of the solute; (2) swelling of the particles due to solvation; (3) nonspherical shape of the particles. A number of theoretical attempts have been made to evaluate the coefficient of the higher terms in the power series, for example, eqs 6 and 7, by going back to through Einstein’s derivation, superimposing the effects of neighboring particles, and studying the effect of undiluted solutions. A few theoretical values were obtained from different models such as 14.1, 12.6, and 7.35. These values account for the so-called “crowding effect” of particles and their “hydrodynamic interactions”. In surfactant-based systems, as is the case of the present study, these interactions become significant and the nature of interface as well as the size and shape of micelles will primarily be established by them. Several approaches have been proposed by Israelachvili et al.,25,26 Mitchell and Ninham,27 Tanford,28 Eicke and Christen,29 and many more to quantify those interactions in energetic or/and thermodynamic terms, such as, solvent-solvent dispersion interaction, dispersion interactions between the hydrocarbon groups of the micelle and the solvent, dispersion interactions between the apolar groups of the monomers forming the micelle, and Coulombic interactions between the units of ionic groups, which result in (1) repulsive terms between positive charges or negative charges, (2) attractive terms between the positive and negative regions of charge, (3) electrostatic binding energy of the ionic groups within the monomer, etc. On the thermodynamic side, various terms were considered to describe the chemical potential of a micelle such as surface, bulk, curvature, and packing. Each of these terms is assigned to represent a certain interaction, for example, the bulk term is a measure of hydrophobic free energy of removing hydrocarbon tails from water. Other views have been (23) Cheng, P. Y.; Schachman, H. K. J. Polym. Sci. 1955, 16, 19. (24) Eirich, F.; Bunzl, M.; Margaretha, H. Kolloid Z. 1936, 74, 276. (25) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1976, 72, 1525. (26) Israelachvili, J. N.; Marcelja, S.; Horn, R. G. Q. Rev. Biophys. 1980, 3, 121. (27) Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1981, 77, 601. (28) Tanford, C. The hydrophobic effect: formation of micelles and biological membranes; John Wiley & Sons Pub.: New York, 1980; Vol. 5. (29) Eicke, H. E.; Christen, J. Colloid Interface Sci. 1962, 46 (3), 417.
Figure 1. A schematic diagram of the spherical reversed micelle model.
presented by Friberg and Buraczenska.30 To summarize the previous thoughts, undoubtedly any of these interactions will have the upper hand in deciding the final shape and size of the microstrucures and, thus, the nature of the interface. Spherical Model of Reversed Micelles and Basic Structural Parameters. A spherical model of the reversed micelle is shown in Figure 1. The model can be visualized as two concentric spheres, the inner one is composed of the water core where the hydrophilic heads of the surfactant are immersed in the water pool while the outer sphere is the coat, which consists of the hydrocarbon chain of the surfactant molecule extended in the organic phase. The volume fraction of the solution occupied by the solute (water + Span 80 or D2EHPA) in the bulk of the organic phase can be represented by
φ ) (VT - V0)/VT
(8)
where VT and V0 are the total volume of the organic phase (micellar phase) and the solvent, respectively. The measurement of the mass and the density of the micellar phase before and after water solubilization would allow φ to be determined. Knowing the φ value from either viscosity or gravimetric measurements would allow the estimation of the basic structural parameters of aggregates such as the aggregation number, N, water core radius, rH, and, thus, the reversed micelle radius, rm. From this model, the volume of the micelle, Vm, can be represented by
Vm )
4π (r + lc)3 3 H
(9)
where, lc, is the length of the surfactant hydrocarbon chain. In analogous manner, the radius of the water core can be represented by
rH )
(4π3 V )
1/3
H
(10)
where VH is the volume of the water core of the reversed (30) Friberg, S., Buraczewska, I.; Ravey J. C. In Micellization, Solubilization and Microemulsions; Mittal, K. L., Ed.; Plenum Press: New York, 1976; Vol. 2.
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Abou-Nemeh and Bart
micelle. Because the number of water molecules per micelle, NH, is equal to NR, where
nH (moles water) ) nS (moles surfactant)
R)
(11)
R is the molar ratio of water to surfactant in the system. Hence, eq 10 can be represented in terms of the specific volume of water molecule, vH, according to the following equation:
rH )
(4π3 v
H
NR
1/3
)
(12)
The aggregation number of the surfactant can be defined as the ratio of the total number of D2EHPA or Span 80 molecules, NS, to the total number of the reversed micelles, Nm, in the micellar phase, VT, which can be represented by
N)
nSNA NS ) Nm φ (VT/Vm)
(13)
where NA is Avogadro’s number. Thus, by substituting the values of eqs 9 and 12 into eq 13 one obtains
N)
NS nSNA 4π 3 v NR ) Nm φVT 3 4π H
([
1/3
]
3
)
+ 1c
(14)
([ ]
φVT 3 nSNA
4πlc3
1/3
)
1/3
- [vHR]
(15)
3
The value VT/ns is simply the reciprocal of the surfactant concentration, Cs. It should be remarked here that the unit of Cs is mol/m3. Therefore, the final form of eq 15 can be represented by
N)
([ ]
4πlc3 φ 3 CSNA
1/3
)
- [vHR]1/3
-3
(16)
Equation 16 demonstrates the possibility of estimating the aggregation number of spherical microstructures formed in the micellar phase. However, considerable care should be taken when deriving values of the aggregation number from such data when the droplet has regions of different densities.31,32 The values R, Cs, and φ can be obtained experimentally, while lc (nm) can be estimated from the literature. The value of the specific volume of water molecules can be calculated from
vH ) MH/FHNA
talist with the necessary input data to estimate the volume fraction occupied by the reversed micelles. In the present study, the viscosity law proposed by Einstein, eq 5, and its modified versions (6) and (7) were used to estimate this important variable. The output results of the application of eqs 5, 6, and 7, i.e., Φ, is then substituted into eq 16 to estimate the aggregation number, N, and, thus, the size of the micelles. 4. Results and Discussion
In eq 14, N is not explicitly expressed, a rearrangement yields
N)
Figure 2. Specific viscosity, ηsp, of D2EHPA solutions versus the volume fraction, φi)1,3 estimated from eqs 5, 6, and 7.
(17)
where M and FH are the molecular weight and density of water in the droplet. Typical values of vH are 0.0298 and 0.0339 nm3 for FH values 1 and 0.881 g/cm3, respectively. Methodology. The basic objective of the experimental measurements of the density and viscosity of the systems Span 80/n-dodecane and D2EHPA/n-dodecane before and after contacting with water is to provide the experimen(31) Day, R. A.; Robinson, B. H.; Clarke, J. H. R.; Doherty, J. V. J. Chem. Soc., Faraday Trans. 1979, 75, 132. (32) Mathews, M. B.; Hirschhorn, E. J. Colloid Interface Sci. 1952, 15, 86.
4.1. D2EHPA/n-Dodecane/Water System. D2EHPA is a very popular and widely used extractant for nickel, cobalt, and uranium extraction in both LSM and solvent extraction processes.33-35 This extractant is known by many researchers36-38 to form dimers due to hydrogen bonding in most hydrocarbon media of low dielectric constant such as kerosene ( ) 2.2). Such dimers are quite stable at room temperature and undergo reaction with metallic ions, e.g., cobalt to yield tetrahedral cobaltous complexes.39 Baes et al.40 have measured the kinetics of dimerization of D2EHPA in organic solvents and found that the stability constant (k) of the dimer is quite high (log k ) 4.75). This fact is of paramount importance as far as the Einstein equation application is concerned. The validity of the rigid sphere model of the solute molecule is that the size of the latter is relatively large to that of the medium, otherwise, the equation is unapplicable.41 The results of viscosity measurement of the system are shown in Figure 2, which is a plot of the specific viscosity of the solutions versus the volume fraction φ1,3 occupied by the solute (D2EHPA and water). Also, the three equations, i.e., Einstein’s, Guth and Simha’s, and Vand’s, are presented. In the region of low concentrations, i.e., below 7%, Einstein’s theoretical equation and the experimental data are in excellent agreement. Equally, it should be noted that the other two correlations show a good fit to the experimental points. However, this is due to the relatively small values of φ at low solute concentrations, and thus, the square value of φ is even smaller so that the (33) Abou-Nemeh, I.; Van Peteghem A. P. Proc. Second Int. Conf. Sep. Sci. and Technol. ICSST’89, vol. 2. 1989, p 416. (34) Preston, J. S. Hydrometallurgy 1982, 9, 115. (35) Kennedy, J.; Deane, A. M. Inorg. Nucl. Chem. 1961, 19, 142. (36) Kolarik, Z. In Solvent extraction review. Marcus, Y., Ed.; Solvent Extraction and Ion-exchange; Marcel Dekker Inc.: New York, 1971; Vol. 2. (37) Sato, T. J. Inorg. Nucl. Chem. 1964, 26, 311. (38) Ferraro, J. R.; Peppard, D. F. J. Phys. Chem. 1961, 65, 539. (39) Hudson, J. Hydrometallurgy 1982, 9, 149. (40) Baes, C. F., Jr. J. Inorg. Nucl. Chem. 1962, 24, 707. (41) Jones, G.; Tabley, S. R. J. Am. Chem. Soc. 1937, 55, 624.
Water Transport in the LSM Process
Figure 3. Aggregation number, N, of D2EHPA estimated from the proposed model according eq 16 for φ1, φ2, and φ3 versus concentration in n-dodecane.
second term in both equations can be neglected. Consequently, this yields Einstein’s equation. In the region of higher concentrations, i.e., higher than 7% (φ ) 0.1), there is a clear deviating trend between the experimental and the other theoretical curves. However, the trend indicated by the experimental points suggests that Einstein’s equation is the one more likely to fit the experimental data better than the other two. (a) Molecular Structure of Aggregates. The aggregation number of the associates estimated according to the proposed model, eq 16, using φ1,3 values obtained from eqs 5, 6, and 7 versus D2EHPA concentrations are shown in Figure 3. The hydrocarbon tail, lc, of D2EHPA molecule was taken as 0.59 nm.42 From this figure it can be seen that the model predicts the molecular structure of D2EHPA in n-dodecane solutions with varied accuracy depending on the φ1,3 values obtained from the corresponding eqs 5, 6, and 7. For φ1 values estimated from Einstein’s equation, the aggregation number was found to be 2 ( 0.31, while those from Vand’s and Guth and Simha’s were 2 ( 0.46 and 2 ( 0.59, respectively. Accordingly, the percentage correlation error was found to be 16, 23, and 29%, respectively, for the three equations assuming that a dimeric structure was formed. At low concentrations (0.11 M ∼ φ ) 0.027) all equations are in excellent accord with reported data from the literature.40,42 It is not by accident that eqs 6 and 7 show a good matching trend. This fact can be attributed to the relatively small φ2,3 values. Thus the higher terms in eqs 6 and 7 give even smaller values, and therefore, they become negligible in comparison with the first term, which de facto lead to Einstein’s equation. However, at higher concentrations, all graphs show increasingly deviating tendency from the dimeric structure, presumably because the hydrodynamic interactions between the particles become significant at this range of concentrations. Nonetheless, Einstein’s equation shows a matching trend even at higher D2EHPA concentrations, i.e., 0.855 and 1.435 M, which corresponds to φ1 values of about 0.11 and 0.17, respectively. At such high volume fraction of the solute, the distance separating the particles is slightly greater than the diameter of the particles, and thus, the interactions become highly significant, which in turn should result in a deviating trend from the Einstein model. However, the experimental results for this particular system indicate otherwise. In other words, the spherical assumption of aggregates applying the volume fraction estimated ac(42) Lovera, J.; Lovera, P.; Gregoire, P. J. Solid State Chem. 1988, 77, 40.
Langmuir, Vol. 14, No. 16, 1998 4455
Figure 4. Water solubilization by D2EHPA and the molar ratio, R, versus D2EHPA concentrations.
cording to eq 5 is valid for values below 20%. This finding is consistent with analogous results reported earlier by Eirich24 and later by Vand22 on the validity of Einstein’s equation for φ1 values below 20% and its ability to predict simple molecular structures. (b) Water Solubilization and Model Verification. The results of water solubilization and water-to-surfactant molar ratio, R, versus D2EHPA concentrations are depicted in Figure 4. The profile of water solubilization curve is noteworthy, where at 0.043 M D2EHPA it passes through a minimum and successively increases on increasing the carrier concentration. It is quite interesting to notice that at very low D2EHPA concentration, ∼0.002 M, the highest value of water solubilization was observed, and therefore, the highest water-to-surfactant ratio (R ) 5) was thus obtained. Apart from this observation, the extent of water solubilization by D2EHPA dimers is rather obscure and marginal in comparison with other classical surface active agents of analogous chemical structure such as sodium bis-(2-ethylhexyl) sulfosuccinate (AOT). Low water solubilization by D2EHPA dimers can be attributed to the lack of formation of reversed micelles, and dimers do not appear to aggregate unless metal ions or surfactants are present in the system.43 It is more likely, that water solubilization by D2EHPA can take place via hydrates formation between D2EHPA and water molecules, especially, when the former is a strong acid, such hydrates can be detected by NMR or FT-IR techniques.9 Surfactant molecules do not always associate into micelles and, in some cases, do not form closed structures.44 D2EHPA belongs to this group of surfactants. In the absence of a “precursor”, which initiates “gluing” the dimers into clusters or molecular aggregates, D2EHPA molecules remain in the dimeric structure. To verify the hypothesis that D2EHPA does not form spherical structures, the spherical model of microstructures in the organic phase has been tested. A new expression has been introduced, i.e., the average area per adsorbed D2EHPA molecule, Ω. In other words, it is the area occupied by D2EHPA molecule adsorbed at the water core/n-dodecane interface of the reversed micelle and can be represented by the following equation:
Ω ) 4πrH2/N
(18)
(43) Newman, R. D.; Park, S. J. J. Colloid Interface Sci. 1992, 152 (1), 41. (44) Langevin, D. Annu. Rev. Phys. Chem. 1992, 43, 341.
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Abou-Nemeh and Bart Table 1. Span 80 Composition (%) component
ICI data
Abou-Nemeh and Van Peteghem45
sorbitan monooleate sorbitan dioleate sorbitan trioleate sorbitan tetraoleate isosorbide monooleate free sorbitol 1,3,4,6 anhydrous sorbitol isosorbide free oleic acid
19.1 36.5 24.8 6.7 3.9 N.M N.M N.M
36.2 32.3 19.3 3.5 N.Ma 1.6 3.9 3.1
a
N.M, not mentioned.
Figure 5. Water core radius, rH, of D2EHPA molecular aggregates estimated according eq 20 for eqs 5, 6, and 7 versus the molar ratio, R.
From eq 12 the relationship between the water core radius, rH, of the spherical reversed micelle and the molar ratio, R, is equal to
R)
4πrH3 3vHN
(19)
By substituting the value of Ω into eq 19 and solving for rH, we obtain
rH )
3vH R Ω
(20)
As can be seen, the radius of the water pool of the reversed micelle is linearly related to the water-to-surfactant molar ratio, R, assuming that Ω does not vary greatly with R and the specific volume of water molecule is relatively constant within the applied R range. This result is of crucial importance to check the spherical model and the nature of the formed aggregates. In Figure 5, the results of the average “radius” of the water core are plotted against the molar ratio. It shows that the relationship between the water core “radius” of the droplets and the molar ratio is nonlinear. However, as can be seen from this curve, there are some intervals of linearity between r and R, and thus, the curve was divided into three R regions, i.e., for ultralow R, R ∈(0, 0.034, 0.057), very low R, R ∈ (0.057, 0.11), and low R values, R ∈ (0.11, 0.4). The experimental points belonging to the same domain were subjected to regression and showed, indeed, a high value of correlation and the residues squared obtained were 0.996, 0.996, and 0.999, respectively. The data obtained from the regression was used to estimate the aggregation number of D2EHPA assuming the same water core “radius” of the droplet. The results revealed a very high error of predicting the experimental aggregation number, and the percentage errors were 51-60%, 60-70%, and 65-95% for the three R regions, respectively. From the preceding finding, therefore, it can be concluded that, indeed, there is no linear correlation between the water core “radius” derived from the employed model and the molar ratio, R. Consequently, the geometrical nature of microstructures formed by D2EHPA dimers is not spherical and no inverted micelles were found, which is consistent with earlier reported results.43 4.2. Span 80/n-Dodecane/Water System. (a) Water Solubilization by Span 80. Span 80 is a nonionic
Figure 6. Solubility diagram of water in Span 80 micellar solution: A, nonlinear range; B, entire range.
surfactant that is often misleadingly called sorbitan monooleate. Abou-Nemeh and Van Peteghem45 have analyzed Span 80 by means of two analytical techniques, gas chromatography (GC) analysis and gel permeation chromatography (GPC), and found that Span 80 is a mixture of different sorbitan esters (monooleate, dioleate, trioleate, tetraoleate) and starting and byproduct materials (oleic acid, sorbitol, sorbitol isosorbide and water). See Table 1. The concept of micellization in apolar solvents has been much debated in the literature, and the presence of critical micelle concentration (cmc), in particular, has been questioned and casts doubt on reported cmc values.18,46 However, some form of micellization usually occurs, and the microstructures formed solubilize, to a certain extent, water. Numerous examples can be found on the formation of inverted micelles by AOT47-49 and the capability of water solubilization by these structural associates. However, as far as Span 80 is concerned the literature has almost nothing to offer on the subject, apart from a few papers45,50,51 on related subjects of Span 80 interfacial properties. Span 80 readily dissolves in dry n-dodecane to give clear solutions; however, sorbitol, which is strongly hydrophilic compound, precipitates spontaneously from the organic medium. The solubility diagram of water for Span 80 micellar solutions is shown in Figure 6. It should be remarked that only the surface active components of Span (45) Abou-Nemeh, I.; Van Peteghem, A. P. Chem. Ing. Technol. 1990, 62 (5), 420. (46) Kertes, A. S.; Gutmann, H. In Surface and Colloid Science; Matijevic, E., Ed.; Willey-Interscience: New York 1976; Vol. 8, Chapter 3. (47) Kithara, A.; Kobayashi, T.; Tachibana, T. J. Phys. Chem. 1962, 66, 363. (48) Peri, J. B. J. Colloid Interface Sci. 1969, 29, 6. (49) Davies, R.; Graham, D. E.; Brian, V. J. Colloid Interface Sci. 1986, 116 (1), 88. (50) Boyd, J.; Parkinson, C.; Sherman, P. J. Colloid Interface Sci. 1972, 41, 359. (51) Mickucki, B. A.; Osseo-Asare, C. Hydrometallurgy 1986, 16, 209.
Water Transport in the LSM Process
80, i.e., sorbitan monooleate, dioleate, trioleate, tetraoleate, and oleic acid, were taken into account for the average molecular weight calculation, and the extended length of the hydrocarbon chain, lc, of oleic acid was estimated according to the method of Tanford.28 Two different regions were distinguished, i.e., low (see Figure 6B) and high concentrations (Figure 6A), from 0.0005 to 0.012 M and 0.012 to 0.33 M, respectively. The two regions were differentiated by linearly regressing the experimental data points for the best fit with maximum number of points as shown in Figure 6B. However, the remaining points, obviously, fit the nonlinear curve as shown in Figure 6A. According to various authors51-54 the lower limit of concentrations used in this study is well above the cmc of Span 80. It is clear from Figure 6B, that the solubilization limit of water in the nonionic surfactant solutions is directly proportional to the surfactant concentration. This increase in water solubilization with surfactant concentration suggests that water molecules are incorporated into the nonionic micelles. An average of two molecules of water were solubilized by one molecule of the surfactant, and thus, the size and shape of the reversed micelle can be spherical and not large. However, the linear relationship between water solubilization and the surfactant concentration is no more valid at lower Span 80 concentrations. In Figure 6A, a larger amount of water is dissolved in the micellar phase; the molar ratio of water-to-surfactant is about 10-12 at the lower edge (0.001 M) and decreases gradually to reach a value of 6 at the higher edge (0.012 M) of Span 80 concentration. Obviously, unlike Figure 6B, a nonlinear correlation was found between the surfactant concentration and the amount of water solubilized by the microstructures for this low range of Span 80 concentrations. These results indicate that, at the initial stage of solubilization, successive water molecules interact strongly with a dissimilar site in the bulk of the reversed micelle and that there is continued solubilization of water phase by hydrogen bonding between solubilized water molecules. The nature of these microstructures and size will be discussed in the next section. (b) Linear Dimension of Microstructures. To estimate the aggregates size and their dimensions, the proposed model eq 16 and related eqs 5, 6, and 7 were extensively used. Figure 7 displays the results of the reversed micelles linear dimensions as well as those obtained by the light scattering (LS) technique versus Span 80 concentrations. It can be seen that the profile of the three curves shows a trend similar to that obtained by the LS method. Depending on the equation from which the φ values were estimated, the diameter of aggregates features a high value at low surfactant concentration, 0.006 M, with a characteristic steep fall from 6 and 8 nm to 4 and 5 nm for φ1 and φ2 estimated from Vand’s and Einstein’s equation, respectively, and reaching a minimum at about 0.02-0.03 M. Moreover, an addional common characteristic is the smooth leveling off tendency of all curves including the optical one at about 0.03 M. On comparison of the estimated diameter from the model for the three different φ1, φ2 , and φ3 values with the optical data, it can be seen that the model predictions using eqs 5 and 7, φ1 and φ3, respectively, are slightly higher than those obtained by the LS technique. However, the best estimation of the aggregate linear dimension seems to follow the application of φ2 values obtained from Vand’s (52) Bhattacharyya, D. N.; Kelkar, R. Y. J. Colloid Interface Sci. 1983, 92, 260. (53) Zhi-Jian, Y.; Newman, J. J. Am. Chem. Soc. 1992, 116, 4075. (54) Becher, P.; Arai, H. J. Colloid Interface Sci. 1968, 27 (4), 634.
Langmuir, Vol. 14, No. 16, 1998 4457
Figure 7. Aggregate diameter predicted by the model using various φ1, φ2, and φ3 values and those obtained by the light scattering versus Span 80 concentration in n-dodecane.
Figure 8. Aggregation number, N, estimated according to eq 16 for eqs 5, 6, and 7 versus Span 80 concentration in n-dodecane.
equation. The percentage average error (PAE) that can be committed using the present model and applying the φ2 values is less than 13%, while on using φ1 and φ3 values, the PAE is decisively higher and can be less than 60% and 300%, respectively, depending on the range of Span 80 concentration. The size of microstructures formed in the organic phase by Span 80 seems to be rather small, which is about 5 nm in diameter on the average. A possible explanation of such behavior can be attributed to the structure of the solvent, which remains basically unaltered by the presence of the amphiphilic molecules. The hydrophobic interactions between the surfactant hydrocarbon chain and the solvent molecules is just as favorable as with other surfactant tails. Therefore, in such a situation there is no tendency that ultimately favors the formation of larger aggregates, and hence, smaller microstructures are formed. This finding is quite consistent with the theoretical calculations earlier reported by Ruckenstein and Nagarajan.18 (c) Morphology of Microstructures. The model actually predicts in the first place the N value, i.e., the aggregation number of the microstructures at a given surfactant concentration. The linear dimension can be estimated accordingly, assuming as earlier mentioned the spherical shape of the reversed micelles. The results of the data processing are shown in Figure 8. The aggregation number, N, values estimated according to eq 16 for
4458 Langmuir, Vol. 14, No. 16, 1998
various φi)1,3 are plotted versus the molar concentration of Span 80. The figure shows that the size distribution is monotonically decreasing (all curves) or possesses a minimum (φ2, φ3) in the range of relatively small concentrations of amphiphile (0.012-0.035 M). It is worth observing that at low surfactant concentrations the amphiphiles are present in aggregates with N < 25 and N < 167 for φ1, φ2 values, respectively. The data collected using φ3 seems to be out of reasonable range of size of aggregates. Similar observations were reported by other authors55 regarding the inapplicability of Guth and Simha’s equation for low surfactant concentrations. The next phenomenon that is worth noting here is that above 0.036 M no characteristic change was observed except that the size of aggregates shows a more leveling off tendency than a slight gradual change versus concentration. The change of apparent aggregation number is independent of the concentration of surfactant. Such a system can be characterized by a constancy of surfactant monomer over a wide range and by narrow distribution of the micellar size. The aggregates formed within this region of amphiphile concentrations are rather small, i.e., N < 22 and N < 50 for φ2 and φ1, respectively. Ravey et al.56 obtained some direct experimental evidence of such a morphology of microstructures using small-angle neutron scattering for nonionic surfactants in decane; the aggregation size distribution profile was identical to the one obtained in the present study and the size of aggregates varied 60 < N < 20. Kijiro Kon-no57 reported that the apparent aggregation number of sorbitan monooleate (one of the major components of Span 80) in n-heptane using vapor pressure osmometry was found to fall within the range 4 < N < 7, which is slightly lower than the finding of the present study, i.e., 3 < N < 20, depending on the applied surfactant concentration. The possible explanation of such deviation can be attributed to the fact that Span 80 is a mixture of five amphiphiles contributing to a greater or lesser extend to the formation of so-called “mixed reversed micelles”. Such micelles are usually larger in size and magnitude and, thus, characterized by higher solubilizing power. This fact was experimentally verified for the Span 80 and D2EHPA mixed system.58 The formation of small microstructures in the organic phase can be attributed to the fact that the structure of the organic medium is basically unchanged by the presence of the surfactant molecules. Nevertheless, the dipoledipole interactions that take place between the polar headgroups of amphiphiles, which constitute the main attractive force for aggregation, lead to the formation of relatively small aggregates. (d) Nonspherical Reversed Micelles. In this section, the procedure presented earlier regarding the verification of the spherical shape of reversed micelles is applied. In Figure 9, the water core radii, rH, of aggregates estimated from the model are depicted versus the molar ratio, R. The points are the experimental data, while the solid lines are the estimated values from the linear regression. As can be seen, the best fit to a straight line was obtained for φ1 values estimated from Einstein’s equation with a residue squared of 0.96, which was expected. Basically, this is due to the fact that one of the fundamental assumptions in Einstein’s equation is that the particles are solid spheres. No linear correlation was found for the (55) Robins, D. C.; Thomas, I. L. J. Colloid Interface Sci. 1968, 26 (4), 415. (56) Ravey, J. C., Buzier, M.; Picot C. J. Colloid Interface Sci. 1984, 97, 9. (57) Kijiro Kon-no Surface and Colloid Science; Matijevic, E., Ed.; Plenum Press: New York, 1993; Vol. 15, p 125. (58) Ju¨ngling, H. Ph.D. Dissertation, Technical University Graz, 1995.
Abou-Nemeh and Bart
Figure 9. Water core radius, rH, versus the molar ratio, R.
experimental data obtained from Guth and Simha’s equation. From the previous section we have seen that the linear dimension of aggregates can be more accurately described by the model using φ2 values; therefore the focus here will be on this particular point. The results of the linear regression have shown that a weak and almost nonlinear correlation was obtained for φ2 estimated from Vand’s equation with a residue square of 0.87. Therefore, following the assumptions of the presented model one may conclude that the reversed micelles formed by Span 80 are nonspherical. In a similar approach, Ravey et al.56 have studied the micellar structure of tetraethylene glycol n-dodecyl ether (C12EO4) in decane by means of smallangle neutron scattering. The most probable morphologies of the aggregates can be determined within a precision of ca. 10%. Some of the experimental and theoretical results have the same aggregation profile similar to those obtained in this study (Figure 8), which suggest that the normal picture of small spherical micelles is not supported in nonpolar solvents. The most probable microstructure that can be formed is hanklike aggregates that spontaneously form after water addition to the Span 80/decane system or discoid-shaped reversed micelles. Any further addition of water to the system should result in phase separation with the formation of a lamellar liquid crystalline phase, which took place in this study. From the preceding results the structural considerations indicate that the spherical reversed micelle microstructure is not applicable in the case of nonaqueous media. There seems to be more than one possible geometric arrangement, which depends primarily on the physicochemical properties of the solvent and amphiphile and their interactions. The shape of the aggregates is more determined by the headgroup interactions and their ability to form organized arrangements. 5. Conclusions The concepts of colloid and interface science have shown to be very efficient and useful tools in advancing the fundamental understanding of water transport in the LSM process. The following conclusions can be drawn from this study: D2EHPA does not form reversed micellar microstructures in n-dodecane solutions, and according to the present model the major microstructures formed were dimers. Water solubilization by D2EHPA is low in comparison with other surfactants of similar chemical structure, which is another fact suggesting the lack of reversed micellar structures.
Water Transport in the LSM Process
Span 80, on the other hand, does form various microstructures in n-dodecane that are relatively small in size, and their shape is presumably nonspherical. The amount of water solubilized by Span 80 varies with the variation of concentration. A nonlinear correlation was found for the concentration range from 0.0005 to 0.012 M; however, above this range an excellent linear correlation was established. This study reveals unequivocally that Span 80 is the main decisive factor causing water transport in LSM process, where water is encapsulated (solubilized) in the reversed micelle. Such a condition is well established within the emulsion globule, where the surfactant molecules are distributed over an enormous number of internal aqueous phase droplets. Consequently, the formation of reversed micelles with a significant amount of water is quite realistic. Those “buckets” full of water will act as a mobile vehicle transporting the water from one interface (feed/membrane) to another (membrane/ aqueous internal phase). Most certainly, the microstructures of reversed micelles and other association aggregates of D2EHPA and Span 80/n-dodecane/water system, which is a standard system in LSM, requires further investigation. 6. Symbols Cs ) surfactant concentration, mol/m3 K ) stability constant lc ) hydrocarbon chain length, nm MH ) molecular weight of water, g/mol N ) aggregation number NA ) Avogadro’s number, 6.023 × 1023 Nm ) total number of reversed micelles
Langmuir, Vol. 14, No. 16, 1998 4459 Ns ) total number of surfactant molecules nH ) moles of water ns ) moles of surfactant R ) molar ratio, moles water/moles surfactant rH ) water core radius, nm rm ) reversed micelle radius, nm VH ) volume of water core of the reversed micelle, nm3 Vm ) volume of reversed micelle, nm3 vH ) volume of water molecule, nm3 VT ) volume of micellar phase, mL Vo ) volume of solvent, mL Greek Symbols η ) dynamic viscosity, cP φ ) volume fraction occupied by the solute, mL/mL F ) density of water in the droplet, g/cm3 Ω ) average area per adsorbed surfactant molecule at the interface, nm2 Subscripts 1,2,3 ) indices refer to the φi values estimated according to Einstein’s, Vand’s, and Guth and Simha’s equations. o ) solvent, organic sp ) specific T ) total H ) water
Acknowledgment. Dr. I. Abou-Nemeh expresses his gratitude to Professor J. Willems, Rektor of the University of Ghent, for allowing use of the facilities of the Academic Computing Center during the execution of this work, and the Christian-Doppler-Society, Vienna, for funding this work. LA9710637
