Langmuir 2007, 23, 4765-4774
4765
Reverse-Micelle Formation in the Partitioning of Trivalent f-Element Cations by Biphasic Systems Containing a Tetraalkyldiglycolamide Mark P. Jensen,*,† Tsuyoshi Yaita,‡ and Renato Chiarizia† Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439, and Actinide Coordination Chemistry Group, Synchrotron Radiation Research Center, Japan Atomic Energy Agency, Hyogo 679-5148, Japan ReceiVed NoVember 1, 2006. In Final Form: January 31, 2007 The conditions for reverse-micelle formation were studied for solutions of tetra-n-octyldiglycolamide (TODGA) in alkane diluents equilibrated with aqueous solutions of nitric or hydrochloric acids in the presence and absence of Nd3+. Small-angle neutron scattering, vapor-pressure osmometry, and tensiometry are all consistent with the partial formation of TODGA dimers at the lowest acidities, transitioning to a polydisperse mixture containing TODGA monomers, dimers, and small reverse-micelles of TODGA tetramers at aqueous nitric acid acidities of 0.7 M or higher in the absence of Nd. Application of the Baxter model to the samples containing 0.005-0.015 M Nd reveals the persistence of tetrameric TODGA reverse-micelles with significant interparticle attraction between the polar cores of the micelles that increases with increasing organic phase concentrations of acid or Nd. Our experimental findings suggest that the peculiar behavior of TODGA with respect to the extraction of trivalent lanthanide and actinide cations arises from the affinity of these metal cations for the preformed TODGA reverse-micelle tetramers.
Introduction The chemical separation of metal ions by biphasic liquidliquid extraction of neutral, organophilic, metal complexes from an aqueous phase into an organic solvent is an important technology for purifying, recycling, or disposing of solutions containing metal ions. The ligands, or extractants, used to complex and impart organic phase solubility to the metal ions are generally surface-active amphiphiles,1,2 containing both polar metal binding functionalities, and nonpolar moieties, such as alkyl or aryl groups, which are required to make the resulting metal-ligand complexes organophilic. Although common surfactants, such as dialkylnapthalenesulfonates or dialkylphosphates, are also important metal ion extractants, the chemical and thermodynamic models used to describe biphasic metal extraction systems are often approached from the standpoint of metal ion coordination chemistry,3 generally considering interligand interactions, such as self-association, as perturbations to the metal-ligand complexation and extraction equilibria. While this has merits, the interligand interactions of the amphiphilic ligands can dominate the metal-ligand partitioning equilibria, for example, by the formation of reverse-micelle-like aggregates.2,4,5 Because of the * To whom correspondence should be addressed. E-mail: mjensen@ anl.gov. † Chemistry Division, Argonne National Laboratory. ‡ Actinide Coordination Chemistry Group, Synchrotron Radition Research Center, Japan Atomic Energy Agency. (1) Kertes, A. S.; Gutmann, H., Surfactants in Organic Solvents: The Physical Chemistry of Aggregation and Micellization. In Surface and Colloid Science; Matijevic, E., Ed. Wiley-Interscience: New York, 1976; Vol. 8, pp 193-295. (2) Osseo-Assare, K. AdV. Colloid Interf. Sci. 1991, 37, 123. (3) (a) Sekine, T.; Hasegawa, Y. SolVent Extraction Chemistry; Marcel Dekker: New York, 1977. (b) Aguilar, M., Graphical treatment of liquid-liquid equilibrium data. In DeVelopments in SolVent Extraction; Alegret, S., Ed. Ellis Horwood: West Sussex, England, 1988; pp 87-118. (4) Markovits, G. Y.; Choppin, G. R. Solvent Extraction with Sulfonic Acids. In Ion Exchange and SolVent Extraction; Marinsky, J. A., Marcus, Y., Eds. Marcel Dekker: New York, 1973; Vol. 3, pp 51-81. (5) (a) Neuman, R. D.; Zhou, N.-F.; Wu, J.; Jones, M. A.; Gaonkar, A. G.; Park, S. J.; Agrawal, M. L. Sep. Sci. Technol. 1990, 25, 1655. (b) Gaonkar, A. G.; Neuman, R. D. J. Colloid Interface Sci. 1987, 119, 251. (c) Neuman, R. D.; Ibrahim, T. H. Langmuir 1999, 15, 10. (d) Steytler, D. C.; Jenta, T. R.; Robinson, B. H.; Eastoe, J.; Heenan, R. K. Langmuir 1996, 12, 1483. (e) Yu, Z. J.; Ibrahim, T. H.; Neuman, R. D. SolVent Extr. Ion Exch. 1998, 16, 1437.
amphiphilic nature of the extractant molecules, applications of approaches that combine the concepts of coordination chemistry and surfactant chemistry have been fruitful for understanding the chemical species and energetic driving forces responsible for a variety of phenomena in the extraction of metal ions into organic solvents by extractants such as bis(2-ethylhexyl)phosphoric acid,5 tributylphosphate (TBP),2,6-8 and alkyl-substituted malonamides.9-11 The newly developed neutral extractant, N,N,N′,N′-tetra(noctyl)-3-oxapentane-1,5-diamide (tetra-n-octyldiglycolamide or TODGA, Figure 1) is being studied for the separation of the long-lived transplutonium radionuclides americium and curium from spent nuclear fuel and radioactive waste.12 The metalcentered, coordination chemistry-based approaches used to understand the behavior of the actinide-TODGA complexes in biphasic alkane/aqueous nitric acid systems suggest that TODGA and related tridentate diamide extractants13,14 will be excellent actinide (An) and lanthanide (Ln) extractants. However, the studies of metal ion-TODGA complexes in organic solvents present unusual, though beneficial, features that are difficult to reconcile within the framework of the traditional coordination chemistry interpretations of solvent extraction behavior, even when the behavior of other diamide extractants15 is considered. The form of the extracted actinide-TODGA complex appears to change as the nitric acid concentration in the aqueous phase changes, while at the same time significant amounts of nitric (6) Chiarizia, R.; Nash, K. L.; Jensen, M. P.; Thiyagarajan, P.; Littrell, K. C. Langmuir 2003, 19, 9592. (7) Nave, S.; Mandin, C.; Martinet, L.; Berthon, L.; Testard, F.; Madic, C.; Zemb, T. Phys. Chem. Chem. Phys. 2004, 6, 799. (8) Chiarizia, R.; Jensen, M. P.; Borkowski, M.; Thiyagarajan, P.; Littrell, K. C. SolVent Extr. Ion Exch. 2004, 22, 325. (9) Erlinger, C.; Belloni, L.; Zemb, T.; Madic, C. Langmuir 1999, 15, 2290. (10) (a) Abe´cassis, B.; Testard, F.; Zemb, T.; Berthon, L.; Madic, C. Langmuir 2003, 19, 6638. (b) Lefranc¸ ois, L.; Delpuech, J.-J.; He´brant, M.; Chrisment, J.; Tondre, C. J. Phys. Chem. B 2001, 105, 2551. (11) Erlinger, C.; Gazeau, D.; Zemb, T.; Madic, C.; Lefranc¸ ois, L.; Hebrant, M.; Tondre, C. SolVent Extr. Ion Exch. 1998, 16, 707. (12) Tachimori, S.; Suzuki, S.; Sasaki, Y. J. Atom. Energy Soc. Jpn. 2001, 43, 1235. (13) Sasaki, Y.; Sugo, Y.; Suzuki, S.; Tachimori, S. SolVent Extr. Ion Exch. 2001, 19, 91. (14) Sasaki, Y.; Tachimori, S. SolVent Extr. Ion Exch. 2002, 20, 21.
10.1021/la0631926 CCC: $37.00 © 2007 American Chemical Society Published on Web 03/29/2007
4766 Langmuir, Vol. 23, No. 9, 2007
Figure 1. Structure of N,N,N′,N′-tetra(n-octyl)-3-oxapentane-1,5diamide or tetra(n-octyl)diglycolamide (TODGA).
acid are co-extracted into the organic phase with the metalTODGA species.13,16 Moreover, measurements based on simple equilibrium thermodynamics suggest the participation of four TODGA molecules in the extraction of An3+ or Ln3+ nitrates,17,18 which is more TODGA than can be reasonably accommodated in the inner coordination sphere of these cations.19,20 Although these observations are difficult to understand in the context of a metal-centered perspective, we have shown that the presence of water and nitric acid drives the formation of a polydisperse mixture of TODGA monomers and aggregates in 0.1 M TODGA/n-alkane solutions in the absence of any metal cations and suggested that the presence of such aggregates may account for the unusual features of the extraction of trivalent f-element cations by TODGA.21 A detailed investigation of the nature and size of these metal-free aggregates was not undertaken, however. Concurrent studies of more concentrated, metal-free TODGA/dodecane solutions by Nave et al. using small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS) indicated the presence of tetrameric reverse-micelles for all TODGA concentrations and acidities studied.22 To gain further insight into the nature and structure of the TODGA aggregates present in the extracted Ln3+ and An3+ complexes, we have extended our SANS studies to include solutions containing a trivalent metal ion, neodymium. Neodymium is a representative lanthanide and close chemical analogue of the trivalent actinides in complexation reactions involving hard oxygen donor atoms, as encountered in the TODGA-nitric acid system.23 It is also nearly the same size as the important minor (15) (a) Lumetta, G. J.; Rapko, B. M.; Hay, B. P.; Garza, P. A.; Hutchison, J. E.; Gilbertson, R. D. SolVent Extr. Ion Exch. 2003, 21, 29. (b) Mowafy, E. A.; Aly, H. F. SolVent Extr. Ion Exch. 2002, 20, 177. (c) Spjuth, L.; Liljenzin, J. O.; Hudson, M. J.; Drew, M. G. B.; Iveson, P. B.; Madic, C. SolVent Extr. Ion Exch. 2000, 18, 1. (d) McNamara, B. K.; Lumetta, G. J.; Rapko, B. M. SolVent Extr. Ion Exch. 1999, 17, 1403. (e) Spjuth, L.; Liljenzin, J. O.; Skalberg, M.; Hudson, M. J.; Chan, G. Y. S.; Drew, M. G. B.; Feaviour, M.; Iveson, P. B.; Madic, C. Radiochim. Acta 1997, 78, 39. (f) Nigond, L.; Condamines, N.; Cordier, P. Y.; Livet, J.; Madic, C.; Cuillerdier, C.; Musikas, C.; Hudson, M. J. Sep. Sci. Technol. 1995, 30, 2075. (g) Nigond, L.; Musikas, C.; Cuillerdier, C. SolVent Extr. Ion Exch. 1994, 12, 297. (h) Cuillerdier, C.; Musikas, C.; Hoel, P.; Nigond, L.; Vitart, X. Sep. Sci. Technol. 1991, 26, 1229. (i) Diss, R.; Wipff, G. Phys. Chem. Chem. Phys. 2005, 7, 264. (j) Sinkov, S. I.; Rapko, B. M.; Lumetta, G. J.; Hay, B. P.; Hutchison, J. E.; Parks, B. W. Inorg. Chem. 2004, 43, 8404. (k) Shashilov, V. A.; Ermolenkov, V. V.; Lednev, I. K. Inorg. Chem. 2006, 45, 3606. (l) Parks, B. W.; Gilbertson, R. D.; Hutchison, J. E.; Healey, E. R.; Weakley, T. J. R.; Rapko, B. M.; Hay, B. P.; Sinkov, S. I.; Broker, G. A.; Rogers, R. D. Inorg. Chem. 2006, 45, 1498. (16) Tachimori, S.; Suzuki, H.; Sasaki, Y.; Apichaibukol, A. SolVent Extr. Ion Exch. 2003, 21, 707. (17) Ansari, S. A.; Pathak, P. N.; Husain, M.; Prasad, A. K.; Parmar, V. S. Radiochim. Acta 2006, 94, 307. (18) Zhu, Z.-X.; Sasaki, Y.; Suzuki, H.; Suzuki, S.; Kimura, T. Anal. Chim. Acta 2004, 527, 163. (19) (a) Hirata, M.; Guilbaud, P.; Dobler, M.; Tachimori, S. Phys. Chem. Chem. Phys. 2003, 5, 691. (b) Dobler, M.; Hirata, M. Phys. Chem. Chem. Phys. 2004, 6, 1672. (20) Narita, H.; Yaita, T.; Tachimori, S. Extraction Behavior for Trivalent Lanthanides with Amides and EXAFS Study of their Complexes. In SolVent Extraction for the 21st Century: Proceedings of ISEC’99; Cox, M., Hidalgo, M., Valiente, M., Eds.; Society of Chemical Industry: London, 2001; Vol. 1, pp 693-696. (21) Yaita, T.; Herlinger, A. W.; Thiyagarajan, P.; Jensen, M. P. SolVent Extr. Ion Exch. 2004, 22, 553. (22) Nave, S.; Modolo, G.; Madic, C.; Testard, F. SolVent Extr. Ion Exch. 2004, 22, 527. (23) Choppin, G. R.; Jensen, M. P., Actinides in Solution: Complexation and Kinetics. In The Chemistry of the Actinide and Transactinide Elements, 3rd ed.; Morss, L. R., Edelstein, N. M., Fuger, J., Eds.; Springer: Dordrecht, Netherlands, 2006; Vol. 4, pp 2524-2621.
Jensen et al.
actinide Am. We have interpreted the SANS results of both Nd-containing and metal-free TODGA solutions using an implementation of the Baxter model that accounts for polydispersity in both aggregate size and interparticle attraction. We find that the size and shape of the TODGA aggregates change with the acid, water, and metal content of the organic phase, undergoing a transition from a mixture of ellipsoidal TODGA monomers and dimers at low acidities and in the absence of metal, to a mixture of TODGA monomers and roughly spherical, small reverse-micelle-like aggregates containing four TODGA molecules when the aqueous acidity reaches 2 M HNO3. This is in general agreement with the formation of (TODGA)4 reverse-micelles in metal-free water-nitric acid/alkane-TODGA systems that was reported at higher TODGA concentrations.22 In addition, we find that these TODGA tetramers persist as Ndcontaining species over a wide range of acidities in the presence of Nd salts, even as phase splitting of the organic phase (i.e., third phase formation) is approached. This formation of tetrameric TODGA reverse-micelles by nitric acid or salts of trivalent f-element cations in the organic phase provides a mechanism for the superior extraction of actinide and lanthanide ions by TODGA,14 as well as explaining the change in the form of the extracted complex in polar organic solvents and the participation of more molecules of TODGA in the extraction equilibrium than can be accommodated in the inner coordination sphere of a trivalent f-element ion. Experimental Section Tetra-n-octyldiglycolamide (99%) was purchased from Kanto Chemical Company, Japan, and was used as received. Solutions of 0.10 M TODGA were prepared by dissolution of a weighed amount of the extractant in n-octane (Alfa-AESAR, 99.7%) or n-octane-d18 (Aldrich, 98 atom%). Solutions of nitric and hydrochloric acids were prepared by dilution of Ultrex grade (Baker) acids with deionized water and were standardized by titration with standard NaOH to the phenolphthalein endpoint. A stock solution of 0.5 M Nd was prepared by dissolving 99.99% Nd2O3 in a slight excess of an appropriate warm acid. The Nd concentration of this solution was determined by titration with EDTA using xylenol orange as an indicator24 with an uncertainty better than (0.2%, while the small amount of excess acid was determined after cation exchange on Dowex 50 by titration with standard NaOH to the phenolphthalein endpoint. All solutions were prepared and equilibrated at room temperature (23 ( 1 °C). Equilibrium loading of the organic phases with water, acid, and Nd(NO3)3 or NdCl3, as appropriate, was ensured by preequilibrating the organic phases (1.00-2.00 mL) twice with two volumes of fresh, Nd-free aqueous phases of the appropriate acidity. The resulting pre-equilibrated organic phases were contacted a final time for 2 min with an equal volume of fresh aqueous phase at the same concentration of acid used in the pre-equilibration steps. When organic phases containing Nd were desired, the aqueous phase for the final equilibration also contained Nd(NO3)3 or NdCl3. The ratio of the volumes of the aqueous phase and organic phase were varied as needed to achieve high Nd loading of the organic phase without formation of a third liquid phase.25 The water content of selected organic phases was measured by Karl Fischer titration in duplicate, giving an estimated uncertainty of (0.002 M. The equilibrium acid concentration of the organic phases also was measured by contacting the loaded organic phases three times with equal volumes of water and titrating the combined aqueous solutions with NaOH. The amount of Nd in the organic phases was calculated from the difference in the aqueous phase Nd concentration before and after the equilibration as determined by spectrophotometry at 575.3 nm. (24) Flaschka, H. A.; Barnard, A. J., In ComprehensiVe Analytical Chemistry; Wilson, D. W., Wilson, C. L., Eds.; Elsevier: New York, 1960; Chapter VII-9. (25) Chiarizia, R.; Jensen, M. P.; Borkowski, M.; Ferraro, J. R.; Thiyagarajan, P.; Littrell, K. C. SolVent Extr. Ion Exch. 2003, 21, 1.
ReVerse-Micelle Formation in TODGA Partitioning
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The surface tension of nitric acid loaded, TODGA/n-octane solutions and the interfacial tension between the organic and aqueous phases in these systems were measured as a function of the equilibrium nitric acid concentration by the Du Nouy ring method with a Fisher Model 20 Surface Tensiometer at 23.0 ( 0.5 °C. The interface was allowed to age for 30 s after complete disengagement of the phases before measurement of the interfacial tensions. The measured interfacial tensions were corrected to real tensions with a calibration curve provided by the manufacturer and based on the ring dimensions and densities of the phases. The calibration of the tensiometer was verified by measuring the surface tension of n-octane. The value obtained, 21.4 ( 0.5 dynes/cm, is in good agreement with the surface tension expected from measurements by other methods (21.326 and 21.527 dynes/cm). SANS measurements were made on 0.0995 M TODGA/octaned18 solutions in 2 mm path length Suprasil cells at 25.0 ( 0.1 °C. Neutrons of wavelengths (λ) between 0.5 and 14 Å, were produced at the Argonne National Laboratory Intense Pulsed Neutron Source, and the scattered neutrons were measured with the time-of-flight neutron diffractometer (SAND), with a useful data range between Q ) 0.0035 and 0.6 Å-1, where Q ) 4π sin(θ)/λ and 2θ is the scattering angle.28 The differential scattering cross-sections, I(Q), were corrected for the background scattering of the instrument, cells, and solvent. The resulting data were placed on an absolute scale using a mixture of deuterated and hydrogenous high-molecularweight polystyrenes with a known absolute cross-section.29 Molecular models of TODGA monomers and aggregates containing nitric acid and water were studied to determine the radius of gyration of the TODGA monomer, dimer, and tetramer. Computations were performed using the MM3(2000) force field30 as implemented in the TINKER suite of programs31 with extensions for amide32 and nitrate33 complexation. Directional hydrogen bonding and bond lengths corrected for electronegativity are both implemented in this MM3 treatment. Water parameters were adapted from the AMOEBA model.34 All uncertainties are reported at the 95% confidence level. SANS Modeling. For a monodisperse system of isotropic particles, the differential scattering cross section can be expressed as
One of the best-known of these solutions, the Baxter model for hard spheres with surface adhesion,37 has been used to investigate the phase behavior of organic solutions of malonamide,9,11 tributylphosphate,6-8 and TODGA22 extractants, as well as other reverse-micelle forming surfactants such as aerosol OT.38,39 The interparticle potential used in the Baxter model, U(r) (in units of kBT), combines an incompressible hard sphere potential of diameter, dHS, with an infinitely deep and narrow square attractive well of width δ. The potential within the attractive well, expressed as a function of the distance between the centers of two spherical particles, r, is
I(Q) ) Np(Fp - Fs)2Vp2 P(Q)S(Q) + Ibkg
where the indexes i and j each represent a particular solute particle composition (i.e., (TODGA)i or (TODGA)j), Bi(Q)2 is the particle form factor (P(Q)) for the i-th solute, and the partial structure factor Sij(Q) accounts for interparticle interactions between the i-th and j-th solutes, as previously described.44 The partial structure factors required by eq 3 also can be calculated under the Baxter model.39,44 In previous studies employing a polydisperse form of the Baxter model, the interparticle attraction, and thus the Baxter parameter for the attraction between the i-th and j-th particles, τij, was taken to be constant for all of the particle sizes considered.39,44 This assumption becomes less realistic as the polydispersity of a sample increases. The interparticle attraction principally responsible for variations in S(Q) under the Baxter model arises from dispersion (induced dipole) interactions between the polar cores of these particles.9 Therefore, the magnitude of the attractive force between two particles should be related to the polarizability of the polar cores45 and the distance between the polar cores. To account for these differences in the interparticle attraction, we approximate the change in the dispersion energy between polar cores assuming that the size of the polar core varies linearly with aggregate volume and that a polar core’s polarizability is directly
(1)
where Np is the number density of the scattering particles; Vp is the particle volume; NpVp is the volume fraction of the particles (η); Fp and Fs are the scattering length densities of the solute particles and the solvent, respectively; P(Q) is the particle form factor, which is determined by the particle shape;35 S(Q) is the structure factor; and Ibkg represents the background from incoherent scattering. For sufficiently dilute solutions, interparticle interactions can be neglected and S(Q) ) 1 for all values of Q. When interparticle interactions cannot be neglected, S(Q) often can be estimated from one of several approximate closed-form solutions to the Ornstein-Zernike integral.36 (26) Vogel, A. I. J. Chem. Soc. 1946, 133. (27) Quayle, O. R.; Day, R. A.; Brown, G. M. J. Am. Chem. Soc. 1944, 66, 938. (28) Thiyagarajan, P.; Urban, V.; Littrell, K.; Ku, C.; Wozniak, D. G.; Belch, H.; Vitt, R.; Toeller, J.; Leach, D.; Haumann, J. R.; Ostrowski, G. E.; Donley, L. I.; Hammonds, J.; Carpenter, J. M.; Crawford, R. K., The New Small-Angle Diffractometer SAND at IPNS. In ICANS XIV: The Fourteenth Meeting of the International Collaboration on AdVanced Neutron Sources, June 14-19, 1998, StarVed Rock Lodge, Utica, Illinois; Carpenter, J. M., Tobin, C., Eds.; National Technical Information Service: Springfield, VA, 1998; Vol. 2, pp 864-878. (29) Thiyagarajan, P.; Epperson, J. E.; Crawford, R. K.; Carpenter, J. M.; Klippert, T. E.; Wozniak, D. G. J. Appl. Crystallogr. 1997, 30, 280. (30) Allinger, N. L.; Yuh, Y. H.; Lii, J.-H. J. Am. Chem. Soc. 1989, 111, 8551. (31) (a) Ponder, J. W.; Richards, F. M. J. Comput. Chem. 1987, 8, 1016. (b) Kundrot, C. E.; Ponder, J. W.; Richards, F. M. J. Comput. Chem. 1991, 12, 402. (c) Pappu, R. V.; Hart, R. K.; Ponder, J. W. J. Phys. Chem. B 1998, 102, 9725. (32) Hay, B. P.; Clement, O.; Sandrone, G.; Dixon, D. A. Inorg. Chem. 1998, 37, 5887. (33) Hay, B. P. Inorg. Chem. 1991, 30, 2876. (34) Ren, P.; Ponder, J. W. J. Phys. Chem. B 2003, 107, 5933. (35) Pedersen, J. S. AdV. Colloid Interface Sci. 1997, 70, 171. (36) Ornstein, L. S.; Zernike, F. Proc. Acad. Sci. 1914, 17, 793.
(
U(r)/kBT ) lim ln 12τ δf0
δ dhs + δ
)
dHS e r e dHS + δ
(2)
Therefore, the dimensionless Baxter temperature parameter, τ, provides a useful measure of the interparticle attraction, and its inverse, τ-1, is commonly referred to as the stickiness parameter. Outside of the attractive well, U(r) ) ∞ when r < dHS, and U(r) ) 0 when r > (dHS + δ ). Given values for τ and the volume fraction, η, S(Q) is easily calculated from a series of closed form algebraic equations.37,40 Although the condition of an infinitely deep and narrow attractive well clearly is not satisfied in real solutions, the values of S(Q) calculated from the Baxter potential are generally good approximations of the structure factors derived from Monte Carlo simulations of spheres with surface adhesion,41 and under the approximations used to generate analytical solutions for the structure factor from attractive square well potentials, S(Q) is relatively insensitive to the width of the attractive well when δ/dHS < 0.1.38,42 When a solution is polydisperse, containing a mixture of p different types of interacting solute particles, a different form of eq 1 should be employed,43 I(Q) ) Ibkg + p
p
∑ ∑ (N N ) i j
1/2
(Fi - Fs)(Fj - Fs)ViVjBi(Q)Bj(Q)Sij(Q) (3)
i)1 j)1
(37) Baxter, R. J. J. Chem. Phys. 1968, 49, 2770. (38) Regnaut, C.; Ravey, J. C. J. Chem. Phys. 1989, 91, 1211. (39) Robertus, C.; Philipse, W. H.; Joosten, J. G. H.; Levine, Y. K. J. Chem. Phys. 1989, 90, 4482. (40) Menon, S. V. G.; Kelkar, V. K.; Manohar, C. Phys. ReV. A 1991, 43, 1130. (41) Gazzillo, D.; Giacometti, A. J. Chem. Phys. 2004, 120, 4742. (42) Menon, S. V. G.; Manohar, C.; Rao, K. S. J. Chem. Phys. 1991, 95, 9186. (43) Guinier, A.; Fournet, G., Small Angle Scattering of X-rays; John-Wiley and Sons: New York, 1955. (44) Duits, M. H. G.; May, R. P.; Vrij, A.; de Kruif, C. G. Langmuir 1991, 7, 62. (45) Chiarizia, R.; Jensen, M. P.; Rickert, P. G.; Kolarik, Z.; Borkowski, M.; Thiyagarajan, P. Langmuir 2004, 20, 10798.
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Table 1. Non-interacting Ellipsoids of Rotation with Semi-axes of Lengths Ra (the Rotation Axis) and Rb Provide the Best Fit to the SANS Data for the Low Acidity Solutions That Do Not Contain Nda [HNO3]aq (M)
[Nd]org (mM)
η
(Fp - Fs)2 (1021 cm-4)b
Ra (Å)
Rb (Å)
Ibkg (cm-1)c
χred2
0 0.0102 0.098 0.484 0.700 1.02 2.02 4.0c 0.484 0.484 0.484 1.02 2.02 4.0d
0 0 0 0 0 0 0 0 5.0 10.0 14.3 10.5 10.4 10.9
0.0642 0.0644 0.0644 0.0647 0.0649 0.0653 0.0675 0.0643 0.0654 0.0663 0.0673 0.0673 0.0681 0.0649
4.11 4.18 4.17 3.99 3.86 3.64 3.09 4.09 4.04 3.90 3.66 3.44 3.43 3.69
2.42 (5) 2.45 (4) 2.46 (4) 2.58 (4) 2.70 (4) 3.01 (4) 4.77 (3) 2.44 (3) 2.93 (3) 3.28 (1) 4.01 (1) 4.18 (2) 3.93 (1) 4.10 (2)
12.63 (13) 12.77 (10) 12.87 (10) 13.23 (10) 13.43 (10) 13.82 (9) 17.26 (7) 13.53 (9) 16.10 (8) 19.25 (6) 25.13 (6) 21.60 (6) 27.72 (6) 20.99 (6)
0.035 0.038 0.039 0.046 0.038 0.037 0.063 0.038 0.029 0.033 0.040 0.037 0.044 0.034
1.2 1.0 1.0 1.0 1.5 1.2 8.7 1.4 1.8 15 123 41 226 21
a Uncertainties in the last digits of the fitted parameters are given at the 95% confidence level in parentheses. b Fs ) 6.43 × 1010 cm-2. c Uncertainty in fitted Ibkg: ( 0.001. d 4.0 M HCl.
proportional to its size for a fixed concentration of water, acid, TODGA, and Nd. For the particle sizes and values of τij encountered in this work, this means that the stronger dispersion forces between two tetrameric aggregates give values for τ44-1 that are ca. 30% larger than τ14-1, the stickiness parameter for monomer-tetramer interactions. The greater polarizability of the larger polar cores of the tetrameric aggregates is partially offset by the inability of the polar cores of two tetramers to approach as closely as the polar core of a tetramer and a dipolar monomer. Analysis of the SANS data began by fitting the data for each solution to eq 1 under the assumption that interparticle attractions were negligible, i.e., S(Q) ) 1, and testing a variety of form factors.35 In the error-weighted, nonlinear least-squares fitting of the data, the particle volume fraction and scattering length densities (Table 1) were held constant for each solution at the values appropriate for the known [TODGA], [H2O]org, [HNO3]org, and [Nd]org, while both the geometric parameters of the particle for a given form factor (e.g., the particle radius) and Ibkg were allowed to vary. The resulting weight-average aggregation number of TODGA, nw, is easily calculated from the average particle volume as previously described.21 The data were also fit to eq 3 assuming a mixture of interacting, ellipsoidal TODGA monomers and spherical TODGA n-mers of physical radius Rtot and hard sphere radius RHS (RHS ) dHS/2 and Rtot g RHS) that contain all of the extracted nitric acid and water. If Rtot is larger than RHS, interpenetration of the solute particles is indicated.9 In this case, the physical TODGA micelles are not perfect hard spheres, but there is a distance, RHS, at which they behave as hard spheres. As previously discussed,7,22 the organic chains surrounding the polar core of a reverse-micelle with a physical radius Rtot may interpenetrate to a distance of Rtot - RHS, where RHS is larger than the radius of the micelles’ polar cores. At this distance, a balance is struck between the attractive van der Waals forces between the polar cores that draw reverse-micelles together and the sometimes attractive,46 but inherently limiting, steric stabilization of the organic shell of the reverse-micelles. In this work, the sum of these opposing forces is approximated by the Baxter square well.7 Modeling the interparticle attractions in the system was possible because of several assumptions. Attractive interactions between TODGA monomers, shown to be of little importance in the lowacidity Nd-free samples (vide infra), were not considered (i.e., S11(Q) ) 1). Interactions between the spherical n-mers were characterized by the volume fraction of the n-mer and one Baxter parameter, τnn. Interactions between the spherical oligomers and the ellipsoidal monomers were also included by approximating the ellipsoids as incompressible spheres of equivalent radii,47 and using the appropriate volume fractions, and the Baxter parameter τn1
calculated by rescaling the fit parameter τnn for the smaller polar portion and closer approach of the monomers (vide supra). In each of these fits, four parameters Ibkg, Rtot, RHS, and τnn were allowed to vary. The number of monomers per TODGA aggregate, n, was calculated from the particle volume, correcting for the volume fraction of the non-TODGA components in each aggregate. For the Ndcontaining 2 M HNO3 solution only, it was also necessary to allow the [(TODGA)n]/[TODGA] ratio to vary as a fifth parameter to account for the presence of TODGA aggregates that do not contain Nd, which were required by the values of Np and [Nd]org. The form factor of the ellipsoidal monomers was calculated using the known molecular volume of the monomers (1070 Å3/TODGA) and the eccentricity of the ellipsoids calculated from the oblate ellipsoid of rotation fits of the low acidity, Nd-free samples (Ra/Rb ≈ 1:6, Table 1). Statistically, this model gave significantly better fits than a simple Baxter model that considered only spherical oligomers with Rtot ) RHS as implemented by Chiarizia et al.8,45 (Supporting Information) or an approach that used eq 3 and included the form factor for ellipsoidal monomers but neglected monomer-oligomer interactions by defining S1n(Q) ) Sn1(Q) ) 1. More complicated models based on eq 3, such as interacting monomer, dimer, n-mer mixtures, or models allowing for polydispersity in the n-mers did not improve the quality of the fit.
(46) Huang, J. S.; Safran, S. A.; Kim, M. W.; Grest, G. S.; Kotlarchyk, M.; Quirke, N. Phys. ReV. Lett. 1984, 53, 592. (47) Isihara, A. J. Chem. Phys. 1950, 18, 1446.
(48) Hutchinson, E.; Shinoda, K. An Outline of the Solvent Properties of Surfactant Solutions. In SolVent Properties of Surfactant Solutions; Shinoda, K., Ed.; Marcel Dekker: New York, 1967; Vol. 2, pp 1-26.
Results and Discussion Metal-Free Solutions. Since TODGA is amphiphilic, the aggregation of the equilibrated metal-free TODGA solutions in n-octane suggested by scattering and vapor pressure osmometry measurements in the previous work21,22 was further investigated by surface and interfacial tensiometry. Tensiometry is often used to study micellar solutions, and changes in the slope of the tensiometric curves are taken as indicators of changes in the aggregation state of the solutes, particularly micellization.48 Figure 2A depicts the dependence of the surface and interfacial tensions of the equilibrated 0.10 M TODGA-containing organic phase as a function of the equilibrium nitric acid concentration of the aqueous phase. The slopes of both the surface and the interfacial tension curves change when the equilibrated aqueous phase contains ca. 0.7 M HNO3 ([HNO3]org ) 0.010 M, [H2O]org ) 0.021 M), indicating a change in the aggregation state of TODGA. As expected, the critical concentration derived from Figure 2, 0.7 ( 0.1 M aqueous HNO3, is not as well defined as those found for aqueous surfactant solutions because the comparatively small aggregation numbers encountered in organic solutions generally
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Figure 3. SANS data from Nd-free 0.10 M TODGA in deuterated n-octane equilibrated with aqueous solutions containing various concentrations of nitric or hydrochloric acid (points) are generally well represented as non-interacting ellipsoids of rotation (lines). Equilibrium aqueous acid concentrations are indicated on the figure. For the 0 M HNO3 sample, the uncertainties in the data used to weight the fits are indicated as error bars when the uncertainty is larger than the data points. For clarity, each of the other data sets are shifted vertically by increasing factors of 2 (except for 4.0 M HCl, which is shifted down by a factor of 4) and their experimental uncertainties, which are similar to those shown, are omitted.
Figure 2. Breaks in the surface (0) and interfacial (O) tensions of 0.10 M TODGA in n-octane equilibrated with varying concentrations of nitric acid (panel A) corresponds well with a rapid increase in the water content (1) of the organic phase (panel B) and the onset of changes in the speciation of TODGA (panel C) derived from SANS and VPO measurements, with the fraction of TODGA present as monomer (9), dimer (b), and tetramer (2) indicated at each acidity. Dotted vertical lines indicate [HNO3]aq ) 0.7 ( 0.1 M.
causes the critical concentrations to be more poorly defined in organic solutions than in aqueous solutions.1,49 Nevertheless, the tensiometry data suggest that the TODGA amphiphiles begin to form small reversed micelles with a critical micelle acidity of 0.7 M aqueous HNO3 in contact with Nd-free 0.10 M TODGA/ n-octane solutions. This is in agreement with the data presented in Figure 2B, which show that a rapid increase in the organic phase water concentration, indicative of reverse-micelle formation, begins when the aqueous phase acidity reaches 0.7 M HNO3. The observation of a critical micelle acidity in the tensiometry data caused us to examine the results of SANS measurements on similar Nd-free solutions of 0.10 M TODGA for evidence of micellization. The scattering data were first fit to eq 1, as described above, assuming that interparticle attractions were negligible in these semidilute solutions (η ≈ 0.065). Form factors for both uniform and nonuniform (core-shell) spheres, cylinders, or ellipsoids of rotation,35 as well as polydisperse nonuniform spheres50 were tested. The uniform ellipsoid of rotation form factor gave the best fit of the model to the data (Figure 3 and (49) (a) Fendler, J. H. Acc. Chem. Res. 1976, 9, 153. (b) Ruckenstein, E.; Nagarajan, R. J. Phys. Chem. 1980, 84, 1349. (50) Bartlett, P.; Ottewill, R. H. J. Chem. Phys. 1992, 96, 3306.
Table 1). This model gave statistically better fits, as reflected by a 1-2 order of magnitude decrease in the reduced chi-squared, χ2red,51 than either the uniform sphere or uniform cylinder models for each solution. It also was superior to all of the core-shell models, as the core radii and shell thicknesses required to adequately reproduce the experimental data were always very physically unrealistic when the dimensions of TODGA and the organic phase concentrations of water and acid were considered. However, as indicated by the χ2red values in Table 1, none of the tested models reproduced the scattering data well for the metalfree TODGA solution contacted with 2 M HNO3 (or for the Nd-containing solutions). Because even the best model of non-interacting particles failed to fit the 2 M HNO3 SANS data well for Q < 0.05 Å-1, monodisperse (eq 1) and polydisperse (eq 3) models that consider interparticle interactions using the Baxter formalism37 to calculate the structure factor were also tested on the SANS data for the solution contacted with 2 M HNO3. The classical, monodisperse, Baxter model gave a statistically poorer fit than the non-interacting ellipsoid model (Supporting Information). In contrast, models based on eq 3, considering mixtures of interacting monomers and oligomers of TODGA, gave significantly better fits. The best fitting model included interacting TODGA monomers and tetramers, as described in the SANS Modeling section above. The relative contributions of the monomer, monomer-oligomer, and oligomer-oligomer terms of eq 3 to the overall fit of the metal-free 2 M HNO3 SANS data are summarized in Figure 4. The parameters that best represent the data can be found in Table 2. On the basis of the ability of the polydisperse interacting particle models to reproduce the 2 M HNO3 data, the SANS data of the lower acidity, metal-free solutions were also refit using the series of interacting models. In contrast to the 2 M HNO3 sample, the non-interacting uniform ellipsoid of rotation model still gave the best fits of the lower-acidity scattering data. The interacting models either reproduced the lower acidity data more poorly or they yielded geometric parameters and aggregation numbers that were physically inconsistent with independent tensiometric and (51) Bevington, P. R.; Robinson, D. K., Data Reduction and Error Analysis for the Physical Sciences, 3rd ed.; McGraw Hill: Boston, 2003.
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expressions for np, nw, and the known total concentration of TODGA, ct:
ct ) [TODGA] + 2[(TODGA)2] + n[(TODGA)n] (5) np )
nw )
Figure 4. According to the polydisperse interacting particle model (s), terms accounting for scattering between TODGA oligomers (- · · -) are the primary contributors to the background corrected experimental SANS data (0) for 0.10 M TODGA in deuterated n-octane equilibrated with 2.0 M HNO3, but monomer-monomer (- - -) and monomer-oligomer (· · ·) interactions should also be considered, as together they can account for 20% or more of the scattering.
osmometric21 measurements. Thus, it appears that the interparticle attractions reflected in S(Q) are negligible for 0.10 M TODGA in contact with metal-free aqueous solutions at or below an acidity of ∼1 M HNO3. While the onset of significant reverse-micelle formation implied by the tensiometry data begins at lower aqueous acidities (ca. 0.7 M HNO3), the modeling of the metal-free SANS results suggests that the combination of the aggregation numbers and the concentrations of TODGA oligomers in the 0.10 M TODGA solution (Figure 2C) remains small enough to have little effect on the neutron scattering until the aqueous nitric acid concentration exceeds 1 M. The low aggregation numbers observed for the metal-free 0.10 M TODGA solutions (Table 3) suggest significant concentrations of TODGA monomer likely persist in all of the metal-free solutions studied. In solutions containing a mixture of monomers and n-mers, n, the stoichiometric aggregation number of a (TODGA)n aggregate in equilibrium with the TODGA monomer, can be calculated from the number-average aggregation number, np, which we previously determined by osmometric measurements,21 and the weight-average aggregation number, nw, which we derive from small-angle scattering measurements, via the equation21
( )
n ) np
nw - 1 np - 1
(4)
(For notational simplicity, the acid, counterions and water will be ignored. An aggregate containing n molecules of TODGA will be written as (TODGA)n, and a Nd-containing aggregate will be written as Nd(TODGA)n). Applying eq 4 to the aggregation numbers of the metal-free TODGA solutions (Table 3) demonstrates the presence of a monomer-dimer equilibrium (i.e., n ) 2) in the lowest acidity solutions (0-0.5 M aqueous HNO3). At 0.7 M HNO3 and above, the stoichiometric aggregation number begins to increase beyond 2, eventually suggesting the presence of a monomer-tetramer mixture in the 2 M HNO3 sample. Having identified the presence of monomers, dimers, and higher n-mers in the 0.10 M TODGA solutions at different acidities using eq 4, the concentrations of TODGA, (TODGA)2, and (TODGA)n can be calculated for any value of n > 2 from the
ct [TODGA] + [(TODGA)2] + [(TODGA)n]
(6)
[TODGA] + 4[(TODGA)2] + n2[(TODGA)n] (7) ct
The aggregation numbers from our SANS data are best represented when n ) 4, and the resulting concentrations of monomer, dimer, and tetramer calculated from the measured aggregation numbers for n ) 4 are shown in Figure 2C. In accord with the tensiometry results, these calculations show that the concentration of TODGA tetramers in 0.10 M TODGA solutions first begins to increase when the equilibrium aqueous phase nitric acid concentration is ca. 0.7 M, and the tetramer concentration increases rapidly when the aqueous acidity exceeds 1 M HNO3. Interestingly, the increase in the tetramer concentration with increasing acidity has minimal effect on the monomer concentration and comes primarily at the expense of the dimer concentration. When the aqueous nitric acid concentration reaches 2 M, the (TODGA)2 dimer has been completely converted to (TODGA)4. The [(TODGA)4]/[TODGA] ratio calculated from the speciation calculations, 0.58, is in excellent agreement with the tetramer/monomer ratio derived from fitting the SANS data to the model (Table 2). The validity of this speciation model is further illustrated by its ability to account for the experimental average radius of gyration measured for each of the solutions from the average particle dimensions given in Table 1. The radii of gyration, Rg, for the lowest energy conformation of TODGA, (TODGA)2, and (TODGA)4‚HNO3 in vacuo were computed for energy-minimized models of these molecules with the TINKER suite of molecular mechanics programs. TODGA aggregates containing the full amount of water and nitric acid suggested by the actual solution compositions of the organic phases were never stable in these calculations, presumably due to the absence of solvent in our simple calculations. The closest stable aggregate was used instead (e.g., (TODGA)4‚HNO3 rather than (TODGA)4‚2HNO3‚2H2O). Nevertheless, this approximation has little effect on the shape or extent of the particles or values of the radius of gyration, Rg, calculated from the molecular models. The computed Rg values were 7.06, 8.76, and 9.25 Å, for the monomer, dimer, and tetramer, respectively. The gyration radii of other TODGA n-mers (n ) 3-8) were also computed from molecular models for comparison. The appropriate, computed, radii of gyration were then combined with the solution speciation determined from the experimental aggregation numbers at different values of n (n ) 3-8), and were used to calculate a value of Rg for each solution via the equation for a z-average quantity, Rg2 ) [TODGA]Rg,12 + 4[(TODGA)2]Rg,22 + n2[(TODGA)n]Rg,n2 [TODGA] + 4[(TODGA)2] + n2[(TODGA)n]
(8) where the radius of gyration calculated for each species by molecular mechanics is indicated by its stoichiometric aggregation number, for example Rg,n. The experimentally measured average Rg values for the various solutions (Table 3) were only reproduced
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Table 2. Fitting SANS Data Using the Polydisperse Baxter Model with Monomer-Oligomer and Oligomer-Oligomer Interactions Indicates the Formation of TODGA Tetramers (n ) 4) and No Significant Difference in the Hard Sphere or Total Radius of the Nd-Free and Nd-Loaded Micellesa [HNO3]aq (M) 2.02 0.484 0.484 0.484 1.02 2.02 4.0d c
[Nd]org (mM)
RHS (Å)
0 5.0 10.0 14.3 10.5 10.4 10.9
τnn
U(r) (kBT)b
0.122 (5) 0.080 (3) 0.074 (6) 0.077 (1) 0.073 (2) 0.081 (1) 0.077 (4)
-2.0 -2.4 -2.5 -2.5 -2.5 -2.4 -2.5
Rtot (Å)
7.3 (3) 6.7 (6) 6.6 (8) 7.0 (3) 6.9 (4) 7.1 (3) 6.9 (5)
10.6 (4) 10.5 (8) 10.1 (9) 10.0 (3) 10.3 (5) 10.1 (2) 10.6 (5)
Σ[(TODGA)n]/[TODGA] 0.58 (16)
