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Evaluation of Electrostatic Potential Induced by Anion-Dominated Partition into Zwitterionic Micelles and Origin of Selectivity in Anion Uptake Kenji Iso and Tetsuo Okada* Department of Chemistry, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan Received March 9, 2000. In Final Form: September 5, 2000 The surface potentials of n-dodecyltrimethylammoniopropanesulfonic acid (DDAPS) micelles in various electrolytes have been evaluated by capillary electrophoresis. This zwitterionic micelle has an inner cationic surface and an outer anionic surface and accommodates anions better than cations, indicating that a negative surface potential is induced by anion-dominated partition. Selectivity terms, i.e., solvation changes of ions and ion association between ions and charged groups in the DDAPS micelles, are introduced into the Poisson-Boltzmann equation for the spherical geometry. This model allows the interpretation of differences in the ionic partition and surface potential between electrolytes. The selectivity parameters have been determined by assuming agreement between the zeta potential determined by capillary electrophoresis and the calculated outer surface potential of the micelle. The obtained selectivity parameters can also explain the potentiometrically evaluated partition of ClO4- and I-. It has been confirmed that capillary electrophoresis has wide applicability in surface potential measurements and can detect surface potentials of less than 1 mV. The selectivity origin in the partition into the DDAPS micelles is also discussed on the basis of evaluated parameters. The hydration changes mainly govern the uptake of well-hydrated anions, whereas poorly hydrated anions are partitioned into the micelle principally by ion-pair formation with the cationic groups in the micelles.
Introduction Electrokinetic phenomena have been studied by various approaches in order to probe molecular interactions occurring on surfaces or at interfaces as well as to understand the structures of electrical double layers.1-7 Electrophoresis, electroosmosis, and streaming potential are often characterized by the ζ potential, which is, in turn, experimentally evaluated utilizing these electrokinetic phenomena. It has been known that the ζ potential characterizes well the surface properties of porous materials, membranes, polymer latices, micelles, etc.5-7 Electrophoresis is one of the most powerful tools not only for separating ionic compounds but also for studying the electrokinetic natures of colloidal particles.6-7 In particular, the developments of capillary electrophoresis (CE) have enhanced the applicability and versatility of * Author to whom correspondence should be addressed. Telephone and fax: +81-3-5734-2612. E-mail:
[email protected]. (1) Cevc, G. Biochim. Biophys. Acta 1990, 311, 1031-1033. (2) Brawn, G. E., Jr.; Henrich, V. E.; Casey, W. H.; Clark, D. L.; Eggleston, C.; Felmy, A.; Goodman, D. W.; Gra¨tzel, M.; Maciel, G.; McCarthy, M. I.; Nealson, K. H.; Sverjensky, D. A.; Toney, M. F.; Zachara, J. M. Chem. Rev. 1999, 99, 77. (3) (a) Hayes, R. A.; Bo¨hmer, M. R.; Fokkink, G. J. Langmuir 1999, 15, 2865. (b) Hu, K.; Chai, Z.; Whitesell, J. K.; Bard, A. J. Langmuir 1999, 15, 3343. (c) Teschke, O.; de Souza, E. F.; Ceotto, G. Langmuir 1999, 15, 4935. (4) (a) Szymczyk, A.; Fievet, P.; Mullet, M.; Reggiani, J. C.; Pagetti, J. J. Membr. Sci. 1998, 143, 189. (b) Mo¨ckel, D.; Staude, E.; Dal-Cin, M.; Darcovich, K.; Guiver, M. J. Membr. Sci. 1998, 145, 211. (c) Ricq, L.; Pagetti, J. J. Membr. Sci. 1999, 155, 9. (d) Ricq, L.; Pierre, A.; Reggiani, J.-C.; Pagetti, J.; Foissy, A. Colloids Surf. A 1998, 138, 310. (e) Peeters, J. M. M.; Mulder, M. H. V.; Strathmann, H. Colloids Surf. A 1999, 150, 247. (5) (a) Eunstan, D. E.; White, L. R. J. Colloid Interface Sci. 1990, 134, 147. (b) Hely, T. W.; Drummond, C. J.; Grieser, F.; Murray, B. S. Langmuir 1990, 6, 506. (6) (a) Cai, J.; Rassi, Z. E. J. Chromatogr. 1992, 608, 31. (b) Lee, C. S.; McManigill, D.; Wu, C.-T.; Patel. B. Anal. Chem. 1991, 63, 1519. (c) Hayes, M. A.; Kheterpal, I.; Ewing, A. G. Anal. Chem. 1993, 65, 27. (7) (a) Yoon, R.-H.; Yordan, J. L. J. Colloid Interface Sci. 1986, 113, 430. (b) Morini, M. A.; Schulz, P. C. Colloid Polym. Sci. 1997, 275, 802.
electrophoretic methods.8 In this technique, a very high voltage (10-30 kV) is applied between the two ends of a capillary made of, for example, fused silica having a 50100 µm internal diameter. Solutes introduced at one end of the capillary are separated on the basis of differences in their electrophoretic mobility and are then detected by a detector placed at the other end. This technique allows for a considerable reduction of sample and electrolyte consumption and provides very high-resolution separation (theoretical plate numbers exceeding several tens of thousands). Micelles have played very important roles in the developments of CE methodology; i.e., micellar electrolytes have enabled the electrophoretic separation of electrically neutral compounds.8b Despite its background and its high efficiency, CE has not been well recognized as a tool suitable for studies of colloid and interfacial chemistry. A possible reason for this oversight is that the separation efficiencies of CE are so high that most researchers have focused their attentions on challenging separations that are difficult by other methods.9 Elucidation of the origin of selectivity in the partition of ions into micelles is one of the important tasks in micellar chemistry. The micellar partition selectivity is closely related to various other phenomena, including ionexchange selectivity, potentiometric responses, etc.10 In this work, we have studied the surface potential of zwitterionic micelles with CE. Because the imbalance between cation and anion partition into zwitterionic micelles induces the potential on the outer surface of micelles that intrinsically have no net charges, studying (8) (a) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, 1298. (b) Terabe, S.; Otsuka, K.; Ando, T. Anal. Chem. 1985, 57, 834. (c) Okada, T. J. Chromatogr. A 1997, 771, 275. (9) (a) Beale, S. C. Anal. Chem. 1998, 70, 279R. (b) Miller, M. L.; Khaledi, M. G.; Shea, D. Anal. Chem. 1997, 69, 1223. (c) Hutterer, K. M.; Jorgenson, J. W. Anal. Chem. 1999, 71, 1293. (10) (a) Okada, T. Bunseki Kagaku 1995, 44, 579 and references therein. (b) Moody, G. J.; Thomas, J. D. R. Selective Ion Sensitive Electrodes; Merrow: Watford Hertz, U.K., 1971.
10.1021/la0003544 CCC: $19.00 © 2000 American Chemical Society Published on Web 11/05/2000
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the surface potential provides significant insights into the thermodynamic origin of partition selectivity. We assumed two possible origins dominating the partition selectivity: (1) the solvation change of an ion upon going from bulk to the micelle and (2) ion association between an ion and the charged groups of the micelles. Although we employed chromatography in our previous work,11 chromatographic separation of ions with micellar mobile phases is based on very complex mechanisms, which prevent the development of a reasonable mathematical model. In contrast, the separation principle of CE is much simpler than that of chromatography. Also, CE is capable of detecting very small surface potentials, as shown in detail below. In the present work, the electrostatic potential of a zwitterionic micelle, which has an inner positive and an outer negative surface, has been evaluated by CE and discussed on the basis of a model derived from the Poisson-Boltzmann equation including selectivity parameters. These parameters agree with those obtained from potentiometry and allow the discussion of the origins of selectivity. Experimental Section The capillary electrophoretic system was composed of a Matsusada Precision Devices high-voltage power supply (model HCZE-30P No. 25), a JASCO UV-visible detector (model 870-CE), and a fused-silica capillary. Currents ranged from 10 to 70 µA, depending on the concentration and nature of the running electrolyte, under a 12-kV applied voltage. Sample solutions were introduced from the anodic end by siphoning. The CE system was set in a thermostated incubator to keep temperature constant at 25 °C. Potentiometric titration was carried out with a Denver pH meter BASIC and a homemade perchlorateselective electrode, composed of a PVC matrix, dioctylphthalate as a plastisizer, and tris-bathophenanthlorine Fe(II) perchlorate as a selective carrier. n-Dodecyltrimethylammoniopropanesulfonic acid (DDAPS) was purchased from Tokyo Kasei and recrystallized from methanol-acetone twice. Other reagents were of analytical grade. Solutions were prepared in distilled deionized water. Results and Discussion Electrostatic Potential of the DDAPS Micelles. The DDAPS micelles themselves should have no net charge. No electrostatic potential can be detected outside the micelles when they are present in pure water. However, in contact with electrolytes, a nonzero electrostatic potential emerges because of an imbalance between anion and cation partitioning. Various investigations have focused on this feature of zwitterionic micelles and revealed that the partition of anions is dominant in the systems of zwitterionic micelles having inner positive and outer negative charges, such as DDAPS.11-12 The theoretical details of the electrostatic potential calculation for the DDAPS micelles are shown in our previous work.11 An outline is briefly described here. (11) Masudo, T.; Okada, T. Phys. Chem. Chem. Phys. 1999, 1, 3577. (12) (a) Chevalier, Y.; Kamenka, N.; Chorro, M.; Zana, R. Langmuir 1996, 12, 3225. (b) Kamenka, N.; Chevalier, Y.; Zana, R. Langmuir 1995, 11, 3351. (c) Gruen, D. W. R. Prog. Colloid Polymer Sci. 1985, 70, 6. (d) Hayter, J. B.; Penfold, J. Colloid Polymer Sci. 1983, 261, 1022. (e) Hu, W.; Takeuchi, T.; Haraguchi, H. Anal. Chem. 1993, 65, 2204. (f) Hu, W.; Tao, H.; Haraguchi, H. Anal. Chem. 1994, 66, 2514. (g) Kamenka, N.; Chorro, M.; Chevalier, Y.; Levy, H.; Zana. R. Langmuir 1995, 11, 4234.
Iso and Okada
Light scattering and neutron diffraction studies have indicated that the DDAPS micelles are spherical with a radius (RB) of 26 Å.12(a) This radius is slightly larger than expected from the molar volume measurements. In this study, based on molecular modeling, RB was assumed to be 23.4 Å, and the radius of the inner core (RA) was 19.4 Å. Figure 1 schematically illustrates the structure of a DDAPS micelle. The entrapment of ions should principally occur in the dipolar layer but not in the inner core; the dipolar layer is defined as the part between the outer anionic surface and the inner cationic surface. The thickness of the dipolar layer (4 Å) is comparable to typical ionic sizes (ca. 1 Å for naked ions and ca. 3 Å for solvated ions). We discuss the thermodynamically averaged behaviors of ions at the micelle/solution interface but do not intend to study their dynamics and structures. Thus, the sizes of ions relative to the thickness of the dipolar layer do not matter for the following discussions. If electrostatic potential is solely responsible for the distribution of ions, then the Poisson-Boltzmann equation for an appropriate geometry (the spherical geometry is suitable for the DDAPS micelles) can describe the spatial distribution of the ions. If the standard chemical potential of an ion is constant throughout the system, this consideration must be correct. However, the standard chemical potential is not constant throughout the system. This term (∆µ°i) can be introduced in the PoissonBoltzmann equation for a sphere as
F ∂2ψ 2 ∂ψ )+ 2 r ∂r ∂r 0
∑zin°i exp(
)
-ziFψ - ∆µ°i RT
(1)
where zi and n°i are the charge and the concentration, respectively, of an ion i in the bulk. ∆µ°i can be regarded as the energy of transfer of an ion from the bulk to the position under consideration. In the DDAPS micellar system, the standard chemical potential in the bulk should be different from that in the dipolar layer of the micelle. Although this term can be gradually changed from bulk to the micelle, a stepwise change was assumed here to facilitate equation derivations; i.e., ∆µ°i ) 0 outside the micelle, whereas ∆µ°i is a particular constant inside the dipolar layer. In the dipolar layer, the hydration of ions should be different from that in the bulk because of the interaction of water molecules with micellar domains. This hydration change in the dipolar layer is represented by the averaged hydration energy change, ∆µ°i, in this paper (see Figure 1). Equation 1 thus predicts that ion distributions throughout the system are determined by the combination of a continuous change in the electrostatic potential with a stepwise solvation change. The Debye-Hu¨ckel approximation allows us to analytically solve eq 1. The following boundary conditions are necessary to relate the density of charged groups at the micellar surface to the electrostatic potential (eq 3) and to maintain the continuity of the radial potential distribution (eq 4):
-
σRA 0
)
|
dψdip dr
r)+RA
ψdip(RB) ) ψout(RB)
(3) (4)
where σRA is the charge density at RA and ψdip and ψout are the electrostatic potential in the dipolar layer and outside the micelle, respectively. Another possible mechanism for the partition of ions is their ion association with ionic groups of surfactant
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Langmuir, Vol. 16, No. 24, 2000 9201
molecules. The association of a cation (C+) with the sulfonate group is, for example, represented by
-SO3- + C+ ) -SO3-C+ ΓSO3C
(
Kip(cation) )
)
(5)
-FψRB
ΓSO3n°C exp
RT
where Kip(cation) is the association constant and ΓSO3 and ΓSO3C are the surface concentrations of free sulfonate groups and associated sulfonate groups, respectively. A similar equilibrium can be assumed for an anion (see Figure 1), i.e., the interaction of an anion with an ammonium group in a DDAPS molecule. The electrical neutrality of the solution can be represented by
δdip + δout + δip(RA) + δip(RB) ) 0
(6)
where δdip, δout, δip(RA), and δ ip(RB) are the net charges in the dipolar and outer layers and at the micellar inner and outer surfaces, respectively.
∫RR ∑zi exp(
δdip ) 4πFn°i
Fn°i 0
δout ) 4π
δip(RA) )
∫R ∑ ∞
B
(
zi exp
(
)
FψRA - ∆µ°anion
RT FψRA - ∆µ°anion
(
1 + n°iKip(anion) exp
)
Figure 1. Schematic representation of a DDAPS micelle and the interaction of the micelle and ions.
-ziFψout 2 r dr RT
σRAARAn°iKip(anion) exp
δip(RB) )
)
-ziFψdip - ∆µ°i 2 r dr RT
B
A
(
σRBARBn°iKip(cation) exp
(
1 + n°iKip(cation) exp
RT
)
)
-FψRB
RT -FψRB RT
)
where ARA and ARB are the micellar surface areas at RA and RB, respectively, and Kip(anion) is the ion association constant of anions at the inner surface. The first and second terms in eq 6 denote the total charges accumulated in the dipolar layer and the outside, and the third and forth terms represent the charges condensed at the inner and the outer surface through ion association. Thus, if appropriate standard chemical potential terms and/or ion association constants are substituted in the above equations, we can calculate the radial concentration distributions of ions as well as the electrostatic potentials at the inner and outer surfaces. Capillary Electrophoretic Determination of ζ Potential. Micellar uptake of ions should be evaluated for various types of electrolytes to discuss the origin of selectivity. CE is a suitable choice for this purpose because of its high applicability and versatility. In CE experiments, the DDAPS micelle was injected in a capillary filled with a running electrolyte also containing the DDAPS micelles from the anodic end. Because the DDAPS micelles themselves have no effective absorption bands, pyrene was solubilized in the injected sample (the concentration of pyrene in a sample solution was lower than 0.8 mM). The solubility of pyrene in water is so low that spiked pyrene should be present only inside the micelle; thus, the detection of the electrophoretic migration of the DDAPS micelles is made possible. Acetone (ca. 5%) was
Figure 2. Typical electropherograms obtained with NaCl and NaClO4 running electrolytes. The concentrations of the electrolytes and DDAPS were 50 mM. Peaks: (a) acetone and (b) pyrene solbilized in the DDAPS micelles. Applied voltage, 12 kV. Detection, 250 nm.
used as an electroosmotic marker. To keep the electroosmotic flow preferably high, all of the running solutions were buffered at ca. pH ) 9.0 by addition of sodium tetraborate. The knowledge of anion-exchange selectivity or hydration suggests that the affinity of borate to the DDAPS micelles is weak. No significant migration was confirmed for the DDAPS micelles in a borate buffer when the concentration is kept as low as 3 mM. Figure 2 shows typical electropherograms of DDAPS micelles with Cland ClO4- running electrolytes. The first peak is acetone, and the second is pyrene solubilized in the DDAPS micelles. The separation of the DDAPS micelle from the acetone peak indicates that the micelle has a negative surface charge. The mobility of the micelle under given conditions (m) is represented by
m) v)L
(
v E
)
1 1 tapp teo
where v is the apparent velocity of the micelle, E is the magnitude of the applied electric field, L is the effective length of the capillary (the length between the injection
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end and the detection window), and tapp and teo are the migration times of the micelle and the electroosmotic flow, respectively. The thickness of the electrical double layer is an important factor in discussing the electrophoretic behaviors of colloidal particles; the Debye-Hu¨ckel parameter, κ, is a useful measure in this regard. The ionic strengths of the running electrolytes ranged from 10 to 80 mM, which corresponds to the range of κ from 3.3 × 108 to 9.3 × 108 m-1. There are various equations capable of relating the electrophoretic mobility of a particle to its ζ potential; it is known that their applicability depends on the ranges of the product of κ and the radius of a migrating colloid. In the present instance, κRB ranges from 0.77 to 2.18. When the ζ potential is not very high, the following Henry’s equation is applicable to the determination of the ζ potential based on electrophoretic mobility:13
m)
0ζ f(κRB) η
where η is the viscosity of the medium and f(κRB) is a Henry’s coefficient. We can thus determine the ζ potential from m. The resolution (Rs) between closely migrating solute bands is given by8(a)
Rs )
m1 - m2 4x2
x
V D(m j + meo)
(8)
where m1, m2, m j , and meo are the electrophoretic mobility of solute 1, that of solute 2, their mean mobility, and the mobility of an electroosmotic flow, respectively, and V and D are the applied voltage and the diffusion coefficient, respectively, of the solutes. The resolution between the DDAPS micelles and electroosmotic flow marker (acetone) is given by substituting m1 ) 0 into eq 8. Figure 3 shows selected results of calculations based on eq 8. Figure 3A illustrates changes in resolution with varying m2 and meo, where the anodic migration of a solute is assumed (m2 < 0). The resolution becomes large with increasing m2 and decreasing mο, indicating that the lower electroosmotic flow rates, the better the resolution, although running times become longer with decreasing electroosmotic flow rate. Figure 3B indicates the ζ potential that can be detected by the present approach under a given meo. If two peaks have the almost identical peak intensity, then Rs ) 1 is a requirement for baseline separation between them. In the present application, baseline separation is not necessary to detect two peaks; Rs ) 0.5 will be enough. Figure 3B clearly implies that a very small potential (
