Langmuir 1996,11, 4267-4277
4267
Electrostatic Effects on the Phase Behavior of Aqueous Cetyltrimethylammonium Bromide and Sodium Octyl Sulfate Mixtures with Added Sodium Bromide Laura L. Brasher, Kathleen L. Herrington,? and Eric W. Kaler* Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received May 1, 1995. I n Final Form: August 11, 1995@ Electrostatic interactions play a prominent role in setting the phase behavior of mixtures of oppositely charged surfactants and lead to the formation of a variety of microstructures,includinga novel equilibrium vesicle phase. Addition of a monovalent salt alters the electrostatic contribution to the free energy of aggregationand thus changes the equilibriumphase behavior and aggregate properties. Here we present observations for the catanionicmixture cetyltrimethylammonium bromide (CTAB)and sodium octyl sulfate (SOS) with added sodium bromide (NaBr). The phase behavior ofthis surfactant system changes markedly when electrolyte is added. At certain compositions,there is a vesicle-to-micelle transition with increasing salt concentration,and surfacecharge densitymeasurements, deduced from electrophoretic light scattering experiments, show that aggregate composition changes with added electrolyte. A thermodynamic cell model has been developed, supported by a new method of calculatingvesicle electrostatic free energy, to quantify the various free energy contributionsto aggregation. The cell model provides insight into how solution conditions such as composition and ionic strength affect phase behavior and related properties.
Introduction The range of microstructure observed in mixtures of oppositely charged surfactants with variations in solution composition is largely a result of electrostatic interactions between charged head groups. By adjusting composition, these interactions (along with hydrophobic tail chain packing considerations) can be tuned to produce aggregates with characteristic geometries ranging from spherical to cylindrical to planar. Of particular interest in catanionic mixtures is the formation of vesicle phases, which are not observed when either surfactant is mixed alone with Unlike the metastable unilamellar vesicles formed from biological lipids, oppositely charged surfactant vesicles are thermodynamically This stability arises from highly nonideal mixing of the two kinds of ~ u r f a c t a n t s . l , ~ - ~ A growing body of literature confirms the potential for vesicles in such roles as drug delivery devices and microreact~rs.~-l~ The manner in which the vesicle/ micelle transition proceeds is also of interest for protein reconstitution procedures, wherein a protein-laden vesicle is solubilizedto purify a protein fraction and then reformed
* Author to whom correspondence should be addressed. Phone: (302)831-3553.Fax: (302)831-4466.E-mail:
[email protected]. Current address: W. L. Gore &Associates, Inc., 297 Blue Ball Road, Elkton, MD 21921. Abstract published in Advance ACS Abstracts, November 1, 1995. (1)Herrington, K. L. Phase Behavior and Microstructure in Aqueous Mixtures of Oppositely Charged Surfactants. PhD Dissertation, University of Delaware, 1994. (2)Kaler, E.W.; Herrington, K. L.; Murthy, A. K.; Zasadzinski, J. A. J. Phys. Chem. 1992,96, 6698-6707. (3)Kaler, E.W.; Murthy, A. K.; Rodriguez, B. E.; Zasadzinski, J. A. N. Science 1989,245,1371-1374. (4)Safran, S. A. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes; Addison-Wesley: New York, 1994. ( 5 ) Safran, S.A.; Pincus, P.; Andelman, D. Science 1990,248,354. (6)Safran, S. A,; Pincus, P.; Andelman, D.; Mackintosh, F. C. Phys. Reu. A 1991,43,1071. (7)Bhandarkar, S.;Bose, A. J . Colloid Interface Sci. 1990,135,531. (8)Fendler, J . H. Membrane Mimetic Chemistry;John Wiley & Sons, Inc.: New York, 1982. (9)Lasic, D.D. Liposomes: From Physics to Applications; Elsevier: Amsterdam: New York, 1993. (10)Liposomes: From Biophysics to Therapeutics; Ostro, M. J., Ed.; Marcel Dekker: New York, 1987.
' @
-
with the newly purified ~ r 0 t e i n . l l - l ~The similarities between synthetic vesicles and cell membranes invite theoretical studies to learn more about the formation and functionality of cells in the body. The vast potential for vesicle application drives the need for a deeper understanding of the physics of vesicle formation. Knowledge of how surfactant architecture and composition affects vesicle stability is critical. For example, catanionic mixtures rich in the shorter hydrophobic chain have an increased propensity for forming vesicles over compositions rich in the longer chain.lJ4 Also, we have demonstrated the stabilizing effect on vesicle formation of a branched tail in mixtures of the straight-chained cetyltrimethylammonium tosylate and the branched sodium dodecylbenzenesulfonate.1s2 Surfactants aggregate because of the free energy benefit ofremoving surfactant tails from direct contact with water. The preferred geometry of the aggregate and its composition and size arise from a delicate balance between this hydrophobic free energy and the other components of the total free energy of aggregation that disfavor aggregation. These unfavorable components include the interfacial free energy for exposure to water of the hydrophobic inner core not shielded by polar head groups, the electrostatic free energy associated with establishing a charged surface, the chain packing free energy of restricting the hydrocarbon tails to the aggregate core, the steric free energy arising from head group crowding at the interface, and the entropic losses of confining monomers to large aggregates. The electrostatic free energy contribution, Gel, depends strongly on salt concentration and favors aggregates of overall neutral charge. Both inter- and intra-aggregate electrostatic interactions are important in setting the stability of all charged (11)Helenius, A,; Simons, K. Biochim. Biophys. Acta 1975,415,2979. (12)Klausner, R. D.; Renswoude, J. v. Reconstitution of Membrane Proteins. In Methods in Enzymology; Academic Press, Inc.: New York, 1984;Vol. 104,pp 340-347. (13)Racker, E. Reconstitution of Membrane Processes. In Methods in Enzymology; Academic Press, Inc.: New York, 1979;Vol. 55,pp 699711. (14)Yatcilla, M. T.;Herrington, K. L.; Brasher, L. L.; Kaler, E. W.; Chiruvolu, S. C. Submitted to J. Phys. Chem.
0743-7463/95/2411-4267$09.00/0 0 1995 American Chemical Society
4268 Langmuir, Vol. 11, No. 11, 1995
Brasher et al.
amphiphile assemblies. The addition of monovalent or micelles,31 without rigorously solving the PBE, and divalent electrolyte to lipid vesicles generally tends to H a ~ t e rhas ~ ~ shown that renormalizing the surface potential makes the solution self-consistent and more screen the interactions between v e s i ~ l e s . ~Typically, ~-~~ accurate. the vesicles flocculate at some critical concentration of salt. They then may or may not fuse to form larger For a spherical bilayer shell geometry, the PBE must structures, depending both on the vesicle charge and on be solved consistently over the two aqueous regions inside the particular electrolyte. Divalent salts tend to induce and outside the bilayer. Mille and V a n d e r k ~ o i ~solved ~B~ fusion, probably due to specific binding.17J9-20Electrothe PBE numerically for a vesicular geometry allowing statics is relevant to in vivo biological studies as well; the for different surface charge densities on the inner and outer monolayer surfaces of the bilayer and explored the surface charge density on in vivo membranes determines case in which the aqueous interior is non-neutral, which interactions with other molecules, and the potential implies a potential drop across the bilayer. Other workers gradient across cell bilayers serves to pump protons in have developed numerical techniques for approximating the process of energy production.21 the potential distributions within a spherical aqueous The inadequacies of the Poisson-Boltzmann equation cavity given the inner surface potential and charge (PBE) are w e l l - d ~ c u m e n t e d , ~yet ~ - ~it~ remains the d e n ~ ity.~ Mitchell ~ - ~ ~ and Ninham38have extended their primary model description of the electric field and ionic analytical derivation for micellar electrostatics to vesicle species concentrations around a charged colloidal particle. geometries, assuming equal potentials (implying an Solving the PBE numerically gives direct information on electroneutral interior aqueous core) and equal surface the entire distribution of ion concentrations and potential charge densities across the bilayer. The assumption of over the volume surrounding a charged particle. The equal surface charge densities is not satisfactory for our numerical solution of the full nonlinearized PBE has been purposes because differences in monolayer compositions successfullyimplemented in the calculation of electrostatic play a role in setting the total free energy of aggregation. free energy in cell model calculations for micellar The assumption of equipotential monolayers, however, ge~metries.~ Given ~ - ~values ~ ofthe electrostatic potential leads to very small differences in the surface potential and the ion concentrations as a function of distance from from the unequal surface potential case.34 a charged particle, the electrostatic free energy can be The paper is organized as follows. A Theory section calculated as the sum of an enthalpic term describing the first provides background information about electrowork of establishing a charged interface and an entropic phoretic light scattering (ELS) experiments and on the term accounting for the order imposed on ionic species thermodynamic cell model. The Results section then around the s u r f a ~ e .Unfortunately, ~ ~ ~ ~ ~ , ~ solution ~ of the shows the effectsof added electrolyte on the aqueous phase full PBE combined with numerical integration to obtain behavior of the oppositely charged surfactant pair cetylthe total electrostatic free energy is computationally trimethylammonium bromide (CTAB)and sodium n-octyl intensive, so a simpler means of calculating electrostatic sulfate (SOS). CTAB is a cationic surfactant with a 16free energy is needed. carbon hydrophobic tail; SOS is an anionic surfactant with The electrostatic free energy of a colloidal particle can an 8-carbon tail. The results obtained here are, at some also be calculated as an integral of the surface potential compositions, quite different from those in biological lipid over the surface charge density.30 This requires no systems with added salt. Instead of a progression to knowledge of the potential away from the surface, and “flatter”microstructure with increasing salt concentration Overbeek has elegantly shown the equivalency of this (i.e., vesicles to flat lamellae), we observe a vesicle-tosurface integration with that of the volume i n t e g r a t i ~ n . ~ ~ micelle phase transition at these compositions. Vesicle Thus only a functional dependence of surface potential on surface charge density, deduced from ELS measurements, surface charge density is required to calculate the is reported next. Finally, cell model calculations of the optimum vesicle concentration as a function of added salt electrostatic free energy. Evans, Mitchell, and Ninham are employed to interpret the experimental data. A simple (EMN) have derived such a relationship for charged method of calculating the electrostatic free energy for unilamellar vesicles was developed to expedite these (15)Day, E. P.; Kwok, A. Y. W.; Hark, S. K.; Ho, J. T.; Vail, W. J.; computations. This approximation is in analogy with the Bentz, J.; Nir, S. Proc. Natl. Acad. Sci. U.S.A. 1980, 77, 4026-4029. (16) Lis, L. J.;Lis, W. T.; Parsegian, V. A,; Rand, R. P. Biochemistry EMN/Hayter t e ~ h n i q u e ~but l , ~allows ~ for asymmetry in 1981,20, 1771-1777. the surface charge and surface potential. A similar (17) Lis, L. J.; Parsegian, V. A,; Rand, R. P. Biochemistry 1981,20, approach has been developed recently.39 1761-1770. (18) Nir, S.; Bentz, J.; Diizgiines, N. J . Colloid Interface Sci. 1981, 84, 266-269. (19) Ohki, S.; Diizgiines, N.; Leonards, K. Biochemistry 1982, 21, 2127-2133. (20) Papahadjopoulos, D.; Vail, W. J.;Newton, C.; Nir, S.;Jacobson, K.; Poste, G.; Lazo, R. Biochim. Biophys. Acta 1977, 465, 579-598. (21) Stryer, L. Biochemistry, 3rd ed.; W. H. Freeman and Company: New York, 1988. (22) Guldbrand,L.; Jonsson, B.; Wennerstrom, H.; Linse, P. J.Chem. Phys. 1984,80, 2221-2228. (23) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press, Inc.: San Diego, 1992. (24) Kirkwood, J. G. J . Chem. Phys. 1934,2, 767. (25) Bogard, M. A. Thermodynamic Modeling of Phase Equilibria in
Ionic Surfactant-WaterSystems. Master’s Thesis, North Carolina State University, 1986. (26) Gunnarsson, G.; Jonsson, B.; Wennerstrom, H. J. Phys. Chem. 1980,84, 3114-3121. (27) Herrington, K. L.; Kaler, E. W.; Miller, D. D.; Zasadzinski, J. A,; Chiruvolu, S. J. Phys. Chem. 1993, 97, 13792-13802. (28) Marcus, R. A. J. Chem. Phys. 1955,23, 1057-1068. (29) Overbeek, J. T. G. Colloids Sur6 1990, 51, 61-75. (30)Venvey, E. J. W.; Overbeek, J. T. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948.
Theory Electrophoretic Light Scattering. The electrophoretic mobility U of a particle of radius R is given by: (31) Evans, D. F.; Mitchell, D. J.; Ninham, B. W. J. Phys. Chem. 1984,88, 6344-6348. (32) Hayter, J. B. Langmuir 1992,8, 2873-2876. (33) Mille, M.; Vanderkooi, G. J. Colloid Interface Sci. 1977,61,455474. (34) Mille, M. R. Electrochemical Properties of Spherical Poly-
electrolytes-Micellar and Liposomal Membrane Models. PhD Dissertation, University of Wisconsin-Madison, 1976. (35) Curry, J. E.; Feller, S. E.; McQuanie, D. A. J. Colloid Interface Sci. 1991, 143, 527-531. (36) Lampert, M. A,; Martinelli, R. U. Chem. Phys. 1984,88, 399413.
(37)Tenchov, B. G.; Koynova, R. D.; Raytchev, B. D. J . Colloid Interface Sci. 1984, 102, 337-347. (38) Mitchell, D. J.; Ninham, B. W. Langmuir 1989,5, 1121-1123. (39) Yuet, P.; Blankschtein, D. Langmuir 1996, 11, 1925-1933.
Electrostatic Effects on Phase Behavior
U = v/E
Langmuir, Vol. 11, No. 11, 1995 4269
(1)
where u is the terminal velocity (reached when the force of the electric field on the particle matches the viscous drag) and E is the applied electric field. U is related to the zeta potential, 5, via Henry's equation:40 (2) where 7 and E are the viscosity and dielectric constant of the medium and EO is the permittivity in a vacuum. Henry's function f l ( ~ Rvaries ) from 1.0 at K R = 0 to 1.5 as KR (the Smoluchowski limit). The inverse Debye length K is
--
(3) with pi" the concentration of the ith ionic species in the bulk, zi its ckiarge, e the charge on an electron, kg the Boltzmann constant, and T the temperature. When the Debye length is much smaller than the particle radius (KR 1)and 5 is small (> 1 (see Results). The mobilities were measured on a Coulter Doppler Electrophoretic derivations of the electrostatics equations are in the Light Scattering Analyzer (DELSA) 440. The system utilizes a Appendix. 5 mW HeNe laser, and d a t a are reported for scattered intensity Electrophoretic light scattering experiments yield a a t a n effective scattering angle of 17.lo, corrected from the mechanical angle for refraction. Since the applied electric field surface charge density at the plane of shear, and the produces flow in the sample cell due to electroosmosis, measurepotential there is significantly lower than that at the ments were made in the stationary layer, determined by locating surface because of screening by counterions and waters the cell wall and moving a predetermined distance from it. The of hydration. As in the EMN picture of a dressed micelle,31 instrument was r u n in current mode, with the current limited this surface charge density given by ELS is much smaller to the minimum current producing a 10 Hz frequency shift. The than that of the "bare" vesicle. From cell model calculamaximum current was 3.0 A for the highest salt concentration tions of surface charge density, we can obtain an estimate measured. The zeta potential was calculated from electrophoretic of the "dressed" surface charge density by multiplication mobility by eq 1. of the vesicle surface charge by degree of ionization, 6. This degree of ionization is calculated using H a y t e r ' ~ ~ ~ Results restatement of EMNs ion binding equation, uiz. Phase Behavior. The phase behavior ofdilute aqueous CTAB/SOS without added salt, and in the presence of 0.5, 2.0, and 4.0 wt % NaBr, is presented in Figure 1. The results represent observations collected on several hundred samples after equilibration for 2 months. Phase boundaries are delineated only after visual observations where xo = K R ~ s is , a dimensionless surface charge density remain unchanged over an extended period of time. Most equal to lue/kBTccoKI, and w = xO(z0 lY2, with zo = compositions equilibrate within 1-2 weeks, but samples cosh(eqd2k~T)and q o = surface potential. that contain vesicles o r a viscous phase require longer equilibration times. Vesicle phases are identified first (46)Szleifer, I.;Ben-Shaul, A,; Gelbart, W. M. J . Chem. Phys. 1985,
+
83,3612-3620. (47)Szleifer, I.; Kramer, D.; Ben-Shaul, A,; Gelbart, W. M.; Safran, S . A. J. Chem. Phys. 1990,92,6800-6817. (48)Szleifer, I.; Kramer, D.; Ben-Shaul, A,; Roux, D.; Gelbart, W. M. Phys. Reu. Lett. 1988,60, 1966-1969.
(49)Rosen, M.J. J . Colloid Interface Sci. 1981,79,587-588. (50) Reid, V.W.; Longman, G. F.;Heinerth, E. Tenside 1967,4,292304. (51)Koppel, D.E.J. Chem. Phys. 1972,57,4814-4820.
Electrostatic Effects on Phase Behavior
Langmuir, Vol. 11, No. 11, 1995 4271
4.0
I
0.0 l
0.0
Eouin
I
I /
I
I
' 1.0
O
2.0 wt%
b
1
\I
I
3.0
E 4.0
0.0
'4.u I
2.0 wt%
d
I
3.0
8
1.o
sos
3.0
4.0
sos
4.0 Equimolar
3.0
PPT+Clear
m
5
2.0
2.0
ep
5
5 1.O
0.0
0.0
1.0
1.o
2.0
3.0
4.0
0.0
0.0
1.O
2.0
3.0
4.0
sos wt% sos Figure 1. Phase behavior of CTABISOSlH20 with no added salt (a) and at three concentrations of added NaBr: 0.5 (b), 2.0 (c), and 4.0 wt % (d). Dotted lines represent equimolar CTABISOS composition, at 61.4% CTAB. (a) With no added salt, one-phase vesicle lobes (V) exist at dilute CTAB-rich and SOS-rich compositions. Samples here appear bluish and are isotropic. One-phase rodlike (R) and spherical (M) micelles form near the CTAB and SOS axes, respectively. Rodlike and spherical micellar phases are both clear, yet scatter more light than pure water. Rodlike micellar samples are viscous and viscoelastic. At intermediate mixing ratios, much of the phase behavior is dominated by vesicles in equilibrium with a lamellar phase (L),which appears as birefringent clouds above the vesicles. The CTAB-rich R and V phases are separated by a narrow two-phase region of rods and vesicles in equilibrium. SOS-richmicelles transformabruptlyto vesicles at most concentrations,though around 3.0w t % an intervening region of rodlike growth occurs. Unresolved multiphase regions are at concentrations above those of the vesicle lobes. (b)At 0.5 wt % NaBr, the smaller vesicle lobe disappears, and the larger SOS-rich lobe shrinks. The CTAB-rich rodlike micelle phase now coexists with a precipitate (PPT).(c) With additional salt, the one-phaseSOS-richvesicle lobe completely disappearsin favor of the micellar phase at lower mixing ratios and of vesiclellamellar coexistence at higher CTAB content. (d) With 4.0 w t % NaBr, the entire CTAB-rich side of the phase diagram is dominated by a clear isotropic liquid in equilibrium with precipitate. Samples here are no longer viscous or viscoelastic. The one-phase micellar region M extends farther toward more CTAB-rich mixing ratios. The multiphase region is at some compositions a clear streaming birefringent phase over an isotropic bluish phase and at other compositions is a clear isotropic phase that scatters more light than water over a clear phase. wt%
visually by the characteristic isotropic blue appearance and then by QLS measurements to verify that aggregate sizes are in the range typical of vesicles. Further, cryoTEM obsellrations of similar samples have confirmed the existence ofvesicles in such phases. The long equilibration time is necessary for the samples containing vesicles to distinguish between single-phase vesicle regions and twophase vesicletlamellar regions, since small amounts of lamellar structure develop slowly compared to other phases. Visual observations and QLS measurements over a time period of 9 months and longer confirm the stability of the vesicle phase relative to a lamellar phase in onephase regions. As discussed the mixture of oppositely charged surfactants CTAB and SOS is actually a five-component system, comprising CTAB, SOS, CTA+-OS, and NaBr. Such a system requires a phase pyramid to accurately describe all phase behavior. For clarity, we instead show phase behavior in two-dimensional plots of wt % CTAB versus wt % SOS at constant added salt concentration.
The phase behavior of CTABlSOSIH20 (Figure l a ) with no added salt has been presented in detail e1~ewhere.l~ One-phase vesicle lobes are located at dilute CTAB-rich and SOS-rich compositions, with the SOS-rich lobe extending to higher surfactant concentration (3.5 wt % compared to 1.0 wt % for CTAB-rich). Vesicle samples appear bluish and isotropic. Solutions near the SOS binary axis contain spherical or globular micelles; they appear clear, yet scatter more light than water. Rodlike micelles form near the CTAB axis, extending to a mixing ratio of 80120 CTABISOS,and are viscous andviscoelastic. Between mixing ratios 80120 and 75/25 CTABISOS, vesicles coexist with rodlike micelles. Much of the phase behavior at compositions between the two vesicle lobes is dominated by vesicles in equilibrium with a lower density lamellar phase, which appears as birefringent clouds above the vesicle phase. SOS-rich micelles transform abruptly to vesicles at more dilute concentrations, although around 3.0 wt %, an intervening region of rodlike growth occurs. Unresolved multiphase regions are at concentrations above those of the vesicle lobes.
Brasher et al.
4272 Langmuir, Vol. 11, No. 11, 1995
1200 0.20 -
3 ‘Oo0
1-
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2
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0.15
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. .
I
.
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i
i I
1.5
.
. .
.
0.0
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wt% surfactant
Figure 2. Absorbance data measured at 400 nm wavelength for 0.5 (O), 1.0 (w),and 2.0 (A)w t % NaBr as a function of surfactant concentration, at a constant mixing ratio 20180 CTABISOS. The dotted lines denote the midpoints of the turbidity increases at the micellar phase boundaries.
The addition of excess electrolyte markedly alters the phase behavior of CTAB/SOS/HzO (parts b-d of Figure 1). The most conspicuous effect is the destabilization of the large one-phase vesicle lobe with increasing amounts of added NaBr. The vesicle region shrinks in all dimensions. Vesicles still form in the water-rich corner of the lobe, but small turbid clouds form over the vesicle phase after the addition of salt. These clouds are either lamellar or multilamellar vesicle (MLV) phases or a fine dispersion ofprecipitate. Efforts to isolate and examine these wispy aggregates failed. Adding NaBr also drives the two-phase lamellar/vesicle region on the CTAB-rich side of the vesicle lobe to more SOS-rich compositions. The lamellar phase becomes increasingly favorable as salt is added, as observed visually by the increasing predominance of a turbid white birefringent phase over the vesicle phase. The vesicle/micelle phase boundary, however, shifts to compositions richer in CTAB with increasing NaBr. Thus, overall, the most SOS-rich section of the larger vesicle lobe becomes unstable with respect to the neighboring micelle phase, while the most CTAB-rich section of the lobe becomes unstable with respect to the lamellar phase. As in the salt-free case, highly viscous and viscoelastic solutions form on the CTAB-rich side ofthe phase diagram. These phases probably contain rodlike micelles. At intermediate salt concentration, though, the rodlike micellar phase coexists with a precipitate. At still higher salt concentration (4.0wt % NaBr), solutions are no longer viscous or viscoelastic, and the CTAB-rich micellar region expands with increasing salt concentration. The increasing stability of the SOS-rich micellar phase over bilayer phases with added electrolyte is represented quantitatively in a plot of absorbance versus surfactant concentration at constant CTAB/SOS ratio, for various salt concentrations (Figure 2). At 20180 CTABISOS, dilution of 2.0 wt % surfactant samples produces first a slow increase in absorbance, followed by a drastic jump in the absorbance at the VesicleAamellar phase boundary. The midpoint of this turbidity jump clearly moves to lower surfactant concentrations as the NaBr content increases, indicating an increase in extent of the micellar phase. Alternatively, the phase transition from vesicles to micellescan be monitored by recording an apparent radius measured by QLS as a function of salt concentration. In Figure 3, the apparent radius as a function of salt concentrationis given for a sample at 2.0 wt % surfactant, 30/70 CTABISOS. With no added salt, the vesicles have an apparent radius of approximately 1300 A. The
clear
400-
2.0
4.0 6.0 wt% NaBr
8.0
10.0
Figure 3. Apparent radius versus wt % NaBr, as measured by QLS at 2.0 w t % 30170 CTABISOS. At low NaBr content, samples are bluish and apparent radii are greater than 1000 A, indicative of vesicles. Between 1.4 and 2.5 wt % NaBr, samples become two-phase and viscous, so that QLS measurement is not possible. At 3.0 wt % NaBr, samples are again one-phase, though now clear and nonviscous. Apparent radii at high salt are less than 200 A and decrease with added salt. , ” . 3-
-3.2
1
-4.0 1 0.0
0
0.2
0.4
7 0.6
t
-40
0 0.8
wt% NaBr
Figure 4. Electrophoretic mobility and zeta potential as a function of added NaBr. Mobilities (solid data points) were measured by ELS, and zeta potentials (open data points) were calculated using eq 2.
apparent radius changes little (-15%) with small amounts of NaBr, and solutions continue to appear bluish and isotropic. Samples then become viscous and phase separate at intermediate NaBr concentrations, between 1.4 and 2.5 wt %. With further addition of salt, solutions clear and form a single phase. The apparent radius of aggregates in these samples is much smaller, less than 200 at 3.0 wt % NaBr, and then decreases further with salt to -100 A at 6.0 wt %. Electrophoretic Light Scattering. More information about the changes of the vesicles in response to addition of salt comes from electrophoretic light scattering experiments. Zeta potential measurements were made as a function of NaBr concentration on the vesicle phase at 2.0 wt % surfactant, 30/70 CTAEVSOS. ELS measurements were limited to salt concentrations low enough (up to 0.75 wt % NaBr) that the sample composition remained in the vesicle phase. ELS results are shown in Figure 4. As more electrolyte is added, the magnitude of the electrophoretic mobility U ranges from -3.9 at no added salt to -3.6pm.cm4V.s) at 0.75 wt % NaBr. The zeta potential 5, calculated by eq 2, decreases steadily over this range, from -58 to -47 mV. Figure 5 shows surface charge density o calculated from Hayter’s equation (eq 4). Clearly, the magnitude of the apparent vesicle surface charge density increases with
A
Langmuir, Vol. 11, No. 11, 1995 4273
Electrostatic Effects on Phase Behavior
Table 1. Comparison of Numerical and Approximate Electrostatics Results’ KRI
Gel (J/mol)
YO
UouJUin
numerical
approx
numerical
approx
numerical
approx
cell model
surface int
51.0 159.8 222.1 248.2
67.8 164.2 224.3 249.7
1.0042 1.0037 1.0099 1.0033
1.0042 1.0038 0.0045 1.0034
-7.10 -4.84 -4.19 -3.98
-6.54 -4.78 -4.17 -3.97
8.26 5.58 4.81 4.58
8.41 5.70 4.86 4.59
7.8 35.6 51.0
10.7 15.1 47.8 67.8
1.0045 1.0045 1.0044 1.0042
1.0045 1.0045 1.0043 1.0042
-10.83 -10.16 -7.82 -7.10
-10.23 -9.54 -7.23 -6.54
0.36 0.66 4.69 8.26
0.36 0.67 4.75 8.41
39.4 60.3 58.4 40.0
70.5 64.9 62.0 58.9
1.0026 1.0107 1.0133 1.0050
1.0025 1.0108 1.0133 1.0050
-8.69 -4.65 4.21 7.23
16.13 1.83 1.30 7.60
16.58 1.85 1.31 7.69
3.6 4.2 7.8
2.7 5.3 10.7
1.0196 1.0095 1.0045
1.0188 1.0091 1.0045
-10.85d -10.85d -10.85d
0.36 0.36 0.36
0.36 0.36 0.36
[NaBrl (M) 0
0.2 0.4 0.5 wt % surf 0.05 0.1 1.0 2.0
11.1
ClCTABb
0.066 0.389 0.598 0.851
Ric
250 500 1000
-7.53 4.51 4.10 6.46 -10.23 -10.23 -10.23
*
Unless otherwise noted, calculations are for 2%, 30/70 CTAJ3/SOS,Xagg,c*~ =Xagg,s0s = 0.9, R1= 1000 A, t = 20 .&,Xin = 0.5. X a g g , c ~ ~ the bulk mixing ratio is varied. 0.05 wt % surfactant. Dimensionless center potential is -1.91 for 250 A, -0.58 for 500 A, and -0.028 for 1000 A. a
= Xagg,sos = 0.9, and
Table 2. Comparison of Electrostatics Results for Unequal and Equal Surface Potentials, Using the Approximate Method of Calculation. For the Equipotential Case, Xi, Was Held Constant at 0.5. For the Unequal Potential Calculations, Xi, Was 0.45 for R1 = 260 A and 0.49 for All Others UouJuin YO Gel (J/mol) Ri (A) KRI unequal equal Yout Yin equal unequal equal 250 1000 1000 1000
2.7 10.7 67.8 248.6
1.0586 1.0602 1.0602 0.9510
1.0188 1.0045 1.0042 1.0035
-10.26 -10.28 -6.59 -3.92
electrolyte concentration, from -3.2 x C/m2with no added salt, to -4.2 x C/m2at 0.75 wt % NaBr. These correspond to changes from 5.0 nm2/charge(0 wt % NaBr) to 3.8 nm2/charge. Similar results, also reported in Figure 5, are obtained for either calculating zeta potential in the Smoluchowski limit offdKR) 1(with Hayter’s equation for a) or calculating surface charge density with the Debye-Huckel equation (and using Henry’s function in eq 2). Model Results. The simple approximate method of calculating electrostatic free energy in the cell model was compared with exact results from numerically solving the nonlinear PBE over a range of surfactant composition and salinity. These are shown in Table 1 for an overall surfactant concentration of 2.0 wt %, assuming a radius of 1000 (as suggested from QLS measurements), a bilayer thickness of 20 A (chosen as an intermediate to the maximum chain lengths of the two surfactant), and the fraction of each surfactant aggregated xagg,CTAB Xagg,sos = 0.9. Results for varying surfactant concentration and vesicle radius are also presented. The quantities of most interest, the surface charge density asymmetry and the electrostatic free energy, are in excellent agreement with the full numerical results for a wide range of surfactant and NaBr concentrations, and for surfactant mixing ratios of 0.1-0.9 CTAB. The surface potentials are also in good agreement but begin to show significant error at vesicle compositions much richer in one component. The approximation improves with added salt. Results are shown in Table 2 for the more general case of nonequal surface potentials across the bilayer. The potential drop is small in all cases, and the free energy is not much different from the equipotential case. Hence all subsequent cell model electrostatics calculations were carried out with the assumption of equipotential bilayers.
-10.23 - 10.23 -6.54 -3.97
-10.18 -10.18 -6.48 -4.03
0.37 0.37 8.44 4.61
0.36 0.36 8.41 4.60
-
A
4 -0.045 I -0.050 ? 0.0
.
, 0.2
,
.
0.4 wt%
.
.
, 0.6
0.8
NaBr
Figure 5. Surface charge densities determined from ELS (symbols) together with cell model results for surface charge density as a function of added NaBr (solid line). W represents data reduction with eq 2 for 5 and eq 5 for u, 0 with eq 2 and eq 4, and A with eq 2 in the Smoluchowski limit and eq 5. Cell model calculations for 2.0 wt % 30/70 CTAB/SOS were made as a function of added salt concentration with the vesicle radiusR1 held constant at 1000 The results for vesicle composition with added salt are given in Figure 6. The fraction of CTAB molecules incorporated in the vesicle is calculated to be = 0.226 (mole fraction) with no added salt and decreases sharply with small amounts of added NaBr. At high salt concentration, asymptotically approaches the bulk molar mixing ratio (0.214CTAB). The predicted change invesicle composition is a consequence of an increasing optimum Xagg,sos.In other words, almost all ofthe CTAB is always aggregated, so the optimumXagg,cTAB remains approximately constant with added salt, and the change inXagg,sos dominates the change in vesicle composition.
A.
Brasher et al.
4274 Langmuir, Vol. 11, No. 11, 1995
0.0
1.o wt%
2.0 NaBr
3.0
4.0
Figure 6. Cell model results for vesicle composition as a function of added NaBr. Composition is given as the mole fraction CTAB in the vesicle. With salt, the vesicle composition decreases sharply at first and then asymptotically approaches the bulk mixing ratio (dotted line). The cell model results for the apparent surface charge density as a function of salt concentration are shown together with those from electrophoretic mobility measurements in Figure 5. Again, the solution composition was 2.0 wt % 30/70 CT@/SOS, and the vesicle radius was held constant at 1000A. The predicted surface charge densities ranged from -0.0234 C/m2with no added salt to -0.0381 C/m2 at 0.77 wt % NaBr. These predictions are in very good agreement with the experimental surface charge densities regardless of the method used for data reduction.
Discussion A large portion of the SOS-rich vesicle lobe is destabilized to the neighboring two-phase vesicleflamellar coexistence region upon the addition of salt. This transition is expected, since screening of intra-aggregate electrostatic repulsion should lead to larger, flatter structures. For example, it is well-known that salt can drive a transition to rodlike micelles in aqueous surfactant solutions that form spherical micelles without added salt.52,53Increased screening between charged head groups produces a smaller effective head group area,23 and consideration of surfactant packing parameters suggests that decreasing the effectivearea per head group (while maintaining a constant hydrophobic tail volume per molecule) should produce flatter microstructure. Moreover, interaggregate screening is expected to promote vesicle destabilization if the vesicles are stabilized by repulsive forces, as in DLVO t h e ~ r y . There ~ ~ , ~are ~ many reports in the biological lipid literature of vesicle flocculation with added monovalent sa1t.15J9n54Vesicle flocculation could be a step in the transition from vesicle to lamellar or MLV structures with added salt. Finally, recall that an increase in electrolyte concentration means that more of the surfactant is aggregated, as evidenced in the pure component case by the depression of the cmc with increasing salt c ~ n c e n t r a t i o n .If~ ~vesicles remain the thermodynamically preferred microstructure with this increase in aggregated surfactant, then the number density of vesicles increases. Eventually the increase in vesicle number density leads to close-packing of the (52) Missel, P. J.; Mazer, N. A.; Benedek, G . B.; Young, C. Y.; Carey, M. C. J . Phys. Chem. 1980,84,1044-1057. (53) Soderman, 0.;Jonstromer, M. J . Chem. SOC.,Faraday Trans. 1993,89,1759-1764. (54) Bartucci, R.; Sportelli, L. Colloid Polym. Sei. 1993,271,262267.
vesicles, and subsequently some of the surfactant will go into the lamellar phase. On the other hand, at certain compositions in the CTAEV SOS system, the morphology proceeds from vesicle to micelle with increasing salt concentration (see Figure 1). The phase transition from large vesicles to much smaller micelles of high curvature is contrary to conventional wisdom, which holds that screening of intra- and interaggregate electrostatic repulsion should lead to larger, flatter structures. Consideration of the relevant free energy terms for aggregation of mixed surfactants, however, provides insight to the salt-induced vesicle/ micelle phase transition. Unlike pure component surfactant solutions, mixed surfactant systems have the added degree of freedom of adjusting aggregate composition to attain the lowest possible free energy state for given conditions. In terms ofthe cell model, Ghyd drives aggregation,while Gelopposes it. For single ionic surfactants at very low surfactant concentrations (below the cmc), the counterion concentration is relatively small, so that the electrostatic free energy penalty for a one-component ionic surfactant to micellize is prohibitively high. At the cmc, enough counterions are available to screen the micelle, lowering Gelto a level where the hydrophobic free energy can balance electrostatics and the other contributions to the free energy of aggregation. Mixtures of oppositely charged surfactants, on the other hand, can form aggregates of nearly equimolar composition and at much lower surfactant concentrations with small electrostatic free energy contributions. By forming aggregates of more neutral composition than the bulk mixing ratio, the system realizes a favorable hydrophobic free energy gain with a relatively small electrostatic free energy penalty. Of all the contributions to the total free energy of aggregation, only the electrostatic free energy is sensitive to electrolyte concentration. With no added salt, Gel is relatively high and thus favors a more electroneutral aggregate, as discussed above. Upon addition of electrolyte, the increased ion concentration shields the charged aggregate and reduces Gel for a given aggregate composition. In view of the then diminished role of electrostatic free energy, the total free energy balance shifts slightly in favor of the hydrophobic contribution. As a response, more of the majority monomeric surfactant is incorporated into the aggregate, producing a more highly charged assembly, but with a favorable decrease in Ghyd. (See Figure 6.) At high concentrations of added salt, the aggregate composition approaches that of the bulk. Micelles may become the thermodynamically preferred microstructure at this higher aggregate surface charge density, but this comparison of free energies has yet not been made. Of course, the entropy of mixing certainly favors the much smaller micelles. Within the cell model, then, the optimum curvature is not found through an explicit accounting of salt’sscreening effect on area per head group. Rather, the decrease in effective area arises as a result of the decrease in Gelwith added salt. That is, for a given aggregate composition, the reduction in Gel favors a transition to lower curvature (larger size), requiring a smaller area per head group. Surface charge density is an experimentally measurable physical property directly related to the vesicle composition. As the composition asymmetry of the vesicle increases with salt, so too does the surface charge density. Predicted surface charge densities match the experimental values very well with all three of the methods used to analyze the ELS data. The combination of Henry’s equation (eq 2) for the zeta potential and Hayter’s potentiallsurface charge density relation (eq 5) gives the
Electrostatic Effects on Phase Behavior
poorest agreement of the three. Replacing either Henry’s equation with the Smoluchowski equation or Hayter’s equation with the Debye-Huckel expression (eq 4) significantly improves the match between model and experiment. This is curious since theoretically Henry’s and Hayter’s formulas should be the most accurate under the given conditions. The agreement of the model with the crude methods of data analysis is likely due to the fortuitous cancellation of errors, perhaps arising from vesicle deformation or from an anomalous surface cond u ~ t i v i t y .Nevertheless, ~~~~~ the trend of increasing surface charge density with increasing salt concentrationis clearly captured. The agreement is especially impressive considering that, outside the use of independentlymeasured vesicles sizes to simplifycalculations, the only parameters invoked in the cell model prediction were those that were derived from pure component cmc data. Overall, our approximation provides a rapid way to calculate the electrostatic free energy. Agreement between exact surface potentials and approximations is within 15%for the range of compositions checked. More importantly, the electrostaticfree energy calculated using the approximation is within 2% of the numerical results for all cases. The approximation deviates from the exact results when the solution composition, and thus generally the monomer composition, is far from equimolar. This error arises from the implicit assumption in the derivation that p y = p1 = pbulk/2. Under these circumstances, the mass balance over aqueous ionic species is not satisfied. However, for most cases of interest, i.e., at compositions that form vesicles in oppositely charged surfactant solutions, the accuracy of the approximation is well within reasonable limits. Furthermore, with small amounts of added electrolyte, the excess salt swamps any counterion/ co-ion composition asymmetry, and the approximation becomes excellent. Finally, we expect, and limited experimental observations confirm, that the general pattern of added electrolyte driving a vesicle-to-micelletransition will hold for mixtures of oppositely charged surfactant having highly asymmetric hydrophobic tail lengths. Then, at concentrationsbetween their two cmc’s and bulk compositions rich in the shorter chain surfactant, vesicles may form with a composition different from that of the bulk, since the shorter chain surfactant monomer is more soluble in water. Added salt will tend to drive the aggregate composition toward that of the bulk, as discussed above, and micelles may become the favored structure.
Conclusions Electrostatic forces are important in setting the aggregation behavior of ionic surfactant systems. With mixtures of oppositely charged surfactants, the electrostatic contribution to the free energy of aggregation tends to favor aggregates with more nearly neutral charges. However, with an increase in solution ionic strength, the electrostatic free energy penalty for a given charge composition is significantly reduced, and so a more highly charged aggregate can form with a compensating favorable change in the hydrophobic free energy of the system. The charge asymmetry continues to increase with added electrolyte until the bulk mixing ratio is reached. At some overall solution compositions, the change in aggregate composition drives a phase transition. For the (55)Overbeek, J. T. G.; Wiersema, P. H. “he Interpretation of Electrophoretic Mobilities. In EZectrophoresis: Theory, Methods, and Applications; Bier, M., Ed.; Academic Press Inc.: New York,1967;Vol. 2, pp 1-52. ( 5 6 )Zukoski, C. F.; Saville, D. A. J. Colloid Interface Sci. 1986,114, 32.
Langmuir, Vol. 11, No. 11, 1995 4275
k water
Figure 7. Vesicle cell, modeled as a spherical bilayer (region 11) enclosingan inner aqueousregion (region I) and surrounded by an outer region of water (region 111).
more equimolar section of the SOS-rich vesicle lobe, a transition from one-phase vesicles to vesicle/lamellar coexistence occurs. In the most SOS-rich region of the vesicle lobe, though, large unilamellar vesicles transform to much smaller, highly curved spherical micelles. This vesicle/micelle transition contrasts with observations made of monovalent electrolyte addition to lipid vesicles, which in general simply flocculate as intervesicular electrostatic repulsions are screened. The surface charge density measurements from ELS provide supporting evidence that the vesicle composition does change in the way described by the cell model. The close agreement between measured and calculated surface charge densities is further evidence of the reliability of such cell model predictions. Further, we have met the need for a simpler method of calculating bilayer charge asymmetries and electrostatic free energy with an approximation to the full nonlinear PBE. The results of this technique give very good agreement with numerical solutions for electrostatic free energy over a wide range of compositions. At the compositions of physical relevance to vesicle formation in mixed surfactant systems, the agreement between approximation and exact solution is excellent.
Acknowledgment. We are grateful for the financial support of the National Science Foundation (CTS-9102719 and CTS-9319447). ELS experiments were performed at the Dupont Company, Deepwater, NJ, with the cooperation of R. Thomas and D. Glaspey. Appendix Derivations are presented here for calculation of the surface potential and electrostaticfree energy for a vesicle geometry. Figure 7 depicts the vesicle cell, with the vesicle modeled as a perfectly spherical bilayer (region 11) enclosing an inner aqueous region (region I) and surrounded by an outer region of water (region 111). Beginning with the nonlinear PBE in spherical coordinates
and introducing the following dimensionless variables
4276 Langmuir, Vol. 11, No. 11, 1995
Brasher et al. Similarly, inside the vesicle, the PBE is integrated from the vesicle center to the inner bilayer:
we arrive at a dimensionless PBE:
V 2 y ( x )=
&2
+ 2x d x = sinh y 0
Ix
( A . l l )
2
Thus the situation is described by three equations (eqs A.4, A.7, andA.ll) and four unknowns (yo, yc,si,,,and s,,,~), and there is not a unique solution. Approximations for the center potential in a spherical ~ a v i t y 3can ~-~ be~utilized to obtain a solution for yc. In mixed surfactant systems, though, the Debye length K - ~is typically small compared to the inner bilayer radius Ro (xin = K& >> 1). Thus potentials generally decay to zero at the center, and we can set yc = 0. This assumption has been verified by numerical solution of the PBE. With ye = 0, the inner surface charge density simplifies to
[l - (1
+ w ~ , ~ ) ' ~ ]where Win
Then sOut is related to yo as
where wout=
Win
=
X&O
2
+ 1) (A.12)
and together with the charge balance and outer surface charge density relations, the surface potential may be easily solved with a simple one-parameter root-solving algorithm. Again, following the derivation of H a ~ t e rthe , ~ ~elec-
Electrostatic Effects on Phase Behavior
Langmuir, Vol. 11, No. 11, 1995 4277
trostatic free energy outside the vesicle, per unit charge, is calculated as
with
These results have the same form as the simpler results for equal surface potentials but now include a term accounting for the potential drop across the bilayer. To solve for the two surface potential gradients, we solve the PBE with the assumption of no charges within the bilayer: (A.21) Inside the vesicle, the analogous integration gives Solution of this ODE,given the boundary conditions, yields
Here gel,out = Gel,ouJQout, where &out = (a0uJe)4nR~2. ge1,in is defined in a similar way. The sum of the inner and outer electrostatic free energies gives the overall electrostatic contribution to the free energy of aggregation. In practice, the procedure to calculate the overall vesicle electrostatic free energy begins with calculating the total surface charge density for the bilayer as a whole, given the vesicle radius, bilayer thickness, and overall composition. Next a surface charge density asymmetry across the bilayer is chosen so that soutand sincan be calculated. The outer surface potential yo is found by a simple oneparameter root-solvingalgorithm from combination of eqs A.4, A.7, and A.12. A G e l is calculated as the sum of the inner and outer free energies (eqs A.13 and A.14). If we do not assume electroneutrality of the vesicle’s inner core, surface potentials on either side of the bilayer are not generally equal. This is a direct result of Gauss’s law, which gives the following new surface boundary conditions: I11
I1
I1
dy - I_ dy = -sOut at dx E d x I1
E
* I1
E d x
-
x = xOut (A.15)
I
dx
= -sin at x = xin
(A.16)
where €I1 is the dielectric constant in the bilayer, and 6 is that for the aqueous regions I and 111. Now the PBE integration gives
Combining the equations above, sout= sout(equalpotentials)
+ -‘I
Yout
€
in
xout (l/Xin - l/xout) (A.23)
and E”
sin= sin(equalpotentials) - E
Yout
in
XinS(l/Xin- l/xout) (A.24)
By removing the assumption of electroneutrality in the inner aqueous core, then the outer and inner surface charge densities bout and .sin) must be varied independently in the cell model free energy minimization. Thus the charge balance relation (A.4)is not used here. The outer and inner surface potentials are found with a twoparameter root-solving algorithm from eqs A.23 and A.24, respectively. Finally, the free energies when yc = 0 are given by ke1,out
= pgel,out(equal potentials) I1
€ -
E
Yout
- Yin
(A.25)
S0,~,,;(l~x;, - l/xout)
,8gel,in = pgel,,(equal potentials)
+
where
and
The above derivations represent a much simpler and faster means of calculating the electrostatic free energy than t h e , full numerical solution. This free energy calculation previously accounted for a significant portion of the total cpu time for each iteration in the cell model free energy minimization. Furthermore, results are well within reasonable limits of accuracy, as compared to the full numerical solution of the PBE and numerical integration to obtain A G e l . LA950339C
