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Notes Electrophoretic Nuclear Magnetic Resonance (ENMR)sA New Tool for Studying Counterion Binding in Mixed Surfactant Systems Peter C. Griffiths,*,† Alison Paul,† Peter Stilbs,‡ and Erik Pettersson‡ Department of Chemistry, Cardiff University, P.O. Box 912, Cardiff CF10 3TB, U.K., and Department of Physical Chemistry, Royal Institute of Technology, Stockholm, Sweden S-100 44 Received May 9, 2003. In Final Form: July 15, 2003
Mixtures of surfactants are used widely in industrial and domestic formulations. While each component has a particular function (e.g. surface tension lowering, wetting, active ingredient deposition, and control of stability or rheology), the properties of the complex mixture are invariably different from those of the individual components. Understanding the interactions between the various components is therefore crucial to optimizing their performance. Our recent interest has focused on the binary surfactant mixture comprising the anionic surfactant sodium dodecylsulfate (SDS) and the sugar-based nonionic surfactant dodecyl malonobis-N-methylglucamide (C12BNMG). The onset of micellization,1 which follows the commonly observed synergistic behavior,2 and the composition3 and size/shape4,5 of the mixed micelle have been measured by surface tension, pulsed-gradient spin-echo NMR (PGSENMR), small-angle neutron scattering (SANS), and timeresolved fluorescence quenching measurements. In essence, exchanging one SDS molecule for a C12BNMG molecule has little effect on the structure of the micelle except to displace a volume of water from the headgroup region commensurate with the difference in respective headgroup volumes of the anionic and nonionic surfactants.6 More importantly, the micellar charge varies as the sodium counterions become more freely available on addition of the nonionic surfactant, at least over the majority of the composition range. Here, we show that ENMR is an ideal technique for probing counterion binding, since classical methods for measuring counterion binding (e.g. conductivity) cannot be applied to mixed surfactant systems, as the micelle composition changes with dilution. † ‡
Cardiff University. Royal Institute of Technology.
(1) Griffiths, P. C.; Roe, J. A.; Jenkins, R. L.; Reeve, J.; Cheung, A. Y. F.; Hall, D. G.; Pitt, A. R.; Howe, A. M. Langmuir 2000, 16, 9983. (2) Rubingh, D. N. Solution Chemistry of Surfactants; Plenum: New York, 1979. (3) Griffiths, P. C.; Stilbs, P.; Paulsen, K.; Howe, A. M.; Pitt, A. R. J. Phys. Chem. B 1997, 101, 915. (4) Griffiths, P. C.; Whatton, M. L.; Kwan, W.; Abbott, R. J.; Pitt, A. R.; Howe, A. M.; King, S. M.; Heenan, R. H. J. Colloid Interface Sci. 1999, 215, 114. (5) Bales, B. L.; Ranganathan, R.; Griffiths, P. C. J. Phys. Chem. 2001, 105, 7465-7473. (6) Griffiths, P. C.; Bales, B. L.; Howe, A. M.; Pitt, A. R.; Roe, J. A. J. Phys. Chem. B 2000, 104, 264.
The electrophoretic nuclear magnetic resonance (ENMR) technique was conceived by Holtz et al.7,8 and subsequently developed by Johnson9-11 and others.12,13 The measurements presented in this Note were conducted as described previously.15 The coherent motion induced by the electric field results in a phase shift of the spin-echo given by
I(G,δ,∆,ν) )
[
(
I0 cos(γGδν∆) exp -γ2δ2G2 ∆ -
) ]
δ D (1) 3 s
where I is the integral of the relaxation-weighted Fourier transformed peak intensity in the absence (I0) and presence (I(G,δ,∆,ν)) of flow and field gradients. ν is the velocity in the presence of the electric field, the “electrophoretic velocity”. The exponential term accounts for the attenuation due to diffusion. Typical experimental parameters using a stimulated echo sequence were τ ) 10 ms, diffusion time (∆) ) 0.5 s, gradient pulses 1 ms in duration (δ), and intensity (G) ) 0.44 T/m. The attenuation of the signal due to relaxation was approximately 30%. Where the double layer is thin or flat, that is, the “large particle limit” (κr . 1, where 1/κ is the Debye length and r is the particle radius), the electrophoretic mobility is often presented as the ζ-potential (Helmholtz-Smoluchowski equation):
u( )
0rζ η
(2)
0 is the dielectric constant of the vacuum, and r is the relative dielectric constant of the solution. In the case of smaller particles, the curvature represents a major theoretical challenge. Henry14 showed that the electrophoretic mobility depends on κr and ranges from the Helmholtz-Smoluchowski limit at low κr to a value larger by 50% at high κr. Indeed, the Henry equation, for large potentials, deviates significantly from a linear interpolation between these two limits over the range 1 < κr < 10. For ions with a small radius r and at low ionic strengths, the electrophoretic mobility scales inversely with size and viscosity η:8
u( )
ze 6πηr
(3)
Colloidal systems rarely fall into one of these two limiting cases; for surfactants such as that presented here, 0.4 < (7) Holz, M.; Mu¨ller, C. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 141. (8) Holz, M. Chem. Soc. Rev. 1994, 23, 165. (9) Johnson, C. S., Jr. Electrophoretic NMR. Encyclopedia of Nuclear Magnetic Resonance; Wiley & Sons: New York, 1996 and references therein. (10) Saarinen, T. R.; Johnson, C. S., Jr. J. Am. Chem. Soc. 1988, 110, 3332. (11) Johnson, C. S., Jr.; He, Q. In Electrophoretic NMR in Advances in Magnetic Resonance; Warren, W. S., Ed.; Academic Press: San Diego, CA, 1989; p 133. (12) He, Q. H.; Liu, Y. M.; Sun, H. H.; Li, E. C. J. Magn. Reson. 1999, 141, 355. (13) He, Q. H.; Lin, W.; Liu, Y. M.; Li, E. C. J. Magn. Reson. 2000, 147, 361.
10.1021/la034793p CCC: $25.00 © 2003 American Chemical Society Published on Web 08/16/2003
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Notes
κr < 1 and only approximate or relative values of the ζ-potential can be obtained. The electrophoretic mobility measured in an ENMR experiment contains contributions from the unimer and micelle that must be decoupled to extract the true micelle electrophoretic mobility15 via a two-state model:16
umicelle ) (
u( - punimeruunimer ( (1 - punimer)
(4)
where punimer represents the concentration of SDS unimer present, taken as equal to the cmc.3 Our electrophoretic mobility data, for example, uSDSmicelle (50 mM SDS/D2O) ) 3.0 × 10-8 m2 V-1 s-1, are ( in good agreement with the early data of Stigter and (100 mM SDS/H2O) ) Mysels,17 who recorded uSDSmicelle ( 3.8 × 10-8 m2 V-1 s-1 from a fluorescence tracer technique. The purpose of this communication is to illustrate how ENMR may be used to probe the ionic character of mixed surfactant micelles using a relatively novel NMR technique, based on using pulsed-field gradients to couple time and molecular displacement, that is, a diffusion experiment rather than a relaxation one.16 We compare the electrophoretic mobilities of mixed micelles formed by SDS and two quite different nonionic surfactants: one comprising a bulky sugar-based headgroup and one comprising a short oligomeric ethylene oxide fragment. The electrophoretic mobility of the mixed anionic/ nonionic surfactant system comprising the SDS/tetra(ethylene oxide) dodecyl ether C12E4 system increasess albeit after an initial dropswith increasing nonionic composition, whereas that of the SDS/C12BNMG system decreases. This implies that the two micellar systems evolve differently with composition. The size and shape of the SDS/C12BNMG micelles are largely invariant with composition,4 so changes in the electrophoretic mobility reflect the counterion binding. SDS/C12E4 micelles grow with increasing nonionic composition,18-20 and thus, changes in the electrophoretic mobility may arise due to changes in both micelle size/shape and counterion binding. Consider these electrophoretic mobility data in the context of the small particle approach (eq 3). For mixed anionic-nonionic surfactant micelles of composition xSDS, the effective charge on the micelle, eeffective, arises due to mixedmicelle : counterion dissociation characterized by RNa + mixedmicelle xSDSNmixedmicelle eeffective ∝ RNa + agg
(5)
An equivalent spherical micelle radius (We make the simplifying assumption that the polar shell thickness is mixedmicelle , may be calculated from largely constant.), rspherical knowledge of the aggregation numbersthe number of surfactant molecules per micellesand the volume of a dodecyl tail: (14) Henry, D. C. Proc. R. Soc. (London) 1931, A133, 106. (15) Griffiths, P. C.; Pettersson, E.; Stilbs, P.; Cheung, A. Y. F.; Howe, A. M.; Pitt, A. R. Langmuir 2001, 17 (22), 7178. (16) Stilbs, P. NMR Studies of Polymer-Surfactant Systems; Surfactant Science Series 77; Marcel Dekker Inc.: New York, 1998. (17) Stigter, D.; Mysels, K. J. J. Phys. Chem. 1955, 59, 45. (18) Iglesis, E.; Montenegro, L. Phys. Chem. Chem. Phys. 1999, 1, 4865. (19) Moises de Oliveira, H. P.; Gehlen, M. H. Langmuir 2002, 18, 3792. (20) Penfold, J.; Staples, E.; Thompson, L.; Tucker, I.; Hines, J.; Thomas, R. K.; Lu, J. R.; Warren, N. J. Phys. Chem. B 1999, 103, 5204.
Figure 1. Degree of sodium counterion dissociation versus micelle composition for SDS/C12BNMG (b) (20 °C) and SDS/ C12E4 (O) (25 °C) calculated via the small particle limit.
Figure 2. ζ-Potential calculated from the electrophoretic mobility as described in the text (large particle limit) versus micelle composition for SDS/C12BNMG (b) (20 °C) and SDS/ C12E4 (O) (25 °C). mixedmicelle rspherical )
(
)
tail 3NaggVdodecyl 4π
1/3
(6)
Accordingly, eq 3 may be recast
umixedmicelle (
∝
mixedmicelle RNa xSDSNmixedmicelle + agg
(
)
tail 3Nmixedmicelle Vdodecyl agg 6πη 4π
1/3
(7)
from which an approximate value for the dissociation of the counterion can be obtained. For the SDS/C12BNMG casesthose micelles whose aggregation number is invariant with compositionschanges in the micelle electrophoretic mobility can be used directly to estimate mixedmicelle pureSDSmicelle RNa given that RNa ) 0.27: + +
umixedmicelle (
) pureSDSmicelle
u(
mixedmicelle RNa + pureSDSmicelle RNa +
(8)
mixedmicelle versus micelle composition, The behavior of RNa + xSDS, is shown in Figure 1. As the fraction of SDS decreases, mixedmicelle RNa remains constant to xSDS ) 0.8 before in+
Notes
creasing steadily. Indeed, it reaches a maximum at xSDS ∼ 0.3 (not shown15). The increase can be rationalized by considering that as the sulfate headgroups become more diluted over the micelle surface, the electrostatic repulsion associated with the counterion dissociation decreases. For the SDS/C12E4 case, the change in aggregation number18-20 must also be considered via eqs 6 and 7. This behavior is also shown in Figure 1. Now, a linear mixedmicelle on composition is observed over dependence of RNa + the whole mole fraction range examined. The degree of counterion binding is significantly greater over the whole mole fraction range for the SDS/C12E4 case compared to the SDS/C12BNMG case. However, this increase in mixedmicelle is not consistent with the micelle growth. The RNa + elongation of the micelle is a consequence of a decrease in the headgroup area, a trend not normally associated with an increase in ionic character. Now, consider these data within the large particle limit. Figure 2 shows the ζ-potential calculated via eq 2; the two surfactant series are quite different. For the SDS/C12BNMG, over the mole fraction range presented, the ζ-potential decreases with increasing nonionic content. Since the aggregation number is largely invariant, the micelle as a whole is acquiring a more nonionic character. mixedmicelle The degree of sodium counterion dissociation RNa + over this range 0.8 < xSDS < 1.0 is roughly constant (Figure 3). The SDS/C12E4 case is ostensibly rather different; the electrophoretic mobility increases with increasing nonionic character. However, the aggregation number also inmixedmicelle creases over this range, such that again RNa is + largely constant and comparable to that of the SDS/C12BNMG case. This behavior is far more consistent with the increase in aggregation number. We have therefore shown that ENMR experiments are a very useful method for characterizing the ionic character
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Figure 3. Sodium counterion dissociation calculated from the ζ-potential via the large particle limit versus micelle composition for SDS/C12BNMG (b) (20 °C) and SDS/C12E4 (O) (25 °C).
of mixed ionic-nonionic surfactant micelles, providing an insight into counterion binding that is not obtainable mixedmicelle from any other technique. The values RNa for two + quite different binary surfactant systems are shown to be very similar, which suggests that the “large particle limit” is more appropriate for describing the ionic character of surfactant micelles. Acknowledgment. P.C.G. and A.P. would like to acknowledge the financial support of the Leverhulme Trust. P.S. thanks NFR (the now discontinued Swedish Natural Science Research Council) and its successor VR (The Swedish Research Council). LA034793P
