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Langmuir 1990, 6, 506-508
Letters Electrostatic Surface Potential and Critical Micelle Concentration Relationship for Ionic Micelles Thomas W. Healy,*Pt Calum J. Drummond,$ Franz Grieser,t and Brent S. Murrayt Department of Physical Chemistry, The University of Melbourne, Parkville, Victoria, 3052, Australia, and CSIRO, Division of Chemicals and Polymers, Bayview Avenue, Private Bag 10, Clayton, Victoria, 3168, Australia Received August 2, 1989. I n Final Form: November 17, 1989 The relationship between the micellar interfacial electrostatic potential (\kpro as measured by reliable acid-base indicator techniques, and the critical micelle concentration (cm$:or dodecyltrimethylammonium bromide/NaBr, dodecyltrimethylammonium chloride/NaCl, sodium dodecyl sulfate/NaCl, sodium dodecyl sulfate/NaClO,, and sodium decyl sulfate/NaClO, systems has been examined. For these dilute micellar systems, it has been found that ~A\kpro,,~/unit change in log cmc is circa 59 mV at 25 “C. A thermodynamic treatment, appropriate for the objective of interpreting the relationship between \Ilprobe and the cmc, demonstrates that this form of behavior is consistent with \k being equal to the mean electrostatic potential at the micellar surface, i.e., the thermodynamic or &%it interfacial potential (\ko) of the micelle. Furthermore, it is consistent to regard the aqueous surfactant monomer species as the potential-determining ion in the charged micellar systems. Introduction Within surfactant self-assembly physics and chemistry, various views of the micellar state are tolerated. At one level, micelles are regarded as strongly timeaveraged flickering clusters and there is an understandable focus on the dynamics of motion of amphiphiles within the core and shell of the micelle and the bulk aqueous environment.’” A t another level, the thermodynamic view insists that micelles can be treated as a separate phase and can be examined as discrete objects having a true thermodynamic id en tit^.^-^ Neither view has absolute validity; the validity of each must be considered in context, as a means to an end, i.e., a real understanding of micellar self-assembly systems. Molecular spectroscopic probe studies have generated significant results on the nature of micellar systems. Provided that one understands the important physicochemical rigor one must apply to such probe studies, it is possible to generate reliable data on the mean electrostatic potential experienced by headgroup entities in the headgroup domains of micelles.6 Data on aggregation numbers, the mean hydrophobic environments experienced by core probes, and the mean “interfacial dielectric constant’’ domains experienced by micelle surface-aqueous solution probes can also be extracted.6 Our own and other mean electrostatic interfacial potential measurements have been obtained on a range of ionic micelle~.~-l’The practice is to report probe potentials
* To whom correspondence should be addressed. +
The University of Melbourne.
* CSIRO,Division of Chemicals and Polymers.
(1) Aniansson, E. A. G. J.Phys. Chem. 1978,82,2805. ( 2 ) Wall, S.N.; Aniansson, E. A. G. J. Phys. Chem. 1980,84,727. (3)Stigter, D. J. Colloid Interface Sci. 1974,47,473. (4)Mitchell, D. J.; Ninham, B. W. J. Chem. SOC.,Faraday Trans. 2 1981,77,601. (5) Gunnarsson, G.; Jonsson, B.; Wennerstrom, H. J. Phys. Chem. 1980,84,3114. (6) Grieser, F.; Drummond, C. J. J. Phys. Chem. 1988,92,5580. (7)Drummond, C. J. Grieser, F.; Healy, T. W. Faraday Discuss. Chem. SOC.1986,81,95.
0743-7463 /90/2406-0506$02.50IO
(\kprobe) for ionic micelles in terms of the “total” aqueous electrolyte concentration; cmc + [electrolyte], and to seek an understanding of the variation of versus total ionic strength. Electrolyte is added to effect a change in potential and simultaneously produces an often ignored change in the cmc relative to changes in the operational variable of cmc + [electrolyte]. The present communication concerns three important interrelated questions. First, how does \kprOb vary with the activity of surfactant monomer in solution, i.e., cmc? Second, how does \kproberelate to the thermodynamic interfacial (9Jor Nernst potential? Third, can the aqueous surfactant monomer species be regarded as a potentialdetermining ion (pdi) in charged micellar systems? To address these questions, we have pooled literature values of \kprobe measured for different micellar systems and have reanalyzed the data in a general thermodynamic framework. Results and Discussion It has been demonstrated elsewhere that, for certain micellar systems, reliable \kprobe values may be determined by using a select group of acid-base indicatorse6 Reliable \kprobedata for micellar dodecyltrimethylammonium bromide (DTAB)/NaBr,’ dodecyltrimethylammonium chloride (DTAC)/NaC1,8 sodium dodecyl sulfate (SDS)/NaCl,lO~llSDS/NaC10,,12 and sodium decyl sulfate (SDeS)/NaClO, (ref 12) systems are iven in Table I. Most of the electrostatic potentialsss1%* ” have been determined by using the relationship
\kprobe= 2.303(kT/e)(pK:
- pK,Oba)
(1)
(8)Drummond, C. J.; Grieser, F.; Healy, T. W. Chem. Phys. Lett. 1987,140,493. (9) Kibblewhite, J.; Drummond, C. J.; Grieser, F.; Healy, T. W. J. Phys. Chem. 1987,91,4658. (10)Hartland, G. V.;Grieser, F.; White, L. R. J. Chem. SOC.,Faraday Trans. 1, 1987,83,591. (11)Fernandez, M. S.;Fromherz, P. J. Phys. Chem. 1977,81, 1755. (12)Frahm, J.: Diekmann, S.:Haase, A. Ber. Bunsen-Ges. Phvs. Chem. 1980,84,566.
0 1990 American Chemical Societv
Langmuir, Vol. 6, No. 2, 1990 507
Letters
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Table I. Literature cmc [Electrolyte], log cmc, and gnmk Results for Micellar Systems Studied. cmc + [electrolyte], system mol dm-9 logcmc qamb DTAB/NaBr* 0.0148 -1.828 +118 0.0218 -1.926 +lo9 +96 0.0401 -2.081 +85 0.0718 -2.230 +83 0.1047 -2.326 +58 0.3333 -2.620 +48 0.6667 -2.797 -2.900 f44 Loo00 +18 4.0020 -3.377 +129 0.0193 -1.712 DTAC / NaCl* -1.803 +125 0.0269 -1.948 +118 0.0456 +lo9 0.0751 -2.085 -2.183 +lo5 0.1076 +85 0.3333 -2.493 +75 0.6660 -2.683 +69 1.oOoo -2.194 +47 4.oo00 -3.174 -2.090 -141 0.008 SDS/NaCl' -125 0.020 -2.393 -2.448 -122 0.025 -2.732 -110 0.065 -95 0.102 -2.857 -85 0.202 -3.044 -13 0.302 -3.154 -72 0.382 -3.219 -67 0.481 -3.281 SDS/NaCld 0.0081 -2.090 -134 0.0521 -2.670 -119 -101 0.1014 -2.857 0.2009 -3.044 -91 0.4006 -3.231 -68 SDS/NaClO/ 0.0084 -2.073 -130 0.0153 -2.277 -120 0.0359 -2.542 -100 0.1018 -2.738 -77 SDeS/NaClO,' 0.0327 -1.485 -95 0.0393 -1.533 -90 0.0569 -1.622 -90 0.1154 -1.812 -79
100
o
A
n "
0.5
0.0
rod
1 .o
1.5
Alogl0 cmc
Figure 1. LA!# as a function of Alog cmc for micellar DTAB/ NaBr ( o ) , D?" /NaCl ( 6 ) : SDS/NaCl (0),lo SDS/NaCl (A)," SDS/NaClO, (D)," and SDeS/NaClO, (A)" systems at 25 "C. The line drawn represenh a gradient of 59 mV/unit change in A log cmc. The gradient and correlation coefficient for the unweighted least-squares fit are 58.7 mV/unit change in A log cmc and 0.979,respectively.
tration (i.e., the cmc). Hence, as shown in Figure 1,the results of Table I were normalized by plotting IAqprobel versus A log cmc. For each micellar system, lA\kprobel and A log cmc are defined relative to the smallest qprobe and cmc values that were measured in the system (see Table I). The line drawn on Figure 1 represents a slope of 59 mV. Thus, the normalization procedure for the six data sets reveals a master curve with a gradient of 59 mV. To continue further, we view the micellar systems "electrochemically'' following a general thermodynamic treatment. In the treatment, we assume as a rudimentary approximation that one can add a surfactant monomer to the micelle without changing its properties (Le., we assume that the micellar phase is analogous to a macroscopic phase and the surfactant monomer ion becomes the potential-determining ion). For any ionic micellar Systems studied were DTAB/NaBr, DTAC/NaCl, SDS/NaCI, system, with micelles of mean aggregation number ( m ) SDS/NaClO,, and SDeS/NaClO,, at 25 O C . * Reference 8. Indicator: 2,6-diphenyl-4-(2,4,6-triphenyl-l-pyridinio)phenoxide as the representative entities (a narrow size distribution (i.e., E,(30)). Reference 10. Indicator: 4-heptadecyl-7-hydroxyis frequently the case for ionic micelles even in the prescoumarin. Reference 11. Indicator: 4-heptadecyl-7-aminocouence of electrolyte''), the chemical potential of an marin. e Reference 12. Dual indicators: 4-undecyl-7-hydroxyamphiphile in a micelle may be expressed as coumarin and 4-heptadecyl-7-aminocoumarin. where qprobe, k, T , e , pK,: and pKaobs denote the mean field electrostatic potential at the average site of residence for the prototropic part of an acid-base indicator, the Boltzmann constant, the absolute temperature, the elementary electrostatic charge, the intrinsic pK, of the indicator residing at the aqueous/surfactant interface in the absence of any electrostatic field, and the apparent pK, of the indicator residing at the charged aqueous/ surfactant interface, respectively. Details of how the pK,O value is determined can be found in refs 6, 7, and 11. A dual acid-base indicator technique, which is described comprehensively in ref 11,was also employed to obtain some of the electrostatic potentials.12 The cmc values quoted in Table I were either interpolated or obtained directly from information contained in a number of literature source^.^^-^' Our main objective was to arrive at an understanding of how \Eprobe varies with surfactant monomer concen(13) Ozeki, S.; Ikeda, S. J. Colloid Interface Sci. 1982,87, 424. (14) Ozeki, S.; Ikeda, S. Bull. Chem. SOC.Jpn. 1981,54,552. (15) Emerson, M. F.; Holtzer, A. J. Phys. Chem. 1967, 71, 1898. (16)Mysels, K. J.; Princen, L. H. J . Phys. Chem. 1969.63, 1696. (17) Hayashi, S.; Ikeda, S. J. Phys. Chem. 1980,84,744.
Pmic,(m)
= Pomic,(m) + ze$, + Pdipole
(2)
In this equation, pomic,.(m) is the standard chemical potential of an amphiphile in a micellar state, z the valency of the charged amphiphile monomer, \E, the mean electrostatic potential at the plane of surfactant headgroups in a micelle, and pdipolethe chemical potential due to dipoles. Equation 2 does not separately take into account terms that include electrostatic interaction, mixing entropy, and hydrophobic interaction contributions to p,ic,(m). S,l9 The chemical potential of amphiphile monomer in aqueous solution is given by (3)
where aaqis the activity of amphiphile monomer in aqueous solution (i.e., the single-ion activity of the surfactant molecule in aqueous solution) and goasis the standard chemical potential of amphiphile monomer in aqueous solution (independent of aeq). (18)Warr, G. G.; Grieser, F.; Evans, D. F. J. Chem. SOC.,Faraday Trans 1 1986,82, 1829. (19)Johnson, I.; Olofsson, G.; Jonsson, B. J. Chem. SOC., Faraday Trans. 1 1987,83,3331.
508 Langmuir, Vol. 6, No. 2, 1990
The condition of equilibrium between the amphiphile monomer in aqueous solution and amphiphile in the micellar state allows the following equation to be generated: *o = ( k T / z e )In
uaq
+ b 0 a q - p"mie,(m) - pdipole)/Ze (4)
This equation provides a direct connection between the micellar surface potential and the amphiphile monomer concentration in equilibrium with the micelle (i.e., the cmc). If the monomer concentration is altered, for example, by adding electrolyte to the micelle solution, \ko will change accordingly: not because the ionic strength is being changed but because the ionic amphiphile is the potential-determining ion (pdi). Provided that the set of terms occurring after the first term in eq 4 does not change appreciably with a change in electrolyte level (the factor that changes the cmc in the micellar systems under examination), it follows that for a charged univalent surfactant, Le., z = 1, at 25 "C dl\k,l/d log uaq= 59.16 mV (5) Therefore, the experimental observationthat lA\kpmbl/ unit change in log cmc is 59 mV (Figure 1) implies that for each of the dilute micellar systems studied, within experimental error, (i) the set of terms occurring after the first term in eq 4 is invariant (see below), (ii) log cmc is a reasonable approximation for log uaq,and (iii) \kprobe is equivalent to \ko. In connection with claim ii, we note that in the aqueous micellar solutions that contain a large amount of electrolyte it is unlikely that the activity coefficient of amphiphile monomer in aqueous solution, yaq, referred to infinite dilution, is 1.0. Nevertheless, the reality of the scatter of the experimental data about the line with gradient 59 mV (Figure 1) and the relationship log uaq= log cmc + log yap (6) is that yaq values would probably have to be less than 0.6 (i.e., log yaq < -0.22) before any nonequivalence of log uaqand log cmc would become apparent. In order to substantiate claim iii, let us consider the scenario that \kprobe does not equal \k, but relates to a potential out from the plane of the surfactant headgroups (i.e., in the diffuse region of the electrical double layer). In any plane out from the micelle surface, the electrostatic potential will depend on both \k, and the electrolyte level in solution. In this scenario, therefore, a lA\kprobel of 59 mV per unit change in log cmc can only occur if, for each micellar system, the distance out from the plane of the surfactant headgroups at which \kprobe is measured (Le., the average residential site for the acidbase indicators' prototropic moieties) varies in a unique manner with the cmc. I t is unlikely that the difference acid-base indicators, identified in Table I, respond to cmc changes by changing their average location out from the plane of the surfactant headgroups in the same unique manner. Thus, the implication is that \kprobe is equal to
Letters
Incorporating this allowance leads to additional terms on the right-hand side of eq 4 (e.g., terms that separately take into account contributions due to electrostatic interactions, mixing entropies, and hydrophobic interactions). The fact that IA\kprobel/unitchange in log cmc is constant at 59 mV indicates that these contributions are invariant under the experimental conditions considered in this communication. The invariance of these contributions, and indeed of [paqo- pom i c , ( m i l , is ~ r o b a bly not surprising since for each of the mice lar systems examined (i) the micellar size and shape do not change significantly with [electrolyte], (ii) the micellar solvating environment is unlikely to vary greatly with [electrolyte], and (iii) there is only a dilute concentration of micelles and amphiphile monomer in aqueous solution. That the pdipole term does not vary significantly with [electrolyte] can also be inferred from the observation that the effective interfacial dielectric constant of the micelle (eeff) hardely alters with increasing levels of electrolyte.* In essence, the experimental conditions are such that the relationship between \kprobe and cmc can be adequately explained by assuming that the micellar state behaves like a bulk phase. I t is therefore internally self-consistent to define the surfactant monomer ion as the potential-determining ion, to equate electrochemical potentials, and to expect the relationship shown in Figure 1, where 9,('\kprobe) obeys the Nernst equation. I t is noted that eq 5 should not be considered as a general rule for all micellar systems until more systems have been examined. In other words, it remains to be seen whether or not the ability of Nernstian surfaces to provide maximum charge regulation" will result in eq 5 adequately describing the \k,/cmc behavior of all aqueous micellar systems. In summary, a thermodynamic treatment, appropriate for the present objective of elucidating the relationship between \kprob and cmc, has allowed us to interpret the experimental observation that lA\k,,,,l/unit change in log cmc is circa 59 mV in dilute micellar DTAB/ NaBr, DTAC/NaCl, SDS/NaCl, SDS/NaClO,, and SDeS/NaClO, systems. It has been shown that the experwas measured as imental conditions, under which qProbe a function of cmc (electrolyte level), are such that the relationship between \kprobe and the cmc can be adequately explained by assuming that the micellar state behaves like a bulk phase. The empirical relationship between \kprobe and cmc is consistent with \kprobe being a true measure of the "electrochemical" surface potential of the micelle (\ko)and with the aqueous surfactant monomer species being the potential-determining ion in the charged micellar systems.
Acknowledgment. This work was supported by an Australian Research Council Program Grant entitled "Surface Spectroscopy of Aqueous Interfaces". We thank Dr. Derek Chan and Prof. Lee White for helpful discussions.
*@
Treating the micellar phase as a macroscopic phase is, of course, an oversimplification. More sophisticated treatments than the one given in the present communication (e.g., that of Jonsson and Wennerstrom based on the cell model5.") allow the properties of the micellar system to change when a surfactant monomer is added to a micelle.
Registry No. SDS, 151-21-3;DTAB, 1119-94-4;DTAC, 11200-5; SDeS, 142-87-0; NaBr, 7647-15-6; NaCl, 7647-14-5; NaClO,, 7601-89-0. (20) Healy, T.W.; Chan, 1980,52,1207.
D.Y. C.;White, L. R. Pure Appl. Chem.
