J. Phys. Chem. 1986, 90, 1853-1859
1853
itations apply, however, for most of the alternative experimental methods as well). Studies are now in progress to extend this method to other biopolymers solubilized in AOT (for example, larger proteins or larger biological structures which have been recently solubilized in hydrocarbon micellar solutions, like plasmidsz7 or bacterial cells2*) as well to other surfactant systems, in order to test the
generality of the conclusions reached in this paper.
Acknowledgment. We gratefully acknowledge the collaboration of Professor Waks and his group. Registry No. AOT, 577-1 1-7; PNPS, 100655-52-5; a-chymotrypsin, 9004-07-3; lysozyme, 9001-63-2; 2-naphthoic acid, 93-09-4; potassium dichromate, 7778-50-9; isooctane, 540-84- 1,
(27) Imre, V. E.; Luisi, P. L. Biochem. Biophys. Res. Commun. 1982,107, 5 38-545.
(28) Haring, G.; Luisi, P. L.; Meussdoerffer, F. Biochem. Biophys. Res. Commun. 1985, 127, 911-915.
Counterion Specificity as the Determinant of Surfactant Aggregation J. E. Brady, D. F. Evans,* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
G. G. Warr, F. Grieser, Department of Physical Chemistry, The University of Melbourne. Parkville, 3052, Victoria, Australia
and B. W. Ninham Department of Applied Mathematics, Research School of Physical Sciences, Australian National University, A.C.T., Australia (Received: July 29, 1985; In Final Form: December 13, 1985)
Aggregation numbers and critical micelle concentrations are reported for dodecyltrimethylammonium salts with hydroxide and a range of carboxylates as counterion, with and without added salt. The micelles are unusual in that cmcs are higher and the aggregation numbers and ion binding parameters much lower than those for the corresponding bromides. Aggregation numbers change slowly (29 to 49) with added salt up to 1 M. The micellar properties parallel those of corresponding double-chaineddimethylammonium salts which exhibit normal behavior (insoluble, lamellar phase) for bromides and anomalous behavior (highly soluble, spontaneous vesicles) for carboxylates and hydroxide. With increasing surfactant concentration the vesicles revert to micelles. An explanation of these phenomena is given.
Introduction The old problem of specific ion effects has been with us for a very long time. For lyophilic colloids the classic example is contained in the observation of different flocculation and repeptization properties of 1:1 electrolytes as one progresses through the lyotropic series. The phenomenon has been quantified for the alkali metal ions in mica interactions across aqueous electrolyte solutions by direct force measurements.' Again, for association colloids there has long been a keen appreciation of counterion specificity as a determinant of aggregation properties. But with the most studied systems which use alkali metal or halide counterions, differences in cmcs, counterion binding, and aggregation numbers are quite subtle and difficult to pin down. Especially is this so when the effects are studied by techniques which because of theoretical and experimental uncertainties use swamping amounts of However specific counterion effects, which change head group area, curvature at the surfactant-water interface, and interactions between aggregates do show up dramatically in multicomponent systems, like microemulsions, and for double-chained surfactants in water. The phase changes exhibited by three-component ionic microemulsions in response to changes in counterion are huge.3 R. M. J . Colloid Interface Sci. 1981, 83, 531. (2) Mitchell, D. J.; Ninham, B. W.; Evans, D. F. J. Phys. Chem. 1984,88, 5855. Evans, D. F.; Mukherjee, S.; Mitchell, D. J.; Ninham, B. W. J . Colloid Interface Sci. 1983, 93, 184. (3) Evans, D. F.; Mitchell, D. J.; Ninham, B. W. J . Phys. Chem., in press. (1) Pashley,
0022-3654/86/2090-1853$01.50/0
This is because ionic microemulsions, often close to zero curvature surfaces, and with weak interactions, must almost by definition be acutely sensitive to counterion type and, further, show a strong co-ion ~pecificity.~ Some notable examples of counterion specificity have been shown in recent work on the aggregation properties of various double-chained cationic surfactant^.^-^ Thus the surfactant didodecyldimethylammonium bromide behaves much as might be expected. In water it is soluble up to about M beyond which it forms a lamellar phase. But if the bromide counterion is replaced by hydroxide, or a range of carboxylates, the surfactant is freely soluble, forming clear solutions up to 1 M. The system forms spontaneous vesicles. That by itself is not surprising.I0 What is, is that the diameter of the vesicles shrink with increasing concentration from about 1000-1500 8, at M,6 to 300 8, at (4) Talmon, Y.; Evans, D. F.; Ninham, B. W. Science 1983, 221, 1047. (5) Hashimoto, S.;Thomas, J. K.; Evans, D. F.; Mukherjee, S.; Ninham, B. W. J . Colloid Interface Sci. 1983, 95, 594. ( 6 ) Ninham, B. W.; Evans, D. F.; Wei, G. J. J . Phys. Chem. 1983, 87, 5020. (7) Kachar, B.; Evans, D. F.; Ninham, B. W . J . Colloid Interface Sci. 1984, 100, 287. (8) Brady, J.; Evans, D. F.; Ninham, B. W.; Kachar, B. J . Am. Chem. Soc. 1984. 106. 4279. (9) Evans, D. F.; Brady, J.; Kachar, B.; Ninham, B. W. J . Solution Chem. 1985, 14, 141. (10) Mitchell, D. J.; Ninham, B. W . J . Chem. Soc., Faraday Trans. 2 1981, 77, 601.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 9, 1986
1854
M$ and to micelles of aggregation number around 40 beyond. Eventually, at a high enough surfactant concentration, they revert to a lamellar phase.” The addition of salt of the same counterion does not induce flocculation. At least in this high salt case the Debye length is well approximated by that of the added electrolyte, and interactions between aggregates are stroligly screened. The phenomenon therefore requires for its explanation two circumstances: (1) The repulsive barrier to flocculation must have no attractive minimum. ( 2 ) The head group area must be relatively large to impose more stiffness on the chains for hydroxide than for bromide. Both conditions can be satisfied by a strongly hydrated counterion. A large hydrated counterion cannot sit too close to the surfactant water interface, which is then highly charged.I2 Indeed direct force measurements confirm that this is so.13 Apart from the intrinsic interest of double-chained surfactants as membrane mimetic systems, the ubiquitous Occurrence of sialic acid residues attached to macromolecules in the glycocalyx of cells indicates that carboxylates deserve more attention than they have so far received. The interpretation of the phenomena described above at a level comparable with that which is in principle achievable with the much better characterizable single-chained micellar systems is more difficult. There is therefore a good motivation for parallel studies on both single- and double-chained surfactant? with hydroxide or carboxylate as counterion. We report here such studies. The aggregation properties of dodecyl- and tetradecyltrimethylammonium salts for a variety of counterions have been characterized through cmcs and ion binding parameters deduced from conductance measurements and micelle aggregatioi numbers derived from fluorescence mea~urernents.’~-’~ The measured parameters and their patterns are consistent with earlier data for micelle-forming surfactants with hydroxide,”-I9 carboxylate^,*^-^^ and sulfatez4 as counterions. They are also consistent with inferences from direct force measurement^.'^ The aggregation patterns observed with corresponding double-chained surfactants are also reported. There are major qualitative differences between the two extremes represented by hydroxide and bromide as counterion for both double- and single-chained surfactants. In spite of this it seems that the unusual properties observed for hydroxides and carboxylates fall into place as a consistent generalization of what has previously been known for halide and alkali metal ions.
Methods The dodecyltrimethylammonium and didodecyldimethylammonium salts were prepared by combining the hydroxide (ion exchanged, REXYN 201 Fisher, from the bromide salt) with a stoichiometric amount of the appropriate acid.* The concentrations of the hydroxides were determined by titration with HCl in water-methanol mixtures ( 10:90 v/v) using pH-saturated calomel electrodes Surfactant salts were also prepared from the bromide by direct ion exchange of the desired carboxylate. Samples prepared by either method gave the same results. The same (1 1) Laughlin, R. G., private communication. (12) Evans, D. F.; Ninham, B. W. J . Phys. Chem. 1983, 87, 5025. (13) Pashley, R. M.; McGuiggan, P.; Ninham, B. W.; Evans, D. F.; Brady, J. D. J . Colloid Interface Sci., in press. (14) Turro, N . J.; YeKta, A. J . Am. Chem. SOC.1978, 100, 5951. (1 5) Warr. G. G.; Grieser, F. J . Chem. SOC.,Faraday Trans. 1, in press. (16) Warr, G. G.; Grieser, F.; Evans, D. F. J . Trans. Soc., Faraday Trans. I , in press. (17) Lianos, P.; Zana, R. J . Phys. Chem. 1980, 84, 3339. (18) Bunton, C . A.; Gan, L. H.; Moffatt, J. R.; Romsted, L. S.; Savelli, G. J . Phys. Chem. 1981, 85, 4118. (19) Athanassakis, V.; Moffatt, J. R.; Bunton, C. A,; Dorshow, R. B. Savelli. G.: Nicoli. D. F. Chem. Phvs. Lett. 1985. 115. 467. (20) Somasundaran, P , Healy, T W , Fuerstenau, D W J Phys Chem 1964~.68. 3565 (21) Mukerjee, P.; Mysels, K. J.; Kapauan, P. J . Phys. Chem. 1967, 71. 4166. (22) Anacker, E. W.; Ghose, H. M. J . Phys. Chem. 1963, 67. 1714. (23) Anacker, E. W.; Underwood, R. L. J . Phys. Chem. 1981, 85, 2465. Underwood. A . L.; Anacker, E. W. J . Colloid Interface Sci. 1984, 100, 128. (24) Wasik, S. P.: Hubbard, W. D. J . Res. Natl. Bur. Stand. 1964, 68A. ~
359.
~~
~
Brady et al. TABLE I: Data for Dodecyltrimethylammonium Salts‘ anion cmc. mM N --p,b % bromide 14.5 54 26.3 hydroxide 33.9 (30.5)‘ 29 (20)c 76 24 f 4e 63 f 3’ 34 formate 27.9 64 acetate 34 30.5 69 acetate with 30.9 67 equimolar acetic acid propionate 26.6 42 59 butyrate 21.7 47 46 tartarate( I-) 19.7 52 37.5 tartarate(2-) 18.0 45 24.5
a,
A2
Rhc,
A
62 78
17 13.4
74 74
14.2 14.2
69 67 64.4 67.5
15.2 15.6 16.3 15.5
‘‘Errors in aggregation number are estimated to be f 5 . For further comparison with S D S cmc = 8 m M , N = 58, p N 0.1-0.25. ’Percent dissociation (conductance) = 1 - q. ‘Data from ref 17. dData from ref 19. eDetermined by dynamic fluorescence.I6 fFrom a plot of log cmc vs. log (cmc [NaOH]).
+
TABLE 11: Effects of Added Salt
Dodecyltrimethylammonium Hydroxide (DTAOH) cmc. m M N 0.0 33.9 29 0.1 39 42 0.2 0.5 48 6.7 49 1 .o 4.0
cmc added NaOH. M
Dodecyltrimethylammonium Acetate (DTAOAc) cmc, m M iv 0.0 30.5 34 0.03 58
cmc added NaOAc, M
0.10 0.40 0.85 0.73 HAC equimolar HAC
55 61 60 34 30.9
Tetradecyltrimethylammonium Hydroxide (TTAOH)“ cmc added NaOH. M
cmc, m M
N
0.c 0.10 0.50 I .oo
8.0 2.0 0.70 0.22
45 60 65 70
a
From ref 5
TABLE 111: Effects of Chain Length DTAOH TDAOH H D A O H (hexadecyl) DTABr TTABr
cmc, m M 31 (30.5)O 8 (7.2)4 ( 1 .8).l 14.4 3.3‘
N 29 (20)d 45’ (42)a (46)‘ 57 7Oa
QFromref 17. *From ref 5 . ‘From ref 33
precautions used previously for hydroxides were employed to exclude carbon dioxide contamination.6 The conductance measurements were carried out using a flow dilution conductivity cells similar to that of ref 25. Fluorescence quenching experiments were performed on a Spex Fluorolog 222 fluorometer exciting at 453.5 mm and monitoring emissions between 610 and 650 nm. The fluorophore used was ruthenium (11) (4,4’-di-n-octyl-2,2’-bipyridyl)bis( 2,2’-bipyridyl) and the quencher was 9-methylanthracene. The fluorescence properties of this fluorophore in micelles and vesicles has been 9-Methyldescribed at length in several publication^.^^.^' (25) Eagland, D.; Franks, F. Chem. Ind. 1965, 1601. (26) Johansen, 0.;Kowala, C.; Mau, A. W.-H.; Sasse, W. H. F. Ausr. J . Chem. 1979, 32, 1435. (27) W a n . G. G.; Grieser, F. Chem. Phys. Lett. 1985, 116, 505.
Surfactant Aggregation
The Journal of Physical Chemistry, Vol. 90, No. 9, 1986 1855
3.0
-
-‘E
-
2.0
0
E z n
P X Y
Y I .o
0
CONC (mM)
Figure 1. Specific conductance vs. concentration for dodecyltrimethylammonium salts: (A) bromide, (B) formate, (C) acetate, (D) propionate, (E) butyrate, (F) tartarate( I-), (G) tartarate(2-).
anthracene was supplied by Tokyo Kasei and was used as received.
Results: Single-Chained Surfactants Tables 1-111 list data for DTA salts, and for hydroxides and acetates as a function of added electrolyte, respectively. Note that the cmcs as obtained from data of Figure 1 are much higher and aggregation numbers much lower than those for surfactants most commonly studied in the past, like DTAB or SDS (cmc = 8X M, N = 58). Our results for dodecyltrimethylammonium carboxylates are in agreement with the behavior observed by Underwood and Anacker using decyltrimethylammonium surf a c t a n t ~ As . ~ ~the size of the bare carboxylate counterion increases there is a systematic decrease in cmcs and corresponding increase in aggregation number. Aggregation numbers for the longer chained carboxylates may reflect the uptake of the hydrophobic portion of the counterion into the micelle interior. The results for acetate with added acetic acid definitely rule out the possibility that the carboxylates, through hydrolysis, are a poor man’s hydroxide. The degree of micellar dissociation p = 1 - q, where q is the fraction of “bound” charge, is extracted from conductance data by plotting the ratio of the specific conductances above and below the cmc. This estimate is purely phenomenological, without a firm theoretical basis. However, it is known from earlier work that this provides estimates consistent with other methods for extracting this parameter. The slopes of the specific conductance below the cmc are determined mainly by the intrinsic mobilities of the various counterions. The slopes above the cmc measure contributions due to counterions, monomer, and micelles. Differences above the cmc reflect variations in counterion “binding”, aggregation number, and interactions. Note that the effective charge is strikingly different for bromide as compared to hydroxide and the carboxylates. In Table I head group areas, a, and hydrocarbon core radii, R,,, have been computed by assuming spherical micelles, with an oil-like hydrocarbon interior, by taking Nu = (4a/3)Rhc3,Nu = 4aRhc2. Here u is the known volume of the hydrocarbon tail estimated as u = (27.4 + 26.9~1) AIo) where n is close to the number of carbon atoms per chain. If the micelles contained water, and the chains were therefore stretched to a larger radius, the head group area would take on ridiculous values, and that
possibility can be excluded. [From X-ray measurements on the lamellar phase of DDAB the head group area is 68 A2,28and from force measurements on (C,,),(Me),NoAc or Br, the bilayer head group area is 66 A2.I3 The fully extended chain length is I = (1.5 + 1.26n) A = 16.7 A.10] Effects of added salt (Table 11) show large differences from those usually observed. There is a slow increase in aggregation number up to 1 M added salt. This contrasts with DTAB with added alkali halides which usually go over to gels by 0.5 M.
Results: Double-Chained Surfactants Conductance data on the corresponding didodecyldimethylammonium salts are given in Figure 2. There are no discernible breaks characteristic of cmc-like behavior over the concentration M). There is a transition in range studied (5 X 10-,-4 X the magnitude of the conductance from hydroxide through acetate to proponate to bromide which parallels those changes in aggregation properties of the single-chained analogues. But here it is quite clear that there are very large differences in counterion binding. Video-enhanced differential interference contrast microscopy (VEDICM)7 shows that DDAOH contains vesicles at concentrations < M. No structures are visible at lo-’ M. Cold stage microscopy4 and scanning electron microscopy show M, and that the vesicles have a diameter 1000-1500 %, at at M these are smaller, with a diameter 300 f 50 A. By contrast, with DDAB, at low concentrations M) the solutions contain vesicles, which aggregate to form liposomes with increased surfactant concentration. Under VEDICM,7 after partial titration of DDAOH with HBr, the number of visible vesicles increases dramatically, indicating that the clear solutions contain a mixture of vesicles and micelles (micelles are undetected by VEDICM or electron microscopy). Figures 3 and 4 show the effect of titration on conductance by HBr and HOAc, respectively. There is a gradual change from that characteristic of hydroxide to that characteristic of bromide or acetate, as would be expected. Addition of salt (to 1 M) to DDAOH (NaOH) or DDAOAc (NaOAc) solutions does not induce flocculation. The solutions remain clear. For the higher carboxylates the solutions become cloudy at lower, but still high salt concentrations, again indicative (28) Fontel, K., private communication
Brady et al.
1856 The Journal of Physical Chemistry, Vol. 90, No. 9, 1986 1
1
1
1
I
I
I
I
I
I
I
.
b
l
1
1
1
1
1
1
1
1
1
1
1
1
-
-
3.0
. .
.
..
.
.
. . . . . . . . . . . . . .. . . . . .. . ..
x 1.0
8
-
. . . ... . . .
e;
-
. C
0 E
-
-
-
. *
t
-
-
-
-
I
n
I
I
1
2QO
0
1
30.0
1
1
I
I
1
I
1
4QO
1
60.0
CONC (mM)
Figure 2. Specific conductance vs. concentration for didodecyldimethylammonium salts: (A) hydroxide, (B) formate, (C) acetate, (D)propionate, (E) butyrate, (F) bromide. ‘2*o
ea
eI)
~
6 .O
4 .O
Y 2.0
4.0 0
CONC (mM)
0
0
200
40.0
60.0
CONC (mM)
Change in specific conductance of didodecyldimethylammonium hydroxide upon titration with hydrobromic acid: (A) DDAoH’ (B) DDAoH (2/3):DDABr )(‘ DDAoH (”’): DDABr (2/3).
Figure 3.
of behavior intermediate between that of bromide and hydroxide. There is then for the double-chained compounds a qualitative difference between the two extremes represented by hydroxide and bromide. These differences are dramatic and counterintuitive. For bromide, the surfactants are iIlsoluble beyond about 1o4 M, and form lamellar phase at higher concentrations. This is expected. For hydroxide, the surfactants are soluble up to 1 M (form clear solutions), and the aggregates formed are spontaneous vesicles which are stable, being reversible to temperature cycles. This is surprising. With increased surfactant the vesicles shrink in size and become micelles of aggregation number about 40. Beyond ca. 1 M concentration the system phase separates to form lamellar phase as is required by thermodynamics.’ I
Figure 4. Change in specific conductance of didodecyldimethylammonium hydroxide upon titration with acetic acid: (A) DDAOH, (B) DDAOH (3/4):DDAAc (1/4), (C) DDAOH (1/2):DDAAc(l/2),(D) DDAOH (1/4):DDAAc (3/4), (E) DDAAc.
The transition from vesicles to micelle with increasing surfactant for DDAOH and D D A O A ~is analogous to but the of the to micelle equilibrium for single-chained surfactants. To quantify this phenomenon, we have studied the transition with a fluorescence The theory of transient fluorescence from a micelle-bound fluorophore quenched by micelle-bound quenchers~~16,29,30 is easily extended to describe a solution containing a mixture of micelles and comparatively macroscopic structures, such as vesicles, Following previous assumptions concerning the mode of probe and quencher distributions,’5,30 the quencher-average aggregation number of a micellar solution is 1
I
7
7
( i ) Q ’ = - In [F(O)/F,(O)] = - In [C’iXi/CiX,exp(-vi)] r>l
i>l
(1) (29) Almgren, M.; Lofroth, J. E. J . Cdloid Interface Sci. 1981, X I , 486. (30) Almgren, M.; Lofroth, J. E. J . Chenz. Phys. 1982, 76. 2734.
The Journal of Physical Chemistry, Vol, 90, No. 9, 1986 1857
Surfactant Aggregation with 17 the scaled quencher concentration of 17 = [quencher]/ [surfactant in micelles], F(0) is the fluorescence intensity at time t = 0, F,(O) is the t = 0 intensity from probes in micelles containing no quenchers, and Xiis the mole fraction of micelles of size i in Note also that lim,,o (i)Q' = (i)w', the weight-average aggregation number of the micellar s o l u t i ~ n . ' ~In * 'a~solution ~ ~ ~ of monodisperse micelles (i)Q' is a constant, N , for all 7 values.15 In the case of rapid quenching, such as occurs in solutions of small micelle^,'^,^^ the fraction of light emitted from micelles containing probe plus quencher is small and eq 1 may be simplified to
0.80 1.00
0)
W J -I W
u
a!
r
040
-
P
0
E q L
040
0.20
where I(?) is the steady-state fluorescence intensity from a solution with quencher concentration 7. In large structures such as vesicles the probability of encounter between probe and quencher is small under conditions where micelle-bound probes will be quenched. At quencher concentrations normally used, there is effectively no quenching observed in solutions of vesicles only and even in solutions containing very large (rodlike) micelles quenching is minimal." Thus in a solution of micelles plus vesicles the fluorescence intensity may be regarded as arising from two contributions: fluorescence from probes bound to micelles, Z,,(o), and that from probes bound to vesicles, I,,, which will be a constant. It is convenient to rewrite the size distribution function X , as two, well-separated micelle and vesicle size distribution functions, Yi and Zi, respectively. When the micellar portion of the solution is totally quenched, there will be residual fluorescence from probes in vesicles, i.e., lim ( I ( q ) / I ( O ) )= I v / I ( 0 ) = x i Z , / x i ( Y ,
Ils-0
i>l
1>1
+ Zi)
(3)
which corresponds to the fraction of the total surfactant taken up in vesicles. The fluorescence intensity at some finite quencher concentration 17 is then
(4) Experimentally, I,,/Z(O) is determined from a plot of Z(q)/I(O) against T - I , which is extrapolated to 11-l = 0. In order to examine the micellar component of this solution it is necessary to determine the fraction of micelles containing no quencher molecules, and hence the concentration of mi~e1les.l~ Invoking a Poisson distribution of quenchers in micelles of any given size,14,15*30 the fraction of micelles containing no quenchers is C i Y i exp(-vi)/CiY, = ~ m ( ~ ) / I r n ( O ) = ( I ( d - I,,)/(I(O) - 1,)
i> I
i> I
Hence the quencher-average aggregation number of micelles in this solution is
-
0
J I
-3.0
I
l
l
- 2.0
I
1
1
1
1
-1.0
Log Conc. (MIL)
Figure 5. Fraction of didodecyldimethylammonium salt in micelles vs. concentration: 0, butyrate, 0 , acetate, A, hydroxide. Vesicles predominate at low concentrations, micelles at high values.
TABLE I V Specific Counterion Effects for Single- and Double-Chained Surfactants DTAB cmc = 14.5 X lo-' M, N = 57, p = 0.2, sphere-to-rod transition at c = 0.3 M DDAB insoluble above M, lamellar phase forms thereafter; forms mixture of single-walled vesicles, liposomes, micelles, flocculations in salt DTAOH cmc = 33.9 X lo-' M, N = 20-29, = 0.6-0.8, small change in aggregation number with added salt DDAOH soluble at least at 1 M; clear solution; does not flocculate with added salt; single-walled vesicles? M; 300 A, M; diameter 1000-1500 A, micelles ( N = 40) a t lo-' M; collapse to lamellar phase -1 M force measurements between bilayers adsorbed on mica as a function of salt well fitted with nonlinear Poisson-Boltzmann equation (double-layer theory), p = 0.1; energy of interaction shows attractive minimum due to van der Waals forces: bilayers are "soft": forms metastable vesicles in water on sonication; chain melting temperature 40 O C in lamellar phase, 28 OC in sonicated vesicle phase force measurements well fitted by Poisson-Boltzmann description up to lo-* M NaAc with = 1; bilayers completely dissociated and extremely stiff; no potential maximum, and forces purely repulsive; soluble in water, forming clear solution to M; structures have appeared; open random network of single bilayers in square array; all solutions clear on heating to 40 OC microemulsions with alkanes form easily with DDAB; with alkanes cannot form with DDAOH
mented by results from direct force measurement^.'^
In all of the surfactants studied the micelles were determined to be monodisperse and were identified by a single aggregation number, N . The aggregation numbers of each of the double-chain surfactants were independent of total surfactant concentration, within experimental accuracy. Figure 5 shows the percentage of surfactant in micelles in the solutions as a function of surfactant concentration. The transition occurs over the range 10-3-10-1. Changes here reflect those in the Debye length of the interacting particles as the aggregates reorganize from vesicles to micelles. In Table IV we have contrasted briefly the extremes of behavior exhibited with variation of counterion. The table has been aug-
Spontaneous Vesicles At first sight the phenomena listed above pose a puzzle of some complexity, linked only by the common thread of counterion specificity. If attention is focussed on the single- and doublechained ionic surfactants most studied, i.e. those cationic or anionic surfactants with halides or metal alkali ions as counterion, the pattern observed is as follows: for (micelle-forming) single-chained surfactants, addition of salt decreases the head group area. This results in micellar growth to rods with a further salt increase, and transformation to lamellar phase. The same sequence is followed (above the Krafft point or below the critical temperature) with increasing surfactant concentration. (The situation is here more complicated, as the sequence micelle-hexagonal phase-lamellar phase with increased surfactant (rather than salt) depends on
1858
The Journal of Physical Chemistry, Vol. 90, No. 9, 1986
induced changes in head group area, possibly the existence of a potential minimum, and packing properties imposed on the system at very low water content.) In terms of a theory3' which assumes the chains are fluid, and ignores interactions, we have spherical < v/al < I / * ; micelles u/al rods or globular micelles vesicles, liposomes, lamellar phase '/* < u / a l < 1; u / a l > 1 reversed phases. Here u is the hydrocarbon chain volume, a the head group area, and I the hydrocarbon chain length (for vesicles the outer hydrocarbon chain length). The situation for the hydroxide and carboxylate surfactants is very different, almost the obverse of the above. Micelles do not grow with added salt, double-chained surfactants are highly soluble, form spontaneous vesicles rather than lamellar phase, and with increasing salt the aggregates transform from vesicles to micelles. How can these observations be explained'? There are two levels at which they can be understood, the one qualitative and the other quantitative. At the first level, paradoxically, the apparently complex phenomenon of spontaneous vesicle formation is easiest and we deal with it first. It turns out that in a more sophisticated theory'O of self-assembly these phenomena emerge naturally and had already been predicted. 'The hydrocarbon chains are not strictly fluid and, depending on the head group interaction, will have varying stiffness. Ignore interactions for the moment. 1 hen quite general considerations allow prediction of vesicle size as a function of v/al. If the chains are fairly stiff, then theory'" predicts that bilayers form at u/al 0.5. Subsequently as c/al increases with decreased head group area, the system forms spontaneous vesicles, micelles, then vesicles, and ultimately bilayers at u / a l 1 . 'The proof is complex, involving a complicated nonlinear optiniization of aggregate free energies, and we refer to ref 10 fur details. For the moment it is sufficient to note that the prediction is purely a consequence of geometry and dimensional arguments. 'This phenomenon is exactly what is observed. It is not universal, and for very nuid chains the "normal" behavior is predicted. We need, in addition to chain stiffness, the requirement that interactions between aggregates be strongly repulsive. We see from Table IV that both conditions seem to be met. At a qualitative level then, the theory sensibly explains the behavior of the double-chained surfactants. Both micellar properties and force measurements show that with hydroxide or carboxylates as counterions aggregates are essentially fully dissociated, implying strong repulsive interactions between aggregates, high head group repulsion, and stiff chains. For bromides, there is a high degree of "binding", an attractive potential minimum in interactions, less head group repulsion, and fluid chains. The picture that emerges is that, e.g. for hydroxides, as surfactant concentration increases, the head group area increases and u / a / ranges over an appropriate range. This is difficult to quantify Rithout an estimate of the effective Debye length of the interacting vesicle suspension. By contrast for bromides, because of the lower degree of dissociation [ ~ / a l 0.821, head group area changes little with increased surfactant, and the system flocculates.
-
-
The Equilibrium Model and Dressed Micelles W-hilethe curious behavior induced by changes in counterion is readily understood at a qualitative level, its quantification in terms of cmcs and aggregation numbers for the micelle-forming single-chained surfactants is not such an easy matter. We here develop a detailed analysis. 'The upshot is that the data can be rationalized provided we admit that the hydroxides and carboxylates differ from bromides and other counterions in that the former are strongly hydrated. '['hey are therefore constrained to reside at the micellar surface a distance of 4---68, further out from the hydrocarbon core than do bromides and behave as if strongly dissociated. Much of the intuition on ionic micellar aggregates is derived from the equilibrium model. This assumes that the monomermicelle aggregation process is described by a n equation of the form K e n , " I I ~ Q n,,
Here monomer ( n l ) , counterion
(ti,).
(7)
and micelle (n,) cnncen
Brady et al. trations are coupled only through the condition of charge neutrality and species inventory
n, = n ,
+ Nn,
= n,
+ Qn,
-
n3
(8)
where n3 represents co-ion concentration and n, surfactant concentration. The micelle is viewed as an aggregate of N monomers with Q counterions "bound". If no is defined as 1/K, = Nndv(n3
+ no)Q
(9)
it can be shown that for large N the system exhibits a cmc = no. Hence 1
In no = - - In (NK,) - q In (no + n3), q = Q / N (10) N and a plot of In cmc vs. In (cmc + salt) yields both the fraction of "bound" charge and the assumed hydrophobic free energy of transfer of a monomer to micelle. This (phenomenological) model yields sensible results for a system like SDS. The curves are linear, and hydrophobic free energies of transfer so estimated are as expected. No conclusion can be drawn concerning any conjectured ion binding parameter from our cmc data because the salt concentration spanned is too wide. [Our focus has been on aggre0.5 as deduced by both gation number.] However, taking q Bunton'* and Zana," consistent with conductance data, we infer that the bulk free energy of transfer is gB= In (NK,) N 6500 cal/mol, while for SDS ( q 3~ 0.8), gB = 9500 cal/mol. To reconcile these differences it is necessary to examine the origins of the equilibrium model. In a first principle theory of micellization in the pseudophase approximation we have k 7 In cmc = gB+ g, + g,,, (11) where g, is the hydrophobic free energy of transfer of the hydrocarbon tail of a monomer from water to the more-or-less oil-like interior of a micelle. This term is nearly independent of salt. The term g, is a net surface free energy, and g,,, a contribution due to interactions between micelles. 'Io a first approximation this can be ignored. The term g, arises from many unquantified forces: e.g. hard core and hydration forces between head groups, entropic terms, a large contribution from chain packing and electrostatic forces. All these effects are opposed by an attractive force due to exposure of the hydrocarbon to water. If it is assumed that'2,32 where gelrepresents the electrostatic contribution, y is taken to be independent of salt concentration and a is the head group area, then the optimal micelle is determined by
a
-g
aa
E
=y
a
-
-g
da
e'
=y
.-
Tel
=0
Since gelcan be calculated explicitly y is determined, and indeed turns out to be virtually constant as a function of salt, in agreement with assumption. (y is not the surface tension at the oil-water interface, 50 dyn/cm. Its value, typically 15 dyn/cm for SDS or DDTAB, represents the interfacial tension minus a term due to chain packing.) It can be shown that in the limit of high surface charge and large radius g5 can be written in the form 9kT I n (nl + n, n3) gq' g, (14)
-
+
+
where q is the adsorption excess of counterions, coions, and monomers about a micelle, and g,' is independent of salt. That is, the equilibrium model has a sensible foundation in some limiting cases. A plot of In cmc vs. In (cmc salt) then yields not the bulk free energy of transfer gB,but rather gB+ gq'. But the approximate form eq 14 is asymptotic and can be expected to hold only when q = 1, which it is for SDS or DTAB. For highly charged micelles (small q ) the form eq 14 fails, and
+
(31) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J . Chem.Soc., faraday Trans. 2 1976,72, 1525. (32) Evans, D. F.; Mitchell, D. J.; Ninham, B. W . J . Phys. C'hem. 1984, 88, 6344. ( 3 3 ) Evans, D. F.; Wightman. P. J. J . Colloid Interface Sei. 1982,86, 515.
The Journal of Physical Chemistry, Vol. 90, No. 9, 1986 1859
Surfactant Aggregation we are forced to revert to theory rather than phenomenology. The required expressions are rather ~ o m p l i c a t e d : ~ ~ gel
{
= k T Yo - 4
I[ ( y2
q=r = 1
-
+
+
[;
;(
2 - ;4( l +
N
In ? ' I 2 ( 1
1
+ $)I/*]
+
-3']
+ (1 +
The problem is reconciled if we take this circumstance into account by an ion exclusion model, i.e. take core size into account properly. The calculations [assuming the worst possible scenario, that the inner part of the double layer also has dielectric constant 801 are inordinately more tedious than previously. The hydrophobic free energy of transfer then emerges correctly, as does the adsorption excess, if the (hydrated) hydroxide sits out about a further 4 A from the micellar head group surface.
(17)
where
Yo = E' e'o z = cosh y 0 / 2 =
[
(1
+ $)2
+
:] -z 112
TABLE V DTAB N = 57, cmc = 0.0147 M, K-' = 25.1 k',Rhc = 16.8 A, a = 62.4 A2,s = 36, yo = 6.86 ge1/kT= 4.69, ya/kT = 2.66, g , / k T = 7.34, K , = 9200 cal/mol, q(ca1cd) = 0.85 DTAOH N = 29, cmc = 0.034 M, K-' = 16.5, R,, = 13.4 A, a = 78.2 A2,s = 18.9, yo = 5.44 g,,/kT = 3.433, ya/kT = 2.52, g J k T = 5.9s. K , = 7900 cal/mol, q(calcd) = 0.74
2
(19)
The surface charge per unit area is u = e / a , IL0 is the surface potential, and R the radius of the micelle. There are various ways of writing these expressions, and the last form of eq 17 is probably exact. Once aggregation numbers are determined, hydrocarbon core radius Rhcand head group area a are known, e.g. if a spherical geometry is assumed Nu = (4r/3)RhC3, N a = 4aRh2, where u is the known volume of the monomer hydrocarbon tail. We make the following comment: the surface free energy is derived from an approximate solution to the nonlinear PoissonBoltzmann equation and can be expected to fail for small radii and at high salt. It ignores interactions between micelles on the grounds that at the cmc the concentration of micelles is small. It assumes that the Debye length is given by eq 18, i.e. it ignores the contribution of micelles. The last two assumptions, together with the pseudophase approximation, can lead to serious error at zero or low (of the order of the cmc) salt concentration. The theory assumes further that the dielectric constant c is that of water = 80 up to the hydrocarbon core interface and ignores image effects. Despite these deficiencies this theory does remarkably well. Typical results are listed in ref 12 and 32. The predicted hydrophobic free energies of transfer for SDS range from 9700 (zero salt) to 9500 (0.3 M) cal/mol, and the same values emerge for DTACI. The predicted free energies of transfer are about what one expects and the theory holds consistently as chain length varies. Further ion binding parameters are given correctly. Now consider the problem at hand. We perform the same calculations for dodecyltrimethylammonium bromide and hydroxide. The results are given in Table V. For DTAOH the hydrophobic free energy of transfer is too low, and the ion binding parameter q much too high. The resolution is immediate: the one free parameter [implicit] in this theory is the position of the electrostatic surface potential. Table V assumes R = Rhc.While this is a reasonable approximation for SDS or DTAB, it is patently in error for DTAOH. The hydroxide counterion is hydrated and sits further from the surface than does the bromide counterion.
Conclusion This work began as an attempt to understand some peculiar and unexpected aggregation properties of double-chained cationic surfactants with hydroxide and carboxylates as counterion. Their very high solubility, insensitivity to salt, the formation of spontaneous thermodynamically stable vesicles-instead of lamellar phase-and most striking of all, the vesicle to micel!e transition with increasing surfactant concentration ail seem at first to be counterintuitive. These phenomena, for double-chained surfactants, had already been predicted theoretically.'0 Theory requires the simultaneous fulfillment of several conditions: relatively stiff chains, strong repulsive interactions being paramount. We have shown that all the evidence is that these conditions are met through the simple postulate-borne out in particular by direct force measurements between bilayers-that the counterion is strongly hydrated. The phenomena are mimicked, albeit in low key, by the corresponding single-chained surfactants. Their cmcs, aggregation numbers, and consistent hydrophobic free energies of transfer all fit semiquantitatively into the scheme of things. It is unlikely that more detailed theoretical modeling can be used at the present time to extract much more information than micellar studies than we presently have. This is because, for highly charged micelles, the pseudophase approximation, our lack of knowledge of the Debye length in the absence of salt, coupled with the flexibility-and additional parameters-required to take account of the so-called inner nature of the double-layer reduce any such theories to curve-fitting. The more interesting and accessible problems, which mimic in the large the more subtle counterion effects in biology, e.g. in phospholipid-cation specific self-assembly, are those involving double-chained surfactants. Acknowledgment. The ruthenium(I1) (4,4'-di-n-octyi-2,2'bipyridyl)bis(bipyridyl) used in this work was kindly provided by Drs. W. H. F. Sasse and D. N. Furlong of the CSIRO Division of Applied Organic Chemistry, Port Melbourne, Australia. We thank Dr. D. Thomas of the Department of Biochemistry, University of Minnesota for making available the fluorometer on which the fluorescence experiments were performed. G.G.W. acknowledges the receipt of a Commonwealth Postgraduate Research Award from the Austrlian Government. J.E.B. thanks Minnesota Mining and Manufacturing Corporation for support as a visiting postdoctoral fellow. D.F.E. acknowledges support by the U.S. Army DAAG 29-84-K-0152. Registry No. DTAOH, 14898-63-6; DTABr, 11 19-94-4; DTAOAc, 22214-02-4; DDAOH, 23381-53-5; DDAAc, 16613-01-7; DDABr, 3282-73-3; NaOH, 1310-73-2; NaOAc, 127-09-3; dodecyltrimethylammonium formate, 100859-15-2; dodecyltrimethylammonium propionate, 100859-16-3;dodecyltrimethylammonium butyrate, 100859-17-4; dodecyltrimethylammonium tartarate, 100859-18-5; didodecyldimethylammonium formate, 90790-95-7;didodecyldirnethylamrnonium propionate, 90790-96-8; didodecyldimethylarnmonium butyrate, 9079097-9.
