J . Phys. Chem. 1989, 93, 1448-1451
1448
Orientational Order and Dynamics of a Wlicellariy Associated Organic Counterion Mikael Jansson,* Puyong Li, Institute of Physical Chemistry, Uppsala University, Box 532, S-751 21 Uppsala. Sweden
Ulf Henriksson, and Peter Stilbs Department of Physical Chemistry, The Royal Institute of Technology, S-10044, Stockholm 70, Sweden (Received: March 25, 1988; In Final Form: July 22, 1988)
Multifield 13Cand *H relaxation data were obtained for 0.2 M solutions of decylammonium butanoate and decylammonium acetate. The data were analyzed within the two-step model for relaxation of micellarly associated surfactants. The evaluated correlation times and order parameters for the butanoate ion indicate that the charged headgroup is anchored at the hydrocarbon-water interface and that the hydrocarbon tail is oriented toward the hydrocarbon core of the micelle. It was also found that the orientation and dynamics of the decylammonium ion were significantly affected by the micellar inclusion of the organic counterion.
1. Introduction In two previous communications we have systematically investigated the effect of different organic counterions on the aggregation of decylammonium amphiphiIes.lv2 It was found that the degree of counterion binding is strongly dependent on the hydrophobic character of the counterion and that the critical micelle concentration (cmc) decreased in the presence of the larger and more hydrophobic counterions. Amphiphilic compounds containing both a cationic and an anionic surfactant in an equimolar ratio are referred to as catanionic surfactant^.^ Due to the pronounced amphiphilic character of butanoate, micelles formed by decylammonium butanoate (DABut) can be regarded as intermediates between cationic and catanionic micelles. The object of this study is to examine the orientation and dynamics of the micellarly bound counterion and, hence, investigate whether the organic counterion is more accurately described as a co-amphiphile in a mixed micelle rather than a counterion. Information of dynamics and conformation of amphiphiles can be obtained from nuclear magnetic spin relaxation data. The application of the so-called two-step model has been shown to give relevant information on alkyl chain order and correlation times corresponding to different dynamical modes in surfactant systems.*-* A two-step model analysis has here been performed on multifield I3C T I and nuclear Overhauser enhancement (NOE) data, for both the decylammonium ion and the butanoate ion, in a 0.2 M solution of decylammonium butanoate (cmc = 0.037 M). In order to sample relaxation rates at lower N M R frequencies and hence to test the applicability of the two-step model to counterion relaxation data, *H TI measurements were performed on deuteriated butanoate ions. The study also includes I3C N M R relaxation data for decylammonium acetate (DAAc). Since specific counterion effects due to the hydrophobic character of the counterion are at most modest in this system, a comparison of the order and correlation times of the amphiphile and the counterion in the two decylammonium systems would reveal the influence of organic counterions on micellar conformation and dynamics. 2. Experimental Section The decylammonium surfactants were synthesized from decylamine (Merck) and the acid corresponding to the specific counterion. Butyric-2,2-d2 acid and butyric-3,3-d2 acid were obtained from IC Chemikalien GmbH, whereas acetic acid and butyric acid were obtained from EGA. Surfactants that did not contain deuterium nuclei were dissolved in deuterium oxide (99.8% w/w enriched, Norsk Hydro), whereas surfactants with deuteriated counterions were dissolved in distilled water.
The variable-field I3C T , measurements were performed on 0.2 M solutions of decylammonium acetate and decylammonium butanoate at four different frequencies: 101.0, 75.7, 25.1, and 15.1 MHz. The instruments used were a Bruker AM-400 spectrometer, a Varian XL-300 spectrometer, a JEOL FX- 100 spectrometer, and a JEOL FX-60 spectrometer, with D 2 0 as an internal lock substance. Nuclear Overhauser enhancements were determined at 75.7 MHz on the Varian XL-300 spectrometer. When T I data were collected, the inversion-recovery technique was e m p l ~ y e dusing , ~ 16 T values, whereas the NOE's were obtained by the dynamic NOE technique,I0 using the same number of T values. 2H T I measurements were performed on 0.2 M solutions of decylammonium butanoate-2,2-d2 and decylammonium butanoate-3,3-d2 on the Bruker AM-400 spectrometer, the Varian XL-300 spectrometer, the JEOL FX- 100 spectrometer, and a Bruker MSL-90 spectrometer with a variable-field facility. Measurements were performed at four different frequencies-1 3.8, 9.0, 7.0, and 4.0 MHz-on the Bruker MSL-90 spectrometer. Self-diffusion coefficients were obtained by the Fourier transform pulsed field gradient spin-echo method" on a JEOL FX-100 spectrometer. All measurements were made at 25 OC.
3. Theoretical Considerations In this study we have extracted information of counterion and amphiphile motion and orientation from the field dependence of spin-lattice relaxation rates and nuclear Overhauser enhancements by application of the two-step model. Spin-spin relaxation rates could in principle also have been used, but as they are more difficult to determine accurately, such measurements were not attempted in the study. This section gives a short outline of the theoretical foundations of the two-step model. A more extensive treatment can be found in ref 5. In the so-called Redfield limit, Le., when the motion causing the relaxation is more rapid than the strength of the interaction that is averaged, the relaxation rates can be formulated as a product of an interaction constant squared and a linear combination of spectral densities.12 The relevant relaxation equations ( I ) Jansson, M.; Stilbs, P. J . Phys. Chem. 1985,89, 4868. ( 2 ) Jansson, M.; Stilbs, P. J . Phys. Chem. 1987, 91, 113. (3) Jokela, P.;Jonsson, B.; Wennerstrom, H. Prog. Colloid Polym. Sci. 1985, 70, 17. (4) Wennerstrom, H.; Lindman, B.; Siiderman, 0.;Drakenberg, H.; Rosenholm, J. B. J . Am. Chem. SOC.1979, 101, 6860. ( 5 ) Halle, B.; Wennerstrom, H. J . Chem. Phys. 1981, 75, 1928. Stilbs, P. J . Phys. Chem. 1984, 88, (6) Walderhaug, H.; Soderman, 0.; 1655
( 7 ) Siiderman, 0.;Walderhaug, H.; Henriksson, U.; Stilbs, P. J . Phys. Chem. 1985, 89, 3693. (8) Jansson, M.; Li,P.; Stilbs, P. J . Phys. Chem. 1987, 91, 5279. (9) Vold, R.L.;Waugh, J. S.; Klein, M. P.; Phelps, D. E. J . Chem. Phys. 1968, 48, 3831. ( I O ) Freeman, R.; Hill, H . D. W.; Kaptein, R. J . Magn. Reson. 1972, 7 , q-7
JLI.
'To whom correspondence should be addressed
0022-3654/89/2093-1448$01.50/0
( I I ) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, I .
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1449
Micellarly Associated Organic Counterions for isotropic systems are given below. For the deuterium nuclei the spin-lattice relaxation rate is given by
R, = ( 3 ~ ~ / 2 O ) x ' ( J (+ w )4J(2w))
(1)
while the spin-lattice relaxation rate and nuclear Overhauser enhancement of a 13C nucleus dominantly governed by dipoledipole interactions are given by13 Rl = ( N / 2 0 ) X ( ~ o Y H Y C ~ / ~ * ~ C - H ~ ) ~ (-J W( W C ) H+ 3J(wC) -k ~ J ( w H + OC)) (2) 7 = (1 / 2 0 ) Y H 3 y C ( h h/4*rC-H3)2(NT1)
(6J(wH + wC) - J(wH - wC)) ( 3 ) where x is the quadrupolar coupling constant in frequency units, po is the permeability under vacuum, Y~ and y c are the magnetogyric ratios of the proton and the carbon nuclei, N, is the number of directly bonded protons to carbon i , h is Planck's constant divided by 2*, rC-His the C-H bond length, and wHand wC denote angular Larmor frequencies of protons and carbons, respectively. The J(w)'s represent various reduced spectral densities at the indicated angular frequencies. It is assumed in the two-step model, as applied to spherical micelle^,^^^*^ that a fast, slightly anisotropic, local chain motion is superimposed on a slow isotropic overall motion of the micelle. If the autocorrelation functions of the fast and slow motions are single exponential, the relevant reduced spectral densities will be given by
J(w) = ( 1
- S2)2r,' + 2S27;/( 1 + (~7,s)')
S = ( 1 / 2 ) ( 3 COS' 0 - 1 )
(4)
where 7,f and 7; denote the correlation times of the fast and slow motions, respectively. S is the order parameter, and B is the angle between the C-H vector (or for the RIDdata the electric field gradient at the deuterium nucleus) and a local director perpendicular to the micellar surface. Since the symmetry of the deuterium electric field gradient is along the C-D bond, correlation times and order parameters evaluated from 13Cand 2H relaxation data refer to identical system parameters (assuming there is not isotopic effect in the motion of the C-H,D vector). The observed R I values have to be corrected for the presence of amphiphiles and counterions that are not associated to the micelle. This was done by assuming the applicability of a two-site relaxation rate model R I = pR,(mic) ( 1 - p)R,(free) (5)
+
where p denotes the fraction of micellized species, R1the observed relaxation rate, Rl(mic) the relaxation rate of the micellized species, and R,(free) the relaxation rate of the free species, which was measured on a sample with a surfactant concentration below the cmc. The NOE values of the micellized species were calculated by a method proposed by Heatley,14 where the NOE value is evaluated from the expression of the dynamic equilibrium between free and micellized molecules R,(mic)(NOE(mic) - N 0 E ) p = Rl(free)(NOE - NOE(free))(l - p ) ( 6 )
TABLE I: Micellar Self-Diffusion Coefficients and Fractions of Micellarly Associated Amphiphiles and Counterions for 0.2 M Solutions of Decylammonium Butanoate and Decylammonium Acetate at 25 OC
D,, 10I2m2/s DABut DAAc
85 f 5 93 5
*
P. 0.836 0.750
P C
0.610 0.430
data of the counterion and the micelle, it reflects the amount of counterions diffusing with the micelle rather than the counterions regarded "bound" to the micelle in other contexts, like spin relaxation. This might lead to an underestimation in the calculated R,(mic) and NOE(mic) values. However, the field dependence and the relative magnitudes of motional and order parameters at different segments of the counterion, which is the main concern of this work, do not critically depend on the p value. The individual fast correlation times, the order parameters, and the slow correlation time were extracted by fitting the parameters in eq 1-4 to the corrected R I C ,RID, and NOE values. The evaluational procedure is described in ref 6 . 4. Results and Discussion
When the two-step model is applied to surfactant relaxation data, it is assumed that one correlation time is sufficient to characterize the slow overall isotropic motion of the micelle, limiting the applicability of the model to spherical aggregates only. Information on the size and shape of micelles can be. obtained from micellar self-diffusion coefficients.I5 The micellar self-diffusion coefficients of DABut and DAAc at the relevant concentration and temperature are listed in Table I. Since the dynamics of micelles in solution reflects intermicellar interactions as well, the interpretation of diffusion data in terms of micellar size and shape is not straightforward. The observed magnitude of D,, -90 X lo-'' m2/s, is however typical for small spherical micelles at this temperature. Furthermore, we have a previous paper demonstrated, by taking the contributions to the micellar self-diffusion coefficient from electrostatic micelle-micelle interactons into account via a kinetic theory of interacting Brownian particles, that dodecylammonium acetate forms spherical miceles at 0.1 M.I6 This strongly suggests that DAAc also would form spherical aggregates at 0.2 M. Due to the higher fraction of bound counterions in the DABut system (Table I), ionic headgroup repulsions are reduced as compared to the DAAc system, and micelles formed by DABut could be expected to be larger than those formed by DAAc. The micellar self-diffusion coefficients indicate, however, that the difference in micellar size is at most modest. The conclusion is that the two-step model can be used in the analysis of N M R relaxation data in both systems. Both deuterium and carbon relaxation data are used in the calculation of correlation times and order parameters of the butanoate ion. The evaluation of these parameters requires a knowledge of the dipolar and quadrupolar interaction constants in eq 1-3. The ratio between the dipolar and the quadrupolar interaction constants can be calculated from the 13C and 2H relaxation rates obtained under extreme narrowing conditions via eq 1 and 2:"
where NOE denotes the observed NOE value, NOE(mic) the NOE value of the micellized species, and NOE(free) the NOE value of the free species. NOE for the free species was assumed to be 2.99, which is the theoretical value at extreme narrowing conditions. The fractions of micellarly associated amphiphiles and counterions were calculated from N M R self-diffusion measurements using the procedure outlined in ref 1 . Since the fraction of micellarly associated counterions is evaluated from the self-diffusion
QCC and DCC represent the quadrupolar and dipolar interaction constants; R I Dand R I Crepresent the measured spin-lattice relaxation rates corresponding to the moton of the C-D and C-H bond vectors at a surfactant concentration below the cmc (0.02 M). x can be calculated by setting rC-Hto 1.09 A, which is the value most commonly used for the length of the carbon-proton bond vector. Table I1 shows the T I values for the nonassociated
(12) Abragram, A . The Principles of Nuclear Magnetism; Clarendon: Oxford, 1961; Chapter 8. (13) Doddrell, D.: Glushko, V.; Allerhand, A . J. Chem. Phys. 1972, 56, 3683. (14) Heatley, F. J. Chem. SOC.,Faraday Trans. 1 1987, 8, 2593.
(15) Nilsson, P.-G.; Wennerstrom, H.; Lindman, B. Chem. Scr. 1985, 25, 67. (16) Jansson, M.; Rymdtn, R.; Linse, P., submitted for publication in J. Phys. Chem. (17) Soderman, 0 .J. Magn. Reson. 1986, 68, 296.
1450 The Journal of Physical Chemistry, Vol. 93, No. 4 , 1989
Jansson et al.
TABLE 11: Measured TI Values of the a- and &Positions of Butanoate in a 0.020 M Solution of Decvlammonium Butanoate a
3.40
0.358
P
3.55
0.362
169 166
“The x values were calculated from eq 5 .
015
010 -
005
I
\
.
-
-
4120
i ;
O o o L ;
R:
L
1
5
6
;
8
9 1 0
H y d r o c a r b o n Choln P o s i t i o n
6
Figure 2. Calculated order parameters versus the hydrocarbon chain
3
060
lo6
lo7
lo8
R:
lo9
v /HZ
position (relative to the charge headgroup) for the decylammonium ion in DABut (0),the decylammonium ion in DAAC ( O ) , butanoate (O),
and acetate (m). Since it was not possible to resolve the peaks from carbons 5 and 6 at lower magnetic fields, an average value is given in the figure. The error limits of S for the different segments of the decylammonium ion are of the same magnitude in both systems. Estimated error limits correspond to 80% confidence intervals.
Figure 1. Experimental values of RIC for the a-carbon (A) and the 6-carbon (A)in butanoate and RIDfor butanoate-2,2-d2(0)and butanoate-3,3-d2(0).respectively. The NOE values of the a-carbon (v)and the @-carbon(V)are shown at the top of the figure. The curves correspond to the R , and NOE values calculated with the two-step model.
ion and the corresponding x values. The values obtained for x are in good agreement with the value most commonly used, 170 kHz.’* Figure 1 shows the experimental R , and 9 values for the butanoate ions, corrected for the presence of nonassociated species, and the calculated relaxation rates according to the two-step model. The decreased frequency dependence of R , at both high and low frequencies, which is predicted by the two-step model, is experimentaly sampled by the combined use of the carbon and deuterium relaxation rates. Although experimental RZDvalues were not used in the evaluation of the order parameters and correlation times, the observed line widths of the deuterium resonances at 61.4 MHz, - 4 Hz, are in good qualitative agreement with the R,D values predicted by the model. In Figures 2 and 3 the calculated order parameters and fast correlation times for butanoate and the decylammonium ions are displayed. Comparing S and 7,f at the carbon adjacent to the functional group of the two ions shows that both parameters are a factor of 2 smaller for the counterion. This demonstrates that the headgroup of the counterion is not as firmly anchored at the micelle surface as the amphiphile, which can be attributed to the smaller size of the butanoate ion. Although the magnitudes differ, the general features of the order parameter and fast correlation time profiles of the counterion and the amphiphile are quite similar; S and 7: decrease along the carbon chain toward the terminal methyl group. This implies that the number of possible orientations of the C-H,D bond is more limited and that the motion of the alkyl chain is more restricted closer to the charged headgroup. Since Table I shows that the relaxation rates at the aand @-positionsin butanoate are almost identical for the nonassociated counterion, this is clearly an effect of the micellar association of the counterion, which supports the concept of the hydrocarbon tail of butanoate being oriented into the micellar hydrocarbon moiety, forming what is essentially mixed, or catanionic, micelles with the decylammonium ion. Figures 2 and 3 also show the order parameter and correlation time evaluated for the methyl group of the acetate ions. Since the calculations of these parameters were based on only four T I values and one NOE value, all in the high-frequency region of the spectral densities, it is not possible to conclude whether the (18) Mantsch, H.; Saito, H.; Smith, C. Prog. Nucl. Magn. Reson. Specrrosc. 1977, 11, 2 1 1 .
0
1
2
3
L
5
6
7
8
9
10
H y d r o c a r b o n Chain Pos~tion
Figure 3. Calculated fast correlation times versus the hydrocarbon chain
position (relative to the charge headgroup) for the decylammonium ion in DABut (0),the decylammonium ion in DAAC ( O ) , butanoate (O),
and acetate (m). Since it was not possible to resolve the peaks from carbons 5 and 6 at lower magnetic fields, an average value is given in the figure. The error limits of correlation times for the different segments of the decylammonium ion are of the same magnitude in both systems. Estimated error limits correspond to 80% confidence intervals. two-step model also applies to the acetate data. The lower relaxation rates and the weaker field dependence observed for acetate indicate, however, that the motions of butanoate are considerably more restricted than for the smaller acetate ion. The influence of large hydrophobic counterions on the order and the dynamics of the decylammonium ion is demonstrated by comparing order parameters and correlation times of the amphiphile in DABut and DAAc. Surfactants with acetate and chloride as counterions have usually almost the same critical micelle concentrations, indicating that any specific effects due to the counterion hydrophobicity are minor. Figures 2 and 3 show that the micellar inclusion of butanoate affects both the order and correlation time profiles of the amphiphile. Even though the uncertainties of the determintions of S and 72 are rather large, it is clearly seen that the presence of butanoate increases the order and decreases the mobility of the decylammonium chain. Either this may be caused by a closer packing of the alkyl chains due to the reduced electrostatic repulsion between the ionic headgroups in the DABut system or it may be a consequence of a different packing of the alkyl chains upon the micellar inclusion of the hydrocarbon tail of butanoate. NCry et al. have shown that a transition from spherical micelles to rodlike micelles corresponds to an increase in the fast correlation times of the same magnitude as the difference between the 7: values of DAAc and DABut.19
J . Phys. Chem. 1989, 93, 1451-1457
TABLE 111: Slow Correlation Times Evaluated from the Two-step Model Calculations"
system DA in DABut DA in DAAc But in DABut
r:,
*
ns
3.7 1.0 3.0 f 1.0 1.5 f 0.2
"The error limits correspond to 80% confidence intervals. However, in this case the micellar self-diffusion coefficients exclude such an explanation for the observed difference between the two systems. The correlation times for the slow motions of the decylammonium and butanoate ions are shown in Table 111. As the I3C measurements only sample the high-frequency region of the spectral density function, the accuracy of the 7,1determination is not optimal, which is indicated by the large error limits in the table. The 7: value of butanoate is much better defined, due to the low-frequency 2H data collected for the counterion. It is usually assumed that both aggregate tumbling and amphiphile diffusion over the curved surface contribute to the slow motion in micellar systems. The theory for spin relaxation in systems of that geometry has recently been discussed by Halle.zo The slow correlation time for the counterion is shorter than for the amphiphile, which can be rationalized by assuming that the lateral diffusion of the butanoate ion at the micellar surface is faster (19) N h y , H.; Saderman, 0.; Canet, D.; Walderhaug, H.; Lindman, B. J . Phys. Chem. 1986, 90,5802. (20) Halle, B. Mol. Phys. 1987, 61, 963.
1451
compared to the amphiphile. Since the 7,f and S values of butanoate indicate that the ion is less firmly anchored at the micelle surface than the decylammonium ion, this appears to be a reasonable assumption. It is not plausible that the exchange of the butanoate ion between the micelle and solution should contribute to 7,". Yiv et al. have measured the dissociation rate constant of 1-pentanol in ionic micelles to be 1.8 X lo7 S-I.~' Although butanoate is less hydrophobic than pentanol this should, with regard to the micellar residence time, be more than compensated by the electrostatic attraction between the micelle surface and the counterion. Therefore, the micelle-counterion dissociation rate constant is probably considerably smaller than lo9 s-I. 5. Conclusions
The evaluated correlation times and order parameters of butanoate indicate that the ionic headgroup is anchored at the micelle surface while the hydrocarbon chain is oriented into the hydrocarbon moiety of the micelle. The motional characteristics of the decylammonium ion are affected by the micellar inclusion of the counterion; the order is increased and the motion is slowed down for the chain segments closest to the hydrocarbon-water interface. It was also found that the slow correlation time, corresponding to the tumbling of the micelle and the lateral diffusion of the amphiphile a t the micelle surface, is shorter for the organic counterion as compared to the decylammonium amphiphile. Registry No. Decylammonium butanoate, 73702-94-0; decylammonium acetate, 2016-38-8. (21) Yiv, S.; Zana, R. J. Colloid Interface Sci. 1978, 65, 286.
Influences of Counterion Hydrophobicity on the Formation of Ionic Micelles Mikael Jansson* Institute of Physical Chemistry, Uppsala University, Box 532, S - 751 21 Uppsala, Sweden
and Bengt Jonsson Physical Chemistry 1 , Chemical Center, University of Lund. P.O. Box 124, S-221 00 Lund, Sweden (Received: May 1 1 , 1988)
Influences of counterion hydrophobicity on the formation of ionic micelles, formed by decylammonium surfactants, were studied both experimentally and theoretically. A theoretical model was proposed from which the distribution function of amphiphiles and counterions in the micellar system, modeled by a cell model, could be calculated. The degree of micellization of counterions, as predicted from the calculations, was found to be high even for the least hydrophobic counterion examined, acetate. The relevance of the model can be tested by calculating self-diffusion coefficients from the distribution functions of counterions and amphiphiles in the cell and comparing them to experimental self-diffusion data, measured with the NMR pulsed-gradient spin-echo technique. Good agreements were obtained between the measured and the calculated concentration dependence of self-diffusion coefficients of the ions.
1. Introduction
The reduction of headgroup repulsions of micellized amphiphiles by counterions is an important aspect of micelle formation of ionic surfactants. The distribution of counterions in the vicinity of charged micelles has usually been described by the PoissonBoltzmann theory.' However, if interactions between counterions and micelles of nonelectrostatical origin, Le., specific counterion effects, are taken into account, the theory clearly has to be extended. This paper focuses on the effects of counterion hydrophobicity on the formation of ionic micelles, which have been investigated both experimentally and theoretically. The systems studied entail micelles formed by decylammonium ions and
carboxylic counterions with different chain lengths, ranging in size from acetate to hexanoate. Due to the pronounced amphiphilic nature of these counterions, the micellization of counterions, as well as decylammonium ions, has to be considered. The surface charge densities of micelles formed in the presence of hydrophobic counterion are thus lower as compared to micelles formed by surfactants with inorganic counterions. The distribution of amphiphiles and counterions between the micelle and the water part may be calculated from the expressions of the chemical potentials of the molecules in the micelle and the water part. With the combined use of the chemical potential expressions and the (1) Jonsson, B.; Wennerstrom, H.; Halle, B. J . Phys. Chem. 1980, 84,
*To whom correspondence should be addressed.
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2119.
0 1989 American Chemical Society
