The Journal of
Physical Chemistry
0 Copyright, 1990, by the American Chemical Society
VOLUME 94, NUMBER 7 APRIL 5,1990
LETTERS NMR Relaxation Studies of Internal Motions: A Comparison between Micelles and Related Systems P. J. Bratt, D. G.Gillies,* L. H. Sutcliffe, and A. J. Williamst Chemistry Department, Royal Holloway and Bedford New College, University of London, Egham, Surrey, TW2O OEX, UK (Received: October 19, 1989; In Final Form: January 16, 1990)
Multifrequency relaxation studies combined with the “two-step” model for molecular motion have shown striking similarities between correlation times for the fast motions at each of the last four carbons of aliphatic chains in surfactant and other systems. Determination of activation energies in nonsurfactant systems of 12 and 15 kJ mol-! for the methyl and methylene groups, respectively, enabled correlation times for all data to be expressed at 298 K. The values for the correlation times are very similar; averages were 4.9,1 I , 14,and 19 ps (starting with the methyl carbon), indicating similar molecular motions in micellar and nonmicellar systems.
NMR relaxation measurements ( T I ,T2,and NOE) provide a powerful means for studying the molecular dynamics of alkyl chains. In particular, I3Crelaxation measurements have been used with great success in the investigation of the molecular dynamics of biomolecules, polymers, and micelles. Recent work on micelles has shown that the dependence of relaxation rates upon radiofrequency can be explained by invoking two types of A slow motion in the order of nanoseconds is due to molecular tumbling and intramicellar amphiphile diffusion, while a faster motion with a correlation time in the order of picoseconds is due to the internal motions of the alkyl chain within the micelle. These latter motions are due to bond isomerizations, distortions, and librations. This approach has become known as the ”two-step” model* and is equivalent to the “model-free” a p p r ~ a c h .The ~ purpose of this Letter is to demonstrate the similarity between the internal correlation times of alkyl chains in different compounds. Results from this laboratory are included but details of the experimental methods and analysis
TABLE I: ComDounds and Their Abbreviations
Author to whom all correspondence should be addressed. ‘Present address: Chemistry Division, National Research Council, Ottawa, Canada. K1 A OR9.
( I ) Halle, B.; Wennerstrom, H. J . Chem. Phys. 1981, 75. 1928. (2) Drakenberg. T.; Lindman, E.; Rosenholme, J. B.; SMerman, 0.; Wennerstrom, H. J . Am. Chem. SOC.1979, 101, 6860.
abbrevn SOBS
SDS CTAC DOTAC DECAM NaCB OAXS SAS-2 SAS-3 1 phiClO 5phiClO C 14S7
CTAB DAPS
name of compound sodium p-(octy1)benzenesulfonate sodium dodecyl sulfate hexadecyltrimethylammonium chloride dodecvltrimethvlammonium chloride decylahnonium chloride sodium octanoate sodium 2-(3-dodecyl)-4,5-dimethylbenzenesulfonate sodium 2-dodecyl sulfate sodium 3-dodecyl sulfate sodium 44 1-decyl)benzenesulfonate sodium 4-(5-decyl)benzenesulfonate sodium 7-tetradecyl sulfate cetylammonium bromide (decyldimethy1ammonio)propyl sulfate
are given el~ewhere.~All the compounds referred to in this paper are listed in Table I .
0022-3654/90/2094-2727$02.50/00 I990 American Chemical Society
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The Journal of Physical Chemistry, Vol. 94, No. 7, I990
Letters
TABLE 11: Internal (Fast) Correlation Times, rr(298)/p, at Carbons for Some Micelles" in Water micelle
CI
c2
NaCs" NaC: SOBSI2 SOBSi4 CTAC~~ CTAB2'
DOTAP19 DOTAC' DOTACZ5 DAPS9 DECAM6 SDS24 SDS26-c av one std dev
21 22
24 27 23
c3
27 22 20 24 20
c4
23 20 24 21 25 18'
26 34
40
13 33 38
15 39
c5
c7
40 30 28 24 24 24 23 55' 16
C6 16 29 34 25 24 27 24 23 24 44 16
16 35 32 24 23 27 23 24 22 37 18
43 26 6
43 24 5
43 25 6
C8 17 29 29 22 24 29 22 22 19 36
ClO 13 15 18 13 15 13 15 14 13 17 13
CI, 8.6 13 12 8.9 II 8.8 10 11
18
15 22 23 17 20 21 18 18 18 26 14
43 25 5
34 19 4
24 14 2
15 11 2
c9
11
14 9.6
CMe 4.0 7.7 5.5 3.9 4.2 5.1 5.0 4.6 5.0 3.3 4.0 4.8 9.1 4.9 1 .o
'Using data extracted from the literature. 'Unresolved. C N o t included in the averages.
If the usual assumption is made that the relaxation of a 13C nucleus is due to the dipole-dipole interaction with directly bonded protons, then the general expressions for T I and the nuclear Overhauser enhancement, 7, are given bys R, = l / T , =
where N, is the number of protons directly attached to the carbon atom, r is the carbon to hydrogen bond length (0.1 105 nm), and yc and yH are the respective carbon and proton magnetogyric ratios. Finally, the J ( w ) ' s are the spectral densities in terms of the resonance frequencies of the carbon and the proton. According to the two-step model or the model-free approach, the motions that bring about spin relaxation are a fast, slightly anisotropic, motion superimposed upon a slow, isotropic, motion. The spectral density is given by2
where TI and T~ denote the fast and slow motions respectively. The order parameter, S, is given by S = ( 3 COS2 0 - 1 ) / 2
(4)
where 0 is the angle between the C-H vector and some local director. The average is taken over a time long enough to provide an average of the fast local motion, but short enough not to include the slow motion. It is assumed that the fast local motions occur in an environment that has on the average a 3-fold or higher symmetry and that the symmetry axis is the local director. According to the two-step model, the three parameters T,I 7s. and 9 determine the observed relaxation behavior within a micelle. In order to extract these parameters, at least four independent measurements of T I and/or 7 are required. In general, the experimental difficulties associated with an accurate determination of T2preclude its use, and hence a typical data set consists of three T,'s obtained at different radiofrequencies and one 7 . The success of this model in its application to micelles is well documented.613 (3) Lipari, G.;Szabo, A. (a) J. Am. Cfiem. SOC.1982, 104, 4546; (b) J . Am. Cfiem. SOC.1982, 104, 4559.
(4) Bull, L. M.; Gillies, D. G.; Matthews, S . J.; Sutcliffe, L. H.; Williams, A. J. Unpublished work. (5) Doddrell. D.; Glushko, V.;Allerhand, A. J . Cfiem. Pfiys. 1972, 56, 3683. . ...
(6) Ngry, H.;Sijderman, 0.;Canet, D.; Walderhaug, H.;Lindman, B. J . Pfiys. Cfiem. 1986. 90, 5802. (7) M e r m a n , 0.;Henrickson, U.; Stilbs, P.;Walderhaug, H.J. Pfiys. Cfiem. 1985, 89, 3693.
Because the internal motions are complex, 7f should be regarded as an effective correlation time corresponding to the integral over the correlation function. For strict application of eq 3 the overall motion should be isotropic, but it has been shown experimentally that the internal correlation times are relatively insensitive to changes in overall motion.6 The thrust of the present Letter is that despite the simplifying assumptions there is a consistency about the Tf values extracted from diverse situations. Allowing for the fact that different compounds have been examined at various temperatures, using different levels of NMR technology and using various techniques for the determination of T I and 7, it can be stated that generally there is a decrease in S2 and 7f from the anchor position to a minimum at the terminal methyl group. Studies in this laboratory4 have included the application of the two-step model to multiple frequency relaxation data obtained as a function of temperature for a synthetic lubricant molecule, polydecene, and for its model compound tri-n-octylamine, (TNO); for a given temperature, the results show a similar trend for S2 and 7falong the alkyl chains. Since the studies on these two compounds were carried out over a wide temperature range, the activation energies associated with 7Sand Tf were evaluated. In order to allow a direct comparison between the values of T f for the different micelles examined it was assumed that the activation energies associated with T ~ obtained , from the data analysis on polydecene and TNO, are also applicable to micelles. This allows literature values of 7ffor micelles at particular temperatures to be normalized to a common temperature of 298 K. The relaxation studies4 on polydecene and T N O give average values of Ea(7r) = 12 f 2 kJ mol-' for the methyl groups and 15.3 f 2.4 and 14.4 f 0.7 kJ mol-', respectively, for the four carbon atoms along the chain from the methyl group; an activation energy of 15 kJ mol-' is generally accepted as being appropriate for the trans-gauche isomerizations within a methylene chain.I5-I9 Thus a literature (8) Ahlnas, T.; Sderman, 0. Colloid Surf. 1984, 12, 125. (9) Jansson, M.; Li, P.; Stilbs, P. J. Pfiys. Cfiem. 1987, 91, 5279. (IO) Siiderman, 0.;Walderhaug, H.Lungmuir 1986, 2, 57. ( I I ) Henricksson, U.; Siiderman, 0. J . Cfiem. Soc., Faraday Trans. I 1981.83, I5 15. (12) Siiderman, 0.;Stilbs, P.; Walderhaug, H. J. Pfiys. Cfiem. 1984.88, 1655. ( I 3) Ahlnas, T.;Hjelm, C.; Lindman, B.; Siiderman, 0. J. Pfiys. Cfiem. 1983, 87, 822. (14) Ahlnas, T.;Lindman, B.; Rapacki, K.; Siiderman, 0.; Stilbs, P.; Walderhaug, H. Faraday Discuss. Cfiem. SOC.1983, 76, 317. (15) Steele, D. J. Cfiem. Soc., Faraday Trans. 2 1985, 8 / , 1077. (16) Taylor, W. J. J. Cfiem. Pfiys. 1948, 16, 257. (17) Piercy, J. E.; Rao, M. G.S . J. Cfiem. Pfiys. 1967, 46, 3651. (18) Pitzer, K. S. J. Cfiem. Pfiys. 1940, 8, 71 I . (19) Ito, K. J. Am. Cfiem.SOC.1953, 75, 2430. (20) Hartley, G. S . J . Cfiem. Soc. 1938, 1968. (21) Howarth, 0. W. J. Cfiem. Soc., Faraday Trans. 2 1979, 75, 863. (22) Axelson, D. E.; Hochman, J.; Levy, G. C.; Schwartz, R. J. Am. Cfiem. SOC.1980, 102, 5723. (23) Belmajdoub, A.; Brondeau, J.; Canet, D.; Elbayed, K.; Lattes, A,; Rico, I. J. Pfiys. Cfiem. 1988, 92, 3569.
The Journal of Physical Chemistry, Vol. 94, No. 7, 1990 2729
Letters
TABLE 111: Internal (Fast) Correlation Times. r,(298)/w, at Carbons for Some Micellesa in Water micelle Cl c2 c3 c4 c5 c6 Cl SOBS I phiClO 5phiCIO OAXS SAS-2 SAS-3 c I4S7 a Data
38.4
26. I
23.2
98.7 34.7 39.7
134 33.2 33.9
32.4 33.1
37.2 27.4
26.1 27.4 96.9
74.1 27.1 35.2 102
70. I 25.2 28.4 75.5 I02
28.7 31.3 28.4 46.5 81.7
28.6 26.3 63.5 96.9 41.0 31.3 25.9 33.0 52.5
C8
c9
c10
CMe
27.1 24.4 35.8 61.2 13.3 23.7 18.5 27.4 37.5
16.7 14.9 23.8 44.1 19.1 16.1 12.0 19.1 20.3
13.9 10.6 17.4
5.2 4.6 6.8 7.6 5.1 5.3 4.7 5.8 5.8
22.1 13.2 19.9 9.5 13.4 12.9
obtained in the present work.
value of rf can be normalized to 298 K by using the standard Arrhenius temperature dependence referenced to 298 K and given by 7f(T) = ~ ~ ( 2 9 exp[E,(T1 8) - 298-’)/R] (5) where E, is assumed to be 15 and 12 kJ mol-’ for CH2 and CH3, respectively. Table I 1 lists the internal correlation times, temperature corrected to 298 K, from literature data for a series of micelles. In many of the systems studied, a shallow maximum is observed in the value of 7f near the center of the chain. This is due to the fact that groups in the middle of a chain require cooperative motions of several other groups in the same molecule to change conformation. The low values of TI for the last four carbons of the chain imply that the interior of a micelle must be similar to that of a neat alkane. Included in Table 111 are the internal correlation times obtained in the present study. SOBS is known to form spherical micelles under these conditions; the other systems are dilute enough to make the reasonable assumption that the micelles are spherical. The multifield relaxation data were analyzed according to the method of Ntry et aL6 It can be seen that, after correcting for temperature, there is a strong similarity between the values of T f for the last four carbons in the alkyl chain, again implying that the interior of a micelle must be very similar from one system to another. An indication of the general validity of this observation is indicated in Table I 1 for SDS studied by Ellena et a1.26 The correlation times extracted from the two-step model are 80-1 50% larger than expected. However, Soderman et al.24have examined SDS micelles in detail and have established that the internal correlation times extracted by Ellena and co-workers are incorrect. The error can be traced to the fact that in interpreting the relaxation data the overall correlation time was calculated by means of equations for micellar rotational tumbling and surfactant diffusion over the micellar surface; these required an estimate of the radius of the micelle and viscosity of the solution. The resulting overall correlation time extracted was a factor of 4 greater than that obtained by Sderman et al.,24who analyzed multifrequency relaxation data only. This example suggests that if there is a large discrepancy between 7;s determined for the last four carbons in the alkyl chain and the generally accepted values then the accuracy of the data should be questioned. The similarity between the internal correlation times discussed above and those exhibited by both polydecene and T N 0 4 indicates that the pattern is typical for most alkyl chains, and not just for micelles, especially for the last four carbons in the chain. Essentially this is restating that the interior of a micelle is the same as in bulk n-alkyl phases2’ It has been proposed that, with
TABLE IV: Fast Correlation Times, rf(298)/ps, at Carbons for Some Poly(n-alkyl methacrylates)*’ Dolvmer C, C, C, C, C, .C , PBMA PHMA
28
60
27 34
40 16
25 12
6 6
increasing chain length, the viscosity of the micelle interior approaches that of the corresponding n-alkyl chain,28*29 with the last segments having conformations similar to liquid hydrocarbons. This suggestion is in keeping with the conclusions made here. In view of the obvious experimental problems involved, the agreement between the internal correlation time profiles listed in Table I1 is very good, which indicates that the activation barrier corresponding to the gauchetrans isomerization barrier is useful in characterizing related systems. The general applicability of our approach led us to attempt to extend it to the internal correlation times for n-alkyl chains in some polymers. Howarth21 has analyzed the relaxation data for poly(n-butyl methacrylate) (PBMA) and poly(n-hexyl methacrylate) (PHMA) using a functionally equivalent spectral density to the two-step model and has extracted the internal correlation time profiles. Applying the normalization given above, q(298) values for these two compounds were obtained and they are given in Table IV. Despite the inevitable errors involved in the method of analysis and experimental procedures, the usual motional parameters are found for the terminal methyl group. The values for the other carbons in the chains are different; the sudden rise of ~ d 2 9 8along ) the PBMA chain is probably due to the shortness of the chain which restricts the number of conformers. Conclusions
This paper indicates that there is good consistency between extracted and normalized internal correlation times for a series of micelles. The similarity in internal correlation times between those in a micelle and those demonstrated by both polydecene and tri-n-octylamine lends weight to the hypothesis that the interior of a micelle is very similar to a liquid hydrocarbon. The general agreement between the correlation time gradients along the hydrocarbon chain shown by the various compounds discussed here indicates that the method of multifrequency relaxation studies is widely applicable to alkyl chains. Furthermore, the close similarity of correlation times (normalized to 298 K) for the last four carbons in the alkyl chain can be regarded as a test of reliability of experimental data. Acknowledgmenf. We thank Shell Chemicals UK, Chester, for financial assistance and Dr. G. E. Hawkes and the ULIRS NMR service at Queen Mary College and King’s College for the use of the Bruker WH400 and WM250 spectrometers, respectively.
(24) Carlstrom, G.; Olsson, U.;SMerman, 0.: Wong, T. C. J. Chem. Soc., Faraday Trans. l 1988,84,4475.
(25) Sijderman, 0. Private communication. (26) Cafiso, D. S.;Dominey, R. N.; Ellena, J. F. J . Phys. Chem. lqS7, 91, 131.
(27) Gruen, D. W. R. J. Phyz. Chem. 1985,89, 146.
(28) Lindman, B.;Stilbs, P.;Walderhaug, H. J . Phys. Chem. 1983, 87, 4762. ( 2 9 ) Chachaty, C.; Chevalier, Y. J . Phys. Chem. 1985,89, 875. (30) Rehfield, S.J. J . Colloid Interface Sci. 1970, 34, 518.
