J. Phys. Chem. 1990, 94,113-116
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Carbon-13 NMR Relaxation Study of Molecular Dynamics and Organization of Sodium Poly(styrenesu1fonate) and Dodecyltrimethylammonium Bromide Aggregates in Aqueous Solution Zhisheng Gao, Roderick E. Wasylishen, and Jan C. T. Kwak* Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 453 (Received: February 8, 1989; In Final Form: July 7, 1989)
Aqueous solutions of aggregates of sodium poly(styrenesu1fonate) (PSS) and dodecyltrimethylammonium bromide (DTAB) have been studied by "C NMR relaxation measurements at 8.48 T. The relaxation data are interpreted by use of a "two-step" model. Correlation times for fast motion and order parameters have been calculated as a function of carbon position on the alkyl chain of DTAB in the PSS-DTAB aggregates. A micellar solution of DTAB is also studied for comparison. Slightly larger order parameters are observed for the surfactant alkyl chain (except the last three carbons C10, C11, and C12) in the PSS-DTAB aggregates compared with those in DTAB micelles. On the other hand, for the carbons near the headgroup of DTAB, the correlation times for fast motion in the PSS-DTAB aggregates are much longer than those in the DTAB micelles.
Introduction Interactions between poly(styrenesu1fonate) (PSS) and dodecyltrimethylammonium bromide (DTAB) have been investigated by surfactant-selective electrodes,'V2 fluorescence probe^,^ and proton N M R ~pectroscopy.~It has been shown that a combination of electrostatic and hydrophobic interactions is involved in the formation of the polymer-surfactant aggregates. Proton N M R ring current shifts indicate that the surfactant alkyl chains are located near the aromatic groups in PSS4 A complete understanding of this and other polymersurfactant systems requires further knowledge about the internal motion of surfactant and polymer in the aggregates. In recent years a number of investigations on the molecular dynamics and structural organization of micelles,s-" macromolecules,12-16and bi~membranes".'~have been reported using NMR relaxation methods. For macromolecular alkyl chains and surfactant alkyl chains in micelles the 13Cspin-lattice relaxation times are usually frequency dependent, leading to nuclear Overhauser factors that are less than their maximum value. This observation indicates that the alkyl chain motion is not a simple internal motion but is a combination of motions. In the case of surfactant systems, a "two-step" model has been suggested where the motion of the alkyl chains consists of a "fast" internal mode due to gauchetrans interconversion, torsions, and librations and a i low" motion which is ascribed to tumbling of the whole aggregate and/or diffusion of surfactant monomers over the micelle surface.610 The same interpretation is applied to macromolecular systems in Lipari and Szabo's "model free a p p r o a ~ h " . ' ~In J ~this model the motion of a spherical macromolecule is described by an effective internal motion correlation time and a slow motion correlation time for overall isotropic motion. For macromolecules whose shapes deviate considerably from that of a sphere, or for systems where the notion of "macromolecular shape" loses meaning because the polymers are in the random-coil conformation, the overall motion (or slow motion) may be described by two correlation time^.'^.'^ Two correlation times are also used to describe the slow motions of rod-shaped micelles.8 In this paper, we present the first investigation of molecular dynamics in a polymer-surfactant system. We have studied the PSS-DTAB system by means of I3C relaxation measurements, Le., spin-lattice relaxation times ( T I )and nuclear Overhauser enhancements (NOE). The relaxation measurements were performed at a single field strength of 8.48 T (90.8 MHz). We have analyzed the relaxation data by means of a "two-step" model, using the literature values in a related system to describe the rate of slow motion."J5 In order to compare the results with those for *To whom correspondence should be addressed.
0022-3654/90/2094-0113$02.50/0
a DATB micellar system, we have also determined the spin-lattice relaxation times and NOE's of DTAB in the absence of polymer.
Theory The carbon-13 nuclei of alkyl chains are relaxed almost exclusively by the 'H, 13Cdipolar interactions with directly bonded protons. The spin-lattice relaxation time and nuclear Overhauser enhancement (NOE) are given by'4,15J9 TI-' = ( / . ~ ~ / 4 1 r ) ~ ( N x/4)
where N is the number of directly bonded protons, yHand y c are the proton and carbon magnetogyric ratios, h is Planck's constant divided by 21r, and wH and wc are Larmor frequencies (in rad s-I) for 'H and I3C, respectively. R is the effective C-H bond distance and is taken to be 1.11 %.I4 According to the two-step model the spectral densities in (1) (1) Hayakawa, K.; Kwak, J. C. t. J. Phys. Chem. 1982.86, 3866. (2) Hayakawa, K.; Kwak, J. C. T. J . Phys. Chem. 1983,87, 506. (3) Abuin, E. B.; Scaiano, J. C. J . Am. Chem. Soc. 1984, 106, 6274. (4) Gao, Z.; Kwak, J. C. T.; Wasylishen, R. E. J. Colloid Interface Sci. 1988, 126, 371. ( 5 ) Canet, D.; Brondeau, J.; Nery, H.; Marchal, J. P. Chem. Phys. Lett. 1980, 72, 184. (6) Wennerstrom, H.; Lindman, B.; Soderman, 0.;Drakenberg, T.; Rosenholm, B. J. Am. Chem. Soc. 1979, 101, 6860. (7) Walderhaug, H.; Soderman, 0.;Stilbs, P. J . Phys. Chem. 1984, 88, 1655. (8) Soderman, 0.;Walderhaug, H.; Henriksson, U.; Stilbs, P. J . Phys. Chem. 1985, 89, 3693. (9) Ellena, J . F.; Dominey, R. N.; Cafiso, D. S . J. Phys. Chem. 1987,91, 131. (10) Soderman, 0.;Henriksson, U.; Olsson, U. J . Phys. Chem. 1987, 91, 116. (1 1) Belmajdoub,A,; Elbayed, K.; Brondeau, J.; Canet, D.; Riw, I.; Lattes, A. J . Phys. Chem. 1988, 92, 3569. (12) Yasukawa, T.; Ghesquiere, D.; Chachaty, C. Chem. Phys. Lett. 1977, 45, 279. (13) Ghesquiere, D.; Chachaty, C.; Tsutsumi, A. Macromolecules 1979, 12, 775. (14) Lipari, G.; Szabo. A. J. Am. Chem. Soc. 1982, 104,4546. (15) Lipari, G.; Szabo, A. J. Am. Chem. SOC.1982, 104, 4559. (16) Kitamaru, R. In Applications of N M R Spectroscopy to Problems in
Stereochemistry and Conformational Analysis; Kakeuchi, Y.,Marchand, A. P., Eds.; VCH: Deerfield Beach, FL, 1986; p 75. (17) Brown, M. F.; Williams, G. D. J. Biochem. Biophys. Methods 1985, 11, 71. (18) Brown, M. F. J. Chem. Phys. 1984,80, 2832. (19) Doddrell, D.; Glushko, V.;Allerhand, A. J. Chem. Phys. 1972, 56, 3683.
0 1990 American Chemical Society
774 The Journal of Physical Chemistry, Vol. 94, No. 2, 1990 and (2) are given as a sum involving #(o) and P(w) J ( w ) = (1 - S 2 ) # ( w )
+ Szsl(w)
(3)
where S is an order parameter (vide infra). If the fast and slow motions are described by single-exponential correlation functions, the spectral densities, f ( w ) and P(w), are well described by Jf*s((w)
= (2/5)
-
'C
1
+
f.s
(W7,IS)Z
(4)
Therefore (3) becomes
where 7,' and 7," are the correlation times for the fast local motion in the alkyl chain and the slow overall motion, respectively. When the fast motion is in the extreme narrowing limit, ( W T , ? ~
