Langmuir 1994,10,89CF898
890
Molecular Mobility and Order of Didodecyldimethylammonium Chloride Adsorbed on Silica Particles from 2HNuclear Spin Relaxation Erik Soderlind, Mikael Bjorling, and Peter Stilbs' Department of Physical Chemistry, The Royal Institute of Technology, S-100 44 Stockholm, Sweden Received October 21, 1993. I n Final Form: December 22, 1999 Didodecyldimethylammonium chloride (DDAC) was adsorbed onto two different silicas with different particle radii at pH 10. Bulk adsorption studies for Cab-0-Si1M5 suggest that the surfactant forms a complete bilayer on the solid surface, as judged from the observed plateau adsorption level (r = 1.25 mmollg) and the calculated surface density. In order to further elucidate the structure and dynamics of the adsorbed surfactant, 2H NMR studies on selectively labeled DDAC (DDAC-de, deuterium labeled in the nitrogen bound methyls) were undertaken. Spectra and spin relaxation parameters were recorded for the surfactant adsorbed on silica, in reference to those for DDAC-& dispersed in water and in lamellar liquid crystals. These studies reveal that the exchange between the solid surface and solution is slow on the pertinent NMR time scale. For DDAC-~B adsorbed on large particles a quadrupole splitting corresponding to an order parameter of SDF= 0.0156 is clearly visible. Longitudinal (TI) spin relaxation measurements at different temperatures are consistent with a higher degree of motional constraints in the adsorbed state, as compared to the dissolved state. Transverse (2'2) spin relaxation measurements and the observed deuterium bandshapes point to the existence of modes of slow molecular motions. An attempt was made to characterize these slow motions further, by studying the dependence of Ta on the pulse dispersion in the quadrupolar CPMG (Q-CPMG) pulse sequence. The correlation time for slow molecular motions so-obtained suggests that additional modes of slow motions are more important for adsorbed DDAC-de than for aggregates in solution, the most likely candidate being related to motions caused by a mismatch of the preferred structure of the surfactant bilayer and the silica surface.
Introduction The dynamics and organization of aggregated surfactant molecules in micelles, vesicles, or liquid crystals have attracted considerable attention over the past decades, and NMR spectroscopy has proven particularly useful in such studies.lb Recently, those properties of physisorbed surfactants on solid surfaces were also studied by similar techniques. 2H NMR spectroscopy and spin relaxation measurements were utilized to investigate the adsorbate structure and the molecular dynamics of ionic surfactants on alumina,eJ s i l i ~ aand , ~ ~polystyrene ~ latex.1G12 The chain conformations of adsorbed surfactants on both alumina and silica have also been studied by means of 13C chemical shifts.13 In a study of silica-supported phospholipids both 2H and 3lP NMR were utilized in order to study the physical properties of the adsorbate.14J6 The existence of different modes of molecular motions occurring on widely separated time scales has been revealed in several studies, particularly the 2Hand 31PNMRstudies.
* To whom correspondence should be addressed.
* Abstract published in Advance ACS Abstracts, February 15, 1994. (1) Chachaty, C. Mol. Eng. 1992, 2, 65. (2) Chachaty, C. h o g . Nucl. Magn. Reson. Spectrosc. 1987, 19, 183. (3) Lindman, B.; SBderman, 0.;Stilbs, P. In Surfactants in Solution; Mittal, K. L., Ed.; Plenum Press: New York, 1989; Vol. 7, p 1. (4) Halle, B.; Quiet, P.-0.; Fur4 I. Liq. Cryst. 1993, 14, 227. (5) Khan, A. In Nuclear Magnetic Resonance; Webb, G. A., Ed.; The Royal Society of Chemistry: London, 1991; Vol. 20, p 497. (6) Saderlind, E.; Blum, F. D. J. Colloid Interface Sci. 1993,157,172. (7) Sbderlind, E. Langmuir, in press. (8) SBderlind, E.; Stilbs, P. J. Colloid Interface Sci. 1991, 143, 586. (9) Sbderlind, E.; Stilbs, P. Langmuir 1993,9, 2024. (10) Macdonald, P. M.; Yue, Y.; Rydall, J. R. Langmuir 1992,8,164. (11) Yue, Y.; Rydall, J. R.; Macdonald, P. M. Langmuir 1992,8, 390. (12) Kuebler, S. C.; Macdonald, P. M. Langmuir 1992,8, 397. (13) Sbderlind, E.; Stilbs, P. Langmuir 1993, 9, 1678. (14) Bayerl, T. M.; Bloom, M. Biophys. J. 1990,58, 357. (15) Dolainsky, C.; Mtjps, A.; Bayerl, T. M. J. Chem. Phys. 1993,98, 1712.
Fast motions, such as local reorientations of hydrocarbon chain segments or rotation of the entire molecule about its long axis, were found to dominate the longitudinal relaxati~n.~ In addition to those motions, other considerably slower molecular motions dominating the transverse relaxation were recognized where lateral diffusion of the molecules over the curved solid surface, possibly in conjunction with overall particle tumbling, is the most likely origin.gJ4Js However, other motions may affect the relaxation processes. The structure of the adsorbate (surface micelles, bilayer patches, or complete bilayers) also influences the interpretation of the spin relaxation data. In order to avoid the problem with an unknown adsorbate structure, we have here chosen to study the surfactant didodecyldimethylammoniumchloride (DDAC) which we believe forms a complete bilayer when adsorbed on silica particles. The surfactant chosen was 2H labeled in the nitrogen-bound methyl groups and is consequently abbreviated DDAC-de. The phase behavior of DDAC and related double-tailed surfactants in water is kn0wn,16J7but the adsorption of DDAC on silica or any other solid surface has not to our knowledge been studied before. No adsorption isotherms for DDAC on neither of the silica particles in this study are therefore available. However, the isotherms for many other surfactants, including both single and double chained, adsorbed on various solids have been determined showing the common feature that the adsorption levels off to a plateau value at a surfactant concentration in solution close to the critical micelle concentration, cmc.1GD (16) Kunieda, H.; Shinoda, K. J . Phys. Chem. 1978,82, 1710. (17) Kang, C.; Kahn, A. J. Colloid Interface Sci. 1993, 156, 218. (18) (a) Clunie, J. S.; Ingram, B. T. In Adsorption from Solution at
the Solid/LiquidZnterface;Parfitt, G.D., Rochester,C. H., E&.; Academic Press: New York, 1983; p 105. (b) Hough, D. B.; Rendall, H. M. In Adsorption from Solution at the SolidlLiquid Interface; Parfkt, G . D., Rochester, C. H., Eds.; Academic Press: New York, 1983; p 247.
0743-7463/94/2410-0890$04.50/0 0 1994 American Chemical Society
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Spin Relaxation of Adsorbed DDAC-de
At this point the surface is saturated in the sense that
I
further addition of surfactant to the particle suspension Bo does not alter the adsorption. Instead the surfactantforms micelles in the solution. The aim of this study was to characterize the molecular dynamics, in particular the slow motional modes, of DDAC-de when adsorbed to saturation on silica particles. Therefore, the full adsorption isotherm was not determined, only the plateau adsorption level. In this work both 2H NMR spectra and relaxation rate measurements of DDAC-de adsorbed on silica particles are presented. The data are interpreted in terms of molecular dynamics and ordering within the surfactant bilayer on the surface. The surfactant system in this study bears clear resemblance to vesicular systems, both being essentially spherical bilayers. Therefore, we have partly adopted the spin relaxation theory derived for vesicles,3O assuming that the surfactant molecules undergo similar motions. Experimentally, by using the quadrupolar CPMG (Q-CPMG) pulse sequence3l-33 to determine the Figure 1. z-axes of the relevant reference frames of a double effective transverse relaxation rate Rze, we demonstrate tailed surfactant bilayer, defined as the applied magnetic field, Bo,the bilayer normal or director,D, the long axisof the molecule, the presence of slow motional modes, slower than those M, and the direction of the CSH bond, F. for adsorbed single chained surfactants and also surfactants in vesicles. The experiments in question vary the 0 into the angles relating the different frames to each other. interpulse spacing and the %lownmotional correlation time In is deduced through this pulse frequency d i s p e r s i ~ n . ~ ~ ~ ~Figure 1,the z-axes of the relevant reference frames of a lamellar liquid crystal are defined. The laboratory frame is given by the direction of the magnetic field, Bo,the Theory director frame by the bilayer normal or director, D, the Quadrupolar Splittings. Nuclei with spin I 2 1 molecular frame by the long axis of the surfactant molecule, possess a quadrupole moment (eQ) which interacts with M,and the principal frame of the efg tensor by the CAH the local electric field gradient (efg) tensor, perturbing bond vector, F. The obtained splitting for a planar DDACthe nuclear Zeeman energy levels of the system. For d6 bilayer, which is stationary with respect to Bo, is organic compounds the efg tensor originates from the therefore given electrons in the CSH bond and is axially symmetric about the bond axis (7 = 0). Due to the quadrupolar interactions, the 2H NMR spectrum of a rigid system consists of a superposition of doublets separated by36 where a is the angle between D and Bo as shown in Figure 1. SDM and S m are the molecular order parameter with respect to the bilayer normal and the internal order parameter with respect to the surfactant long axis, respectively, defined as the time average where x is the quadrupole coupling constant and 0 the angle between each C-2H bond and the magnetic field Bo. 3 cos28, - 1 The molecules in a liquid crystalline phase are ordered (3) sij = 2 but not static as in normal crystals; i.e., 8 is time-dependent which reduces the observed splitting. For liquid crystals, where eDM is the angle between D and M and Om the angle it is very useful to introduce other reference frames in between M and F. Consequently, the commonly used addition to the laboratory frame, and decompose the angle order parameter SDFcorresponds to the product of SDM and S m
)
(
(19) Ingram, B. T.;Ottewill, R. H. In Cationic Surfactants; Physical Chemistry; Rubingh, D. N., Holland, P. M., Eds.;Marcel Dekker: New York, 1991; p 87. (20) Rupprecht, H.; Gu, T. Colloid Polym. Sei. 1991,269, 506. (21) Somasundaran,P.; Kunjappu, J. T. Colloids Surf. 1989,37,245. (22) Denoyel, R.;Rouquerol,J. J. ColloidInterface Sci. 1991,143,555. (23) Bijsterbosch, B. H. J. Colloid Interface Sei. 1974,47, 186. (24) Wbgnerud, P.; Olofsson, G. J. Colloid Interface Sci. 1992,153,
392. (25) Esumi, K.; Nagahama, T.; Meguro, K. Colloids Surf. 1991, 57, 149. (26) B6hmer, M. R.; Koopal, L. K. Langmuir 1992,8, 2649. (27) Esumi, K.; Sugimura,A,; Yamada, T.;Meguro, K. Colloids Surf. 1992, 62, 249. (28) Carmona-Ribeiro, A. M.; Midmore, B. R. Langmuir 1992,8,801. (29) Eeumi, K.; Yamada, T. Langmuir 1993,9,622. (30) Halle, B. J. Phys. Chem. 1991,95,6724. (31) Bloom, M.; Sternin, E. Biochemistry 1987,26, 2101. (32) Sbhrer, J.; Grabner, G.; Reimer, D.; Weisz, K.; Mayer, C.; Kothe, G. J. Chem. Phys. 1991,95,672. (33) Bloom, M.; Morrison, C.; Sternin, E.; Thewalt, J. L. In Puked Magnetic Resonance: NMR, ESR and Optics-a recognition of E. L. Hahn; Bagguley, D. M. S., Ed.; Clarendon Press: Oxford, 1992; p 274. (34)Blicharski, J. S. Can. J . Phys. 1986, 64, 733. (35) Blicharski, J. S.;Wolak,A. Acta Phys. Polon. A 1991, 79, 591. (36) Seelig, J. Q. Rev. Biophys. 1977,10, 353.
where eDF is the angle between D and F. For a macroscopically unoriented lamellar liquid crystal all angles a are represented, and the obtained 2H NMR resonance is a so-called Pake pattern. The splitting of the two most prominent components or horns in such a resonance is obtained for a = 90°. 3
A ~ Q ( a = 9 0= ~ )4 xSDF
(5)
Spin Relaxation. The longitudinal and transverse relaxation rates of 2H are given by the following general expressions37 (37) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, 1961.
092 Langmuir, Vol. 10, No.3, 1994
R, = Tl = 3?r2 40 x2(2J(wo) + 8J(2w0))
where J(o)is the reduced spectral density function, x the quadrupole coupling constant, and wo the Larmor frequency. Recently, a restricted rotational diffusion model was presented to account for the spin relaxation of phospholipid vesicles,N a system which bears clear similarities with surfactant bilayers on solid particles. According to that model the spin relaxation is due to three separable modes of motion, represented by individual contributions to the spectral density function
Saderlind et al.
3kT +-6Dht (10) 4rR3q R2 where R is the radius of the sphere, q the solvent viscosity, and Dht the lateral diffusion coefficient. Including only the J(0) term and neglecting the contributions from internal motions and rotational diffusion, R2 becomes 1
-e-
Tht
For Lorentzian NMR lineshapes, R2 can be obtained from the line width, but it may also be determined by using the standard CPMG pulse sequence. Alternatively, the quadrupolar CPMG sequence (Q-CPMG)31 may be employed
(go"), - [ T - (m"), - T I n The J h t term describes internal motions such as transgauche isomerization or methyl rotation, which are sufficientlyfast to give a frequency-independentcontribution to the spectraldensityfunction. J,t(w) describesrestricted rotational diffusion of the molecule, Le., the spinning motion of the molecule around the long axis and the restricted tumbling of this axis relative to the bilayer normal. Finally, Jh&) describes lateral diffusion of the molecule over a curved surface and tumbling of the whole bilayer aggregate. As indicated in eq 8, in the megahertz region it is the restricted rotational diffusion, the lateral diffusion, and the reorientation of the vesicle that produce the frequencydependencein the spectral density function. The restricted diffusion is characterizedby the rotational diffusioncoefficientsDHand D I,but accordingto the model there are 13 distinct reorientational modes with individual effective correlation times T,,,,, all on the nanosecond time scale.N Similar approaches were also used by other authors,where the wobbling and spinning motions of the molecule were accounted for in a somewhat simpler model including only two correlation times. Again, correlationtimes in the nanosecond region or shorter were found. The slowest motions of phospholipid vesicles that contribute to the relaxation are the ones described in Jht, with the joint correlation time for the lateral diffusion and the vesicle tumbling, rht, on the microsecond time scale.N*"OSimilar motions, although faster, are also found in micellar surfactant systems.14 In the case of vesicles, the contribution to the longitudinal relaxation, R1, from those motions is negligible at frequencies YO > 10 MHz,~O whereas the transverse relaxation is entirely dominated by them. This is due to the J(0) term in eq 7 and is manifested in the large magnitude of R2 (Rz>> R I ) . It can be shown that the spectral density function, Jlat(o),is Lorentzian
where SDF is completely analogous to the order parameter defined in eq 4. For spherical aggregates the correlation time is given by (38)Pastor, R. W.: Venable, R. M.:. K a _r ~ l.M.: ~ ..Szabo. A. J. Chem. Phys. .1988,89, 1128.. (39) Lepore,L. S.; Ellena,J. F.;Cafiio, D. S. Biophys. J. 1992,61,767. (40) Ellena, J. F.; Lepore, L. S.; Cafiiso, D. S.J. Phys. Chem. 1993,97,
2952.
This pulse sequence gives echoes at times n(27 + ~(90")), where ~ ( 9 0is~the ) length of the 90° pulse and n = 1,2, ...,N. The effective relaxation rate, Rh, is then evaluated from the signal decay. If there exists a mode of very slow molecular motions with a motional correlationtime, T ~on, the same order as the pulse spacing, T , the obtained R h becomes dependent.^'^^ Provided this motion is described by a Lorentzian spectral density function, R k will be given by3493s 2
R , = R2 - AM2
$tanh
where A M 2 is the change of the second moment of the 2H resonance due to motional narrowing. Typically,the pulse spacingis kept above 20 ps,which is normally much longer than the slow motion correlation time for surfactant aggregates (T >> T ~ ) .Consequently,for micelles and small vesicles, Rze = R2. On the other hand, if sufficiently slow motions indeed are present and attributed to lateral diffusion and particle tumbling ( T ~= Tht), then
Experimental Section Materiale. Didodecylamine waa purchased from ICN Biomedicals, Inc. (Cosa Mesa, CAI, C2HJ from Aldrich Chemie (Steinheim,Germany), and Dowex 1 anion exchange resin from Sigma Chemical Co. (St. Louis,MO). All reagenta were of beet quality available and were used as received. Didodecyldi[W& methylammonium chloride (DDAC-de) was synthesized from didodecylamine and C2HJaccordingto the method proposed by Cope et al.'I using NaOH aa base. The product, didodecyldimethylammoniumiodide,was transformedintothe corresponding hydroxide by ion exchange, and then further to the chloride or bromide by neutralizationwith HC1or HBr. The desired product was dried and recrystallized from acetone. 2H-depleted water, obtained from IC Chemikalien GmbH (Ismaning, Germany), waa wed throughout all experimenta. Nonporous silica of two different particle sizes was used. Silica particles with a radius of R = 320 f 20 nm were from the same source as in previous studies" and were kindly provided by Dr. T. M. Bayerl,Technieche UnivereiW. Miinchen, Germany. The other silicawas Cab-0-Si1grade MS obtainedfrom Fluka Chemie AG (Buchs, Switzerland) with a specific surface area of 200 m2/g according to the manufacturer's specification. The silica was placed under vacuum at room temperature for several hours, to remove excess water. (41) Cope,A. C.; Ciganek, E.;Fleckenatein, L. J.; Meieinger, M.A. P. J. Am. Chem. SOC.1960,82,4651.
Spin Relaxation of Adsorbed DDAC-de Methods. The adsorption sample was prepared by weighing an appropriate amount of silica particles and water (approximately 2% silica) into a screw-capped centrifugation tube. In order to obtain maximum adsorption level, the pH was adjusted to 10 with NaOH. The surfactant was weighed into the tube, which was slowly rotated at 65 O C for 6 h in order to dissolve the Surfactant. The temperature was then gradually decreasedto 25 "Cand the samplewas equilibratedatthis temperature for several days. The suspension was centrifuged at 5700 rpm and excess supernatant was removed for surfactant concentrationanalysis. The relatively denseparticle/water sedimentwas then transferred into a 10-mm NMR tube, which was sealed. The equilibriumconcentration of DDAC-dein the supernatant was determined spectrophotometrically(ShimadzuW-110-02) according to the method by Few et al.& In the Cab-0-Si1silica sample,the obtained DDAC concentrationwas 0.20mM and the corresponding amount adsorbed was r = 1.25 mmol/g. *The bluish-white dispersion of liquid crystals that appears at higher surfactant concentration is very stable with respect to centrifugation.'* However, the supernatant was clear, indicating that no or only very small amounts of liquid crystalline surfactant waspresent in the sample. The melting point of hydrated DDAC is reported to be 26 OC;le hence the solution may be slightly supercooled. The other silica sample was prepared similarly, but with excess surfactant to ensure that the solid surface was saturated. The obtained DDAC-de concentration was in this sample 1.9 mM. An additional NMR sample of 5 wt % DDACde in water, which is above the thermodynamic solubility limit, was also prepared. In order to produce vesicles the solution was sonicated, and a clear solution was obtained. However, after some time the solution became turbid, indicating the presence of larger aggregates such as large vesicles of poesibly dispersed lamellar liquid crystale. The obtained dispersion was stable for several days even when subjected to mild centrifugation (5700 rpm). Lamellar liquid crystalline samples of DDAC-de and DDABde (the corresponding bromide) were prepared by weighing appropriate amounts of surfactant and water into glaae tubes, which were flame sealed. The DDAC-de content was 44 w t % , which is within the relatively wide lamellar phase region,'&' whereas the DDAB-de content was 90 wt % Corresponding to the Lam2phase." The sampleswere heated to 100OC and thereafter slowly cooled to 28 OC (DDAC-de) or 55 "C (DDAB-da). The temperature was elevated in order to avoid surfactant precipitation and, in the caseof DDAB-4, to producea clear quadrupole splitting in the 2H NMR spectrum. 2H NMR spectra were recorded at 30.72 MHz on a Bruker MSL 200/90spectrometer. Longitudinal relaxation times, TI, weremeasured by the standard inversionrecovery pulse sequence, and in the case of transverse relaxation times, Ts,both the standard CPMGand the Q-CPMGsequences(seetheorysection) were employed. In order to suppress the narrow resonance in the spectrum of the adsorption sample, an initial 180" pulse was applied to invert the spins. After a delay, which was sufficiently long to recover most of the magnetization corresponding to the broad component but short enough to suppress the relative intensity ofthe narrowcomponent (typically55ms),theQ-CPMG sequencewas applied. The spin relaxation measurements were performed only for the DDAC-d$Cab-0-Sil M5 system, since the signals from the other sample with larger particles were very weak. The relaxation data were evaluatedby fitting appropriate functions to the data in a nonlinear least-squares procedure as described in ref 44. The 90° pulse length was typically 10ps, the recycle delay 3-5 TI, and the pulse spacing in the Q-CPMG sequence 25-120 pa. The temperature was kept at 25 "C throughout all NMR experimenta except for the liquid crystals (28or 50 O C ) and the dispersed DDAC-& sample (28OC). Bandshape Calculations. In order to correctly account for molecular motions occurring on an intermediate time scale, the bandshape simulations are based on the stochastic Liouville (42)Few, A. V.; Ottewill, R. H. J. Colloid Sci. 1966, 1 1 , 34. (43)Fontell,K.;Cee~e,A.;Lindman,B.;Ninham,B.ActaChem.Scand. 1986,A40, 247. (44)Walderhaug, H.; StMerman, 0.; Stilbs,P. J. Phys. Chem. 1984,88, 1666.
Laugmuir, Vol. 10,No. 3,1994 893
equation for the time evolution of the density operator.- The physical model for the calculations is simii to that described above (see theory section). Further detaile regarding the calculations are given elsewhere.' The parameter set of this model includesthe following parameters: EO,the magneticfield; x , the quadrupole coupling constank S, the order parameter; T,, the correlation time for the isotropic motions that averages the quadrupole coupling; and R,, the residual line broadening due to fast internal motions. The magnetic field was fiied at BO= 4.7 T, the quadrupole coupling constant x = 181 ~ H Z and, the ~ residual line broadening R, = 20 Hz. Only S and 7, were varied to get the best fit to the experimental bandshapea. The bandahape simulation program was kindly provided by Dr. E. Berggren,University of Bologna, Italy. It is written in Fortran, and was run on VAX/VMS workstations.
Results and Discussion The equilibrium concentration in solution of DDAC-de obtained in the adsorption experiment was [DDAC-del= 0.20 mM, which is well below the solubility limit of this surfactant at room temperature, 14-17 mM.lsJ7 However, it is very close to the reported critical micelle concentration, 0.17 mM for DDAW or 0.16 mM for the corresponding bromide (DDAB).61 The obtained amount of surfactant adsorbed onto the silica surface was r = 1.25 mmol/g, which may also be expressed as r = 6.25pmol/m2provided the entire BET area (200m2/g)is available for surfactant adsorption. This value is close to or somewhat larger than the obtained adsorption plateau values for the single-chain CIZ-,CIC,and C l ~ - ~ l t r i m e t h y l a " O n i ~bromides m on the same surface under similar conditions.g*Ba Furthermore, the adsorption plateau level of dioctadecyldimethylammonium chloride (DODAC) on a porous silica .~~ charged polystyrene was I' = 1.1 ~ I I I O U ~On~ negatively particles the plateau values for DODAC and DODAB (the corresponding bromide) were r = 5.8 pmol/m2and I' = 6.6 pmol/m2, respectively.28 Thus, it is reasonably safe to conclude that the adsorption level of DDAC-de in this study corresponds to the adsorption plateau level. The average area occupied per DDAC-de molecule on the saturated silica surface calculated from r and the BET area was A = 26.6 A2. Note that this average molecule area is calculated regardless of the true adsorbate structure, i.e., A = l/(r"d.The area per DDAC molecule may be compared with the cross-sectional area per hydrocarbon chain of DDAB in the lamellar liquid crystalline phases. DDAB forms two different lamellar phases with water, Lam1 and lam^,^ and the respective cross-sectionalareas are 34 and 30 A2per hydrocarbon chain as determined by X-ray diffraction. From the corresponding DODAC and DODAB average areas on polystyrene particles, 28.6 and 25.2 A2,it was concluded that those surfactants form complete bilayers on the solid particles.n These data strongly suggest that DDAC-de also forms a complete bilayer on the silica particles when adsorbed to the saturation level. This is in fact the general observation for ionic double chained surfactants adsorbed on oppositely charged solid s u r f a c e ~ . ~ J ~ JThus, ~ f l - ~due to the spherical shape of the silica particles a curved surfactant bilayer with a radius of curvature determined by the particle radius is obtained. This geometry of the surfactant aggregates clearly resembles the geometry of surfactant vesicles. (45)Kubo, R. J. Math. Phys. 1963,4,174. (46)Freed, J. H.; Bruno, G.V.; P o h z e k , C. F. J.Phys. Chem.1971, 76, 3386. (47)Lynden-Bell, R. M.Mol. Phys. 1971,22,857. (48)Baram, A.;Luz, Z.;Alexander, S.J. Chem. Phys. 1973,68,4658. (49)Berggren, E.Theet, University of Stockholm, Sweden, 1991. (60)Sdderman, 0. J. Magn. Reson. 1986,68,296. (61)"heher, C.;Makayw.i, A. Langmir 1992,8,794.
894 Langmuir, Vol. 10, No.3, 1994
Saderlind et al.
a
a
b
4.00
-3.00
0.00 kHz
3.00
6.00
Figure 2. *HNMR spectra of the unoriented lamellar liquid crystalline phases of (a) DDAC-de recorded at 28 "C and (b) DDAB-de recorded at 60 O C . The temperature was elevated in order to avoid surfactantprecipitation and, in the case of DDAB, to produce a clear quadrupole splitting.
Consequently, the comparison with vesicles and the spin relaxation theory derived for such systems30 is indeed relevant. Figure 2 shows the 2H NMR spectra of the lamellar phases of DDAC-ds (a) and DDAB-ds (b). Both spectra were recorded for unoriented liquid crystals and consist of resonances with clear quadrupole splittings, AvQ(~O"), defined as the peak-to-peak separation. Such splittings appear when the quadrupolar interactions are not completely averaged out by isotropic molecular motions. From the splittings we may directly determine the order parameter, SDF= SDMSMF, using eq 5. Several values of the quadrupole coupling constant, x,have been proposed (167-181kHz); here we used x = 181kHz.60 The recorded quadrupole splittings were 1653 Hz (44% DDAC-d6, 28 "C)and 1728Hz (90%DDAB-de, 50OC),which correspond to the order parameters (disregarding the sign), SDF= 0.0122and 0.0127. These two phases were investigated in order to clarify how the packing of the surfactant molecules in each surfactant layer influences the order parameter. Although each headgroup of the DDAB-de in the Lam2 phase occupies a smaller area in average, we find that SDF is not muchdifferent from that of DDAC-d6 in the lamellar liquid crystal. This conforms with the general finding that the order parameter is independent of surfactant aggregate structure.14 The values obtained here may appear small but are not unexpected since the angle between M and the C-N bond in Figure 1is close to the "magic angle", 5 4 . 7 O . This, in combination with the rapid rotation of the methyl groups, produces a very small value of the internal order parameter, Sm. Figure 3 compares the 2H NMR spectra of DDAC-de adsorbed on silica particles of two different sizes. The uppermost spectrum (a), which was obtained for DDACd13adsorbed on the smaller silica particles Cab-0-Si1 M5
I
4.00
I
-2.00
I
1
0.W
2.00
I
4.00
-
kHz
Figure 3. aH NMR spectra of DDAC-de adsorbed on (a) small silica particles (Cab-0-Sil,R 7 nm) and (b) large particles (R = 320 nm). Inserted is the spectrum of dispersed DDAC-de in water above ita solubility limit under similar conditions of measurement.
(I' = 1.25mmol/g),consistsof asuperpositionofonenarrow resonance upon a broad unsplit resonance. Similarly, the lower spectrum of DDAC-ds on the larger particles (b) also consists of two superposing resonances. However, the broad component is in this case clearly split. Resembling spectra with two or more superposed resonances have been observed previously in aqueous particle/ surfactant dispersions.&12 Based on such spectra, the existence of different molecular domains in which the surfactant moleculescan reside and the chemical exchange rate between those domains were discussed exten~ively.~ In our case, the narrow resonances clearly originate from dissolved DDAC-ds, while the broad components of the spectra originate from adsorbed DDAC-de. This conclusion is also confirmed by the NMR spectrum of a 5 w t % DDACd6 dispersion in water which is inserted in Figure 3a for comparison. Clearly, dissolved or dispersed DDACde gives rise to resonances much sharper than the adsorbate resonances. Furthermore, the chemical exchange rate is, as expected, slow between the surface and the s o l ~ t i o n . ~ Otherwise the spectrum would consist of the populationweighted time average of the two resonances. In principle, the bilayer adsorbate consists of two domains with different radii of curvature and surfactant orientation, the inner layer with the surfactant headgroups pointing toward the solid surface and the outer layer with surfactants in the opposite orientation. For Cl2- and C16-akyltrimethylammonium bromides adsorbed on silica, those two domains have been shown to be indistinguishable by means of 2H NMR spectroscopy.9 For bilayer vesicles a similar situation arises, but it was shown that even if the local ordering is slightly different in the two layers, the observed 2H NMR resonance will not appear appreciably non-lorent-
Langmuir, Vol. 10, No. 3, 1994 895
Spin Relaxation of Adsorbed DDAC-de
-5000
0
so00
Figure 4. Experimental (left) and calculated (right) spectra of DDACl.de adsorbed on silica particles with R = 320 nm. At the top the spectra have been enlargedin order to more clearlydieplay the broad features.
zianegoHence, the broad components of the spectra in Figure 3 also consist of two superposing indistinguishable resonances originating from the two layers of the bilayer. It should also be noted here that the spectra were recorded with too short delays between each scan to allow full longitudinal relaxation of the dissolved molecules. Consequently, the relative intensities of the two components do not reflect the distribution of surfactant molecules between the adsorbate and the solution. In the case of small silica particles (Figure 3a) a Lorentzian bandshape fits well to the broad resonance, whereas for large silica particles (Figure 3b) the broad component resembles a Pake pattern. As indicated in eq 10, the correlation time for the isotropic slow motions increases with increasing surfactant aggregate radius. For sufficiently large aggregate radii the lateral motions of the surfactant molecules become too slow to completely average out the residual anisotropy, and the recorded 2H NMR resonance becomes split. This is indeed the case for the DDAC-de bilayer adsorbed on the large particles, whose radii are approximately R = 320 nm. The resemblance of the lower spectrum in Figure 3 to those of the lamellar phases (Figure 2) indicates that the ordering of the surfactants is similar in the two different in Figure states. From the quadrupole splitting, AVQ(SO~), 3b we may again obtain a value of the order parameter. Using this approach, we arrive at S = 0.009. However, in contrast to the spectra of lamellar phases, the true order parameter does not result from the evaluation, but rather a value that is too small. A closer inspection of the broad features of the spectrum in Figure 3b implies that the slow motions are not in the static regime despite the large particle radius. The effect of such motions is that the residual anisotropy becomes partly averaged. Accordingly, the observed splitting becomes smaller than that predicted from eq 5. To overcome this problem and obtain the true order parameter, we performed a bandshape simulation in which the slow motions were accounted f0r.~0Figure 4 shows the result from a simulation of the bandshape in Figure 3b. In the calculation of the Pake pattern only two parameters were varied, the order parameter and the correlation time for the slow motions, and the best fit to the experimental spectrum was obtained for SDF= 0.0156
f 0.0002 and rn= 1050 f 50 ps. To the so-obtained split component a Lorentzian resonance, centered at YO = -20 Hz and Av1p = 65 Hz, was added. The order parameter is as expected close to that obtained for lamellar liquid crystals, althoughsomewhatlarger. This relatively small variation is significant but not unusual for surfactant molecules in different aggregate structures. However, this result contrasts to those for the anionic surfactants SHBS (sodium 4-(l'-heptylnonyl)benzenesulfonate) and SDS (sodium dodecyl sulfate) adsorbed on alumina, for which the order parameters were slightly smaller than in other aggregates.6~~In the top spectra in Figure 4it is seen that the experimental spectrum is slightly broader at the "foot" of the split component than the calculatedspectrum. It proved impossible with the preaent program to simultaneously obtain a correct splitting and a correct lower part of the resonance. This could indicate that the broad component consists of two or more overlapping resonances with slightlydifferent bandshapes. Such difference may be hue to different order parameters but is more likely an effect of the distribution of slow motion correlation times produced by the particle size distribution. If the slow motions responsible for the averaging of the residual anisotropy are entirely attributed to the lateral motions over a spherical surface, then eq 10 is applicable for estimating the lateral diffusion coefficient of DDAC on silica particles. For spheres with a mean radius R = 320 nm, the correlation time associated with particle tumbling in water is rt = 30 ms at 298 K. This is probably an underestimation for the present system, since the viscosity in the particle/water suspension is likely to be higher than in pure water. The bilayer thickness has also been neglected. In any case, the particle tumbling influences the total correlation time only to a very small extent. Using rt = 30 ms and rn= a t = 1050ps,we obtain Dkt = 1.6 X 10-1l m2/s. The lateral diffusion coefficient for DDAC has not to our knowledge previously been determined,but severalvalues for phospholipidshave been proposed. For liquid crystalline systems values between D u = (0.1-2) X 10-11 m2/s have been reported,m*62while recent studies have suggested that the lateral diffusion in vesicles is slightly faster, Dkt = (10-20) X 10-11 m2/s.N For spherical supported phospholipid vesicles on the same silica as used in the present work, 31P bandshape calculations using Dkt = 0.4 X 10-11 m2/s gave good agreement with experimental spectra. Finally, the lateral diffusion of the single-tailed Surfactant DoTAC (dodecyltrimethylammonium chloride) in the cubic liquid crystalline phase was determined to Dkt = 0.8 X 10-l1 m2/sam In the perspective of thwe data, the diffusion coefficient estimated here does not appear unreasonable. It should be stressed that if other motions than the lateral diffusion and particle tumbling contribute significantly to the averagingof the quadrupolecoupling, then these equations no longer hold and the diffusion coefficient may be very different. There are, however, no immediate indications that this should be the case for DDAC bilayers on large silicaparticles. In order to determine Dktmore accurately, further studies of the lateral diffusion of surfadants on solid surfacesare currently under progress using the pulsed field gradient technique. To further investigatethe dynamicalaspecta of adsorbed surfactants, spin relaxation measurements of DDAC-de on the smaller silica, Cab-0-Si1M5,were performed. Figure (52) Kuo, A,-L.; Wade, C . G . Biochemistry 1979,18,2300. (63) E r i n , P.0.;Khan, A.; Lmdblom, G. J. Phys. Chem. 1982,86,
387.
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Figure 6. Arrhenius plot of the temperature dependence of TI of DDAC-de adsorbed on Cab-O-Siland in a 5 w t 7% dispersion in water. 5 shows the temperature dependence of the longitudinal relaxation time (TI)of adsorbed and dispersed DDAC-de, respectively. The data were collected between 25 and 42 OC, and the TIfor adsorbed DDAC-de increased from 13.9 to 17.8 ms over that range. For dispersed DDAC-de, probably in the form of large vesicles, the TI increased from 18.5 to 27.1 ms. At 25 OC, the observed TI of the narrow component in the spectrum in Figure 3a was around 340 me, and for nonaggregated DDAC-de in solution ([DDAC-de] < 0.2 mM) it was 510 ms. Evidently, the longitudinal relaxation rate (UTI)increases quite dramatically when the surfactant is adsorbed on the solid surface or aggregated in solution. This increase in relaxation rate indicates as expected that aggregated or adsorbed molecules undergo more restricted motions than free molecules. The large differencein TIbetween the narrow and broad resonances in the spectrum in Figure 3a again shows that the narrow component orginates from dissolved nonaggregated surfactant molecules. The shorter 21' of this resonance as compared to the TIof nonaggregated DDACde can be explained by the additional presence of small DDAC-c&aggregatesin the adsorption supernatant. Since the aggregation of free molecules in solution commences around 0.17 mM, a small fraction of the dissolved DDACde molecules will be aggregated at a total concentration of 0.2 mM and the observed TI averaged accordingly. From the linear relationships in Figure 5 it is possible to calculate the apparent activation energy, EA,for the motions that contribute to the relaxation. For adsorbed DDAC-c&11.3kJ/mol and for the dispersed DDAC-de 17.7 kJ/mol were obtained. The physical relevance of these apparent activation energies could however be questioned. For vesicles, it has been shown that several modes of motions may contribute to the longitudinal relaxation even at high magnetic fields.mtPrimarily fast motions, Le., internal motions, such as methyl rotation, spinning of the molecule around its long axis and also tumbling of the molecule with respect to the bilayer normal contribute to TI. Therefore, the apparent activation energies are not associated with any particular motional mode but with several. In any case, the temperature dependence of the TIindicates that the motions that govern the TIrelaxation probably fall in the extreme narrowing regime. This statement may be questionable for adsorbed DDAC-de since the temperature dependence is relatively weak, but
it is probably true for the DDAC-de dispersion. It has also previously been shown that the methyl rotation and the spinning of the molecule indeed fall within the extreme narrowing limit.m*Obviously, the TIrelaxation data are very useful when comparing the fast motions of dispersed and adsorbed DDAC-de. Both for aggregated and adsorbed surfactant, the TI decreases substantially. The decrease of TI that occursupon aggregation in solution or adsorption on solids, respectively, is close to equal, implying that similar constraints are put on the fast motions. However, the TI of adsorbed molecules is slightly shorter than for dispersed molecules, indicating that the fast motional modes contribute differently to the relaxation in the two states. This is also manifested in the apparent activation energies, which differ significantly. Both the shorter TI and the weak temperature dependence of TIof adsorbed DDACde suggest a larger contribution from slower motions to the longitudinal relaxation. This may be due to the presence of different motional modes but is more likely due to slightly different motional rates. The rotational rate of the methyl groups is probably equal for both states. Thus, it is the rotational diffusion,i.e., the spinning of the molecule around its long axis and the wobbling motions of the surfactant with respect to the local normal, that differs. Consequently, one may expect slightly different rotational diffusion coefficients,D#and DL,for dispersed and adsorbed DDAC-de. Alternatively, a different influence on TI of the lateral diffusion of the surfactant molecules may also provide an explanationto the observed dissimilarities. However, it has previously been shown for vesicles that the contribution of the lateral diffusion and the overall aggregate tumbling to the longitudinal relaxation is negligible at high Larmor frequencies.mThis is most likely the case also for the present system, why different rotational diffusion rates appear as a more probable explanation to the observed TI difference. To further elucidate this problem, multifield relaxation data would be useful. Unfortunately, such data are presently not available. Analysis of the transverse (T2) relaxation data shows that additional modes of slow motion contribute to the relaxation. Assuming a Lorentzian bandshape of the broad yomponent in Figure 3a, a T2 of 482 ps is obtained from ' 2 implyingthat the adsorbed the linewidth. Clearly, T2
