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Molecular Dynamics in Dilute Aqueous Solutions of Ethyl(hydroxyethyl)cellulose and Sodium Dodecyl Sulfate As Investigated by Proton NMR Relaxation Hans Evertsson,*,† Stefan Nilsson,† Christopher J. Welch,‡ and Lars-Olof Sundelo¨f† Physical and Organic Pharmaceutical Chemistry, Uppsala University, Uppsala Biomedical Centre, Box 574, S-751 23 Uppsala, Sweden Received April 14, 1998. In Final Form: August 24, 1998 Dilute aqueous solutions of ethyl(hydroxyethyl)cellulose (EHEC) and sodium dodecyl sulfate (SDS) have been investigated by 1H NMR shift and relaxation measurements. The shift measurements indicate no presence of EHEC at the core of the SDS micelles but at and just inside the micellar surface. Both the spin-lattice relaxation time (T1) and the spin-spin relaxation time (T2) imply that molecular motions slow as the system aggregates. T1 measured at both 270 and 400 MHz indicates nonextreme narrowing conditions with molecular motions on the nanosecond time scale. T2 monitors slower dynamics of the EHEC/SDS/ water as compared to both of the systems polyethylene oxide (PEO)/SDS/water and SDS/water, attributed to the rigid EHEC backbone as compared to the more flexible PEO chain. An important observation is that the NMR relaxation data correlate well with the microviscosity in the EHEC/SDS/water system as measured by intramolecular excimer formation of the fluorescent probe 1,3-di(1-pyrenyl)propane (P3P).
Introduction Aqueous polymer-surfactant systems are of great importance in industrial applications such as enhanced oil recovery, detergency, and pharmaceutics due to their amphiphilic aggregation behavior and delicate rheological characteristics. Good reviews1,2 cover the research area, and today a quite detailed description of polymersurfactant interaction in water exists. In the case of nonionic polymer-ionic surfactant systems, a surfactant concentration (here denoted c1) describing the onset of polymer-surfactant interaction is typically reached by increasing the surfactant concentration while keeping the polymer concentration constant. Further increase of the surfactant concentration leads to adsorptive interaction of surfactant with the polymer giving rise to mixed polymer/surfactant micelles, and eventually the polymer becomes saturated with surfactant and free micelles are formed in the system as well. In this laboratory a number of investigations3-13 have been carried out on dilute aqueous solutions of nonionic cellulose ethers and the anionic surfactant sodium dodecyl sulfate (SDS). In particular, the system ethyl(hydroxyethyl)cellulose (EHEC) † ‡
Physical Pharmaceutical Chemistry. Organic Pharmaceutical Chemistry.
(1) Goddard, E. D. Colloids Surf. 1986, 19, 255. (2) Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993. (3) Holmberg, C.; Nilsson, S.; Singh, S. K.; Sundelo¨f, L.-O. J. Phys. Chem. 1992, 96, 871. (4) Nilsson, S.; Holmberg, C.; Sundelo¨f, L.-O. Colloid Polym. Sci. 1994, 272, 338. (5) Nilsson, S.; Holmberg, C.; Sundelo¨f, L.-O. Colloid Polym. Sci. 1995, 273, 83. (6) Nilsson, S. Macromolecules 1995, 28, 7837. (7) Holmberg, C.; Sundelo¨f, L.-O. Langmuir 1996, 12, 883. (8) Holmberg, C. Colloid Polym. Sci. 1996, 274, 836. (9) Holmberg, C.; Nilsson, S.; Sundelo¨f, L.-O. Langmuir 1997, 13, 1392. (10) Evertsson, H.; Nilsson, S.; Holmberg, C.; Sundelo¨f, L.-O. Langmuir 1996, 12, 5781. (11) Evertsson, H.; Nilsson, S. Macromolecules 1997, 30, 2377. (12) Evertsson, H.; Holmberg, C. Colloid Polym. Sci. 1997, 275, 830. (13) Evertsson, H.; Nilsson, S. Carbohydr. Polym. 1998, 35, 135.
fraction CST-103/SDS/water has been thoroughly studied by means of viscometry, equilibrium dialysis, conductometry, dye solubilization, and fluorescence spectroscopy, and a fairly detailed picture has emerged. Some of these studies have addressed the important problem of time dependencies prior to the establishment of a time equilibrium situation. Immediately following c1 a maximum both in bulk viscosity and microviscosity follows, corresponding to EHEC-dominated mixed micelles. At higher SDS concentrations the EHEC content of the mixed micelles decreases, and so does the bulk and microviscosity as the mixed micelles become dominated by SDS. This model is in accord with the findings by Piculell et al.14 who studied a similar EHEC/SDS/water system in the semidilute concentration regime with respect to the polymer by means of bulk viscosity and NMR self-diffusion. NMR is a powerful spectroscopic tool for the investigation of isotropic surfactant and polymer-surfactant systems15-17 capable of yielding both static information such as chemical shift data for determination of, e.g., c1, and dynamic information through NMR self-diffusion and NMR relaxation describing transverse and rotational diffusion, respectively. NMR self-diffusion has been utilized14,18-21 on semidilute EHEC/surfactant/water systems to establish adsorption isotherms of SDS onto EHEC, while NMR relaxation measurements on EHEC/SDS/water systems (14) Piculell, L.; Thuresson, K.; Ericsson, O. Faraday Discuss. 1995, 101, 307. (15) Lindman, B.; So¨derman, O.; Wennerstro¨m, H. In Surfactant Solutions. New Methods of Investigation; Zana, R., Ed.; Marcel Dekker: New York, 1987; Chapter 6. (16) So¨derman, O.; Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 445. (17) So¨derman, O.; Olsson, U. Curr. Opin. Colloid Interface Sci. 1997, 2, 131. (18) Kamenka, N.; Burgaud, I.; Zana, R.; Lindman, B. J. Phys. Chem. 1994, 98, 6785. (19) Walderhaug, H.; Nystro¨m, B.; Hansen, F. K.; Lindman, B. J. Phys. Chem. 1995, 99, 4672. (20) Thuresson, K.; So¨derman, O.; Hansson, P.; Wang, G. J. Phys. Chem. 1996, 100, 4909. (21) Walderhaug, H.; Kjøniksen, A.-L.; Nystro¨m, B. J. Phys. Chem. 1997, 101, 8892.
10.1021/la980422a CCC: $15.00 © 1998 American Chemical Society Published on Web 10/09/1998
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are more rare.20 To give further insight into polymersurfactant interaction, especially the difference between the nonionic polymers PEO and EHEC, and to confirm and evaluate some previous fluorescence microviscosity investigations,11-13 a 1H NMR relaxation investigation is presented here on the very same EHEC fraction as previously studied.3-5,7-13 The dynamics of the mixed EHEC/SDS micelles is examined by the spin-lattice relaxation time (T1) and spin-spin relaxation time (T2) since these give complementary information with respect to the time scale of molecular motions. The results are compared to the well-studied 2 reference system poly(ethylene oxide) (PEO)/SDS/water and put in relation to the basic features of this dilute EHEC/SDS/water system. Experimental Section Materials. Ethyl(hydroxyethyl)cellulose, EHEC fraction CST-103,Mseo ) 0.7, DSethyl ) 1.5, Mw ) 190 000, Mw/Mn ) 2.1 as determined from a combination of size exclusion chromatography, low-angle laser light scattering, and refractive index measurements (SEC/LALLS/RI)22 and an intrinsic viscosity of 455 mL/g4 was obtained from Akzo Nobel AB, Stenungsund, Sweden. The standard procedure of preparing EHEC stock solutions is described in a previous paper.3 After preparation, the EHEC stock solution was rinsed from low molecular weight impurities by dialysis against Milli Q water for 1 week using a Spectra/Por tube dialysis membrane, Specrum Medical Ind., LA, with molecular weight cut off at approximately 12000-14000. The EHEC stock solution was then filtered through 0.8 µm filters (Millex-AA, Millipore, SA, Molsheim, France). All EHEC/SDS/ water solutions were prepared 24 h in advance in order for the time-dependent effects reported earlier4 to settle. For NMR experiments, the EHEC stock solution was freeze-dried and then redissolved in D2O 99.9 atom % Sigma Chemical Co., St. Louis, MO. EHEC fraction CST-103 in water has a cloud point (CP) of 28-37 °C depending on the polymer concentration, and in the presence of SDS the cloud point increases with increasing amount of SDS.4 Poly(ethylene oxide), PEO, Mw ) 300 000 as determined by the producer, was obtained from Janssen Chimica, Geel, Belgium. Analytical grade sodium dodecyl sulfate, SDS (>99%), was obtained from Merck, Darmstadt, Germany, and used as supplied. NMR samples were not degassed. According to numerous equilibrium dialysis and fluorescence probe experiments, SDS seems to be stable in aqueous solution for at least 1 week.10,11 NMR Measurements. All 1H NMR experiments were performed at room temperature (20 ( 1 °C) in a JEOL EX270 or EX400 spectrometer operated at 270 and 400 MHz, respectively. The EX 270 was equipped with an automatic sample changer with a capacity of 16 NMR tubes ensuring consistency within measurement series. For the major part of the data presented in this work, the methyl protons of SDS have been observed since they show significant effects upon system aggregation. For the shift measurements, the residual HOD proton resonance was set to δ ) 4.500 serving as an internal standard. The experiments were run in duplicate, and the experimental error was (5% or less. An NMR spectrum of 5 mM SDS and 0.2 wt % EHEC is shown in Figure 1. NMR chemical shift measurements have been used over the past decades to monitor aggregation processes in surfactant and polymer/surfactant systems23-26 and is today a standard tool for the determination of critical micelle concentrations (cmc’s) and onset of polymersurfactant interactions (c1).15 At room temperature, the observed signal will be an average of the whole population of surfactant molecules, and as in the case of SDS in water, a chemical shift change is observable as the cmc is passed and the average (22) Nilsson, S.; Sundelo¨f, L.-O.; Porsch, B. Carbohydr. Polym. 1995, 28, 265. (23) Muller, N.; Johnson, T. W. J. Phys. Chem. 1969, 73, 2042. (24) Smith, M. L.; Muller, N. J. Colloid Interface Sci. 1975, 52, 507. (25) Cabane, B. J. Phys. Chem. 1977, 81, 1639. (26) Hammarstro¨m, A.; Sundelo¨f, L.-O. Colloid Polym. Sci. 1993, 271, 1129.
Figure 1. 1H NMR spectrum of a 5 mM SDS/0.20 wt % EHEC/ D2O solution at 20 °C. The R-carbon of SDS is the carbon closest to the sulfate headgroup. The protons of carbon 3-11 on SDS occur as a single peak. molecular environment of the hydrocarbon chains of SDS becomes more hydrophobic. NMR relaxation measurements are useful in isotropic surfactant and polymer/surfactant systems since the relaxation times depend on molecular reorientation.15-17 According to the Bloch equations, two distinct correlation times are defined:27 T1, the longitudinal or spin-lattice relaxation time, which is the relaxation of the Bolzmann distribution of spins in the z-direction of the laboratory frame; T2, the transverse or spin-spin relaxation time, which is the loss of coherence in the x-y plane. However, there are several difficulties in the interpretation of relaxation data which make comparison with other techniques quite important. In such comparisons with microviscosity data the parameter of interest is the rotational correlation time τc, which for a small hard sphere immersed in a viscous liquid can be defined as τc ) 1/6Dr where Dr is the rotational diffusion coefficient given by
Dr ) kBT/(8πr3η)
(1)
where kB is the Bolzmann constant, T the absolute temperature, r the radius of the sphere, and η the viscosity of the solvent.28 The average molecular motion is given by the autocorrelation function
G(τ) ) 〈F(t)F(t + τ)〉
(2)
which in the simplest model case of a sphere and a Gaussian process can be expressed as29
G(τ) ) e-(τ/τc)
(3)
Relaxation measurements, however, give information on the spectral density function, J(ω), which is the Fourier transform of the autocorrelation function
J(ω) )
∫
∞
-∞
G(τ)e-iωτ dτ
(4)
which for a small sphere with a single correlation time becomes29
J(ω) )
τc 1 + ω2τc2
(5)
Thus, if the intention is to determine absolute values of correlation times, such a model has to be applied,15,29,30 and measurements (27) Sandstro¨m, J. Dynamic NMR Spectroscopy; Academic Press: London, 1982. (28) Canet, D. Nuclear Magnetic Resonance. Concepts and Methods; John Wiley & Sons Ltd.: Chichester, 1996. (29) Bovey, F. A.; Jelinski, L. W. J. Phys. Chem. 1985, 89, 571. (30) Wennerstro¨m, H.; Lindman, B.; So¨derman, O.; Drakenberg, T.; Rosenholm, J. B. J. Am. Chem. Soc. 1979, 101, 6860.
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Figure 2. Chemical shift, δ, of the methyl protons of SDS as a function of the total SDS concentration, [SDS]tot, for 0.20% polymer/SDS/water solutions at 270 MHz and 20 °C: b, EHEC; 9, PEO; O, SDS only.
Figure 3. Chemical shift, δ, of the protons on the R-carbon of SDS as a function of the total SDS concentration, [SDS]tot, for 0.20% polymer/SDS/water solutions at 270 MHz and 20 °C: b, EHEC; 9, PEO; O, SDS only.
over a broad range of Larmor frequencies, ω0, must be utilized in order to map J(ω) as a function of ω and a decrease in J(ω) is observed at some characteristic frequency ω0 ≈ 1/τc.29 In the case of T1 measurements, 1/T1 is proportional to the spectral density at the Larmor frequency, J(ω0).28 Starting at small τc (small molecules), T1 will decrease as τc increases (e.g., by lowering the temperature) in a region where ω0τc , 1, termed extreme narrowing conditions. With further increase in τc, a minimum in T1 will be reached when ω0τc ≈ 1, beyond which T1 will increase upon further increasing τc.29 1/T2 on the other hand is dependent on the spectral density at zero frequency, J(0), as well,28 and T2 will generally not pass through a minimum with increasing τc but will decrease continuously; cf. eq 5. The aim of this investigation is not to determine absolute values of the correlation times but rather to interpret the relative changes in relaxation times when the system composition is changed in terms of molecular mobility. Nevertheless it is very important to have at least qualitative knowledge of the relationship between 1/T1 and τc. For this reason, reference measurements of T1 in the system EHEC/SDS/water have been made at both 270 and 400 MHz. The spin-lattice relaxation time, T1, was measured using a standard 180-τ-90 inversion recovery pulse sequence31 with >5T1 delay between pulse sequences allowing the spin system to relax to equilibrium. Eleven τ values between 0.2 and 10 s were applied and evaluated by the nonlinear curve fitting software of the spectrometer. The experimental error between duplicate experiments was ≈(5%. The spin-spin relaxation time, T2, was measured by the Carr-Purcell-Meiboom-Gill (CPMG) echotrain pulse sequence,32,33 which gives the true T2, avoiding the B0-field inhomogeneity contributing to T2 if evaluation of band shapes is employed. Twelve echoes were used in the train, and the τ value was set between 3 and 30 ms depending on the system composition in order to achieve an acceptable nonlinear curve fit as evaluated by the spectrometer software program. A delay of >5T1 was allowed between consecutive experiments to relax the spin system to thermal equilibrium. The experimental error was (10% or less. In these relaxation experiments where no deuterations have been made, it is evident that spin diffusion is present,34 tending to average the relaxation times over the whole spin system, making determination of absolute values of T1 and T2 ambiguous for a selected proton.
SDS/water, and EHEC fraction CST-103/SDS/water. There are distinctive shifts on the ppm scale from about 0.53 to 0.56 for all three systems at the respective aggregation concentrations. The binary system SDS/ water shows a break point at [SDS]tot ) 8 mM, which is in good agreement with the literature value of the cmc of SDS (8.2 mM35). PEO/SDS/water and EHEC/SDS/water have their break points, here denoted as the SDS concentration of onset of polymer-surfactant interaction, c1, at [SDS]tot ) 4.5 and 2 mM, respectively, also in agreement with previous studies using other methods such as equilibrium dialysis and fluorescence measurements.5,10,11,13 After the abrupt increase, δ levels off to 0.56-0.57 in the SDS concentration range 15-30 mM for all three systems. The proximity of δ among the systems in this region suggests very similar interior of the “pure” SDS micelles as compared to the mixed polymer/SDS micelles. These results should be compared to the data of Figure 3, which describes the very same parameters and systems with the exception that here the protons on the R-carbon of SDS (the carbon closest to the sulfate group and hence to the charged micelle surface) are monitored. The features of these shifts are not as “clear-cut” as those of the methyl protons, but still informative. At the cmc of the SDS/water system and at c1 of each of the polymer/ SDS systems there is a drop in δ instead of a rise. Contrary to the methyl protons, the magnitudes of the shifts differ among the systems indicating different molecular environments beyond cmc/c1. The binary system SDS/water shows the smallest shift, from 3.735 to 3.715, and the system PEO/SDS/water the largest shift, from 3.735 to 3.695, implying the presence of PEO chains at or just inside the surface of the PEO/SDS micelles, in accord with the findings by Cabane.25 However, using a paramagnetic 1H relaxation technique, Gao and co-workers36 claimed that PEO solubilizes mainly into the interior of SDS micelles. This technique however, requires a high concentration of NaCl (0.2 m) which might “salt in” PEO into SDS micelles. Gjerde et al.37 used an NMR nuclear Overhauser effect spectroscopy experiment to indicate proximity between PEO and the main peak of the SDS chain (the protons of carbons 3-11) even though the
Results and Discussion The chemical shift of the methyl protons of SDS, δ, as a function of the total SDS concentration, [SDS]tot, is presented in Figure 2 for the systems SDS/water, PEO/ (31) Vold, R. L.; Waugh, J. S.; Klein, M. P.; Phelps, D. E. J. Chem. Phys. 1968, 48, 3831. (32) Carr, H. Y.; Purcell, E. M. Phys. Rev. 1954, 94, 630. (33) Meiboom, S.; Gill, D. Rev. Sci. Instrum. 1958, 29, 688. (34) Wennerstro¨m, H.; Lindblom, G. Q. Rev. Biophys. 1977, 10, 67.
(35) Handbook of Pharmaceutical Excipients; American Pharmaceutical Association (AphA): Washington, DC, 1986; p 272. (36) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J. Phys. Chem. 1991, 95, 462. (37) Gjerde, M. I.; Nerdal, W.; Høiland, H. J. Colloid Interface Sci. 1996, 183, 285.
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Figure 4. Spin-lattice relaxation time, T1, of the methyl protons of SDS as a function of the total SDS concentration, [SDS]tot, for 0.20% polymer/SDS/water solutions at 270 MHz and 20 °C: b, EHEC; 9, PEO; O, SDS only.
Figure 5. Spin-lattice relaxation time, T1, of the methyl protons of SDS as a function of the total SDS concentration, [SDS]tot, for 0.20% EHEC/SDS/water solutions at 20 °C: b, 400 MHz; O, 270 MHz.
experiment suffered from spin diffusion. The system of main interest here, EHEC/SDS/water, also shows a large chemical shiftsfrom 3.735 to 3.705sbut not as large as that of PEO/SDS/water. At higher SDS concentrations the EHEC/SDS curve is located between those of SDS and PEO/SDS, an indication of the proximity of EHEC chains at or just inside the surface of SDS micelles. An interesting detail in the δ curve of EHEC/SDS is the weakly developed minimum in δ at [SDS]tot ) 10 mM, suggesting a composition with strong EHEC-SDS interaction. This interaction seems to decrease upon further increase of the SDS concentration. The argumentation in a previous paper using equilibrium dialysis on the very same system10 supports this observation since a breakpoint in the adsorption isotherm at exactly [SDS]tot ) 10 mM was detected. The cooperativity of the binding of SDS onto EHEC increases at this surfactant concentration and is thought to correspond to a change in the interaction process from binding of SDS to partly self-aggregated EHEC below the break point to binding of SDS onto deaggregated single-stranded EHEC chains above the break point. [SDS]tot ) 10 mM corresponds to [SDS]eq ) 4 mM (see methods) and can be seen in Figure 7 below. The spin-lattice relaxation time, T1, has been used to monitor the formation of surfactant and mixed polymersurfactant micelles,25,30,38-40 and generally at cmc or c1 the molecular motions slow with a decrease in T1 as a consequence. Since the interaction pattern of this particular EHEC fraction with SDS is quite complex, the well-studied model system PEO/SDS/water has been incorporated in the study. T1 of the methyl protons of SDS at 270 MHz as a function of the total SDS concentration is presented in Figure 4. In the absence of polymer, T1 has a constant value of ≈2.4 s below the cmc. There is a sudden drop in T1 as the cmc is passed (at about 8 mM SDS) down to T1 ≈ 1.75 s at [SDS]tot ≈ 10 mM followed by slowly decreasing values down to T1 ≈ 1.3 s at 30 mM SDS. The system PEO/ SDS/water shows similar features with a corresponding drop in T1 at c1 ([SDS]tot ≈ 5 mM) down to an asymptotic value of T1 ≈ 1.2 s in the region 15-30 mM SDS. Also the EHEC/SDS/water system shows a strong decrease in
T1 at c1 ≈ 2 mM SDS down to a minimum of T1 ≈ 1 s at [SDS]tot ≈ 5 mM followed by an asymptotic level of T1 ≈ 1-1.1 s in the SDS concentration range 10-30 mM. The somewhat lower values of T1 for the reference system PEO/ SDS/water, as compared to SDS/water, might be attributed to the presence of polymer segments hindering the molecular motions, as also detected by fluorescence microviscosity measurements.13 Concerning the EHEC/ SDS/water system, the sharp decrease in T1 at c1 and the T1 minimum at [SDS]tot ) 5 mM are consistent with earlier findings on the very same system.3,5,10,11 Around this particular composition a maximum in bulk viscosity3 and microviscosity11 has also been detected. The high bulk viscosity is thought to originate in a three-dimensional EHEC network built up by mixed SDS/EHEC micelles as connecting tie points. The average aggregation number of SDS monomers per polymer-bound micelle, Np, as determined by static fluorescence quenching,5,10 is found to be low at this composition, about 10, and EHEC is believed to dominate these mixed EHEC/SDS micelles with a high density of hydrophobic polymer segments inducing a very rigid sructure and a steric hindrance for the motion of fluorescent microviscosity probes.11 The rigidity is also detected as a minimum in T1. As more SDS is added to the system, Np increases to about 50 and SDS begins to dominate the mixed micelles which at the higher SDS concentrations investigated resemble normal free micelles,11 an effect observable in Figure 4 where the curves of the three systems tend to coincide as the SDS concentration is increased. At the higher SDS concentrations, normal free micelles are present in the system as well, which will bias the relaxation and microviscosity data somewhat. It is important to at least qualitatively examine the relationship between the correlation times and the Larmor frequency employed. In Figure 5 T1 is presented as a function of the total SDS concentration at 270 and 400 MHz for 0.20 wt % EHEC solutions. The sharp decrease in T1 at c1 is detectable at both frequencies, but the curves level off at different values of T1. At 270 MHz (6.3 T) the asymptotic value is T1 ≈ 1 s and at 400 MHz (9.4 T) it is ≈1.2 s. Furthermore, the minimum in T1 at [SDS]tot ) 5 mM is not as pronounced at 400 MHz as that at 270 MHz. This implies that non-narrowing conditions are present.29 The two-step model proposed for micellar systems by Wennerstro¨m et al.30 states that T1 is influenced by motions on two separable time scales: the fast local motions of surfactant alkyl chains on a picosecond time
(38) So¨derman, O.; Walderhaug, H.; Henriksson, U.; Stilbs, P. J. Phys. Chem. 1985, 89, 3693. (39) So¨derman, O.; Henriksson, U.; Olsson, U. J. Phys. Chem. 1987, 91, 116. (40) Chari, K.; Antalek, B.; Lin, M. Y.; Sinha, S. K. J. Chem. Phys. 1994, 100, 5294.
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Figure 6. Spin-spin relaxation time, T2, of the methyl protons of SDS as a function of the total SDS concentration, [SDS]tot, for 0.20% polymer/SDS/water solutions at 270 MHz and 20 °C: b, EHEC; 9, PEO; O, SDS only.
scale and the overall motion of the micellar aggregate on a nanosecond time scale. Isotropic surfactant and polymer-surfactant systems typically show an increase in the slow correlation time (describing the overall aggregate tumbling according to the two-step model) from 10-11 s to about 10-9 s when cmc or c1 is passed.15,38-41 This suggests that that the minimum in T1 on the τc scale29 (see methods) is reached as the EHEC/SDS/water system aggregates, since, e.g., at 270 MHz for small monomers below cmc ω0τc ) 2π270 × 106 × 10-11 ≈ 0.017 (ω0τc < 1) and for micelles ω0τc ) 2π270 × 106 × 10-9 ≈ 1.7 (ω0τc > 1). The non-narrowing conditions as here deduced by two different high-field measurements indicate that T1 for the EHEC/ SDS/water system is influenced by motions on the nanosecond time scale in addition to the faster local chain motions. If one wants to correctly map the influence of these slower motions on T1, it is necessary to perform measurements also at very low frequencies.38,39,42 Spin-spin relaxation time (T2) measurements are often used to determine whether slow motions are present in isotropic surfactant and polymer/surfactant systems15 since T2 depends on the spectral density at zero frequency, J(0), as well. T2 for the systems SDS/water, PEO/SDS/ water, and EHEC/SDS/water is presented in Figure 6 as a function of the total SDS concentration at 270 MHz. The faster T2 time scale in Figure 6 as compared to that of T1 in Figure 4 is another indication of nonextreme narrowing conditions.15 The qualitative picture is similar to the T1 measurements with sudden drops at the respective aggregation concentrations implying aggregate growths and slower molecular tumbling, and these findings are in agreement with the ones by Thuresson and co-workers20 on similar EHEC/SDS and hydrophobically modified (HM) EHEC/SDS systems using 2H line width determinations of R-deuterated SDS. The magnitude of the drops in T2, however, differs between the systems as compared to T1. At higher SDS concentrations, the PEO/SDS micelles show T2 values comparable to the binary system SDS/water indicating similar aggregate tumbling and a quite flexible PEO chain, and in this region the experimental error of the two lines overlaps. The EHEC/SDS/water system on the other hand shows a drastic drop in T2 at c1, from 0.65 to 0.1 s, significantly larger than the drops of the other two systems (
