7548
Langmuir 2000, 16, 7548-7550
Growth of C12E8 Micelles with Increasing Temperature. A Convection-Compensated PGSE NMR Study N. Hedin,† T. Y. Yu,‡ and I. Furo´*,† Division of Physical Chemistry, Department of Chemistry, Royal Institute of Technology, SE-100 44 Stockholm, Sweden, and Department of Chemistry, National Taiwan University, TA-10764 Taipei, Taiwan Received April 20, 2000. In Final Form: June 26, 2000
Introduction The self-diffusion coefficient of C12E8 (member of the oligooxyethylene alkyl ether family1 CmEn, where m and n are the numbers of the methylene carbons and the oxyethylene groups, respectively) molecules in D2O is temperature dependent. This phenomenon, detected by both QELS2 (quasielastic light scattering) and PGSE (pulsed-field-gradient spin-echo) NMR,2-4 is usually ascribed to the size of the C12E8 micelles that increases with increasing temperature. This growth can also be sensed by fluorescence quenching.5 Similar NMR and QELS results can also be obtained on other CmEn micellar systems.6 Accurate assessment of the micellar growth requires accurate QELS and PGSE NMR data which, however, may not be easy to obtain by either light scattering or NMR since these dynamic methods (and possibly some other ones, too) are susceptible to errors caused by convection.7-11 Convection may arise whenever the temperature gradient within the sample causes a density gradient with lighter material in the lower part of the container.12 Typically, in NMR probes (with a probe space heated from below) this appears in high-temperature experiments. For a given sample with a particular set of material parameters (viscosity, thermal diffusivity, thermal expansion coefficient) convection appears if the temperature gradient exceeds the value set by the so-called critical Rayleigh number13 Rac. For cylindrical samples (typical for NMR), this temperature gradient is inversely proportional to the fourth power of the radius of the sample tube. Hence, the first and obvious way to suppress convection artifacts is * Corresponding author. Tel: +46 8 790 8592. Fax: +46 8 790 8207. E-mail:
[email protected]. † Royal Institute of Technology. ‡ National Taiwan University. (1) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; Macdonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975. (2) Brown, W.; Pu, Z.; Rymde´n, R. J. Phys. Chem. 1988, 92, 6086. (3) Jonstro¨mer, M.; Jo¨nsson, B.; Lindman, B. J. Phys. Chem. 1991, 95, 3293. (4) Nilsson, P.-G.; Wennerstro¨m, H.; Lindman, B. J. Phys. Chem. 1983, 87, 1377. (5) Binana-Limbele´, W.; Zana, R. J. Colloid Interface Sci. 1988, 121, 81. (6) Brown, W.; Johnson, R.; Stilbs, P.; Lindman, B. J. Phys. Chem. 1983, 87, 4548. (7) Goux, W. J.; Verkruyse, L. A.; Salter, S. J. J. Magn. Reson. 1990, 88, 609. (8) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Microscopy; Clarendon Press: Oxford, UK, 1991. (9) Jerschow, A.; Mu¨ller, N. J. Magn. Reson. 1997, 125, 372. (10) Hedin, H.; Furo´, I. J. Magn. Reson. 1998, 131, 126. (11) Sehgal, A.; Seery, T. A. P. Macromolecules 1999, 32, 7807. (12) Landau, L. D.; Lifshitz, E. M. Fluid Mechanics, 2nd ed.; Pergamon: Oxford, UK, 1987. (13) Bejan, A. Convection Heat Transfer; Wiley: New York, 1995.
to use a narrow sample tube. However, in most NMR probes that are available today, convection sets in for most liquids at less than 5-10 K over room temperature even in 5 mm NMR sample tubes. The effect of convection in NMR diffusion experiments was qualitatively recognized a long time ago (to the authors’ knowledge, it is first mentioned in ref 14) but its effect was seldom quantified or suppressed. In PGSE NMR experiments in micellar solutions, the convection problem was sometimes partially compensated for by, e.g., normalizing3 the surfactant diffusion coefficient with that of free surfactant molecules at a surfactant concentration below cmc. However, this procedure is flawed since convection influences the PGSE results for slowly-diffusing molecules much more than for quickly-diffusing molecules. One would also expect that older experiments2,6 using iron magnets, where the axis of the NMR tube is perpendicular to the gradient direction, are immune to convection problems. Indeed, the effect of convection is much (by about the axial ratio of the NMR sample) reduced in such an arrangement at moderately high temperatures. However, by increasing the temperature and by that the temperature gradient over the sample, convection modes that consist of several convection rolls over each other evolve13,15 in which situation “old” iron magnet and “modern” superconducting magnet geometries are almost equally sensitive to convection artifacts. Since convection does not change strongly the character of the signal decay in diffusion experiments (it remains apparently Gaussian unless convection completely dominates over diffusion, see below), results of previous concentration-dependent studies at high temperatures (where the viscosity varies along the sample series) or of temperature-dependent studies are equally questionable. Although there are solutions available by changing the sample or probe geometry (see ref 10 and references therein), for PGSE NMR the simplest remedy is to make use of the different spatial propagators for flow and diffusion and design pulse sequences that suppress signal attenuation9 that comes from displacement by convection. The best solution is the combination of these approaches as will be demonstrated below. Any PGSE NMR studies on colloidal systems16 that are performed more than a few degrees away from room temperature should consider the occurrence of systematic errors in the obtained diffusion coefficients and structural conclusions based thereupon. This is particularly advisable in modern NMR systems with superconducting magnets where the gradient field direction is usually coparallel to the NMR sample tube axis. Experimental Section A micellar sample of C12E8 (Nikko Chemicals) was made by mixing ∼5 wt % surfactant into D2O (Isotec). A sample tube was filled up to ∼4 cm in a 5 mm o.d. NMR tube and flame sealed ∼2 cm above the liquid surface to prevent long-term evaporation of the solvent. This sample tube was placed coaxially into a 10 mm NMR tube filled with a perfluorinated oil (Krytox 143 AZ, DuPont); this arrangement creates a more even temperature distribution10 within the micellar sample and, in particular, suppresses the “hot spot” at the bottom of the sample tube that appears at elevated temperatures in our pulsed-field-gradient NMR probe (from Cryomagnet System, Indianapolis, IN). The (14) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1. (15) Guthmann, C.; Perrin, B.; Thome´, H. J. Phys. Fr. 1989, 50, 2951. (16) So¨derman, O.; Stilbs, P. Prog. NMR Spectrosc. 1994, 26, 445.
10.1021/la000595b CCC: $19.00 © 2000 American Chemical Society Published on Web 08/18/2000
Notes
Langmuir, Vol. 16, No. 19, 2000 7549
Figure 1. Self-diffusion coefficients of C12E8 micelles (5 wt %) in D2O at 45 °C measured by 1H PGSE NMR using the conventional stimulated echo (STE, 9) and the convectioncompensated double-stimulated echo9 (DSTE, O) experiments. The error bars represent conventional estimates of the (2σ error ranges and are calculated from the deviation of the experimental points from the fitted Stejskal-Tanner17 expression. The diffusion time has been varied by increasing those periods in the two pulse sequences during which the encoding is stored as z magnatization. 1H NMR signal from the rest protons of the perfluorinated oil is small and appears at distinctly high chemical shifts. The temperature was calibrated by an external thermometer and regulated using a Bruker BVT3000 temperature regulator at a flow of ∼800 L/h of regulation air. The 1H NMR experiments were performed on a Bruker DMX 200 spectrometer. We carried out conventional stimulated-echotype (STE)17 and the convection-compensated double-stimulatedecho-type (DSTE)9 PGSE experiments. Both pulse sequences were followed by a longitudinal eddy current delay (LED)18 to suppress the spectral distortions caused by the gradient pulses. The length and the strength of the gradient pulses was varied in the 3-6 ms and 10-50 G/cm ranges, and the decay of the 1H line of the methylene groups with increasing gradient strength G was recorded. Identical (within precision) data were obtained using the 1H lines belonging to the ethyleneoxide groups. In a cylindrical tube, the convection streamlines are mainly parallel to the tube axis13 and to first approximation, convection can be modeled as a flow of equal amount of liquids of equal velocity v both upward and downward. In this system the echo attenuation with increasing gradient strength G becomes19
(
(
I(G) ∼ cos(γδGv∆) exp -γ2δ2G2D ∆ -
δ 3
))
(1)
in a conventional STE experiment where γ is the gyromagnetic ratio, δ the length of the gradient pulses, ∆ the diffusion time, and D the self-diffusion coefficient. As illustrated by eq 1, a clear sign of convection is the failure to fit the experimental data by the conventional StejskalTanner17,20 expression (a Gaussian decay identical to the second part of the formula in eq 1). However, convection may distort the data even if deviations from the Stejskal-Tanner expression are not apparent; the reason is that the cosine function starts out flat, just like a Gaussian function. In fact, for v2∆ , D and δ , ∆, one obtains good quality least-squares fits to a Gaussian function although the obtained apparent diffusion coefficient to first approximation becomes
Dapp ) D +
∆v2 2
(2)
Both these effects are illustrated in Figure 1. First, the diffusion (17) Tanner, J. E. J. Chem. Phys. 1970, 52, 2523.
Figure 2. Temperature-dependent self-diffusion coefficients of C12E8 micelles (5 wt %) in D2O surfactant solution scaled with the solvent viscosity and the temperature; the data have been obtained by the convection-compensated DSTE experiment9 with 360 ms diffusion time. The data are normalized with 1.8 × 10-16 kg m/(s2 K) which is the value of Dη(T)/T at the lowest temperature of the present study (303 K). coefficients obtained by fitting the Stejskal-Tanner expression to the experimental points obtained by the conventional STE experiment are clearly dependent on the diffusion time ∆. Moreover, the larger the ∆ value the larger is the apparent error of the obtained Dapp which indicates that the experimental decay increasingly deviates from the Stejskal-Tanner expression. The true diffusion coefficient D could thus be evaluated from the STE experiment only if the data are extrapolated to ∆ ) 0. On the other hand, the diffusion coefficients obtained by the convection-compensated DSTE experiment are independent (to less than (5%) of the diffusion time and free of convection artifacts. Note that the convection effects cannot be separated from diffusion by simply fitting eq 1 to the experimental points. At low v the cosine and Gaussian functions cannot be well separated while at high v the signal damping by diffusion is small as compared to that by convection. Moreover, instead of a single velocity there exists a velocity distribution in a convecting fluid. As an illustration, fitting eq 1 to our experimental points yields diffusion coefficients that are somewhat (60-80%) lower than the corresponding Dapp values in Figure 1 but still much higher (and increase with increasing ∆) than the true D values obtained by convection compensation.
Result and Discussion The C12E8 molecules exchange rapidly on the time scale of our diffusion experiments and the experimental selfdiffusion coefficient is therefore an average over surfactant molecules free and in a micelle. At the high surfactant concentration (∼0.1 mol/L) of the present study the contribution from free surfactant molecules is negligible because of the very low critical micelle concentration (∼7 × 10-5 mol/L at 25 °C21). Hence, a decreasing diffusion coefficient with increasing temperature (Figure 2) reflects, as previously suggested, micellar growth. Below, this is modeled as elongation of prolate-shaped aggregates with axial ratio F. The diffusion coefficient of such objects can be expressed as22 (18) Gibbs, S. J.; Johnson, C. S. J. Magn. Reson. 1991, 93, 395. (19) Saarinen, T. R.; Johnson, C. S. J. Magn. Reson. 1988, 78, 257. (20) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288. (21) Mukerjee, P.; Mysels, K. J. CMC of Aqueous Surfactant Systems; US National Bureau of Standards: Washington, DC, 1971. (22) Hiemenz, P. C. Principles of Colloid and Surface Chemistry, 2nd ed.; Marcel Dekker Inc.: New York, 1986.
7550
Langmuir, Vol. 16, No. 19, 2000
D0 ) f(F) )
kT f(F) 6πηr
ln(F + xF2 - 1)
xF2 - 1
Notes
(3)
(4)
Here r is the minor axis of the micelle and η the solvent viscosity. (Polydispersity is not considered.) Since the volume fraction of the surfactants is low we shall neglect the effect of steric obstruction on the micellar diffusion. The temperature-dependent self-diffusion data obtained in our micellar solution are presented in Figure 2. As illustrated by eq 3, the raw diffusion data must be normalized with the solvent viscosity and the temperature to reflect micellar size; hence, in Figure 2 we present Dη(T)/T, where η(T) is the temperature-dependent viscosity23 of D2O. Assuming that the micelles are spherical at room temperature, the normalized diffusion data provide (through eq 4) information on the size of the micelles modeled as prolate ellipsoids (Figure 3). The prolate micelle model is less suitable for long and almost certainly flexible aggregates and therefore we do not provide any axial ratios in the 330-350 K region. As clearly seen in Figures 2 and 3, micellar growth starts just above 310 K and continues until the phase separation at ∼350 K. This picture is somewhat different from that obtained earlier by conventional PGSE NMR.2 First, we do not detect any increase of Dη(T)/T in the D in the earlier conventional PGSE NMR experiments2 as would be expected in case of convection. Acknowledgment. The Swedish Natural Science Research Council (NFR) has supported this work. N.H. thanks the Ernst Johnsson Foundation for a scholarship. T.Y.Y. thanks the Royal Institute of Technology for a scholarship. Peter Stilbs is thanked for useful discussions. LA000595B
