9524
J. Phys. Chem. 1992, 96, 9524-9531
Counterion Spln Relaxatlon in Mlcroemulslon Droplets P. Huang Ken&, C. Carlstrbm; I. Fur&*and B. Halle* Physical Chemistry 1, University of Lund, Chemical Center, P.O. Box 124, S-221 00 Lund, Sweden (Received: May 6, 1992; In Final Form: July I O , 1992)
Counterion 23Naspin relaxation data are reported from the microemulsion phase in the AOT/water/isooctane system as a functionof the water/AOT ratio,which determines the size of the aqueous droplets. The W a NMR measurementscomprise three independent relaxation rates, allowing the individual spectral density values to be determined, as well as the seumd-ordcr quadrupolar dynamic shift. The effect on the relaxation obwables of counterion diffusion within the aqueous droplet core is calculated by solving the diffusion equation in the presence of the electrostatic mean field. This allows the 23NaNMR data to be interpreted in terms of the Na' lateral diffusion coefficientD, in the surface region, the residual quadrupole coupling constant XI, and a spectral density contribution Jf due to fast local motions. These quantities have also been determined in a previous 23NaNMR study of the reversed hexagonal phase of the same system, with similar results. Although the prescnt data are basically consistent with the expected microstructure of closed droplets with highly mobile counterions, a model of monodisperse spherical droplets cannot account quantitatively for all the data. This discrepancy is tentatively ascribed to the existence of small reversed micelles coexisting with the classical microemulsion droplets.
Introduction In a typical water-in-oil microemulsion, the water is dispersed in the form of surfactant-coated droplets whose size is controlled primarily by the water/surfactant ratio.'+ Among the many systems that form microemulsions, the ternary system AOT/ water/alkane has long been a favorite candidate for experimental study. (AOT refers to the surfactant sodium bis(2-ethylhexy1)sulfoeuccinate.) Information about droplet size and polydispersity has come mainly from studies of tight scattering and small-angle neutron and X-ray scattering.5-'2 Droplet size, clustering, and coalescence dynamics in AOT-based microemulsions have also been studied by c ~ n d ~ ~ t i v i ~elfdiff~~i~n,~~~'~~' ty,~~*~~ StOppad-flOW kinetics,'* fluorescence quenching,1w1dielectric spectrmpy12u3 and several other techniques. While many aspects of this microemulsion phase are by now well characterized, relatively less is known about the internal structure and dynamics of the aqueous droplet core. Such information canbe obtained by studying the spin relaxation of nuclei residing in the water molecules or the counterions contained in the droplet. In several recent studies24-26the 2Hand 170relaxation of water in microemulsion droplets has been measured and analyzed in terms of water Wbsion and droplet structure. The Z3Na spin relaxation of the counterionsin AOT-stabilized microemulsion droplets was studied in an early but due to instrumental limitations and the incomplete understanding of the relaxation proc*ls at that time, the results of that study are of limited value. In the present work we report the results of an extensive 23Na spin relaxation study of the sodium counterions in the microemulsion phase of the AOT/H20/isooctane system. By meesUring thne independent spin relaxation rates,we can determine the value of the motional spectral density function at three frequencies. Additional independent information is obtained from the second-order quadrupolar dynamic shift. These data, determined for a range of droplet sizes (core radius 2-1 1 nm) at two temperatures,allow us to decisively test various structural and dynamic models. The relaxation data clearly reveal the existence of a dynamic process on the time scale 10-* s, which we identify as counterion diffusion within the droplet. Since the counterions are strongly accumulated near the oppositely charged AOT headgroup, it is natural to model this motion as diffusion on a spherical surface. However, this simple model is not adequate for a quantitative analysis. Numerical calculations reported here show that counterion diffusion into the core causes significant deviations from To whom correspondence should be addreassd. ' Rcaent address: Department of Molecular Biology, Scripps Research Institute, 10666 North Torrey Pines Road, La Jolla, CA 92037. $On leave from the Central Rtsearch Institute for Physics, B u d a p t , Hungary.
0022-3654/92/2096-9524$03.00/0
sample
xw*
4b
b/nmc
Pd
1 2 3 4
9.4 17.7 28.3 34.0 43.6 48.2 61.7 65.6
0.087 0.108 0.133 0.147 0.168 0.177 0.204 0.212
2.11 3.42 5.12 6.04 7.58 8.31 10.5 11.1
0.90 0.86 0.84 0.83 0.82 0.82 0.81 0.8 1
5 6 7 8
'Molar ratio H,O/AOT. bDropletvolume fraction at 20 O C (H20 'Aqueous core radius for monodisperse spherical droplets, calculated according t01-*2~19~20 b/nm = 0 . 1 6 ~+~0.6. dFraction counterions (at 20 "C) within 6 = 0.5 nm of the spherical interface, calculated from eq 14.
+ AOT).
the predictions of the surface diffusion model. Even when this complication is taken into account, however, the data are not fully consistent with a microstructure of monodisperse spherical dpplcts. Neither a unimodal droplet size distribution nor droplet shape fluctuations can remove the inconsistency. Rather, the data suggest a bimodal size distribution, where microemulsion droplets coexist with small reversed micelles. Such a distribution has previously been invoked to explain small-angle X-ray scattering and kinetics data.43 Finally, we compare the results of this study with those of a recent 23Naspin relaxation study of the reversed hexagonal phase of the same system.29
Materials and sample Repntioa AOT (sodium bis(2-ethylhexyl) sulfosuccinate) from Sigma and isooctane (2,2,4trimethylpentane) from Aldrich (99%) were used as supplied. The water was Millipore-filtered H20. Microemulsion samples were made by weighing the components into 'I-mm-i.d.-Pyrex tubes, which were then flamesealed. All samples were made from a stock solution of molar ratio isooctane/AOT no = 35.0, to which water was added to obtain the desired mdar ratio HzO/AOT, denoted XW. The cOmpaPition data for the investigated samples are given in Table I. Figure 1 shows the relevant part of the x r T phase diagram (at fmed xo = 35.0), with the position of the inveatigated samples indicated. The boundarim of the onaphase microemulsion region were established by visual inspection and agree closely with previous results for this system.'* The two-phase region at low temperature contains microemulsion in equilibrium with e x a s water (or normal micellar phase), whereas the two-phase region at high xw, at least at 10 and 20 O C , contains microemulsion in equilibrium with lamellar liquid-crystallinephase. The samples marked by open circles were first thought to be in the onaphase microemulsion region but, on closer inspection, turned out to be 63 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No.23, 1992 9525
23NaNMR in Microemulsions 100
I
I
4
1
"I-
80
j,
%
4 t
60
1
i
4 XW
40
20[ 0 0
5
:
10
, 15
:
20
I
25
1
30
T/"C Figure 1. Apparent stability region of the microemulsion phase (L2) in the AOT/H20/isooctane system with xo = 35.0. In the shaded twophase regions the " u l s i o n phase is in equilibriumwith excess water (L2 + aq) or with a lamellar phase (b+ D). In the latter case, the (dashed) phase boundary is only apparent; careful examination revealed that the samples marked by open circles are biphasic. Samples marked by solid circles were found to be homogeneous.
biphasic. This was established either by extended centrifugation (several days) leading to phase separation.or by a significant deviation from the biexponential transverse 23Narelaxation expected for a homogeneous microemulsion sample. In the former case, the bottom phase had a texture (observed in a polarizing microscope) characteristic of a lamellar phase, but the sample reverted spontaneously to a clear solution on a time scale of days. Whereas the phase-separated sample exhibited a uNa quadrupole splitting of ca. 20 W z , no splitting could be detected from the clear sample, indicating that the dissolved lamellar microcytallites are small (lateral dimensions less than ca. 0.2 pm).
Diffusion Measurements To ensure that the microemulsion samples investigated by uNa NMR consist of discrete water droplets rather than having a bicontinuous topology, we performed water diffusion measurements on several samples using the 'H pulsed-field-gradient spin-echo technique.30 Since this experiment measures the macroscopic water diffusion coefficient, corresponding to rootmean-square displacements of the order 1od m, it readily distinguishes between closed droplets and a bicontinuous microstructure. The samples, contained in 4-mm4.d. glass ampules,were located in a horizontal solenoid probe centered in a quadrupole gradient coil providing an essentially homogeneous magnetic field gradient of ca. 4 mT an-'. The conventional spin-echo pulse sequence with two gradient pulsesmwas used to record the intensity of the water 'H signal with increasing gradient pulse length. The 180' pulse length was ca. 12 ps at a 'H Larmor frequency of 100.13 MHz. The separation between the gradient pulses and the 180' pulse or the echo was at least 10 ms; no phase distortions were seen in the spectra. The water self-diffusion coefficient D in the microemulsion sample was determined from a three-parameter nonlinear least-squares fit. (The other parameters were the initial intensity and the base line.) No significant changes in D were found by varying the delay between the gradient pulses from 20 to 200 ms, indicating unrestricted diffusion on the micrometer length scale. The results of diffusion measurements on samples 4,5, and 7 are shown in Figure 2. A transition from closed droplets to bicontinuous topology is evident for sample 4 above 40 OC as the boundary of the one-phase region is approached. At 10 and 20 OC, however, all the samples investigated by 23NaNMR showed water diffusion coefficients characteristic of closed droplets. In fact, the measured water diffusion ooefficients deviate by less than 20%from the theoretical value D = (1 - 2+)kBT/(6q&) for
2t
0
I-
O
i
Po
@
io
o
io
@
1 -I
0
p.b.
@i
@
io
sb
io
T PC Figure 2. Temperaturedependence of water self-diffusioncoefficient D in microemulsion samples 4 (O), 5 (0),and 7 (A).
+
+
hard spheres of radius R = 6 1.0 nm at volume fraction (cf. Table I) in a medium with the viscosity vo of isooctane.
fjNa Spin Relaxation Measurements The 23NaNMR measurements were performed on a Bruker MSGl00 spectrometerequipped with a 10-mm vertical s a d d l d probe and a 2.35-T(26.485-MHz resonance frequency for 23Na) wide-bore superconducting magnet. The sample volume (ca. 15-mm height in the Pyrex tube) was centered in the coil yielding a spatial rf (B1) inhomogeneity of ca. &lo%. The static magnetic field inhomogeneitywas minimized by shimming on the narrow 'H spectrum; the resulting inhomogeneous broadening in the 23Naspectrum was typically ca. 2 Hz. The temperature was controlled by a Stelar VTC 87 regulator with high airflow (1.5 m3/h), yielding a temperature stability of f0.03 O C . The temperature gradients within the sample are estimated to be less than h0.03 OC. The 180' pulse length (typically around 12 ps) was determined from the zero crossing of the signal with varying pulse length. The 90' and 63.4' pulse lengths were determined by extrapolating from 180' and 360' pulse lengths. Free Induction Decay. When rccarding the free induction decay (FID) signal, the following steps were taken to minimize errors. First, spurious (ghost) signals due to receiver imbalance were suppressed (i) by fine-tuning the amplitude and phase balance of the receiver and (ii) by using the CYCLOPS phase cycle.31 The unsuppressed spurious signals were measured in an off-resonant experiment and were found negligible (S0.296). Second, the aquisition delay was set to 230 ps. A good suppression of any rf-coherent ringing was accomplished by varying the filter width, pulse length, and acquisition delay. The 230-ps delay also ensures that the 23Nasignal from the Pyrex tube has decayed completely before signal aquisition starts. The filter width (100 W z ) was chosen so as to cause negligible distortions in the pass band. To achieve a satisfactory precision, 48 000-96 OOO scans were collected with 120-ms repetition time. (To avoid sample heating, no shorter repetition times were used.) The full spectral width was 71.4 or 83.3 W z , and 1600-2400 points were digitized in the decay. (The signal was recorded in sequential digitization mode; i.e., data points were alternately digitized in the "real" and "imaginary" channels. This has been taken into account when fitting the data.) A typical FID is shown in Figure 3. The obtained signal-tu-noise ratio (calculated as the maximum intensity of the signal in the "real" channel divided by one standarddeviation characterizing the assumedly Gaussian noise) was 300-600. The FID signal S(t) following the single-pulse excitation of an I = 3/2 spin system consists of two components of fixed relative amplit~des~~
The transverse quadrupolar relaxation rates of the slowly and rapidly decaying components are denoted by R2-and R2+,respectively. The two decaying signal components are modulated
9526 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992
3
I
Longitudinal Relaxation. These experiments were carried out with a modified inversion recovery sequenceKx with a detection pulse angle of 63.4". This particular pulse angle cancels the coherence transfer from octupole polarization, which develops under nonextreme narrowing conditions, to the detected singlequantum coherence. Since this experiment exclusively monitors the evolution of the dipole polarization, the line shape does not change with delay time and the two longitudinal relaxation rates R1-and R1+can be obtained from a double-exponential fit with fixed amplitudes according to
I
1
I
I
5
0
10
t/ms
Since R i and R l + do not differ much, we actually performed a single-exponential fit according to S(T) A(1 - 2 exp(-Rl*~)] B (3b) with an effective longitudinal relaxation rate
Figure 3. A typical FID signal recorded on sample 6 at 10 OC.
+
TABLE U "Na Relamtion Rates rad Dynamic Shift" 9.4 17.7 28.3 34.0 43.6 48.2 61.7 65.6
1264 f 20 778 f 12 564 i 9 495 f 7 437 f 6 419f 5 379 f 5 373 f 5
9.4 17.7 28.3 34.0 43.6 48.2
9 1 4 i 14 590f 8 432 f 6 378 f 5 329 f 4 314f 4
Huang KenQ et al.
1372 f 25 852 f 15 616 f 10 540*9 471 f 9 453 f 9 402 f 9 401 i 8 T=20°C 980 f 20 645 i 10 477i8 424*8 368 f 8 354 f 6
1960 f 35 1268 f 20 1106 f 12 1 1 1 7 f 12 1197 f 13 1256 f 13 1509 f 15 1614f 15
*
1340 30 914 f 12 837f 1 1 916f 12 1105 15 1280 f 20
*
260 h 40 240 f 30 266 f 20 259f20 249 f 20 237 f 20 226 f 25 232f 25
(The intensity A and the base line B were parameters of no physical interest.) Monte Carlo simulations showed that the (random and systematic) error in Rl*, obtained from eq 3b, was smaller than the random errors in the individual rates obtained from a doubleexponential fit to eq 3a. Furthermore, the simulation results could be used to correct for the small (
