J. Phys. Chem. 1985,89, 3373-3378
3373
Figure 7 presents two relaxation plots calculated by using the dynamic simulation method for 1000 ellipsoids having size dimensions equal to the average dimensions of the latex particles used in the experiments. These plots made for two widely different initial orientations have nearly equal slopes (slope of -0.1 18 s-' for the initial orientation, B = 9 = fi = 0.01 and -0.1 13 for B = 4 = = r / 2 ) in good agreement with the theoretical value of -0.1 18 s-' (see eq 40). This also c o n f i i the theoretical prediction that for ellipsoids having rotary diffusion coefficients such that D2 + D3 >> D2 - D3 the initial orientation has very little effect on their relaxation behavior. We found that for ellipsoidal particles often D2 is close to D3, even for widely different axis ratios, indicating that eq 40 is often a very useful approximation.
+
0
2
4
6
Time (s) Figure 7. Variation in Rayleigh ratio (e, = loo) as a function of time obtained from the dynamic simulation method for ellipsoids having al = 470 nm, a2 = 330 nm, a3 = 250 nm. See Table I, column 3, for details of other parameters used. Calculations were carried out for 1000 particles; time interval, A? = 0.01 s. Symbols: @ initial orientation, e = @ = $ = 0.01; initial orientation, 0 = @ = $ = 7r/2. then be used to calculate light scattering parameters for each particle as a function of time. Interparticle interactions were neglected and each particle was simply assumed to contribute with equal weight to light scattering. Thus the ensemble average light scattering parameters at a given time were evaluated as number averaged values. The results are presented in terms of Rayleigh ratio, Ru(60),defined by the expression Ru(60)= (1(60)/1,,)$where I(&) is the scattered intensity at scattering angle 6, Io the intensity of perpendicularly polarized incident light, and r the distance between the scatterer and the detector.
Conclusions We have presented a general method which in principle could be used to treat theoretically the relaxation of any property of suspensions that can be expressed as a function of orientation of anisometric particles. The examples discussed in this paper show that for many useful physical properties one can obtain simple expressions relating the relaxation to rotary diffusion coefficients of the rotating particles. The nature of these expressions depends on the physical property and the symmetry properties of the particles being studied. Good agreement was observed between theory and rheo-optical properties of suspensions. Finally, it is clear from this work that relaxation studies provide a direct and simple means to obtain information about size and shape of Brownian particles. Acknowledgment. We thank Dr. H. L. Goldsmith (Montreal General Hospital) and Dr. D. Distler (BASF, Ludwigshafen, West Germany) for supplying the hardened human red blood cells and the ellipsoidal latex particles, respectively.
Aggregation and Dynamical Behavior in Sodium Diethylhexyl Phosphate/Water/Benzene Inverted Micelles A. Faure, A. M. Tistchenko, T. Zemb, and C. Chachaty* Dzpartement de Physico-Chimie, Cen. Saclay, 91 191 Gij-Sur- Yvette Cedex, France (Received: August 14, 1984; In Final Form: March 25, 1985)
The static and dynamical properties of sodium diethyl-2-hexylphosphate/water/benme inverted micelles have been investigated by using several techniques. Proton NMR, densimetry, as well as light and neutron scattering experiments yield a mean aggregation number of 12 1 for a cmc of 8 X lW3 M. The domain of stability of these micelles correspond to water/surfactant ratios W I 6. Above W = 3.5, the release of free water molecules and sodium ions in the micellar core is evidenced by 'H and 23NaNMR and corresponds to the onset of electrical conductivity. The anisotropic motions of water and surfactant molecules have been investigated by multinuclear relaxation experiments. The reorientation of water seems consistent with the lone-pair model of binding to sodium ions.
Introduction The dialkyl phosphates and their alkaline salts are of interest in extraction processes because of their complexing properties toward metal ions (see, for instance, ref 1-4). The surfactant properties of their sodium salt in aqueous solution and their ability to give rise to lyotropic mesophases are currently investigated in our l a b o r a t ~ r y . ~ .Among ~ them the sodium diethyl-2-hexyl (1) Peppard, D. F.; Mason, G. W.; Maier, J. L.; Driscoll, W. J. J . Inorg. Nucl. Chem. 1957,4, 334. (2) Peppard, D. F.; Ferraro, J. R.; Mason, G. W. J . Inorg. Nucl. Chem.
1957, 4, 371. ( 3 ) McDowell, W. J.; Coleman, C. F. J. Inorg. Nucl. Chem. 1%3,25,234. (4) Liem, D. H. Acta Chem. Scand. 1968, 22, 753.
phosphate (NaDEHP) has the particular property to give rise to inverted micelles in organic solvents as already pointed out by Eicke and Christen.' This important ProPrtY, which accounts for the Surfactant activity at the Water/SOlVent interface (See, for out an extensive investigation instan% ref 8), Prompted Us to (5) Belaid, S.;Chachaty, C. J . Colloid Interface Sci. 1982, 86, 277; "In Proceedings of the 4th International Symposium on Surfactants in Solution, Lund, Sweden, 1982"; Mittal, K.L., Lindman, B., Eds.; Plenum Press: New York, 1984; Vol. 1, p 501. (6) Chachaty, C.; Quaegebeur, J. P. J. Phys. Chem. 1983, 87, 4341. (7) Eicke, H.F.; Christen, H . J . Colloid Interface Sci. 1974, 46, 417. (8) Gaonkar, A. G.; Neuman, R. D. Proceedings of the 5th International Symposium of Surfactants in Solution, Bordeaux-Talence,France, July 9-13, 1984, to be published.
0022-3654/85/2089-3373.$01.50/0 0 1985 American Chemical Society
3374 The Journal of Physical Chemistry, Vol. 89, No. 15, 1985
Faure et al.
of NaDEHP aggregation processes in nonpolar solvents and in the presence of water. Most of our experiments were performed with benzene to avoid interferences with ‘H or 13CN M R lines of the surfactant. It was verified however that cyclohexane yields essentially the same results. The present work deals with the physicochemical properties of the reversed micellar NaDEHP/C,H,/H,O solutions, including the determination of the critical micellar concentration and aggregation number by densimetry, light and neutron scattering, and IH N M R as well as a relaxation study of the dynamical behavior of surfactant and water molecules. Up to now, most of the N M R studies on reversed micelles are dealing with AOT.+13 The NaDEHP is of particular interest for comparison with AOT because of its similar structure and of the presence of in the polar head which is a very convenient probe for the motion of surfactant molecules. Materials and Methods Diethyl-2-hexyl phosphate was prepared from diethyl-2-hexanol by reaction with PC13 and S02C1214 in anhydrous benzene. The purity of the obtained acid was checked on ‘H and 31PN M R spectra. It was neutralized by sodium hydroxide in ethanol, until the aqueous solution pH reaches the value of 6. The salt was then carefully dried overnight under high vacuum and kept in a desiccator. The samples were prepared in benzene dried on sodium metal. The quantity of water added was equivalent to a number of water molecules per surfactant W = 4 except for the light scattering and water proton chemical shift measurements where it was taken equal to 3.6 and 3.2, respectively. All the experiments were performed a t 27 f 0.5 OC except for the phase diagram determination which was done at 20 OC. The N M R measurements were carried on Varian XL100, Bruker WH90, and Bruker WM500 spectrometers, the spin-lattice relaxation times being determined by the inversion recovery method. The density data were obtained with a Paar DMA 602 digital densimeter, the conductivity ones with a Tacussel CD6N6 conductimeter. The laser used for the light scattering experiments was a Spectra Physics 164 emitting at a wavelength of 5145 A with a power of 600 mW. Small-angle neutron scattering (SANS) spectra were recorded on spectrometer PACE at the Laboratoire Lton Brillouin, Saclay (France), using a cylindrical collimation geometry. The wavelength was X = 0.5 nm. Samples were held at 28 O C in flat quartz cells of 1- or 2-mm optical path. The sample to detector distance chosen was 0.6 m, in order to obtain high spatial resolution,Is reaching the high q range (0.4 < q < 4.4 nm-’). Counting times varied from 30 min to 4 h, depending on the contrast used. For each sample, three independent contrast conditions were employed: D,O/protonated NaDEHP/protonated solvent, called ”core” since only the aqueous core of the micelle is seen; H20/ protonated NaDEHP/deuterated solvent, called “micelle” since the whole micelle, including the chains of the surfactant gives the contrast; D20/protonated NaDEHP/deuterated solvent, called ”shell” since typical spectra of monodisperse hollow shells are observed in this case. In an Zq4 vs. q representation, the second maximum is higher than the first one.16 Standard data correction from background were used.” (9) Wong, M.; Thomas, J. K.; Nowak, T. J. Am. Chem. SOC.1977,99, 4730. (10) Ueno, M.; Kishimoto, H.; Kyogoku, Y . J . Colloid Interface 1978,63, 113. (1 1) Rouviere, J.; Couret, J. M.; Lindheimer, M.; Dejardin, J. L.; Marrony, R. J. Chim. Phys. Phys.-Chim. Biol. 1979,76, 289. (12) Maitra, A. N.; Eicke, H. F. J. Phys. Chem. 1981,85,2687. (13) Martin, C. A.; Magid, L. J. J. Phys. Chem. 1981,85, 3938. (14) McIvor, R. A.; McCarthy, G. D.; Grant, G. A. Can. J. Chem. 1956, 34, 1819. (15) Cabane, B.; Duplessix, R.; Zemb, T. In ‘Proceedings of the 4th International Symposium on Surfactants in Solution, Lund, Sweden, 1982”; Mittal, K. L., Lindman, B., Eds.; Plenum Press: New York, 1984; Vol. 1, p 373. (16) Hayter, J.; Hayoun, M.; Zemb, T. J. Colloid Interface Sci. 1984, 262, 798. (17) Ghosh, R.; Laue-Langerin Institute Report No. 78GH247T
Figure 1. Determination of the cmc by density measurements. (B) Expanded view of (A).
Figure 2. (A, left) Variation of the Rayleigh ratio RT with the surfactant concentration. (B, right) Determination of the aggregation number.
The inverted micelles have been found to exist in the oil-rich corner of the phase diagram for an added water quantity between W = 1.2 (under which NaDEHP cannot be solubilized in C&) and W = 6 (where a separation in two phases occurs). Static Study The critical micellar concentration (cmc) is known to be far smaller for inverted micelles than for direct ones. We chose densimetry as a sensitive method to determine it. According to Figure 1, the solution density varies linearly against the concentration of amphiphile on both sides of the point 9 X M. These two straight lines yield the partial volumes of the diethyl-2-hexyl phosphate in its monomeric and micellar states by means of the formula1* where p is the density and x the weight fraction of solute. Below the cmc V, = 392 cm3/mol and then the partial volume of the surfactant is 320 cm3/mol for a water/surfactant ratio of 4. It decreases to 310 cm3/mol above the cmc instead of increasing as in most of the direct micelles. This different behavior results possibly from a shrinking proper to amphiphiles with two alkyl chains due to sterical constraints in the aggregated state. For such a small water content, tightly bound to the polar heads as it will be shown later, we can consider that we are dealing with a twocomponent system, the organic solvent and the hydrated surfactant, so that we can dilute the solution with W constant without perturbing the system.’%22 The Figure 2A gives the Rayleigh ratio RT proportional to the intensity diffused by the solution in a direction perpendicular to the incident beam: this ratio appears to increase above lo-* M. This determination is far less accurate (18) Corkill, J. M.; Goodman, J. F.; Walker, T. Truns. Faruduy Soc. 1967, 63,768. (19) Day, R. A.; Robinson, B. H.; Clarke, J. H. R.; Doherty, J. V. J . Chem. Soc., Faraday Trans. 1 1979,75, 132. (20) Zulauf, M.; Eicke, H. F. J. Phys. Chem. 1979,83,480. (21) Elworthy, P. H.; Macintosh, D. S. J. Phys. Chem. 1964,68,3448. (22) Nakagawa, T.; Kuriyama, K.; Inoue, H. J . Colloid Sci. 1960,15,268.
The Journal of Physical Chemistry, Vol. 89, No. 15, 1985 3315
Properties of Inverted Micelles
-ir
-kLJ9d -y -
2I-3-m
-3 Log
y4
Figure 3. (A, left) Water proton chemical shift dependence of surfactant concentration. The solid line is calculated from eq 6 with N = 11.3, the dotted one with N = 2. (B, right) Determination of aggregation number Nand constant K .
but confirms the value of the cmc obtained by density measurements. From Debye's formula
+ 2A2(c - cmc) + 3A3(c - cmc)z
K ( c - cmc)/R = 1 / M
(2)
where K = ( 4 ~ ~ n ~ / X , ~ ) ( d n /l/N), d c ) ~ (n the benzene refraction index = 1.498, dn/dc the variation of the solution index with the concentration (measured by diffractometry) = 9.17 X cm3/g, A,, the light wavelength = 5145 A, R the difference between the ratio RT measured at the concentration c and the one measured at the cmc (RT,), and A, the virial coefficients, we can deduce the molar weight of the micelle and consequently its aggregation number N from the plot of K(c - cmc)/R vs. (c - cmc). Taking cmc = 9 X M, we did find N = 12.8 (Figure 2B). The first virial coefficient A2,which is null for an ideal solution, is negative due to the fact that we are dealing with a bad solvent. The water 'H chemical shift 6 allows a subsidiary determination of the cmc, assuming that for W = 3.5 all the water molecules are bound to the polar head as shown later. The plot of 6 vs. the surfactant concentration shows two limiting values below and above the cmc denoted as 6, and 6,, and corresponding to the 'H shifts of water bound to monomer and aggregated surfactant molecules, respectively (Figure 3A). At the vicinity of the cmc, the observed shift is a weighted average of 6,,,, and 6,,c 6obsd
=
(Wcmmo/
Wc)6mono
+ (Wcmic/
Wc)6m,c
(3)
where c,,,, and c,,, are the surfactant concentration in the monomer and aggregated states. The pseudophase model which assumes that above the cmc the concentration of monomers in solution remains constant and equal to the cmc, gives 6 = 6,,
below the cmc above the cmc 6 = 6,, - (cmc/c)(6,,c -),,6
(4a) (4b)
The eq 4b fits well the experimental data for a value of the cmc of 6.8 X M with a standard deviation (1/N)(E(6ca,Cd - 6obsd)2)1'2
= 0.014 PPm
But the equality 4a does not hold for the concentrations below the cmc. It seems therefore that a preassociation exists below this point. Let us then consider the mass action law model N(M)
2 (MN)
and denote now as 61 the value of the chemical shift for the monomer and 6, the value for an associated species of aggregation number N . The chemical shift at the concentration c is 6 =
(CI/C)~I
+ (CN/C)~N
Figure 4. Id vs. q plots of SANS spectra for (A, top) micelle contrast, (B, bottom) shell contrast; full line is for a 0.5 M solution, dotted line for 0.1 M.
(6 - 6 , ) or ( 6 , - 6) are too small compared to the experimental errors, one gets clearly two straight lines of slopes 2 and 11.3 for the small and large concentration, respectively (Figure 3B). Below the cmc the monomers are involved in a dimerization equilibrium with a constant K = 86 (mol/L)-I, and the profile of the plot becomes inconsistent with the pseudophase model. Above the cmc the aggregates include 11.3 monomers on the average; the micellization constant is then 4 X lo2' ( m ~ l / L ) - ' ~ .We ~ . can calculate the cmc according to the expressionz3 cmc = K-I/N-I = 8 X 10-3 M
It is slightly different from the one measured by densimetry. This difference may be due to a solvent effect which is protonated in density experiments and deuterated in N M R measurements. Such a phenomenon has often been observed in micellar systems. A last model is the multiple equilibrium model which is frequently used for inverted micelles2e26 and gives rise to a distribution of sizes. This model fits the experimental data too but was discarded by small-angle neutron scattering experiments. Typical SANS spectra are shown in Figure 4A,B for two different concentrations of NaDEHP (0.1 and 0.5 M ) and a constant value of W = [H,O]/[NaDEHP] = 4. Figure 4A is the spectrum with contrast condition "micelle", whereas Figure 4B is a "shell" spectra. The spectra obtained are independent of the concentration, since the minima of Zq4vs. q are at the same value of q, where q is the momentum transfer and Z the scattered intensity. Spectra obtained with cyclohexane and benzene are identical. This is not the case with AOT,27where benzene acts as a cosurfactant.28 The minimum of Zq4 vs. q reaches almost zero, indicating that the scatterers are both spherical and monodisperse. This sharp minimum at q 3.5 nm-I is much more pronounced than in the case of AOT?9 Since the micelles are monodisperse, their average mass cannot vary with concentratiodo and the multiple equilibrium model does not hold. We have estimated the micellar radius R from the relation qminR= 4.5 which gives a good approximation for homogeneous spheres, independent of the interaction term S(0).29By this method, one obtains, from the core spectrum, a waterpool radius of 7 A corresponding to 48 water molecules and therefore an aggregation number of 12, since W = 4, and from the micelle spectrum, the external radius of 13 A. It is then possible to calculate the interaction S(0) by the expression29
where Vis the deuterated volume of the micelle. We obtain S(0)
(5)
with c, + cN = c and K = c N / N c I N This . equation can also be written as log c(6 - 6,) = N log ~ ( 6 , - 6) + log N K - ( N - 1) log (6, - 61) (6) If this model holds, the plot of log c(6 - 6 , ) vs. log c (6, - 6) should give a straight line the slope and intercept of which yield the value of N and of the association constant. Removing the points where
(23) Eicke, H. F. Top.Curr. Chem. 1980, 87,85. (24) Muller, N. J. Phys. Chem. 1975, 79, 287. (25) El Seoud, M.I.; El Seoud, 0. A. J. Colloid Interface Sci. 1983, 91, 320. (26) OConnor, C. J.; Lomax, T. D. Tetrahedron Lett. 1983, 24, 2917. (27) Eicke, H. F. J. Colloid Interface Sci. 1979, 68,440. (28) Maitra, A,; Vasta, G.; Eicke, H. F. J. Colloid Interface Sci.1982, 93, 389. (29) Pileni, M.-P.; Zemb, T.; Petit, C. Chem.Phys.Lett.,in press. (30) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem.SOC., Faraday Trans.2 1976, 32, 1525.
3316 The Journal of Physical Chemistry, Vol. UY, 1VO. 202.7 MHZ
*
Paure et al.
1 3 , 1 YUJ
TABLE I: Comparison between Experimental and Calculated TI Values for the Studied Nuclei Using T~ D,, and d Best Fit Parameters'
i
nucleus
'H
freq, MHz 90.0 0.1456 0.14 4.0
T1,cpId Tl,cxptl
A,C % I
0
"See
102
Figure 5. OIPrelaxation rate as a function of surfactant concentration at two frequencies.
= 0.4 for c = 0.1 M. Since the volume fraction of the micelles is 4 = 3.8%, this value is higher than the one predicted by Camahan-Striling formula.'' Therefore, our neutron scattering experiment confirms the presence of an attractive interaction between reverse micelles, already found in AOT systems.'* Neutron scattering of the reverse micelles formed give the following picture: spherical, monodisperse micelles with an aggregation number of 12 in very good agreement with the value already determined by light scattering and N M R chemical shift measurements, formed according to the mass action law model and interacting through an attractive potential. The size of the micelles is independent of concentration. The surface per headgroup is 64 A2 against 60 A2 for AOT.33 For a molecule length of 9 8, and a molar volume of 310 cm3.mol-l, we calculate the sterical parameter defined by Israelachvili and co-worker~:'~u/aol = 0.9, a. being the area per headgroup. Since this value is lower than 1, the head group volume of our molecule is likely too low and so does not allow the formation of large and stable water in oil microemulsions, the opposite of AOT where u/aol = 1.05. Dynamical Behavior The main static data of the micellar system being determined, we are interested in the understanding of its dynamical behavior. For this purpose, we have measured the relaxation times of several nuclei of the surfactant molecule and of the water molecule. Surfactant Molecule. The phosphorus atom a t the center of the polar head is a very convenient probe for the overall molecular motion, allowing relaxation measurements down to lo-' M. Figure 5 givw the variations of relaxation rate l/T1 with the inverse of the solution concentration at two frequencies. It can be said first that this rate is less sensitive than the chemical shift of water proton to the difference between the mass action law model and the pseudophase one. Above the cmc, l/T1 can be written as
TI
= (l/TI)mic - (cmc/C)((l/Tl)mic - (l/TI)mono)
(8)
This equation holds for both models. Below the cmc, l/Tl seems to be constant as expected for the pseudophase model. Taking the K and N values calculated in the first section we deduce that the dimerization is not complete below the cmc: less than onehalf of the surfactant molecules are involved in a dimer at the cmc. The perturbation they cause must be within the measurements uncertainties. According to eq 8 the limiting values ( l/Tl)hc and ( l/Tl)mono can be obtained from the slopes and intercepts of the linear plots of Figure 5. The reorientation rates being obviously larger for monomers than for molecules in micelles, a shorter relaxation time is expected for the latter. An opposite behavior is observed which Can be tentatively explained by the occurrence of a conformational change upon micellization, such as for instance the removal of ethyl protons from the vicinity of the polar head. IH and I3C relaxation measurements were also performed on the first methylene groups a t a single concentration of 0.5 M where the (31) Cazabat, A. M.; Langevin, D. J. Chem. Phys. 1981, 74, 3148. (32) Huang, J. S.; Safran, S. A.; Kim, M. W.; Grest, G. S.; Kotlarchyk, M.;Quirke, N. Phys. Rev. L e r f . 1984, 53, 592. (33) C a b , C.; Delord, P. J. Phys. 1978, 39, 432. (34) Israelachvili, J. N.; Marcelja, S.; Horn, R. G . Q.Reo. Biophys. 1980, 13, 121.
IH 500.1 0.4423 0.482 -8.2
"C 25.2 0.09508
0.103 -7.7
31P
31P 36.5 2.043 2.05 -0.3
202.5 0.8874 0.84 5.6
36.5 3.397 3.365 1
Figure 7. ba-deuterated DEHP sample. c A = (TI,,,, -
Tl,cxptl)/ T1,cxptl.
Figure 6. Representation of the DEHP-molecule at the vicinity of the polar head in its most probable conformation (trans for the POCIC2and POGQ fragments). A is the molecular reorientation axis (bisector of
OOPO,).
monomer contribution is negligibly small. To account for the whole of the data of Table I we have considered that the molecule reorients preferentially about an axis A which is the bisector of the 03P04fragment (Figure 6). The vicinal coupling constants 3Jpocc and 'JpocHmeasured on the I3C and spectra are equal to 7.7 and 3.9 Hz, respectively. They follow a Karplus type relation depending on the dihedral angles POCICz and POCH. Taking for the trans (T) and gauche (G) rotamers the value^^^,^^ 'Ppocc = 8 HZ, 'Ppocc = 2 Hz, 'frpoc~= 20.9 Hz, and ' P p o c H = 1.8 Hz, one finds the conformational probabilities: for the POCIC2 fragment, PT = (3PBspocc - 3Jopocc)/(3frpocc 'J0pocc) = 0.95and for the POCH fragment, PG= ('frpWH 3PBspoCH)/(3frpoCH - 3Pp0cH) = 0.89. The small difference between these two results can be due to the imprecision of the measurements as well as uncertainties on the parameters 3 f r 3 G . The probabilities of the POClC2 trans conformation being equal to 0.9 we shall neglect in the forthcoming calculations the contribution of the gauche one without changing significantly the results. We are now able to calculate the positions of each atom of the first CH2groups relative to 31Pnucleus and the A axis. This leads to the conformation shown in Figure 6. The proton-induced dipolar relaxation rate 1/TI of 31P(or I3C) is l/T1 = (h2/10)y12ys2[Jo(~s - 4 + 3J1(wI) + 6J& + 4 1 (9) where J,(w) are reduced spectral densities of the form T / ( 1 w ~ T ~yr,s ) , being the magnetogyric ratios, and q Sthe Larmor frequencies of 'H (spin S ) and 31Por I3C (spin I). The dipolar relaxation rate of a proton pair is
+
1/TI = (3/lo)-~~h~(J,(wo) + 4Jd2~0))
(10)
For an axial motion of the NaDEHP molecule of correlation time sG and a micelle isotropic overall reorientation of correlation time T ~ The . spectral densities are3' = r-6(A(To/1
Jm(W)
+ W 2 T 0 2 ) + B ( T l / 1 + W 2 T 1 2 ) + c(T2/1 + W 2 7 2 2 ) ) (11)
(35) Lapper, R. D.; Mantsch, H. H.; Smith, I. C. P. J . Am. Chem. SOC. 1973, 95, 2878.
(36) Lapper, R. D.; Smith, I. C . P. J . Am. Chem. SOC.1973, 95, 2880. (37) Woessner, D. E. J . Chem. Phys. 1962.36, 1. (38) Herzfeld, J.; Griffin,R. G.; Haberkom, R. A. Biochemistry 1978, 17,
2711.
The Journal of Physical Chemistry, Vol. 89, No. 15, 1985 3377
Properties of Inverted Micelles
Figure 7. (A, left) DR,ro sets giving computed TI within 10% from the experimental TIfor ‘H at 90 MHz (horizontal stripes), ‘H at 500 MHz (vertical stripes), and ”C at 25 MHz (oblique stripes). (B, right) Domains of compatibility of 31Prelaxation at 36 and 202 MHz for d parameter values equal to 2, 2.2, 2.3, 2.4, and 2.6 A from left to right. *: best fit parameters point.
with DR = (rO-l+ TO-’)/T
