J. Phys. Chem. 1989, 93, 2190-2192
2190
An NMR Paramagnetic Relaxation Method To Determine Distribution Coefficients of Solubllizates in Micellar Systems Zhisheng Gao, Roderick E. Wasylishen, and Jan C. T. Kwak* Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 453 (Received: November 9, 1988: In Final Form: January 31, 1989)
A new technique is reported to measure apparent distribution coefficients of solubilizates in micellar systems, based on NMR paramagnetic relaxation. The degree of solubilization, p , of solubilizates between aqueous and micellar phases can be obtained by comparing the proton spin-lattice relaxation rates of the solubilizate in the absence and in the presence of noncomplexing paramagnetic ions of the same sign of charge as the micelle. The degree of solubilization is reported for 1,4-dioxane, diethyl ketone, 1-pentanol, benzyl alcohol, and benzene in dodecyltrimethylammonium bromide micelles and 1-propanol and benzyl alcohol in sodium dodecyl sulfate micelles. The results agree closely with those obtained from Fourier transform pulsed gradient spin-echo NMR self-diffusion measurements. The NMR paramagnetic relaxation method is applicable in principle to the quantitative determination of solubilization equilibria in many microheterogeneous systems and may be used with a number of NMR-active nuclei in the solubilizate.
Introduction Solubilization processes are involved in many applications of micellar solutions. The micelle-water distribution coefficients of solubilizates are important parameters in the solution chemistry of surfactants.' Although a variety of experimental techniques have been developed to measure micelle-water phase distribution coefficients, including vapor pressure,* c a l ~ r i m e t r y sol~bility,~ ,~.~ fluorescence spectr~photometry,~*' gel filtration,' electromotive force measurements: and N M R self-diffusion measurements,lO,l' many of these methods are difficult to perform and/or subject to considerable error, and some of them are still controversial.12 The Fourier transform N M R pulsed gradient spin-echo (FTPGSE) self-diffusion technique is a well-established methodI3 to study solubilization equilibria. This method offers several advantages over the other methods]' because N M R spectroscopy can identify chemically nonequivalent nuclei in the molecule to be investigated. Also, the FT-PGSE self-diffusion method monitors a concentration-related distribution coefficient and is unaffected by nonideal solution conditions. Unfortunately, the FT-PGSE technique requires a special probe and hardware modification to generate strong pulsed gradients. We report here a simple alternative N M R technique to measure the apparent distribution coefficient of solubilizates in ionic micellar solution, based on paramagnetic relaxation. This technique has the same advantages as the FT-PGSE self-diffusion method in measuring apparent distribution coefficients and can be carried out using any pulse FT N M R spectrometer. The precision of the TI measurement in the present method is at least equal to and possibly better than that of the self-diffusion coefficient measurement by FT-PGSE. The technique involves measuring the rate of 'H N M R spinlattice relaxation for one or more sets of chemically equivalent protons of the solubilizate in micellar solution in the presence and in the absence of a low concentration of some salt where either the cation or the anion is paramagnetic. The charge of the paramagnetic ion should be the same as that of the surfactant headgroup to ensure that the paramagnetic ion is repelled by the micellar surface and resides exclusively in the aqueous phase. Qualitatively, the rate of solubilizate proton relaxation will be significantly enhanced in the presence of the paramagnetic ion if the solubilizate spends the bulk of its time in the aqueous phase. If on the other hand the solubilizate resides predominantly in the micellar phase, the paramagnetic ions will not significantly enhance the proton relaxation rate of solubilizate. The value of p , the mole fraction of solubilizate in the micellar phase or the degree of solubilization, can be evaluated as follows. Under the condition of fast exchange of solubilizate between the *To whom correspondence should be addressed
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aqueous and micellar phases, the observed spin-lattice relaxation rate of solubilizate is a weight average between the solubilizate in the micellar phase and in the aqueous phase.Iel7 In the absence of paramagnetic ion the spin-lattice relaxation rate of solubilizate is given by Rl.obsd = pRl(mic) + ( l -p)Rl(aq)
(1)
where R,(mic) is the spin-lattice relaxation rate of the solubilizate in the micellar phase and Rl(aq) is the spin-lattice relaxation rate of the solubilizate in the aqueous phase. In the presence of paramagnetic ion, the observed spin-lattice relaxation rate of solubilizate is given by
where RP(aq) is the spin-lattice relaxation rate of solubilizate in aqueous phase in the presence of paramagnetic ion. Note that we have assumed that the R,(mic) is not influenced by the presence of the paramagnetic ion; this is a reasonable assumption when the charge of the paramagnetic ion is the same as that of the micellar surface. Subtracting eq 1 from eq 2 and rearranging, one obtains (3)
( I ) Mukerjee, P. In Solution Chemistry ofSurfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. I , p 153. (2) Tucker, E. E.; Christian, S. D. J . Colloid Interfuce Sci. 1985, 104. 562. (3) Roux, A. H.; Hetu, D.; Perron, G.; Desnoyers, J. E. J . Solution Chem. 1984, 13, I . (4) De Lisi, R.; Genova, C.; Testa, R.; Turco Liveri, V. J . Solution Chem. 1984, 13, 121. (5) Ekwall, P.; Mandell, L.; Fontell, K. Mol. Cryst. Liq. Cryst. 1969, 8, 157. (6) Abuin, E. B.; Lissi, E. A. J . Colloid Interface Sci. 1983, 95, 198. (7) Almgren, M.; Grieser, F.; Thomas, J. K . J . Am. Chem. Soc. 1979, 101, 279. (8) Goto, A,; Endo, F.; Ita, K. Chem Pharm. Bull. 1977, 25, 1165. (9) Yamashita, F.; Kwak, J . C. T., to be published. (10) Stilbs, P. J . Colloid Interface Sci. 1981, 80, 608. (1 1 ) Stilbs, P. J . Colloid Interface Sci. 1983, 94, 463. (12) Stilbs, P. J . Colloid Interface Sci. 1988, 122, 593. (13) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, I . (14) Zimmerman, J. R.; Brittin, W. E. J . Phys. Chem. 1957, 61, 1328. (15) Mclaughlin, A. C.; Leigh, Jr., J. S. J . Magn. Reson. 1973, 9, 296. (16) James, T . L. Nuclear Magnetic Resonance in Biochemistry; Academic: New York, 1975; pp 173-211. (17) Chachaty, C.; Ahlnas, T.;Lindstrom, B.; Nery, H.; Tistchenko, A. M. J . Colloid Interface Sri. 1988, 122, 406.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2191
Letters TABLE I:
'H TI of Solubilizate in the Presence and Absence of Paramagnetic Ions and the Degree of Solubilization in DTAB and SDS' solubilizateb*c Tlhd %bsd TI(4 P FT-PGS E
nw
1,4-dioxanediethyl ketone (CH$H2)zCO (CH$H2)2CO benzyl alcohol, C6H6CH20H 1-pentanol, CH3(CH2),CH20H benzene
5.59 f 0.20 4.81 f 0.20 4.40 f 0.15 3.03 f 0.15 2.32 f 0.11 3.92 f 0.18
DTAB/Mn(D20)62+ 6.29 f 0.30 1.25 f 0.06 6.75 f 0.30 1.82 f 0.09 1.84 f 0.09 6.46 f 0.25 9.44 f 0.40 1.73 f 0.08 3.85 f 0.15 1.41 f 0.07 2.85 f 0.14 18.9 f 0.90
1.15 f 0.05 1.44 f 0.07 1.52 f 0.07 1.25 f 0.06 0.91 f 0.04 1.61 f 0.08
0.13 f 0.07 0.37 f 0.07 0.37 f 0.07 0.64 f 0.05 0.67 f 0.05 0.83 f 0.04
0.69d 0.69d 0.85d
1-propanol, CH3CH2CH20H benzyl alcohol, C6H5CH20H
4.03 f 0.16 3.04 f 0.12
SDS/3-Carboxyproxyl 1.99 f 0.08 5.30 f 0.21 2.07 f 0.08 9.10 f 0.30
1.69 f 0.07 1.73 f 0.06
0.37 f 0.07 0.67 f 0.05
0.32 f 0.06e 0.67 f 0.03'
O.lld 0.34d
'All TI values are in seconds. bSolubilizateconcentrations are 4 hL/g of D20,corresponding to ca. 0.04 m. CItalicsindicate the proton resonance on which T , is determined. dReference 1 I . cReference25.
In all cases, R I = l / T l , where T I is the spin-lattice relaxation time. The spin-lattice relaxation rate of solubilizate in the aqueous phase in the presence of paramagnetic ion, RP(aq), is given by (4) where R,,(aq) is the paramagnetic contribution to the spin-lattice relaxation rate of solubilizate in the aqueous phase. If there is no stable complex formed between the paramagnetic ion and the solubilizate, the paramagnetic relaxation of the solubilizate molecule is dominated by intermolecular dipole-dipole interaction modulated by relative translational motion.l* When the solubilizate is neutral, this paramagnetic relaxation is dependent on the concentration of paramagnetic ion but independent of the concentration of the solubilizate, as indicated by Abragam's earlier "independent diffusion" mode119-20 or by Hwang and Freed's recent "force free diffusion" mode1.z1-24 Therefore, RP(aq) can be measured independently in a solution containing the same amount of paramagnetic ions and solubilizate molecules in the absence of surfactant micelles. Rl(aq) can also be easily determined in an aqueous solution containing the solubilizate only. In the present study we demonstrate the feasibility of this paramagnetic relaxation method by measuring ' H spin-lattice relaxation rates of a number of solubilizates in well-studied dodecyltrimethylammonium bromide (DTAB) and sodium dodecyl sulfate (SDS) solutions, with Mn(D20)2+ and 3-carboxyproxyl as paramagnetic ions, respectively. The results for the degree of solubilization and the distribution coefficients will be compared to data derived from FT-PGSE experiments by Stilbs'l~zsand to the results of the thermodynamic measurments of De Lisi et a1.26 in the same systems.
Experimental Section
Dodecyltrimethylammonium bromide (Aldrich) was purified by repeated recrystallization from acetone. The proton TI measurements were performed at 361.053 MHz (8.48 T), using a Nicolet 360 N B spectrometer. Ti'swere measured by using an inversion recovery sequence in which alternate 90' pulses are phase shifted by 180°,27and a composite 180' pulse is used to compensate for imperfect Bl homogeneity.28 All T I values were calculated from peak heights obtained at 12 or more delays, using (18) Kowalewski, J.; Nordenskiold, L.; Benetis, N.; Westlund, P.-0. Prog. Nucl. Mugn.Reson. Spectrosc. 1985, 17, 141. (19) Abragam, A. The Principles of Nucleur Magnetism; Clarendon: Oxford; 1961; Chapter VIII. ( 2 0 ) Hexem, J. G.; Edlund, U.;Levy, G.C. J. Chem. Phys. 1976,64,936. (21) Hwang, L.-P.; Freed, J. H. J . Chem. Phys. 1975, 63, 4017. (22) Freed, J. H. J . Chem. Phys. 1978, 68, 4034. (23) Fries, P. H.; Patey, G.N. J . Chem. Phys. 1984, 80, 6253. (24) Fries, P. H.; Jagannathan, N. R.; Herring, F. G.;Patey, G. N. J . Phys. Chem. 1987, 91, 215. (25) Stilbs, P. J . Colloid Interface Sci. 1982, 87, 385. (26) De Lisi, R.; Milioto, S.;Turco Liveri, V. J . Colloid Interface Sci. 1987, 11 7, 64. (27) Cutnell, J. D.; Bleich, H. E.; Glasel, J. A. J . Mugn. Reson. 1976, 21,
43.
a nonlinear three-parameter least-squares fitting procedure29 available on the Nicolet software. Error limits as reported represent the repeatability of the data in a series of independent experiments and are much larger than the error derived from the least-squares fitting of a single experiment. The error limits obtained from the least-squares fitting of a single experiment are usually less than 1%. The experiments were carried out at 35 f 1 'C for DTAB micellar systems and 25 f 1 O C for SDS micellar systems; 99.9% D 2 0 (Norell) was used as solvent. MnC12 (ACS grade) and 3-carboxyproxyl (Aldrich) were used as paramagnetic agents. The 'H spin-lattice relaxation rates of the surfactant DTAB headgroups (Le., the N-CH, and the a-CH2 protons) are not changed until the Mn(D20),2' concentration is as high as 0.0007 m (mol/kg of DzO). The concentration of Mn(D20)?+ used in this study is 0.0004 m . At this concentration the proton relaxation time of the surfactant DTAB headgroup is the same as that in the absence of M n ( D ~ o ) 6 ~ ' .The sodium salt of 3-carboxyproxyl was prepared by neutralizing 3carboxyproxyl with an equivalent amount of NaOD. In the SDS micellar systems 0.002 m 3-carboxyproxyl was used. At this concentration, the 'H spin-lattice relaxation rate of a-CH2 in SDS is the same as that in the absence of the paramagnetic ion. Also, in a SDS solution containing 2 hL/g of DzO tetramethylsilane (TMS), the IH relaxation times of T M S in the absence and in the presence of 0.005 m 3-carboxyproxyl are the same within experimental error, clearly indicating that the p value of T M S is close to 1 and that the paramagnetic ions have no effect on the relaxation rate of the molecule located inside the micelles.
Results and Discussion The results of five typical solubilizates, 1,4-dioxane, diethyl ketone, I-pentanol, benzyl alcohol, and benzene, in DTAB micelles (with Mn(D20)62+as paramagnetic ion) and of 1-propanol and benzyl alcohol in SDS micelles (with 3-carboxyproxyl as paramagnetic ion) are shown in Table I. The solubilizate concentration is 4 pL/g of D 2 0 (ca. 0.04 m ) ; DTAB and SDS concentrations are 50 mg/g of D 2 0 (0.16 m ) and 70 mg/g of D 2 0 (0.24 m),respectively. Also shown in Table I are the p values measured by Stilbs using the FT-PGSE self-diffusion method for the same surfactant-solubilizate combinations and at similar The results obtained with the paramagnetic relaxation method described in this paper agree closely with those of the FT-PGSE self-diffusion method. If the solubilizate has chemically nonequivalent protons, the best resolved proton resonance (as indicated in table I) is chosen to measure TI. Different proton resonances should give the same result if they are all well-resolved; for instance, the T,'s measured from the methyl protons and the methylene protons of diethyl ketone give the same p value, as shown in Table I. In principle, the paramagnetic relaxation method monitors the time-average mole fraction of solute located inside the micelles (28) Freeman, R.; Kempsell, S. P.; Levitt, M. H. J . Magn.Reson. 1980, 38, 453. (29) Levy, G.C.; Peat, I. R. J . Magn. Reson. 1975, 18, 500.
J . Phys. Chem. 1989, 93, 2192-2193
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TABLE 11: Dependence of p and K, on 1-Pentanol Concentration in DTAB (50 m d g of D,O) Micellar Solution
[pentanol],m 0.037 0.074 0.1 1 1 0.148
P 0.67 0.60 0.66 0.64
f 0.05 f 0.05 f 0.05
f 0.05
Kc 36 f 8 21 f 6 35 f 8 32 f I
while the FT-PGSE self-diffusion method"I3 monitors the time-average mole fraction of solute diffusing with the micelles. The degrees of solubilization obtained with these two methods are in very good agreement, demonstrating that the two techniques measure the same quantity. Goto et aL30 found in gel filtration experiments that the apparent distribution coefficients of alkylparabens in sodium dodecyl sulfate micellar solutions depend on the concentration of the alkylparabens. Zana et aL3' in their study of alcohol solubilization in micellar solution found that the apparent distribution coefficient obtained with the solubility method is about one-quarter of the value obtained in the vapor pressure experiments that were performed at 100- to 1000-fold lower alcohol concentrations. These authors suggest that this discrepancy is due to the dependence of the apparent distribution coefficient on the alcohol concentration. We have measured the degree of solubilization, p , and the apparent distribution coefficient, Kc, of 1-pentanol in DTAB (50 mg/g of D20) micellar solution at four different 1-pentanol concentrations (Table 11). The K, values are calculated from the following equation:]' (30) Goto, A.; Endo, F. J . Colloid Interface Sei.1978, 66,26. (31) Zana, R.; Yiv, S.; Strazielle, C.; Lianos, P. J . Colloid Interface Sei. 1981, 80,208.
Kc
=
(%cellar
phase/ @aqueous phase
- PVaqueous phase/(l
- p)Vmicdlar phase
(5)
In the calculation of Kc we use 0.295 dm3/mol for the partial molar volume of the micellar DTAB.26 Our results show that in the concentration range studied p and Kc are constant within experimental error. The average value of the apparent distribution coefficient, Kc, is found to be 33 f 5, in good agreement with the value of 33 obtained from the application of a mass action model to measurements of heat of mixing at 25 " C by De Lisi et a1.26 In conclusion, the N M R paramagnetic relaxation technique provides a convenient, reliable way to study solubilizationequilibria in micellar systems. This technique has considerable advantages over many other methods used to measure distribution coefficients. The values for the distribution coefficient obtained with this method agree with the values resulting from the FT-PGSE self-diffusion method. From the study of the dependence of the measured apparent distribution coefficient on solubilizate concentration we found that,for 1-pentanol in the concentration range of 0.037-0.148 m (mol/kg of D 2 0 ) the apparent distribution coefficients in DTAB solutions are constant within experimental error. In principle, this method can also be used in other microheterogeneous systems, including microemulsions, reverse micelles, liposomes, and polymer-surfactant solutions. The relaxation of other NMR-active nuclei can also be used to measure distribution coefficients of a number of different solubilizates.
Acknowledgment. This research was supported by the Natural Sciences and Engineering Research Council of Canada. N M R measurements were carried out in the Atlantic Region Magnetic Resonance Centre (ARMRC) at Dalhousie University.
Dlffusion and Nonlinear Reversible Trapping in a One-Dimensional Semiinfinite Model Membrane A. Prock* and W. P. Giering Chemistry Department, Metcalf Cenf e r For Science and Engineering, Boston University, Boston, Massachusetts 02215 (Received: December 13, 1988)
One-dimensional diffusion in the presence of nonlinear reversible trapping is described for the semiinfinite case-a special but experimentally important case. Although the results differ in quantitative aspects, they corroborate qualitatively the existence of sharp, slow-moving steps and pronounced inflections in the concentration profiles as recently reported.
Introduction In recent years a controversy has grown up about whether an electroactive dopant within a conducting polymer can be in thermodynamic equilibrium with dopant in an external phase. Points of contention are the observed disparity in desorption time vs absorption time for a given amount of dopant, and the existence of sharp steps and points of inflection in the concentration profiles of dopant within the conducting polymer. These observations have been interpreted by some researchers as casting doubt on the existence of a state of equilibrium. Reiss and co-workers1s2in addressing this problem have devised an equilibrium model where the interaction of the trap, T, with the dopant, A, is described chemically in terms of an equilibrium constant according to ( I ) Murphy, W. D.; Rabeony, H. M.; Reiss, H. J . Phys. Chem.1988, 92, 7007. (2) Kim, D.-u.; Reiss, H.; Rabeony, H. M. J . Phys. Chem.1988, 92, 2673.
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A + T = AT, a = [A'][T']/[AT'] (1) where the prime refers to concentration normalized to total trap [AT]). A polymer sheet containing a concentration ([TI uniform concentration of homogeneous traps, immersed in the external phase, is treated as a one-dimensional diffusion problem where D turns out to be concentration dependent, vide infra. Numerical solution of the resulting partial differential equation' shows indeed that sharp steps and inflection points in the concentration profile result along with a disparity in absorption and desorption times and that the smaller a, the greater the disparity. This model requires one to solve a "stiff" differential equation,' i.e., where the diffusion coefficient is a sensitive function of material concentration. As the problem is posed, the equation, written in the usual distance and time variables, possesses singular points at the membrane boundaries, and a highly sophisticated method of integration must be employed. However, the concentration profiles presented' are virtually those for the semiinfinite problem. With this special but important case in mind we offer
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0 1989 American Chemical Society
