J. Phys. Chem. 1991, 95,462-467
462
consisting of a hard-sphere repulsion term and a strong and extremely short range attractive term. This model describes droplets whose hydrocarbon tails are strongly attractive to the hydrocarbon tails of adjacent droplets. The SANS fit shows that the tail-tail attractive interactions may be stronger than the longer range van der Waals type attractive interaction between the water cores of the droplets. In the context of this model, the tail-tail attractive potential would be zero for a c8 alkane continuous-phase solvent. These results are in agreement with earlier SANS and light scattering studies of alkane/AOT/water systems. The SANS and light scattering results are still not completely consistent with phase behavior studies of these systems, which suggest that there is a minimum in the interdroplet attractive force for a C5 continuous-phase solvent.38
Acknowledgment. SANS spectra were taken at the scattering facility at the National Institute of Standards and Technology (NIST). We are extremely grateful for the advice and encouragement of Dr. Charles Glinka of NIST, without whose help these measurements could not have been made. This work was supported by the National Science Foundation (PYIA-8351179) and the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the US.Department of Energy (which supported J. L. Fulton and R. D. Smith), under Contract DE-AC06-76L0 1830. Pacific Northwest Laboratory is operated for the DOE by Battelle Memorial Institute. (38) Tingey, J. M.; Fulton, J. L.; Smith, R. D. J . Phys. Chem. 1990, 94, 1994.
Distribution Equilibrium of Poly(ethy1ene oxide) in Sodium Dodecyl Sulfate Micellar Solutions: An NMR Paramagnetic Relaxation Study Zhisheng Gao, Roderick E. Wasylishen, and Jan C. T. Kwak* Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3 (Received: March 14. 1990; In Final Form: June 14, 1990)
The apparent distribution coefficient of poly(ethy1eneoxide) (PEO) in sodium dodecyl sulfate (SDS) micelles has been determined by using the NMR paramagnetic relaxation method. The influence of PEO molecular weight, terminal group, and concentration on the solubilization equilibrium is examined. For low molecular weight PEO (MW < 4000) the degree of solubilization increases with increasing molecular weight. Also, the degree of solubilization of PEO increases when the terminal group of the polymer is changed from -OH to -OCH,. For PEO with a molecular weight higher than 4OO0, the degree of solubilization remains constant at 0.85 0.02 and the solubilization capacity of the SDS micelle is ca. 1.9 PEO monomer units per dodecyl sulfate ion. The location of PEO in the SDS micelles has been investigated by measuring the degree of solubilization in the presence of high concentrations of NaCI. The results suggest that only a small fraction of the PEO is located in the micellar electric double layer.
*
Introduction interactions between polymers and surfactants are generally referred to as “binding” of the surfactant by the polymer. Earlier studies were concerned mainly with interactions between proteins and charged surfactants, where the binding was considered to be site specific.’ In the past two decades, interactions between ionic surfactants and neutral polymers have been investigated extensively because of their importance in industrial processes and in biological systems.2-s Although it is generally recognized that the hydrophobic interaction is the most important interaction between neutral polymers and ionic s u r f a c t a n P and that there are no specific binding sites in the polymer, the term “binding” is still used to describe these interactions. Many binding studies focus on the distribution of the surfactant between monomer and polymersurfactant aggregates, whereas the measurement of the distribution coefficient of the polymer between the aqueous phase and polymersurfactant aggregates has been completely neglected, probably due to the fact that there was no experimental technique available to distinguish between the polymer monomer units in the aqueous phase and in the polymer-surfactant aggregate. I n recent years solubilization in micellar systems and mixed micelle formation have been studied extensi~ely.~.’~ Many techniques have been developed to measure the distribution coefficients of solubilizates or cosurfactants in the micellar and in the aqueous phases, including vapor pressure,” calorimetry,’*J3 solubility,’4fluorescence spectrophotometry,15J6 gel filtration,” emf measurements,I8 and NMR self-diffusion measurement^.'^*^^ Most of these methods are difficult to perform and/or subject to certain limitations, and none of them can be easily applied to
* To whom correspondence should be addressed. 0022-3654/9 1/2095-0462$02.50/0
polymersurfactant systems. We have recently established a new method to measure the distribution coefficients of solubilizates ( I ) Steinhardt, J.; Reynolds, J. A. Multiple Equilibria in Proteins; Academic Press: New York, 1969. (2) Robb, 1. D. In Anionic Surfactants, Physical Chemistry of Surfactant Action; Lucassen Reynders, E. H., Ed.; Marcel Dekker: New York, 1981; Vol. 11, p 109. (3) Goddard, E. D. Colloid Surf. 1986, 19, 255, 301. (4) Saito, S. In Nonionic Surfactants: Physical Chemistry; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; Vol. 23, p 881. (5) Hayakawa, K.; Kwak, J. C. T. In Cationic Surfactants; Holland, P . M., Rubingh, D., Eds.; Marcel Dekker: New York, in press. (6) Francois, J.; Dayantis, J.; Sabbadin, J. Eur. Polym. J . 1985, 21, 165. (7) Perron, G.; Francoeur, J.; Desnoyers, J. E.; Kwak, J. C. T. Can. J . Chem. 1987, 65,990. (8) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J . Colloid Interface Sci. 1990, 137, 137. (9) Mukerjee, P. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. 1, p 153. (10) Scamehorn, J. F. In Phenomena in Mixed Surfactant Systems; Scamehorn, J. F., Ed.; ACS Symposium Series 31 I; American Chemical Society: Washington, DC, 1986; p I. (1 1) Tucker, E. E.; Christian, S.D. J . Colloid Interface Sci. 1985, 104, 562. (12) Roux, A. H.; Hetu, D.; Perron, G.; Desnoyers, J. E. J. Solution Chem. 1984, 13, 1. ( 1 3) De Lisi, R.; Genova, C.; Testa, R.; Turco Liveri, V. J . Solution Chem. 1984, 13, 121. (14) Ekwall, P.; Mandell, L.; Fontell, K. Mol. Cryst. Liq.Cryst. 1969,8, 157 ._.
(15) Abuin, E. B.;Lissi, E. A. J. Colloid Interface Sci. 1983, 95 198. (16) Almgren, M.; Grieser, F.; Thomas, J. K. J. Am. Chem. SOC. 979, 101, 279. (17) Goto, A.; Endo, F.; Ito, K. Chem. Pharm. Bull. 1977, 25, 165. (18) Yamashita, F.; Kwak, J. C. T. To be published. (19) Stilbs, P. J . Colloid Interface Sci. 1981, 80, 608.
0 1991 American Chemical Society
Solubilization of Polymers in Micelles
in micellar solution, based on NMR paramagnetic relaxation.21 This method not only offers the same advantages as the NMR FT-PGSE self-diffusion methodZobut also is unique in the study of polymersurfactant systems because it can distinguish between the monomer unit of the polymer in the aqueous phase and in the polymersurfactant aggregates. Spin-lattice relaxation rates can be easily measured in any pulse FT N M R spectrometer, and hardware modifications as required for the FT-PGSE self-diffusion method22are not necessary. The feasibility of the paramagnetic relaxation method in the case of small solubilizates has been demonstrated in previous paper^.^'**^ The degree of solubilization has been reported for a number of solubilizates in dodecyltrimethylammonium bromide (DTAB), sodium dodecyl sulfate (SDS), and Triton X-100 micellar solutions, using Mn(D20)62+, Mn(EDTA)2-, and 3carboxyproxyl anions as paramagnetic reagents. The results in DTAB and SDS micellar systems agree closely with those obtained from NMR FT-PGSE s e l f - d i f f ~ s i o nand ~ ~ ~thermodynamic ~~ measurements.25 Some preliminary results on the solubilization of polymers in surfactant micellar solutions have also been reported .23 In this paper we present a detailed investigation of the solubilization equilibrium of a neutral water-soluble polymer poly(ethylene oxide) (PEO) in the SDS micellar system, by use of the paramagnetic relaxation technique. Proton spin-lattice relaxation rates of the PEO in SDS micellar solutions are measured in the presence and absence of paramagnetic 3-carboxyproxyl anions. The influence of PEO molecular weight, terminal groups, and concentration on the distribution equilibrium of the polymer between polymer-surfactant aggregates and aqueous solution are reported. Theory The paramagnetic relaxation technique involves measuring the apparent rate of 'H NMR spin-lattice relaxation for one or more sets of chemically equivalent protons of the polymer in micellar solution in the presence and in the absence of a low concentration of a 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 hence resides exclusively in the aqueous phase. Qualitatively, the rate of polymer proton relaxation will be enhanced significantly in the presence of the paramagnetic ion if most of polymer monomer units are located in the aqueous phase. If, on the other hand, the polymer resides predominantly in the miccllar phase, the paramagnetic ions will not significantly enhance the relaxation rate of polymer protons. We define a parameter p as the fraction of a solute solubilized in the micelles
where n,(mic) and n,(aq) are the number of moles of solute S in the micellar and in the aqueous phases, respectively. For the case of polymer as solute, n,(mic) and n,(aq) are expressed in terms of monomer units. The value of p can be evaluated as follows. I f the polymer is under the condition of fast exchange between the aqueous and micellar phases (vide infra), the observed IH spin-lattice relaxation rate of the polymer protons is the weighted average bctween the polymers in the micellar phase and in the aqueous phase.2629 In the absence of paramagnetic ions the IH (20) Stilbs, P. J . Collid Interface Sci. 1983, 94, 463. (21) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J . Phys. Chem. 1989, 93, 2190. (22) Stilbs, P. Prog. Nucl. Magn. Reson. Specirosc. 1987, 19, I . (23) Gao, Z.; Kwak, J. C. T.; Labonte, R.; Marangoni, D. G.; Wasylishen, R. E. Colloid SurJ 1990, 45, 269. (24) Stilbs, P. J . Colloid Interface Sci. 1982, 87, 385. (25) De Lisi, R.; Milioto, S.; Turco, Liveri, V. J . Colloid Interface Sci. 1987, I 17, 64. (26) Zimmerman, J. R.; Brittin, W. E. J. Phys. Chem. 1957, 61, 1328. (27) Mclaughlin, A. C.; Leigh, Jr., J . S. J . Magn. Reson. 1973, 9, 296.
The Journal of Physical Chemistry, Vol. 95,No. 1, I991 463 spin-lattice relaxation rate of the polymer proton is given by
where R,(mic) is the spin-lattice relaxation rate of the polymer protons in the micellar phase and Rl(aq) is the spin-lattice relaxation rate of the polymer protons in the aqueous phase. In the presence of paramagnetic ions, the observed spin-lattice relaxation rate of the polymer protons is given by (3) where R{(aq) is the spin-lattice relaxation rate of polymer protons in the aqueous phase in the presence of paramagnetic ion. Equation 3 is based on the assumption that the R,(mic) is not influenced by the presence of the paramagnetic ion of the same charge as the micellar surface. Subtracting eq 2 from eq 3 and rearranging, we can obtain the mole fraction of polymer in the micellar phase
(4)
In all cases, R l = l / T l , where TI is the spin-lattice relaxation time. R{(aq) and Rl(aq) can be measured directly in aqueous solutions of the polymer in the presence and absence of paramagnetic ions, respectively.2' The question may arise whether for polymers that are partially solubilized in micelles the IH spin-lattice relaxation rates of polymer monomer units in the aqueous phase are the same as those of free polymers in the aqueous phase. However, even if this is not the case, what we use in eq 4 is the difference between R{(aq) and Rl(aq). This difference for free polymers in the aqueous solution is essentially the same as that of polymers partially solubilized in micelles, as will be shown below. The paramagnetic contribution to the 'H spin-lattice relaxation rate of polymer in aqueous phase, Rl,(aq), is given by the difference between R{(aq) and Rl(aq) and is determined by an intermolecular dipolar interaction with unpaired electrons, provided no stable complex is formed between the polymer and the paramagnetic ion3*37 R1Jaq) = Rf(aq) - Rl(aq) = ( 8 ~ 15)(110/4a)~(rirsh/2*)ZS(S / + 1)(Ns7/b3)X [3J(~1,7)+ 7J(ws77)l ( 5 )
where y, and ys are the nuclear and electron magnetogyric ratios and wI and us are the corresponding Larmor frequencies. S is the electron spin, h is the Planck constant, Ns is the number density of the electron spin S , and b is the distance of closest approach. J(w,T)is called the spectral density function, and its precise form is model d e ~ e n d e n t .7~is~the ~ ~translational correlation time which is defined by33-37 7
= b2/(D1 + Ds)
(6)
where D, and D, are the translational diffusion coefficients of I ~
(28) James, T. L. Nuclear Magnetic Resonance in Biochemistry; Academic: New York, 1975; pp 173-211. (29) Chachaty, C.; Ahlnas, T.; Lindstrom, B.; Nery, H.; Tistchenko, A. M. J . Colloid Interface Sci. 1988, 122, 406. (30) Kowalewski, J.; Nordenskiold, L.; Benetis, N.; Westlund, P.-0. frog. Nucl. Magn. Reson. Spectrosc. 1985, 17, 141. (31) Abragam, A. The Principles of Nuclear Magnetism; Clarendon: Oxford, 1961; Chapter VIII. (32) Hexem, J. G.; Edlund, U.; Levy, G . C. J . Chem. Phys. 1976,64,936. (33) Hwang, L.-P.; Freed, J. H. J . Chem. Phys. 1975, 63, 4017. (34) Freed, J. H. J . Chem. Phys. 1978, 68,4034. (35) Ayant, Y . ; Belorizky, E.; Alizon, J.; Gallice, J. J . Phys. (12s. Ulis, ?O, 6253.
464
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The Journal of Physical Chemistry, Vol. 95, No. I , 1991
TABLE I: 'H T I of 0.058 m Benzyl Alcohol and 0.2% PEO 4000 in the Presence and the Absence of 3-Carboxylproxyl Anions and the Degrees of Solubilization in 0.24 m SDS" solubilizate IDroxvll, m Ti nk 7?n h T,(aq) 7Rad P 1.73 f 0.05 0.67 f 0.04 2.07 f 0.06 9.10 f 0.27 3.04 f 0.09 benzyl alcohol 0.002 0.286 f 0.010 0.64f 0.03 9.10 f 0.27 3.04 f 0.09 0.648 f 0.030 C, H ~ - CH OH^ 0.015 0.216f 0.007 0.69f 0.02 0.583 f 0.020 9.10 f 0.27 3.04 f 0.09 0.020 0.84 f 0.03 0.638 f 0.020 0.257f 0.008 0.487f 0.010 0.414f 0.010 PEO 4000 0.0I O 0.188 f 0.006 0.87 f 0.02 0.369f 0.010 0.638 f 0.020 0.487f 0.010 0.015 "All TI valucs arc in seconds. bltalics indicate the proton resonance on which TI is determined.
and S spins, respectively. For the interaction between polymer nuclei and small paramagnetic ions the T value is primarily determined by the translational diffusion coefficient of the paramagnetic ions, which is assumed to be much greater than the translational diffusion coefficient of the polymer. For instance, the translational diffusion coefficients of PEO 5700 (6.6%)'* and 3-carboxyproxyl anion3' in aqueous solution are 3 X IO-'' and 8 X 1 0-Io m2/s, respectively. Therefore, the value of Rl,(aq) for PEO is essentially the same whether the polymer is partially solubilized in the micellar phase or located exclusively in the aqueous phase. In this study, eq 4 is used to calculate the degree of solubilization of PEO in SDS micelles. PEO molecules are assumed to undergo fast exchange ( R e x>> R I , Re, is the exchange rate) between the micellar and the aqueous phases. This assumption is best justified by the recent ultrasonic relaxation data of Takisawa et al.,39which indicated that, in a PEO 300000/sodium decyl sulfate system, the desorption rate of the surfactant from the polymer is 8.6 X 105 s-' .
n
PEO I
?
5.5
...
, . . . 5.0
....
I
Y.5
Y.0
. . , . , . 3.5
1
.
5.0
, . . . , . . , . , . . . . I I 2.5 2.0 1.5
.
.
.
,
.
.
1.0
.
.
,
.
.
.
0.5
PPW
Figure 1. 'H NMR spectrum of 0.75% PEO 4000/0.24m SDS solution, with HOD resonance (6 = 4.63 ppm) as internal reference.
(38) Brown, W.; Stiibs, P. Polymer 1982, 23, 1780. (39) Takisawa, N.;Brown, P.; Bloor, D.; Hall, D. G.; Wyn-Jones, E. J . Chem. Soc.. Faraday Trans. I 1989, 85, 2099. (40)Cutnell, J. D.;Bleich, H. E.; Glasel, J. A. J . Magn. Reson. 1976, 21,
As shown in Figure 1, the proton resonances of PEO are well separated from those of SDS, and hence the spin-lattice relaxation rate of the PEO ethylene protons can be determined with good accuracy. In the PEO/SDS system, the short spin-lattice relaxation times of the PEO protons necessitate the use of relatively high paramagnetic ion concentrations (0.010-0.020 m 3-carboxyproxyl anions) to enhance the relaxation rate of the polymer protons in the aqueous phase substantially. To ensure that the paramagnetic ions have no effect on the ' H spin-lattice relaxation rates of solubilizates in the SDS micellar phase, we have measured the degrees of solubilization of 0.058m benzyl alcohol in 0.24 m SDS micellar solution, using respectively 0.002, 0.015, and 0.020 m 3-carboxyproxyl anions. The three values for p obtained are within experimental error (Table I). When the concentration of 3carboxyproxyl anions is 0.002 m, the paramagnetic relaxation enhancement on the first methylene group (a-CH2) of SDS is not observable.*' At higher concentrations of 3-carboxyproxyl anions, a small effect on the ' H spin-lattice relaxation rate of a-CH2 can be observed, which is due to the dipolar interaction between the paramagnetic ions and the surfactant monomers in the aqueous phase. Our p values for benzyl alcohol in SDS micellar solutions also agree closely with the value p = 0.67 obtained by Stilbs using the FT-PGSE self-diffusion technique.24 There is no significant difference between the measured degrees of solubilization of 0.2% PEO 4000 in SDS micellar solutions using 0.010 and 0.015 m 3-carboxyproxyl anions (Table I). These results demonstrate that the paramagnetic relaxation method yields reliable results even when the concentration of 3-carboxyproxyl anions is as high as 0.020 m. Throughout this work we use 0.01 5 m 3-carboxyproxyl anions to enhance the 'Hspin-lattice relaxation rate of the PEO in the aqueous phase. PEO Molecular Weight and Terminal Group Effects. The solubilization equilibria of 0.2% (ca. 0.045 m ) PEOs with average molecular weights of 200000, 20000, 8000, 4000, 600, and 300, and tetraethylene glycol and tetraethylene glycol dimethyl ether, all in 0.24 m SDS micellar solution, have been studied. The degrees of solubilization calculated from eq 4 and apparent distribution coefficients (from eq 7), are given in Table 11. For PEO
43. (41)Freeman, R.;Kempsell, S . P.; Levitt, M. H. J . Magn. Reson. 1980, 38, 453. (42)Levy, G.C.;Peat. I. R. J . Magn. Reson. 1975, 18, 500
(43)Stark, R.E.;Storrs, R. W.; Kasakevich, M. L. J . Phys. Chem. 1985, 89, 272.
Experimental Section Sodium dodecyl sulfate (Sigma), poly(ethy1ene oxide) polymers PEO 200000 (Aldrich), PEO 20000 (BDH), PEG 8000 (Aldrich), PEG 4000 (BDH), PEG 600, and PEG 300 (Canada Colors and Chemicals), tetraethylene glycol (Aldrich), and tetraethylene glycol dimethyl ether (Aldrich) were used as received. Sodium 3-carboxyproxyl was prepared by neutralizing 3-carboxyproxyl (Aldrich) with an equivalent amount of NaOD. Aqueous SDS solutions were prepared by weight, and the concentrations are given as molalities (mol/kg of D20). For the PEO solutions, concentrations are given as wt % or as molalities on a monomer basis (mol of monomer/kg of D20). D 2 0 (99.9%, Norell) was used as solvent. The proton T I measurements were performed at 361.053 MHz (8.48 T), using a Nicolet 360 NB spectrometer. T,'s were measured by using an inversion recovery sequence in which alternate 90° pulses are phase-shifted by 180°,40and a composite 180' pulse is used to compensate for imperfect B, homogeneity!' The signal intensities of the ethylene protons of PEO and the aromatic protons of benzyl alcohol show single-exponential decay in all T I measurements. T I values were calculated from peak heights obtained at 12 or more different delays, using a nonlinear three-parameter least-squares fitting procedure42available on the Nicolet software. Error limits as reported represent the repeatability of the results in a series of independent experiments and are much larger than the error derived from the least-squares fitting of a single experiment ( < I % ) . All measurements were carried out at 25 3~ 1 O C . Results and Discussion I H Spectrum Assignment and Paramagnetic Ion Concentrations. The 'H NMR spectrum of PEO 4000 (0.75%)/SDS (0.24 m ) is shown in Figure I . The spectrum is assigned by comparison to the spectra of the individual components, Le., PEO and SDS!3
Solubilization of Polymers in Micelles
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 465
TABLE 11: Dependence of Degree of Solubilization and Apparent Distribution Coefficient of WeighP
PEO (0.2%)in SDS (0.24 m ) on POE Molecular ~~
PEO MWb
200000 20000 8000 4000 600 300 197 (TEC)
TI .ow 0.506 f 0.01 0.510 f 0.01 0.476 f 0.01 0.487 f 0.01 0.528f 0.015 0.612 f 0.02 0.814 f 0.03
0.393 f 0.01 0.384f 0.01 0.380f 0.01 0.396 f 0.01 0.357 f 0.01 0.269 f 0.01 0.216 f 0.008
0.754 f 0.02 2.37 f 0.07
0.309 f 0.009 0.532 f 0.016
P
Kc
0.639f 0.02 0.638 f 0.02 0.636 f 0.02 0.638 f 0.02 0.763 f 0.02 0.957 f 0.03 1.19f 0.04
IpW 0.202 f 0.006 0.194 f 0.006 0.191 f 0.006 0.188 f 0.006 0.203 f 0.007 0.216 f 0.008 0.243 f 0.008
0.83 f 0.02 0.83 f 0.02 0.86f 0.02 0.87 f 0.02 0.75 f 0.03 0.42 f 0.05 0.00f 0.07
73 f 10 73 f IO 91 f 15 99f 18 45 f 7 11 f 2 Of1
1.17 f 0.03 3.31 f 0.07
0.234 f 0.006 0.345 f 0.01
0.44f 0.03 0.44 f 0.03
12f 1 12f I
Ip,obd
TEGDM
-CHZ-' -CHj
'All T , values are in seconds. b T E G = tetraethylene nlycol: . _ . TEGDM = tetraethylene glycol dimethyl ether. cItalics indicate the proton resonance on which.T, is determined.
with molecular weight greater than 4000 the degree of solubilization in the SDS micellar phase was found to be 0.85 f 0.02, independent of PEO molecular weight. However, for low molecular weight PEO the degree of solubilization decreases as the number of ethylene oxide units decreases. Tetraethylene glycol is located almost exclusively in the aqueous phase (p = 0.00 f 0.07). The change of the terminal groups of tetraethylene glycol from hydroxy to methoxy (tetraethylene glycol dimethyl ether) leads to a significant increase in the degree of solubilization (p
PA
F
= 0.44 f 0.03). The apparent distribution coefficient of PEO, Kc, was calculated from the equationZo Kc =
Qmic/@aq
= ~ V a q / ( l- P)Vmic
(7)
In the calculation of K, the partial molar volume of micellar SDS is assumed to be 0.250 d ~ n ~ / m o l . ~ ~ The results, presented in Table 11, agree very well with surface tension4 and conductivity measurements,6 which indicate that with increasing PEO molecular weight the tendency toward polymer-surfactant aggregate formation increases strongly at first but remains constant when the PEO molecular weight approaches approximately 4000. The difference in degree of solubilization between tetraethylene glycol and tetraethylene glycol dimethyl ether clearly indicates that the terminal hydroxy groups play an important role in the decreased solubilization of low molecular weight PEO. This result is consistent with the recent results of a dynamic light scattering study of low molecular weight PEO, in which it was found that the change of terminal group from hydroxy to methoxy results in a large difference in the degree of self-aggregation in solution.4s For higher molecular weight PEO the preference of the terminal hydroxy groups for the aqueous phase is compensated by the interaction between the polymer ethylene oxide group and the surfactant. The free energy of the interaction between PEO molecules and SDS micelles may be considered to be the sum of the free energies of interaction between the individual ethylene oxide units of the PEO molecules and the SDS micelles. Therefore, the degree of solubilization will increase with increasing PEO molecular weight. However, a micelle can only accommodate a certain number of ethylene oxide units, and eventually the degree of solubilization in the micellar phase reaches the constant value observed for PEO with molecular weights 4000 or higher (degrees of polymerization >90). PEO Concentration Dependence. In Figures 2 and 3, the degrees of solubilization of PEO 4000 and PEO 8000 in 0.24 m SDS solution arc plotted as a function of the PEO-t&DS concentration ratio. In these figures, [PEO], indicates the total molal concentration of PEO monomers; [SDS], is the total molal concentration of SDS, equal to 0.24 m. At low PEO concentrations the degree of solubilization, p , remains constant: but when the PEO monomer to SDS ratio exceeds I , p decreases. In order to discuss the solubilization capacity of the SDS micelle, we introduce a pa(44)Schwuger, M.J. J. Colloid Interface Sci. 1973,43,491. (45)Bender, T.M.:Pecora, R.J. J. Colloid Interface Sei. 1988, 126,638.
01 0
1
2
3
4
10 6
5
Figure 2. Dependence of p and F (see text for definitions) of PEO 4000 on the PEO-to-SDS concentration ratio. F
P%
I
T
T
I/+ 0
14 0
0 1
2
3
4
5
6
[pEol,/[s~sl, Figure 3. Dependence of p and F of PEO 8000 on the PEO-to-SDS concentration ratio.
rameter, F, the average number of bound polymer monomer units per micellar surfactant molecule, which is given by
F = [PEOlb/[SDSlmic = p[PEOlt/([SDSl, - [SDSlf) (8) where the subscript b stands for bound, mic for micellar, t for total, and f for free or monomer. Since in the present study the concentration of SDS (0.24 m) is much higher than the critical micelle concentration (cmc) (ca. 0.008 m),the [SDS]f term in eq 8 can be ignored. The dependence of F on the PEO-to-SDS concentration ratio is also shown in Figures 2 and 3. With the addition of PEO 4000 or PEO 8000, the F values increase to reach a maximum value of about 1.9 when the total PEO monomer to SDS ratio exceeds 3.5. Apparently, at high PEO concentrations the SDS micelles are saturated with PEO
466
Gao et al.
The Journal of Physical Chemistry, Vol. 95, No. 1. 1991
TABLE 111: Apparent Distribution Coefficients of PEO 4000 and PEO 8000 in 0.24 m S D S Micellar Solution
IPEOl,. % ’ 0.2 0.5 0.75
I .o I .5
2.0 2.5 3.0 3.5 4.0 5.0 6.0
[PEOl,/[SDSl,, mlm 0.19 0.47 0.7I 0.95 I .42 I .89 2.36 2.84 3.3 I 3.78 4.73 5.67
SDS’
Kc
PEO 4000 99f 18 91 f 15 91 f 15 78f 12 59f I I 40 f 6 26 f 5 19 f 2 16 f 2 13 f 2 9f2 7fl
TABLE IV: Influence of Added NaCl on q,ow and Apparent Degrees of Solubilization of Benzyl Alcohol and PEO 8000 in 0.24 m benzyl alcohol
PEO 8000 91 f 15
[NaC113m
78 f 12
0 0.10 0.20
50 f 8
“All T , values are in seconds.
25 f 3 17 f 3 8 f l
monomers, and the maximum value for F, which may be considered to be the solubilization capacity of the SDS micelles for PEO, shows a stoichiometric composition of the PEO/SDS aggregate in excess PEO of approximately 1.9 PEO monomers per dodecyl sulfate ion. Reportcd values for the aggregation number of SDS in PEO/SDS complexes, determined by fluorescence methods, vary from 40 to 60.6346 I f we combine this number with the stoichiometric composition of 1.9 PEO monomer units per SDS ion, we conclude that each aggregate contains 76-1 14 PEO monomer units, depending on the value used for the SDS aggregation number. Note that PEO 4000 and PEO 8000 contain about 90 and 180 monomer units per molecule, respectively. As shown in Figure 3, the degrees of solubilization and the solubilization capacity of the SDS micelles for PEO 8000 are essentially the same as those for PEO 4000, indicating that the solubilization equilibrium of PEO 4000 at different polymer-to-surfactant concentration ratios can be applied to other PEO polymers of higher molecular wcight. The apparent distribution coefficients, K,, of PEO 4000 and PEO 8000 were calculated via eq 7 and are given in Table 111. The dependence of K , on the polymer-to-surfactant concentration ratio at [PEO],/[SDS], > 1 clearly shows the gradual saturation of surfactant micelles by the polymers. Jones first observed two discontinuities in the surface tension curve when SDS was added to a PEO solution of fixed concent r a t i ~ n . ~ This ’ author interpreted the first discontinuity as the concentration at which the surfactant starts to bind to the polymer and the second one as the concentration at which the polymer is saturated by the surfactant and polymer-free surfactant micelles begin to form. The second critical point in fact separates two regions: one containing polymer-surfactant aggregates and another one containing polymer-surfactant aggregates and polymer-free micelles. The concentration ratio of bound surfactant to polymer (on monomer basis) at the second critical point has been determined by a variety of experimental technique^.^^"^^^-^^ For PEO/SDS the following values for this ratio have been reported: 0.3 (surface tension data44,48),0.33 (conductance meas u r e m e n t ~ ~0.41 ~ ) , (dialysis results in 0.1 M NaCISo),and 0.38 (ultracentrifugation6). These surfactant-to-polymer ratios in the range of 0.3-0.4 correspond to a value of 2.5-3.3 for the ratio of [PEO],/[SDS],. As shown in Figures 2 and 3, a [PEO],/[SDS], value in the range of 3.0-3.5 can be also considered to be a critical ratio, above which the solution contains polymer-surfactant aggregates and below which the polymer-surfactant aggregates coexist with polymer-free micelles in solution. It is clear that the results obtained with the paramagnetic relaxation method are in excellent agreement with those obtained by other techniques. (46) Zana, R.; Lianos, P.; Lang, J. J . Phys. Chem. 1985, 89, 41. (47)Jones, M.N . J . Colloid Interface Sci. 1967, 23, 36. (48) Cabane, B. J . Phys. Chem. 1977, 81, 1639. (49) Sasaki, T.; Kushima, K.; Matsuda, K.; Suzuki, H. Bull. Chem. Soc. Jpn. 1980, 53, 1864. (50) Shirahama, K. Colloid Polym. Sci. 1974, 252, 978.
T,&d
P
PEO 8000 q.obsd
P
0.648 f 0.03 0.64 f 0.03 0.294f 0.008 0.63f 0.03 0.593 f 0.02 0.60f 0.03 0.283f 0.008 0.61 f 0.03 0.540 f 0.02 0.54f 0.03 0.263f 0.008 0.55f 0.04
An interesting comparison can be made between PEO/SDS systems and alkyl polyoxyethylene sulfate surfactants of varied ethylene oxide c ~ n t e n t . ~ ’In - ~the ~ alkyl polyoxyethylene sulfate solutions, the cmc values decrease as the number of ethylene oxide groups increase^.^*-^^ Significant differences in micellar hydration and in surface adsorption at the water/air interface are observed between surfactants with one or two ethylene oxide groups and surfactants with more than two ethylene oxide group^.^^^^^ These studies suggest that for surfactants with one or two ethylene oxide groups the decrease in the cmc is due to a hydrophobic contribution from the ethylene oxide groups, while for surfactants with more than two ethylene oxide groups the decrease in the cmc is caused by an increase in the average distances between the charged sulfate group^.^' This can be compared to our observations that in the PEO/SDS aggregate the maximum solubilization capacity per SDS molecule is close to two ethylene oxide groups. Location of PEO in the PEOISDS Aggregates. The structure of the PEO/SDS aggregates is generally considered to be micellelike, with the aggregated SDS surrounded by PE0.3348254 Cabane48estimated that at [PEO],/[SDS], = 3.3 only 10% of the PEO monomer units are adsorbed directly on the micellar surface, while the remainder forms loops in the surrounding aqueous phase. To the contrary, ‘our results clearly indicate that the degree of solubilization of PEO in the SDS micelles is significantly higher than Cabane’s value. One criticism of the FT-PGSE self-diffusion method22in measuring degree of counterion binding is that the method determines the fraction of counterion diffusing with the micelle, which is not necessarily the same as the fraction bound to the micelle.s5 Similarly, it may be argued that the p value measured by use of the paramagnetic relaxation method includes contributions from PEO monomer units located in the electrical double layer around the micelle, if the paramagnetic ions are completely expelled from the micellar surface. We have measured the paramagnetic relaxation of PEO 8000 (3% or 0.68 m ) and of benzyl alcohol (0.058 m) in 0.24 m SDS in the presence of 0.1 and 0.2 m NaCl (Table IV). At such high salt concentrations, the micellar electric double layer is almost completely suppressed and the polymer units residing in the double layer and even some of the polymer units directly adsorbed on the micellar surface may be exposed to the paramagnetic ions. As shown in Table IV, the apparent values of p measured in the presence of high concentration of NaCl are indeed slightly lower than those in the absence of NaCI. For the case of benzyl alcohol the small decrease in p is an indication that some of the solubilizates located close to the micellar surface are now exposed to the paramagnetic ions in the aqueous phase. Treiner et aLS6observed that the addition of NaCl to SDS does not influence the solubilization equilibrium of 1pentanol. The changes in the apparent values of p for PEO 8000 and benzyl alcohol upon the addition of NaCl are almost identical. We conclude from the similarity of the paramagnetic relaxation method data of PEO 8000 and benzyl alcohol that the amount (51) Schwuger, M . J. In Structurelferformance Relationships in Surfactants; Rosen, M. J., Ed.; ACS Symposium Series 253; American Chemical Society: Washington, DC, 1984; p 1. (52) Tokiwa, F.; Ohki, K. J . Phys. Chem. 1967, 71, 1343. (53) Tokiwa, F. J. Phys. Chem. 1968, 72, 1214. (54) Nagarajan, R. Colloid Surf. 1985, 13, 1. (55) Jansson, M.; Li, P.; Henriksson, U.; Stilbs, P. J . Phys. Chem. 1989, 93, 1448. (56)Treiner, C.; Khodja, A. A.; Fromon, M.; Chevalet, J. J . Solution Chem. 1989, 18, 217.
J. Phys. Chem. 1991, 95, 467-471 of PEO residing in the micellar double layer is small and thus that the p values and distribution coefficients reported in Tables 1-1 I I do indeed represent the PEO solubilized in the micellar interior. Conclusion The NMR paramagnetic relaxation technique provides a new method to study solubilization equilibria of polymers in micellar systems bccause it can distinguish the polymer monomer units in the aqueous phase and in the micellar phase. In principle, this technique is applicable to many other polymers than the one reported here and to other microheterogeneous systems. The solubilization equilibria of PEO in SDS micellar solutions clearly indicate that the nature of the interaction between the PEO and SDS is dependent on the PEO molecular weight. The apparent distribution coefficient increases with increasing PEO molecular weight until the PEO molecular weight reaches about 4000. Replacing the terminal hydroxy groups of tetraethylene glycol with methoxy groups (tetraethylene glycol dimethyl ether) leads to a significant increase of the apparent distribution coefficient.
467
The apparent distribution coefficients of PEO in SDS micellar systems are dependent on the PEO-to-SDS concentration ratio. The PEO is saturated by SDS at a concentration ratio of one SDS molecule per PEO monomer unit. Conversely, the solubilization capacity of the SDS micelle is 1.9 PEO monomer units per dodecyl sulfate ion. This value may also be considered as the stoichiometric composition of the PEO/SDS aggregate in excess PEO. These results are applicable to PEO with a molecular weight higher than 4000. Finally, we find that only a very small amount of PEO is located in the electric double layer of the SDS micelles. Acknowledgment. The authors acknowledge the Natural Sciences and Engineering Research Council of Canada for the support of this research and the Killam Trust for the award of a postgraduate scholarship to Z.G.. NMR measurements were carried out in the Atlantic Region Magnetic Resonance Centre (ARMRC) at Dalhousie University. Registry No. PEO,25322-68-3; SDS, 151-21-3; NaCI, 7647-14-5; tetraethylene glycol, 1 12-60-7; tetraethylene glycol dimethyl ether, 14324-8.
Ovalbumin Diffusion at Low Ionic Strength Stephen J. Cibbs,*qt Alice S. Chu, Edwin N. Lightfoot, and Thatcher W. Root Department of Chemical Engineering, University of Wisconsin-Madison, (Received: March 21, 1989; In Final Form: June 26, 1990)
Madison, Wisconsin 53706
Ovalbumin mutual diffusivitiesand intradiffusivities have been determined by the synthetic boundary and pulsed field gradient N M R techniques as a function of protein concentration at pH 5.5 and 4 mM sodium acetate. The pulsed field gradient technique provides efficient and reliable estimates of the ovalbumin intradiffusion coefficient and, in conjunction with the macroscopic boundary-relaxation technique and independent measures of the protein activity coefficient, offers a means of comparing the magnitudes of the frictional coefficients for mutual diffusion and intradiffusion. Ovalbumin diffusivities determined by quasi-elastic light scattering are intermediate in value between those experimentally determined by the NMR and boundary-relaxation techniques.
Introduction Protein diffusion, in spite of its importance in a wide variety of biological transport phenomena, remains poorly characterized; reliable experimental measures of protein intradiffusivities (or tracer diffusivities) and mutual diffusivities are relatively scarce. Instrumental techniques, because of their speed, accuracy, and precision, are attractive for this endeavor, but the most widely employed technique to date, quasi-elastic light scattering (QES), suffers from ambiguities at high protein concentrations and low ionic strength’-3 and frequently yields estimates of protein mutual diffusion coefficients that differ dramatically from classical diaphragm cell or free diffusion measurements.’~~-~ In contrast, pulsed field gradient spin-echo NMR (PFGNMR) allows the unambiguous determination of intradiffusion coefficients.’ The PFGNMR technique, however, has not been widely employed for proteins. We report here on our measurements of ovalbumin diffusion coefficients as determined by the classical synthetic boundary technique, the QES technique, and the PFGNMR technique. We find that, for the system studied, PFGNMR appears to give accurate estimates of protein intradiffusion coefficients and that a reasonable estimate of the concentration dependence of the protein-water mutual diffusivity, as determined by the synthetic boundary technique, can be made from the PFGNMR measurements and a protein activity correction. In addition, we find
’
Present address: Department of Chemistry, CB# 3290 Venable Hall, University of North Carolina, Chapel Hill, NC 27599-3290.
0022-3654/91/2095-0467$02.50/0
that the QES technique effectively measures a diffusivity intermediate in magnitude between the intradiffusivity, as determined by PFGNMR, and the mutual diffusivity, as determined by the synthetic boundary technique. Thermodynamic Framework We shall limit our discussion of protein diffusion to a pseudobinary treatment in which the species P is taken to be the hydrated protein ion and its counterions, and the species W is the solvent. We take as a starting point the generalized StefanMaxwell equations for a two-component system and, neglecting pressure and temperature gradients and external body forces, w ri
(1) Phillies, G. D. J.; Benedek, G . B.; Mazer, N. A. J. Chem. Phys. 1976, 65(5), 1883.
(2) Wills, P. R. J . Chem. Phys. 1979, 70(12), 5865. (3) Russel, W. B.; Glendinning, A. B. J . Chem. Phys. 1981, 74(2), 948. (4) Keller, K. H.; Canales, E. R.; Yum, S . I . J. Phys. Chem. 1971,75,379. ( 5 ) Alpert, S. S.; Banks, G. Biophys. Chem. 1976, 4, 287. (6) Veldkamp, W. B.; Votano, J. R. J . Phys. Chem. 1976, 80, 2794. (7) Ahn, M. K.; Jensen, S . J. K.; Kivelson, D. J . Chem. Phys. 1972,57(7), 2940. (8) Hirschfelder, J. 0.;Curtis, C. F.; Bird, R. B. Molecular Theory OJ Gases and Liquids; Wiley: New York, 1954; p 714.
0 1991 American Chemical Society
