J. Phys. Chem. 1994,98, 2459-2463
2459
Interaction between Nonionic Micelles and a Nonionic Polymer Studied by Fourier Transform NMR Self-Diffusion Kewei Zhang,' Mikael Jonstromer,t and Bjorn Lindman Physical Chemistry 1, Chemical Center, University of Lund, P.O. Box 124, S-22100 Lund, Sweden Received: September 22, 1993; I n Final Form: December 9, 1993"
The interaction between octaethylene glycol mono-n-dodecyl ether (C12Eg) and ethylhydroxyethyl cellulose (EHEC) in aqueous solution has been studied by measuring the C&g self-diffusion coefficient in the presence of EHEC at 25 OC. Micelle diffusion is influenced by the polymer in two ways, i.e. obstruction due to the polymer network and association of micelles to the polymer chains. It is demonstrated that, from studies using polymers of different polarity, a separation between obstruction and association effects can be achieved. It is found that the interaction between a relatively hydrophobic EHEC and the surfactant is dominated by a strong attraction leading to a formation of polymer-surfactant complexes. This observation is consistent with phase diagram findings. Taking into account the obstruction from both micelles and polymer chains, the binding isotherm of C&g to the hydrophobic EHEC is calculated by using a two-site model.
Introduction The understanding of polymer-surfactant interactions is of considerable practical as well as fundamental importance. Most studiesare focused on water-solublenonionicpolymers interacting with ionic surfactants, or polyelectrolytes interacting with an oppositely charged surfactant.14 Only a few studies concerning systems of water-soluble nonionic polymers and nonionic surfactants have been reportede5-9 Generally the interaction for the latter type of system is weak. However, for some less polar polymers, such as polypropylene oxide (PPO) or hydroxypropyl cellulose (HPC), a significant interaction between the polymer and the nonionic surfactants has been demonstrated by either a marked change in the cloud point or by an endothermic enthalpy of mixing.5.6 In a previous report, we investigated the phase behavior of EHEC/C,zE,/water systems with n = 4 and 8, respectively.8 EHEC is ethylhydroxyethyl cellulose and C12En polyethylene glycol mono-n-alkyl ether. The conclusion was that the interaction between the polymer and the surfactant is dominated by strong attractive forces leading to the formation of polymer-surfactant complexes. It is evident that further insight into the nature of the interaction should benefit from a direct study of the binding isotherm. The binding isotherms for several polymer-ionic surfactant systems have been obtained due to the development of surfactant selectiveelectrodes.1° For nonionic surfactant systems, however, this technique fails since it is based upon the determination of the surfactant ion activity. In swh cases, the measurement of surfactant self-diffusion coefficients constitutes an important complement to the selective electrode technique. As will be demonstrated, the self-diffusionapproach gives direct insight into the association of micelles to polymer chains or to a polymer network. In this report, the interaction between EHEC and ClzE8 in water is studied by measuring the surfactant self-diffusion coefficient. Several dilution series were checked with either the C&8 or the EHEC concentration kept constant. In order to quantify the obstruction effect from the polymer chains, recent theoretical and experimental work by Johansson and LofrothlI-15 is most significant. Inter alia these authors investigated the diffusion of nonionic micelles in solutions and gels of an ionic
* To whom correspondence should be addressed. t
Present address: Astra Draco AB, Box 34, 22100 Lund, Sweden. 1994.
* Abstract published in Advance ACS Abstraczs, February 1,
0022-3654/94/2098-2459$04.50/0
polysaccharide, a system where no polymer-micelle association can be anticipated. For our system, a separation of effects due to obstruction and association is crucial, and an approach based on measurements involving polymers differing stronglyin polarity is proposed. Using a noninteracting hydrophilic EHEC, the obstructioneffect can be estimated. Froma two-site model, where the surfactant is assumed to be "bound" to the polymer chains or "free" in the form of micelles in the surrounding solution, the binding isotherm is calculated.
Experimental Section Materials. C12Eg of high quality (>98%) was obtained from Nikko Chemicals, Tokyo, Japan, and used as received. Samples of ethylhydroxyethylcellulose,EHEC, of different polarities were supplied by Berol Nobel AB, Stenungsund, Sweden. One is more nonpolar (Bermocoll CST 103, below referred to as EHEC,; the degree of substitution of ethyl, DScthylris 1.5 and the molar substitution of ethyleneoxide, MSEO,is 0.7) with a cloud point of about 30 OC; theother is more polar (Bermocoll E230G, below referred to as EHEC,; DSethyl= 0.8 and MSEO= 0.8) with a cloud point of about 62 OC. The EHEC samples are water soluble at room temperature. The number average molecular weight is 80 000 and 100 000 for EHEC, and and EHEC,, respectively (given by the manufacturer). The dilute EHEC solution was dialyzed against pure water (Millipore, Bedford, MA, USA) for at least 5 days to remove salt (impurity from the manufacture) and then freeze-dried. 2H20 (99.7 at. % 2H) was obtained from Norsk Hydro, Rjukan, Norway. Self-Diffusion Measurements. Samples were prepared by mixing the bulk solutions of the components into standard 5-mm NMR tubes. The tubes were then flame sealed and equilibrated at 0-5 'C for 24 h before use. All samples were made up with 2H20. The proton self-diffusion studies were performed at 60 MHz on a modified JEOL FX-60 FT NMR spectrometer equipped with a home-built pulsed field gradient unit. All measurements were performed at 25 OC f 0.5 'C. According to Stejskal and Tanner,I6 a spin-echo signal is induced by a 9O0-s-18O0 radio frequency pulse sequence. A magnetic field gradient, G, is applied during a time, 6, as a twin pulse with a time difference A, one before and one after the 180' pulse. The echo signal amplitude, A, for a given chemical species is given by A = A,,F(J,A) exp[(-27/T2 - (rGs)*D(A- 6/3)] 0 1994 American Chemical Society
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Zhang et al.
2460 The Journal of Physical Chemistry, Vol. 98, No. 9, 1994
where A0 is a constant, F(J,A) represents the J-modulation effect, y is the magnetogyric ratio for the nuclei studied, T2 is the transverse relaxation time, and D is the self-diffusion coefficient. For a constant value of T , eq 1 is simplified to A = A, exp[-(yG6)2D(A - 6/3)]
(2)
In our experiments, A is kept constant, while 6 is varied. The self-diffusion coefficient is calculated from eq 2 by a least-squares fit of the observed echo amplitude from at least 10 different values of 6. Moredetails on the method may be found e1~ewhere.l~ The self-diffusionmeasurement directly monitors the random motion of an individual molecule during a time interval, A - 6/3. The relation between the molecular mean square displacement in one dimension, (x2), and the self-diffusion coefficient is given as ( x 2 ) = 2D(A- 6/3)
(3)
where D is the self-diffusion coefficient which typically is in the range of 10-9to 10-l m2 s-l . A used in the present study is 140 ms. During this time the molecules diffuse over a distance from 1 to 20 pm. This length scale is much larger than any micellar size or gyration radius of the polymer. Hence, the observed selfdiffusion coefficients only reflect the mobility of entire micelles, surfactant-polymer complexes, or surfactant monomers. Segmental displacement of the polymer-surfactant complex or surfactant diffusion within the micelles exerts no significant influence on the results.
Model Considerations Compared to some previous self-diffusion ~tudies,~J9 where the interaction between ionic surfactants and polymers has been investigated, this work shows some distinct differences: (i) The critical micelle concentration (cmc) of the nonionic surfactant is so low that for the concentration range investigated (>>cmc) only a negligible fraction is not micellized. Any contribution to the observed surfactant diffusion coefficient, Doh, from C&8 monomers may, therefore, be neglected. Arguments for this assumption have been given by Johansson et al.14and are further discussed below. (ii) According to previous work,20the size of C&8 micelles remains constant when changing the surfactant concentration over a wide range. This simplifies the estimation of the self-diffusion coefficient for the micelle, Dmip (iii) For charged surfactant-polymer systems, any complex formation is an interplay between electrostatic and hydrophobic interactions which are hard to separate. In the present study, only the hydrophobic interaction between the surfactant and the polymer is expected to be of importance. In order to use surfactant self-diffusion data to evaluate the fraction of surfactant micelles bound to the polymer, the following effects have to be considered: (a) ObstructionEffect. The obstruction effect originates from the presence of impenetrable particles leading to an increase in the path length of the diffusing species. In the present work, we have to consider the obstruction effects originating from both the polymer chains and other micelles. Spherical micelles are formed in the binary Cl&/water solutionsover wide temperature and concentration ranges.20The reduced mobility due to obstruction between spherical nonionic micelles is well described by the relationship21322
where D, is the micellar self-diffusioncoefficient in the absence of the polymer, 4, the volume fraction of the micelles including the water of hydration, and Do the self-diffusion coefficient at infinite dilution.
Figure 1. Micelle diffusion in a polymer network. This depends inter alia on micelle size and shape.
The obstruction from the polymer chains has a large influence already at moderate polymer concentrations. As illustrated in Figure 1, the size and shape of the micelles are important factors and others are the polymer radius, the polymer volume fraction, and the polymer persistencelength. The obstruction contributions from the polymer chains can for nonflexible polymer chains and sphericalmicelles be described by a model developed by Johansson et al.11-15
+
where a = $p(Rs a)2/a2, Dmicis the micellar self-diffusion coefficient in the polymer solutions in the absence of strong attractive interactions between the surfactant and the polymer, q5psisthe volume fraction of the polymer, R, is the micellar radius, a is the polymer radius, and El is the exponential integral, Le.,
E , ( x ) = Jxm e+/u du Combining the obstruction effects from both surfactant micelles and polymer chains leads to
Equation 6, which is the one that we will use for calculating the obstruction from both the surfactant micelles and the polymer chains, assumes that the micelle-micelle obstruction is not influenced by the closeness of polymer chains. This is a simplification,but this obstructioneffect is throughout quite small. Also, eq 6 is appropriate to use ifp/a > 10,wherep is the polymer persistencelength and a is the polymer radius.13 This requirement is well fullfilled for the semistiff celluloses.28 (b) Migration of Surfactant Monomers. Besides the translational motions of the free micelles and the surfactant-polymer complexes,the surfactant micelles may diffuse along the polymer chain. The surfactant monomers may also exchange between adjacent micelles, which may contribute significantly to Doh for concentrated surfactant solutions,23 in particular if there is major micellar growth.14 These effects were considered to only give insignificant contributions to the surfactant diffusion in the concentration regime considered, as was also indicated by the experimental data (see below), and are not taken into account in the model presented below. Assuming a distribution of the surfactant only between free micelles and micelles bound to the polymer chains, the observed
Nonionic Micelles-Nonionic Polymer Interaction
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The Journal of Physical Chemistry, Vol. 98, No. 9, 1994 2461
A4,0
10
I
I
I
I
I
I
I
8
I
I
0.5wt%EHEC 0
1.0 wt% EHEC
-
% EHEC Figure 2. Ternary phase diagram of the ClzEs/EHEC,/water
system at31,32,33,and35 OCwithtwotielinesindicated(at35 "C). Thefilled circles refer to the initial sample compositions, and crosses connected with the phase boundary refer to the analytical compositions of the dilute phases. @ I denotes the isotropic one-phase region and @Z the two-phase region.
self-diffusion coefficient, Doh, can be expressed with a simple two-site model:
0
0
1
2
3
4
5
concentrations of the polymer solutions are shown in the figure. The solid line corresponds to eq 4 for polymer-free solutions. The dashed lines are only as an aid to the eye. Temperature T = 298 K.
I -1
+ CX2eaE1(2CX))](1 - pb) + PbDb
7
C!, Eg concentration (wt%) Figure 3. Self-diffusion coefficients of C1zE8 in the hydrophobic EHEC, solutions as a function of the C12E8 concentration (wt %). The
Combining 7 with eq 6, we obtain
Doh = [Do( 1 - 24,)(e"
6
(8)
.o wt%
where Pb is the fraction of the surfactant micelles bound to the polymer and & the self-diffusion coefficient of the polymersurfactant complex. This is the equation that we will employ for calculating the binding isotherm. It is worth noting that eq 6 holds under conditions that the presence of the nonionic polymer does not markedly influence the micellar size. However, as noted, CI2E8 micelles (in contrast to, for example, C1& micelles14~22-24)have little tendency to grow in the presence of the polymer.
Results and Discussion Phase diagrams for the ternary systems of EHEC,/C12E,/ water with n = 4 and 8 have previouslybeen determined at various temperatures. The phase behavior was found to be similar with a minimum in the lower consolute boundary upon addition of EHEC,. Moreover, at temperatures above the lower consolute boundary, phases concentrated in both EHEC, and C12E8 are in equilibrium with solutions dilute in both components (Figure 2). This associative type of phase separation indicates that the interaction between the polymer and the surfactant is attractive. The present study concerns a direct investigation of the interaction between EHEC, and nonionic surfactant in homogeneous solution. The self-diffusion coefficient of Cl2E8 at 25 OC for various EHEC, concentrations is plotted versus the C12Es concentrationin Figure 3. A significantdecreasein D h is induced by addition of EHEC,. At high EHEC, concentrations, D0b becomes almost independent of the Cl2Es concentration. The self-diffusion coefficient of C12Es at fixed surfactant concentrations, 1.O and 5.0 wt %, is plotted as a function of the EHEC, concentration in Figure 4. A significant decrease in Doh is observed even at low polymer concentrations. As mentioned above, the migration of surfactant monomers either through exchange between adjacent micelles or along the polymer chains could contribute to Doh. The former process should be of importance at high surfactant concentrations, since the mean distance between the micelles decreases, and the latter process at high EHEC, concentrations, since the number of
0
' 0
0.5
1
1.5
EHEC" concentration
2
2.5
(~01%)
Figure 4. Self-diffusion coefficients of ClzE8 at two different concentrations, 1.0 and 5.0 wt %, plotted versus the EHEC, concentration (vol 76). The solid lines are only as an aid to the eye. The volume fraction of the polymer was calculated from the partial specific volume u = 0.75
mL/g. Temperature T = 298 K.
diffusion pathways increases. For the present study, both the surfactant and the polymer concentrations would appear to be too low for these processes to be significant. Furthermore, no increase in D0b is observed in the high-concentration regimes of Figures 3 and 4, which indicates that none of the two migration processes contributes significantly to Doh under the conditions investigated. In contrast to the present case, the migration of surfactant monomerswas demonstrated to contribute significantly to Dobina C12b-polymer system.14 For thelatter case, monomer contributions become relatively more important due to a major micellar growth that retards micellar diffusion. From the phase behavior investigations we know that the interactions between Cl2E8 and the rather hydrophobic EHEC, are dominated by an attraction. Therefore, the reduction of the micellar self-diffusion can be expected to be a combination of obstructive and associativeeffects. The obstructive contribution from the micelles can be well described by eq 4, as already mentioned. In order to monitor the obstructive contribution from
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The Journal of Physical Chemistry, Vol. 98, No. 9, 1994 1
Zhang et al.
1 o
EHEC,
e EHECU
/I
VI
N
-E
0
4.5
1
2
3
4
5
6
7
C, ?& concentration ( ~ 1 % )
a
0.4
1
3.5
\
1
i
\
e e ~
".L
0
0.4
0.8
1.2
1.6
2
EHEC concentration ( ~ 0 1 % ) Figure 5. Relativeself-diffusion,DID,,, for L O wt % CliE8 in the EHEC,
(open circles) and EHEC, (filled circles) solutions as a function of the polymer concentration (vol 96). The solid line calculated according to eq 6 with a = 4.5 A and R, = 33.4 A. The volume fraction of the polymer was calculated from the partial specific volume u = 0.75 mL/g. Temperature T = 298 K. the EHEC chains, one way is to measure the self-diffusion of C I ~ inE EHEC ~ solutions in the absence of dominant attractive forces. Fortunately, this is easily realized by choosing a hydrophilicEHEC, sincethere is usually no or very weak attractive interactions between nonionic surfactants and hydrophilicnonionic polymers at ambient temperature. Therefore, the reduction of the surfactant self-diffusion in this case is totally attributed to obstruction effects. In Figure 5 we plot the relative self-diffusion (Dob/Daq)for a constant surfactant concentration of 1.0 wt % in solutions of two different EHEC polymers, one hydrophilic, EHEC,, and another more hydrophobic, EHEC,. Daqis the selfdiffusion coefficient of C12E8measured in the absence of polymer. As expected, the self-diffusionin EHEC, solutions is more rapid than that in EHEC, solutions. In the former case, the reduction of the surfactant mobility is totally attributed to obstruction effects, while in the latter we infer a combination of both obstructive and associative contributions. The solid line in the figure was calculated according to eq 5. The micellar radius, R, = 33.4 A, including the water of hydration, is taken from the previous report.14 The value of the polymer radius, a = 4.5 A, is obtained by fitting eq 5 to the data in Figure 5 for EHEC, solutions. The polymer radius obtained is larger than that obtained for K+-K-carrageenan, which has a similar molecular backbone as EHEC, in coil conformation (a = 3.3 %I) but smaller than that of K+-K-carrageenan in double helix conformation (a = 5.1 A).14J5 The value obtained for EHEC, a = 4.5 A, is reasonable in view of the average degree of substitution. In the present case, in order to use eq 8 to calculate the binding isotherm, it is necessary that the obstruction from the polymer chains is independent of the surfactant concentration. Such an assumption is supported by the fact that the micellar size of C I Z Eremains ~ constant over wide concentration regions. Experimentally,it may be inferred from the insert of Figure 6, in which DID,, of ClzEs in 0.5 wt % EHEC,solutions is plottedvs the ClzEs concentration, that the obstruction from the polymer chains gives DID,, = 0.76, independent of the surfactant concentration within the " e n tra tion region investigated. In Figure 6 we compare the self-diffusionmeasured for 1.O wt % Cl2E8 in EHEC, solutions with that calculated according to eq6withDo=6.6 X mZs-l,whichisconsistentwithprevious results, a = 4.5 A and R, = 33.4 A. The consistency between
0
1
0.5
EHEC,,
concentration
1.5 (vol%'c)
Figure 6. Comparison between the self-diffusion measured for 1.O wt 7%
C12Esin hydrophilicEHEC, (filled circles)solutionsand those calculated m2s-l, a = 4.5 A,and R,= 33.4 according to eq 6 with DO= 6.6 X A (solid line). The volume fraction of the polymer was calculated from the partial specific volume u = 0.75 mL/g. Temperature T = 298 K. Insert: Relative self-diffusion,DID,, of C12E8 in the hydrophilicEHEC, solutions as a function of the surfactant concentration (wt %). The concentration of EHEC, is fixed at 0.5 wt 7%. Temperature T = 298 K. the experimental and the calculated values lends further support to our model calculations. In addition, the self-diffusion coefficient of the polymersurfactant complex, &, is needed for the isotherm calculation according to eq 8. & may be assumed to be considerably lower than Doh,so precise informationis not required and even assuming it to be negligible compared to D0b may be a reasonable approximation. Mainly due to the rapid transverse relaxation rate characterizingthe polymer signals,we were unable to measure the polymer self-diffusion by our equipment. However, recently an improved FT-NMR-PGSE technique in combination with stimulatedecho pulsesequenceswas successfullyused todetermine the EHEC, self-diffusion coefficient to be 6.0 X 10-13 m2 s-1.25 With the values of a, R,, and & at hand, the binding isotherm of C12E8 to EHEC, can easily be calculated from the diffusion data shown in Figures 3 and 4 by using eq 8. The result is presented in Figure 7,in which the amount of C&8 (millimoles) bound per gram of EHEC,, 8, is plotted as a function of the free C12E8 micelleconcentration,C,, (mM). Ckwasobtained by assuming that the aggregation number of the micelles is 1 The solid line in the figure is represented by the Langmuir adsorption isotherm2'
(9) OSat. is
the saturation value, obtained to be roughly 3.5 mmollg EHEC. As can be seen from Figure 7,there is rough agreement between the experimental observation and the Langmuir isotherm. However, the binding process in the present case has not reached the saturation stage. In this study, we have thus directly demonstrated, using the self-diffusionapproach, an association between the hydrophobic EHEC, and nonionic micelles and found that the association approximately follows a Langmuir isotherm. The polymersurfactant interaction is dominated by a strong attractive interaction (from K we obtain a free energy of interaction of ca. -5.8 kJ/(mol of surfactant)) which is consistent with the phase behavior. The polymer solutionsinvestigated are in the semidilute
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The Journal of Physical Chemistry; Vol. 98, No. 9, 1994 2463
1.6
Discussions with B. JBnsson, H. WennerstrBm, U. Olsson, and L. Piculell are gratefully acknowledged. The study has been financed by a grant from the Swedish Research Council for Engineering Sciences.
1.2
References and Notes (1) Robb, I. D. Polymer/Surfactant Interactions. In AnionicSurfactanrs-
M Y
z
E v
a
0.8
0 0
I
I
I
0.2
0.4
0.6
Cmic
I 0.8
(mM)
Figure 7. Calculated binding isotherm of &E8 interacting with hydrophobic EHEC,. The solid line represents the best fit of eq 9.0 is the amount of Cl2E8 bound per gram EHEC and C,,,jc is the free micelle concentration (mM). Temperature T = 298 K.
regime, and we can picture the system as a three-dimensional lattice of points which can associate with the nonionic micelles, where the most favorable points of interaction can be assumed to be those of contact or closeness between two polymer chains. Since the interaction between different C12E8 micelles is repulsive at the experimental temperature,2°.u it is reasonable to assume that micelles should interact independentlywith a polymer network and association of a micelle with a site should only depend on whether that site is occupied or not. This would suggest that a Langmuir isotherm should offer a suitable description,as is indeed found.
Acknowledgment We are grateful to K. Lindell at the Department of Food Technologyand G. Wang at the Department of Thermochemistry for providing us with the EHEC, sample.
Physical Chemistry of Surfactant Action; Reynders, E. L., Ed.; Surfactant Science Series, Vol. 11; Marcel Dekker: New York, 1981;Chapter 3. (2) Goddard, E. D. Colloids Surf. 1986, 19, 255. (3) Goddard, E. D. Colloids Sur- 1986, 19, 301. (4) Goddard, E. D. Anathapadmanabhan, K. P., Eds. Interactions of Surfactants with Polymers and Proteins; CRC Press: Boca Raton, FL, 1993. (5) Wechtrbm, K. FEBS Lett. 1985,192 (2),220. (6) Brackman, J. C.;van Os,N. M.;Engberts, B. F. N. Lungmuir 1988, 4, 1266. (7) Wormuth, K.R. Lungmuir 1991, 7, 1622. (8) Zhang, K.; Karlstrbm, G.; Lindman, B. Colloids Sur-1992,67,147. (9) Penders, M.H. G. M.; Nilsson, S.; Piculell, L.; Lindman, B. J. Phys. Chem. 1993, 97, 11332. (10) Shirahama, K.; Himuro, A.;Tahisawa, N. Colloid Polym. Sci. 1987, 265,96.Shirahama, K.; Santerre, J. P.; Kwak, C. T. Biophys. Chem. 1983, 17, 175. (1 1) Johansson, L.; Skantze, U.; LBfroth, J.-E. Macromolecules 1991,24, 6019. (12) Johansson, L.; Elvingson, C.; Lbfroth, J.-E. Macromolecules 1991, 24, 6024. (13) Johansson, L.; LBfroth, J.-E. J . Chem. Phys. 1993, 98, 7471. (14) Johansson, L.; Hedberg, P.; Lbfroth, J.-E. J . Phys. Chem. 1993,97, 747. (15) Johansson, L. Diffusion and Interaction in Gels and Solutions.
Doctoral Thesis, GBteborg, 1993. (16) Stejskal, E. 0.; Tanner, J. E. J. Chem. Phys. 1965, 42,288. (1 7) Stilbs, P. Prog. Nucl. Reson. Spectrosc. 1987, 19, 1. (18) Carlsmn, A.; Karlstrbm, G.; Lindman, B. J . Phys. Chem. 1989, 93, 3673. (19) Thalberg, K.;van Stam, J.; Lindblad, C.; Almgren, M.;Lidman, B. J. Phys. Chem. 1991.95, 8975. (20) Nilsson, P. G.; Wennerstrtim, H.; Lindman, B. J . Phys. Chem. 1987, 87, 1377. (21) Ohtsuki, T.; Okano, K. J. Chem. Phys. 1987, 77, 1443. (22) Faucomprl, B.;Lindman, B. J . Phys. Chem. 1987, 91, 383. (23) Jonstrbmer, M.; JBnsson, B.; Lindman, B. J. Phys. Chem. 1991,95, 3293. (24) Lindman, B.; Wennerstrbm, H. J . Phys. Chem. 1991, 95, 6053. (25) Stilbs, P.Unpublished data. (26) Zana, R.; Weill, C. J. Phys. Lett. 1985, 46, L-953. (27) Hiemenz, P. C. Principles of Colloid and Surface Chemistry, 2nd ed.; Marcel Dekker, Inc.: New York, 1986;p 398. (28) Kamide, K.; Saito, M.Adu. Polym. Sci. 1987, 83, 1.
