J. Phys. Chem. 1992, 96, 6805-681 1
6805
Complex Formation between Poly(oxyethylene) and Sodium Dodecyl Sulfate Micelles: Light Scattering, Electrophoresis, and Dialysis Equilibrium Studies Jiulia Xia, Paul L.Dubin,* Department of Chemistry, Indiana University-Purdue University at Indianapolis, Indianapolis, Indiana 46205
and Yesook Kim Parenteral Research and Development, Eli Lilly and Company, Indianapolis, Indiana 46285 (Received: February 3, 1992; In Final Form: April 8, 1992)
The structure and behavior of polymer-micelle complexes formed in dilute solutions of poly(ethy1eneoxide) (PEO) and lithium dodecyl sulfate (LDS) in LiCl solution were studied by quasi-elasticlight scattering, electrophoreticlight scattering, static light scattering, and dialysis equilibrium, as a function of polymer molecular weight (M) and ionic strength (I). In 0.4 M LiCI, the diffusion coefficient of the LDS-saturated complex shows an exponential M dependence, i.e. D = kMv. The value of v = -0.55 is typical of nonionic flexible chain polymers (for PEO alone v = -0.52) in good solvents. The electrophoretic mobility, u, of the complex is nearly M-independent, similar to the behavior of polyelectrolytes. These results suggest an overall Gaussian distribution for the PEO-LDS complex, with sufficient chain expansion to yield free-draining behavior. The number of micelles bound per chain increases strongly with ionic strength, as does the electrophoreticmobility. This result can be interpreted on the basis of the contribution of uncharged bound polymer to the friction force per bound micelle. The present results support a micellepolymer interaction mechanism which involves simultaneous binding of Li+ by both the micelle and the polymer.
Introduction Polymer-surfactant complexes have been the subject of continued interest for at least 3 decades.’ Among the first systems studied were those comprised of anionic micelles and nonionic synthetic polymersS2In particular, much attention has been paid to complex formation between poly(oxyethy1ene) (PEO) and sodium dodecyl sulfate (SDS) micelles, which has been studied by surface tension measurements: surfactant ion specific electrodes,’ conductimetry,Sdialysis equilibrium? NMR spectroscopy,7 dye solubilization,8 and viscometry? Neutron scattering experiments carried out by Cabane’O were especially influential in supporting a model quite rich in detail about the structure and arrangement of the bound micelles. These clusters, thought to closely resemble free SDS micelles except for a slightly diminished aggregation number, were considered as bound within the more or less unperturbed domain of the polymer chain, which thus served as a string for this “necklace of beads”.1° Despite the many techniques applied to the characterization of PEO-SDS systems, there has been no compelling model put forward for the nature of the stabilizing interaction. Thus, for example, it has been proposed that the complex is stabilized by hydrophobic interactions between the methylene units of the polymer and those of the surfactant alkyl groups5*”or by iondipole interactions between sulfonate groups and ether oxygens.’* More recently, weI3 suggested-on the basis of a comparison of the effects of Na+, Li+, and NH4+ on the critical micelle concentration (cmc) of PEO-SDS-that the cation plays a role in this interaction, by simultaneously coordinating with the polymer oxygens while being electrostatically bound to the micelle. In addition to the controversial nature of the energetics of PEO-SDS association, unresolved questions arise about the structure of the complex. Thus, for example, the size of SDS micelles increases strongly with ionic strength, and one may ask how earlier models should be modified when the ‘beads” are larger than the “string”. It is appropriate here to point out that one finds no study in which the concentrations of polymer, surfactant, and supporting electrolyte have all been varied systematically. The preceding remarks are intended to indicate the rationale for further investigationS into what might seem a rather thoroughly explored area. However, it is interesting to note that the powerful techniques based on total intensity measurements with visible light (static light scattering) and dynamic measurements of scattering fluctuations (quasi-elasticlight scattering or QELS) have not been 0022-3654/92/2096-6805$03.00/0
TABLE I: Molecular Weights and Wstributions of PEO code M, M,/M, code Mw KIM, SE-2 2.50 X lo4 1.14 SE-30 2.50 X los 1.04 SE-5 3.90 X lo4 1.07 SE-70 5.94 X lo5 1.04 SE-8 8.60 X lo4 1.02 SE-150 9.96 X lo5 1.05 SE-15 1.45 X 10’ 1.03
applied to these systems. In addition, the method of electrophoretic light scattering (ELS), developed by Ware,I4 is found to be quite complementary to the QELS technique and provides additional important insights. The present study then has three goals: (a) to apply light scattering techniques, namely, QELS and ELS, to the characterization of PEO-SDS complexes; (b) to utilize the availability of well-characterized narrow molecular weight distribution (MWD) fractions of PEO to explore the M dependence of the diffusion coefficient and electrophoretic mobility; and (c) to test the hypothesis, previously put forward,I3of the role of the cation in mediating the polymer-micelle interaction. Experimental Section
Materials. Narrow-distribution poly(ethy1ene oxide) (PEO) fractions were purchased from Toyo Soda Manufacturing Co. Ltd. (Tokyo, Japan). The molecular weight (M) and molecular weight distribution of each fraction are shown in Table I. Lithium dodecyl sulfate (LDS) was from Sigma (St. Louis, MO). The oil-soluble dye, orange-OT (l-(o-tolylazo)-2-naphthol), was from Du Pont. Reagent grade LiCl was from Fisher. All solutions were prepared using glass distilled water subsequently passed through one carbon and two ion-exchange filters. Sample Preparation. Except for the M-dependence study, all experiments were carried out with SE-15 and at a polymer concentration of 0.25 g/L. To prepare solutions for light scattering measurements, the desired amounts of PEO and LDS were weighed and dissolved in LiCl solution of desired ionic strength, I . The solutions were then sonicated for 30 min and stirred overnight at rmm temperature to attain equilibrium. All solutions were then made dust-free for light scattering measurements by filtration through 0.2-pm Acrodisc filters from Gelman Science (Ann Arbor, MI). For PEO-LDS dialysis experiments, orange-OT was added to LDS solutions as a UV-visible probe of LDS concentration. The solutions were prepared by adding orangeOT to concentrated LDS solutions in LiCl at desired ionic strength, i.e., 12 g/L LDS for 0 1992 American Chemical Society
6806 The Journal of Physical Chemistry, Vol. 96, No. 16, 1992
Z = 0.05 M, 20 g/L LDS for I = 0.1 M, and 36 g/L LDS for I = 0.4 M. The solutions were sonicated in 100-mL volumetric flasks for 15 min to disperse the dye and then centrifuged at 3300 rpm for 15 min to remove unsolubilized dye particles. Each of the clear solutions obtained was then diluted to several LDS concentrations at constant ionic strength for both dialysis and UV-visible absorbance calibration. This technique assumes that the complexed micelles do not solubilize more dye than the free micelles: if this were the case, then the reduction of dye available for dissolution in the free micelles could reduce the visible absorbance contribution per free micelle. This is unlikely because (a) previous studies support the view that the bound micelle is not larger than the free micelle and (b) we have shown, for a different polymer-micelle system,13that the solubilization efficiency of an anionic micelle is unaltered upon binding to polymer. Metbods. Quasi-Elastic Light Scattering. Quasi-elastic light scattering (QELS)measurements were made at scattering angles from 30' to 150' with a Brookhaven (Holtsville, NY) 72 channel BI-2030 AT digital correlator and using a Jodon 15-mW H e N e laser (Ann Arbor, MI). We obtain the homodyne intensity-intensity correlation function G(q,t), with q, the amplitude of the scattering vector, given by q = (4?rii/X) sin (8/2), where ?I is the refractive index of the medium, X is the wavelength of the excitation light in a vacuum, and 0 is the scattering angle. G(q,t) is related to the time correlation function of concentration fluctuations g(q,t) by G(q,t) = 4 1
+ bg(q,02)
(1)
where A is the experimental base line and b is the fraction of the scattered intensity arising from concentration fluctuations. The quality of the measurements was verified by determining that the difference between the measured value of A and the calculated one was less than 1%. General discussions of QELs data analysis may be found in refs 15 and 16. In general, the correlation function can be expressed as an integral sum of exponential decays weighted over the distribution of relaxation times ~ ( 7 ) :
Xia et al. have already reached Do values for the surfactant-free polymer at a concentration of 0.25 g/L in 0.4 M NaCl. For PEO-LDS complex, our determinations were all made at a polymer concentration of 0.25 g/L and LDS concentration of 9.26 g/L. At this LDS concentration, the scattering intensity Z, for each PEO M fraction reaches a limiting value at a polymer concentration of 0.25 g/L under which conditions $ ( t ) show two exponential decays. Do values extracted from the slow diffusivity mode correspond to the complex, since the fast mode is identical to that observed for pure LDS micelles. We have also confirmed that the extracted slow mode Do values do not change upon either further increasing LDS concentration or decreasing PEO concentration. They therefore correspond to the complex saturated with LDS. Scattering Intensity Measurements. The static scattering intensity, &, was measured as the photon count rate with the Brookhaven system described above, using a scattering angle of 90' with a 200-pm pinhole aperture for the EM1 photomultiplier tube. Each measurement was carried out for 5 min. The average of 10 such measurements was reported as Z,. Electrophoretic Light Scattering. Electrophoretic light scattering (ELS) measurements were made at four scattering angles (8.6', 17.1', 25.6', and 34.2'), using the Coulter (Hialeah, FL) DELSA 440 apparatus. The electric field applied was at constant current from 3 to 10 mA, for different solution ionic strengths. In ELS, the photon-counting heterodyne correlation function for a solution with an electrophoretically monodisperse solute can be written as1* C(7) = &6(7) a. aIexp(-2Dq2r) + a2exp(-Dq%) cos (AUT)
+ +
(5)
where A, cu,, a,,and a2are constants independent of correlation time, T , and 6 ( ~ )is the delta function. D and q have the same definitions as in QELS. The cosine term is due to simultaneous electrophoresis and diffusion. The Fourier transform of eq 5 with respect to time, as stipulated by the Weiner-Khinchine theorem,Ig gives the power spectrum S(w) = j30
In principle, it is possible to obtain the distribution p ( ~ by ) integral transformationof the experimental [G(t)/A- 1]'12,but in practice this presents a formidable problem for numerical analysis, since taking the inverse Laplace transform is numerically an ill-posed problem. Several numerical methods developed so far are devoted to calculating ~ ( 7 ) .In the present work, we analyze the autocorrelation function of PED-LDS complexes by using the CONTIN program, which employs the constrained regularization method." From eq 2, the mean relaxation time, ( T ) , defined as the area of g(t), is given by (7)
= Jmg(t) dt
(3)
S , h dT
This ( T ) value can be resolved from each of the distribution modes ) the fmt moment of the normalized relaxation spectrum. of p ( ~ as Therefore, the diffusion coefficient, which corresponds to each value of ( T), can be calculated using D=
A2
16r2[sin2(8/2)]
(7)
(4)
where D becomes identical, in the limit of high dilution, to the translational diffusion coefficient, Do. In order to ensure that the diffusion coefficients determined from eq 4 are equivalent to translational diffusion coefficients, we have explicitly confirmed that the observed diffusion coefficients
+ aS(w) + w22(a,/*)Dq2 + (2Dq2)2
+
1
1 + (w + A w ) + ~ (Dq2)2 ( w - Aw)* + (04')'
where a is a constant independent of w. In both eqs 5 and 6, Aw is the difference between the angular frequency of the scattered light, a,,and that of the reference beam, a,,which is the same as that of the incident beam in DELSA. Since the frequency of the incident beam is modulated in the scattered light by the amount of the so called Doppler shift frequency, Aw can be given by 2ufi Aw = -Eu sin 8 (7) A where E (V/cm) and u ((pm s-')/(V cm-I)) are the applied electric field strength and electrophoretic mobility, respectively. Therefore, u can be directly evaluated from frequencies of the power spectrum. Detailed discussion on ELS measurements can be found in several reviews. Dialysis Equilibrium. Homemade two component dialysis cells2' with an effective volume capacity of 5.6-mL on each side of 0.02-pm Anopore membrane discs (Alltech Associates, Inc., Deerfield, IL), were used to separate PEO-bound and free LDS micelles. To compartment 1 of the dialysis cell, 5.6 mL of SE-15 PEO aqueous solution, adjusted to the desired ionic strength with LiCl, was added with a Finnpipette (Cole Scientific, Woodland Hills,CA). In compartment 2 a solution of LDS in the same LiCl solution, with dissolved orangeOT, was added. After a magnetic stir bar was placed in each compartment, the cells were sealed by Parafilm O-rings between the membrane and cells. The sealed cells were secured by rubber bands and placed on a magnetic 14~15~18320
Complex Formation between PEO and SDS Micelles
;
h
2.0
0
The Journal of Physical Chemistry, Vol. 96, No. 16, 1992 6807
1 Y
0.0
0
5
10
c, ,
15
0
Figure 1. Intensity of scattered light as a function of LDS surfactant concentration at ionic strengths (M LiC1): 0.05 (A),0.10 (0),and 0.40 ( 0 ) . Lower curves for the L D S upper curves in the presence of 0.25 g/L PEO.
stirrer at room temperature (22 "C) for 50 days to reach dialysis equilibrium, at which time the concentration of LDS in compartment 2 was no longer changed with time. Thus, 2.0-mL samples were taken from compartment 2 for UV-visible spectrophotometry (HP 8450) to determine the equilibrium free LDS concentration in the system, since the concentrations of free LDS in both compartments 1 and 2 are the same at equilibrium. The absorbance at 496 nm is linearly proportional to LDS concentration (C,), and was used to determine C,. The amount of LDS bound by PEO was then calculated by bund
%itid
20
10
30
50
40
60
gil
- &pilib
(8)
where n h u n d is the number of moles of bound LDS; ninitialis the total number moles of LDS added to side 2 initially; and nquilib = 2VmllC,,where Vel, = 5.6 mL is the total number of moles of free LDS in the system at equilibrium.
Results and Discussion Effect of Ionic Strength. Static Light Scattering. The effect of ionic strength, Z, on the scattering intensity of both pure LDS micelle and PEO-LDS complex formed with SE-15 is presented as plots of photon counts I, vs LDS concentration (C,) in Figure 1 . For LDS micelles, we observe that Z, linearly increases with C, at each ionic strength, which suggests that the aggregation number, N, of LDS micelles is independent of C,, in the concentration range of the present study. The thermodynamics of the binding SDS micelles to PEO chains has previously been inferred from neutron scattering.I0 It was shown that SDS micelles fmt bind to PEO with a free energy, AF, of -(1&20)kT. This binding free energy then becomes less favorable with increasing number of bound SDS micelles because of the repulsions among micelles within a PEO-SDS complex. As long as AF > kT, SDS micelles bind to PEO. Saturation occurs when the binding free energy is smaller than kT. The static light scattering results for the complexation of PEO and LDS observed in Figure 1 are consistent with this description. The scattering intensity rapidly increases at low LDS concentration and then slowly reaches a plateau, corresponding to saturation. The scattering intensity of the saturated complex increases with LiCl concentration because the number of micelles bound per PEO chain increases (see dialysis results below) with ionic strength. Despite the expected intermicellar electrostatic repulsive effect, the initial rate of increase of I, with LDS concentration is larger at low ionic strength. This can be interpreted in terms of the effect of the cation on the complexation of PEO and dodecyl sulfate micelles. The influence of Li+, Na+, and NH4+ on the cmc reduction of dodecyl sulfate micelles by PEO has been explained in terms of a direct role of the cation in the PEO-micelle interactionI3 as follows. PEO has been shown to bind Li+ and Na+ in water;2zif the cation is simultaneously bound electrostatically to the micelle, then its interaction with the polymer can provide part of the driving force for polymer-micelle association. However,
[LDS]/lO .'mol dm"
Figure 2. Binding isotherm for the PEO-LDS system in 0.05 M (O), 0.10 M (A),and 0.40 M (0) LiC1. Solid lines are the fits of eq 9. The broken line is from Hill's equation. TABLE II: n and K Values Obtained for PEO SE-15 from Eq 9 at Different Ionic Strengths K X KX I(M) n 104(M-') I(M) n 104(M-') 0.05 0.1
7 16
1.8 1.7
0.2'
0.4
20 26
1.4
"Only carried out at a high LDS concentration.
if the bulk concentration of cation is large compared with the local ex- in the vicinity of the micelle, this effect becomes negligible. We believe this is why the initial rate of increase of Z, with C, in Figure 1 diminishes with increasing LiCl concentration. On the other hand, we cannot rule out the possibility that the scattering intensity is also influenced by the ionic strength via intercomplex interactions, inasmuch as such interparticle repulsion may affect the second virial coefficient. Dialysis Equilibrium. Shown in Figure 2 are binding curves of the PEO-LDS system obtained at different ionic strengths. For elucidation of the ionic strength effect, binding curves are first discussed in terms of a noncooperative isotherm. For a ligandbinding macromolecule with n equivalent binding sites on each macromolecular chain, the degree of binding, Y, can be written asl8
(9) where [L] and [PI are the ligand and polymer molar concentrations, respectively, n is the number of binding sites per polymer chain, and K is the binding constant. To convert the LDS surfactant concentration to [L], i.e. the micelle concentration, we use literature values for the aggregation numbersz3of SDS at different ionic strength, since the measured hydrodynamic sizes for both LDS and SDS in 0.40 M LiCl micelles are the same, e.g. R, = 3 nm. In Figure 2, the dialysis data are fitted to eq 9, as shown by the solid lines. The obtained fitting parameters n and K are given in Table 11, where n is also the maximum number of micelles bound per PEO chain. Clearly, the increase in n with increasing ionic strength can be explained as a consequence of the shielding of the electrostatic repulsion between bound LDS micelles. The n values in Table I1 are consistent with those obtained by neutron scatteringlo for PEO-SDS. It is also of interest to note that the binding constants decrease with increasing ionic strength. This is consistent with the specific effect of Li+ on the binding of LDS to PEO discussed above. The cooperative binding of ligands to macromolecules may be described by Hill's eqz4
Y=
CP-1' 1
+ CTL]'
(10)
where z is an empirical exponent, called Hill's coefficient. The
6808 The Journal of Physical Chemistry, Vol. 96, No. 16, 1992
-
-0'31t'"""' -0.4
I \
I
Xia et al.
I
-0'3 I -0.4
1
\A
I
\
\
t -0.7
-0.7
~
U.0
0.1
0.2
0.3
0.4
0.5
[ LiCl I, M Figure 3. Electrophoretic mobility of the PEO-LDS complex as a
function of ionic strength. Polymer concentration of 0.25 g/L; LDS concentration of 9.26 g/L.
quantity z is a measure of cooperativity; if z = 1, noncooperativity is observed, i.e. a single binding constant governs the independent binding of all ligands. If z > 1, the binding is cooperative, which means that the second ligand binds more readily than the first. If z < 1, then the binding is anticooperative. In cooperative or anticooperative binding, the initial binding usually induces a conformation change in the macromolecule, thus affecting subsequent binding. In eq 10, C and C'are constants related to the binding constant and number of binding sites. Since the overall cooperative binding constant is a function of both the intrinsic binding constant and number of binding sites, C has no clear-cut physical definition. Shirahama6has used eq 10 to analyze dialysis data for PEOSDS in 0.1 M NaCl. He reported highly cooperative binding (z = 20) and a limiting binding ratio of 0.4 SDS per base mol PEO. This binding ratio corresponds to 16 bound micelles, which is the same as the result obtained in Table 11. The dialysis data for I = 0.1 M LiCl in Figure 2 are fitted to eq 10, as shown by the broken curve, yielding z = 2, which is much less than the cooperativity observed by Shirahama for PEO-SDS in the same ionic strength. The cause of the discrepancy might be that our dialysis experiments were carried out at LDS concentrations above the cmc. Even though surfactant binding at very low C, is important for determining cooperativity, it was not investigated in the present dialysis study since we were only interested in determining the LDS micelle binding constant and number of LDS micelles bound per PEO chain. Therefore, the experimental data obtained at other ionic strengths are not further analyzed in terms of eq 10. Electrophoretic Light Scuttering. The electrophoretic mobility of the PEO-LDS complex as a function of ionic strength is shown in Figure 3. Since the number of bound micelles N is strongly dependent on the ionic strength, this result can be interpreted on the basis of the contribution of the polymer segments to the friction force per bound micelle. The motion of the complex at steady state in a field of strength E (V cm-')can be described by balancing the electrostatic force, F,,and frictional force, Ff: F, = Ff
(11)
From the dependence of the electrophoretic mobility on the M of PEO (see below), we deduce that the complex behaves as a free-draining coil, in which each unit of the complex chain acts independently. The electrostatic and frictional forces can then be given by F, = Nq,E Ff = U&
+ Nf,)
(12)
(13)
where q, is the effective charge of a bound micelle;f and f, are the friction coefficients of PEO and the bound L b S micelle, respectively. E is the external field strength and u is the center
'
5
I 25
15 N
Figure 4. Electrophoretic mobility of the PEO-LDS complex vs the number of bound LDS micelles. The solid line is the best fit to eq 14.
of mass velocity of the complex. Substituting eqs 12 and 13 into eq 11, we have
Thus, we can fit the electrophoretic mobility data in Figure 3 against the number of bound micelles. The results are shown in Figure 4, where the triangles are the experimental data and the line is the fitting curve from eq 14. In eq 14, q,, fp, and f, are unknown. However, they can be obtained by using a least q u a m fitting program to fit the experimental data to the equation, which (Ns)/m, and yields f, = 5.1 X lo-" (Ns)/m, fp = 7.1 X q, = 4.6 X C. Assuming that the frictional resistance to flow of the micelle is not affected by the applied field in electrophoresis, the value of fp/f, is the ratio of the hydrodynamic radius of a PEO polymer to that of an LDS micelle in the complex, since f, = 61rqR,. We findfplf, to be much larger than R,(PEO)/R,(LDS) = 3.4, obtained by QELS for isolated PEO polymer and LDS micelle. One explanation is that the binding of LDS to PEO makes the polymer chain more extended in the complex, thus increasing f v The structure change of the bound micelle may also be a factor causingfp/f, > &(PEO)/&(LDS), inasmuch as Cabane' found the micelle aggregation number to diminish upon binding. Since the shear plane of a micelle is located in its electrical double layer, the shear surface charge, deduced from mobility measurement, includes the counterion contribution. Therefore, the ratio of q, in the PEO-LDS complex to that in the pure micelle should provide information about the enhancement of counterion binding upon complexation. We found that q, in the complex is smaller than that of free LDS micelle (8.2 X C) by ca.60%, which suggests that more Li+ ions lie within the shear plane of the bound LDS micelle than the free one. This is consistent with the interpretation of the role of the cation in the binding of dodecyl sulfate micelle to PEO described above. M SDepeaaeneeOf D i f f d coefficht. ~~ @&-Elastic Light Scuttering. To extract the diffusion relaxation time constants of the PEO-LDS complexes, QELS measurements were made at scattering angles from 30° to 150' on 0.25 g/L solutions of PEO at all M's in 0.40 M LiCl containing LDS at concentrations ranging from 0.74 to 9.26 g/L. Shown in Figure 5 are distributions of relaxation times. Clearly, the distribution functions change from a single relaxation to bimodal distributions when the LDS concentration increases from 2.2 to 2.9 g/L. Below C, = 2.2 g/L, the single mode relaxation slows down with increasing C, due to an increase in the number of bound LDS in the complex. At C, 1 2.9 g/L the bimodal distributions exhibit only changes in the relative intensity of the two modes. It is also found that the relaxation times deduced from the fast mode of the bimodal distributions are identical to that obtained for pure LDS micelle. Therefore, we can conclude that the slow mode of the bimodal distributions corresponds to an LDS-saturated complex, while the single relaxation mode observed at lower C, can be attributed to
Complex Formation between PEO and SDS Micelles
The Journal of Physical Chemistry, Vol. 96, No. 16, 1992 6809 TABLE III: Electrophoretic Mobility of PEO-LDS Complexes Formed from PEO of Varying M ,
M, x
P
-0.65
0.25 0.39 0.86 1.45
v
a
M, x
(pm cm V-' s-I)
io+
2.50 5.94 9.96
-0.64 -0.64 -0.62
P
(pm cm V-I s-I)
-0.61 -0.61 -0.60
If the PEO-LDS is an intrapolymer complex, the molecular weight of the complex is proportional to the PEO molecular weight Mc
= 8MPPEO
(15)
Therefore, Dc
k@'55Mp~04'55
(16)
where k2 is the proportionality constant for the PEO-LDS complex. kl = 1.2 X 10" cm2/s and k p S 5= 9.8 X lov5cm2/s are obtained from Figure 6. The value of k@ 55 is smaller than kl which may suggest that the PEO-LDS complex is less flexible than the PEO chain.I5 /3 is related to the number of micelles bound per polymer chain, N, by
v
a
@=N-
+ 1
MPEO
7,
Ps
Figwe 5. Distributionsof relaxation spectra p ( r ) calculated by using the CONTIN program for PED-LDS complexes in 0.40 M LiCl and PEO concentration of 0.25 g/L given with LDS concentration (g/L): (a, top) 0.74 ( O ) , 1.74 (A), and 2.22 (0); (b, bottom) 2.98 (A) and 9.26 (0).
where M,,, is the LDS micelle mass, about 28 OOO for ionic strength 0.40.10,22From the dialysis measurements discussed above, we obtain the mean number of bound micelles per PEO chain at saturation as 26 for SE-15.Thus, from eq 17, 8 = 6.1 and k2 = (9.8 X ~ m ~ / s )= / P2.6~ X~ 10" cm2/s are obtained. According to the blob model proposed by Akcasu and Han,2' the constant k, is proportional to [(l - v)(2 - v)]-I when the ratio of the blob to the chain molecular weight is smaller than 1. Therefore, the result k2 > kl is consistent with the model since Y is larger for the PEO-LDS complex. Since the binding of micella to water soluble polymers is usually expressed as the ratio of moles of bound surfactant to the moles of polymer residue,' y, we have
p
y-
I
M m
NMo
-7.5
'
4.0
\ I 6.0
5.0
log M
Figure 6. Molecular weight dependence of the translational diffusion coefficients of PEO (0)and PED-LDS (0)in 0.40 M LiCI. Polymer concentration of 0.25 g/L.
unsaturated complexes. Using eq 4 the corresponding diffusion coefficient for the LDS-PEO complex of each PEO fraction is obtained from the slow mode relaxation. The diffusion coefficients obtained are plotted vs PEO molecular weight in Figure 6,along with the diffusion coefficient of surfactant-free PEO. The linear plots in Figure 6 show that both PEO and PEO-LDS follow the same scaling law. For PEO, Do = klM-0.52is observed, which has the same 4 M dependence obtained by Brown.25 For the PEGLDS complex, Do is proportional to PEO molecular weight by M-0.55,which suggests that the PEO-LDS complex behaves since the scaling law of Do = like a polymer in good klM-' shows a value of v = 0.5 for a polymer in 8 solvent and 0.5 C v C 0.6 for a polymer in a good solvent.
-
+ 1 = y-MLDS+ 1 MO
where N is the aggregation number of the micelle, and Moand Mm are the molar mass of the polymer unit and LDS surfactant, 44 and 272, respectively. 7 = 0.8 was obtained from small angle neutron scatteringlo at ionic strength 0.40. Therefore, 8 = 6.2 is obtained from eq 18. This /3 value is consistent with the one obtained from dialysis experiment by eq 17. M Dependence of Electrophoretic Mobility. Electrophoretic Light Scattering. The electrophoretic mobilities (u) of PEO-LDS complexes in 0.4 M LiCl are given in Table 111. Clearly, u is nearly independent of molecular weight, which suggests that the electrophoretic mobility corresponds to that of a free draining coil in which each unit of the chain exerts its own independent frictional resistance to motion, i.e. 24
= qo/fo
(19)
where qo andfo are the charge and friction coefficient per chain unit, respectively. For the PEO-LDS complex systems, qo corresponds to micelle charge andfo is the summation of frictional contributions of the micelle and the PEO chain between the adjacent bound LDS micelles, as described by eq 14. The M independence of the mobility further suggests that PED-LDS complexes behave like a polyelectrolyte.28 S p e e u l r t i ~on~ a Model. From measurements of neutron scattering intensity'O and NMR chemical shifts at varying SDS concentration,' the binding ratio y was found to be M-indepenent in the range of 0.2-0.4 mol of SDS per base mol of PEO in 0.1 M NaCl solution. From this result, and from evidence that the
Xia et al.
6810 The Journal of Physical Chemistry, Vol. 96, No. 16, 1992
friction coefficient of polymer electrostatic force frictional force normalized correlation function homodyne intensity-intensity correlation function ionic strength scattering intensity proportionality constants in Do M relationship binding constant ligand concentration monomer molecular weight molecular weight of LDS surfactant molar mass of LDS micelle molar mass of PEO number of micelle binding s i t e per polymer chain number of bound micelles per polymer chain number of moles of bound LDS number of moles of free LDS at equilibrium total number moles of LDS refractive index micelle aggregation number polymer concentration amplitude of scattering vector effective charge of micelle charge of repeating unit of PEO-LDS complex hydrodynamic radius Fourier transform of C(r) electrophoretic mobility center of mass velocity dialysis cell volume degree of binding empirical exponent in cooperative binding isotherm constants independent of correlation time
L
7
-
Figure 7. Schematic representations of the PEO-LDS complex. complex is intrapolymer based on neutron scattering, a structural modello of the complex was proposed. In this model, the PEO chain is adsorbed on SDS micelles: 10%of PEO segments are in direct contact with the micellar surfaces, while the others form loops or strands joining two micelles. The schematic diagram of the model is shown in Figure 7a(left). This structural model appears to be consistent with the macroscopic properties obtained so far for the complex. The properties studied by conductimetry, viscometry, and ultracentrifugation show that the saturated PEO-SDS complex has the properties of a polyelectrolyte with the same linear charge d e n ~ i t y . ~The M dependence of both diffusion coefficient and electrophoretic mobility of the complex, presented in this paper, also demonstrates that the PEO-LDS complex behaves like a polyelectrolyte. While the structural model in Figure 7a(left) is compatible with all the macroscopic properties of the complex, it does not specify the nature of the interaction between the PEO chain and the dodecyl sulfate micelle. Cabane concluded from NMR measurements that the contributions of hydrophobic and electrostatic interactions are comparable, and both occur at the micellar surface.’ Most recently, Kwak et al. concluded from the same NMR technique that PEO units are predominantly solubilized within the micelle.29 The discrepancy between these conclusions is obvious. In a previous study, we found that the dodecyl sulfate cmc-lowering effect of PEO is strongly dependent on the nature of the cation (Li+ > Na+ > NH4+),I3Although it is difficult to rule out the possibility that the hydration nature of the cation may affect in some way the properties of the Stem layer, we suggested more specifically that the cation interacts simultaneously with the micelle (through electrostatic forces) and with the polymer (via coordination complexation), as shown schematically in Figure 7b(right). The cation in the double layer coordinates with the nonionic polymer to form a “pseudopolycation”,which then forms complexes with the anionic micelles. The interaction between the micelle and the polymer is then mostly localized in the electric double layer of the micelle. Three aspects of the current results are relevant to this hypothesis: (a) the micelle binding constant measured by dialysis increases with decreasing ionic strength, (b) the dependence on surfactant concentration of the static light scattering intensity in the PEO-LDS system increases with decreasing ionic strength at low LDS concentration; and (c) the degree of micelle counterion binding appears to increase in the presence of PEO. These three observations support the model represented in Figure 7b(right). Acknowledgment. This research was supported by NSF Grant DMR-9014945. List of Symbols Used A
b
C
c,
c(d
D
DO E fm
h
base line fraction of the scattered intensity constant of cooperative binding surfactant (LDS) concentration heterodyne correlation function diffusion coefficient translational diffusion coefficient electric field strength friction coefficient of micelles friction coefficient of polymer unit
molar mass of complex relative to molar mass of PEO moles of surfactant bound per mole residue of PEO delta function scattering angle relaxation time mean relaxation time distribution function of relaxation time empirical exponent in Do M relationship frequency of reference beam frequency of scattering beam frequency shift
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Registry No. PEO, 25322-68-3; LDS, 2044-56-6; orange-OT, 264617-5; LEI, 7447-41-8; Li, 7439-93-2.
References and Notes Goddard, E. D. Colloids Surf. 1986, 19, 255. Fishman, M. L.; Eirich, F. R. J . Phys. Chem. 1971,75,3135. Schwuaer, M. J. J . Colloid Interfuce Sci. 1973,43,491. FranVTs, J.; Dayantis, J.; Sabbadin, J. Eur. Polym. J . 1985,2l,165. Jones, M. N. J . Colloid Inferface Sci. 1967,23,36. Shirahama, K. Colloid Polym. Sci. 1974,252,978. Cabane, B. J . Phys. Chem. 1977,81,1639. Shirahama, K.; Ide, N. J . Colloid Interfuce Sci. 1976,54,450. Nagarajan, R.;Kalpakci, B. Polym. Prepr. (Am. Chem. Soc., Diu. Polym. Chem.) 1982,23,41. (10) Cabane, B.;Duplessix, R. J. Phys. (Paris) 1982. 43, 1529. (1 1) Ruckenstein, E.; Huber, G.; Hoffman, H. Lungmuir 1987,3, 328. (12) Mori, Y.;Akisada, H.; Saito, M.;Matuura, R. J . Colloid Interfuce Sci. 1976,61, 233. (13) Dubin, P. L.; Gruber, J. H.; Xia, J.; Zhang. H. J . Colloid Interface Sci. 1992,148, 35. (14) Ware, B. R. Adu. Colloid Interfuce Sci. 1974,4, 1. (1 5) Pecora, R. Dynamic Light Scuttering: Applicurion of Photon Correlution Spectroscopy; Plenum Press: New York. 1976. (16) Stock, R.S.;Ray, W. H. J. Polym. Sci., Polym. Phys. Ed. 1985.23. (1) (2) (3) (4) (5) (6) (7) (8) (9)
1393. (17) Provencher, S. W. Compur. Phys. Commun. 1982,27,229. (18) Ware, B. R.; Haas, D. D. In Fat Merhods in Physical Biochemistv und Cell Biology; Shaafi, R. I., Fernandez, S.M., Eds.; Elsevier: Amsterdam, 1983. (19) McQuarrie, D. A. Stutisticul Mechanics; Harper and Row: New York, 1976. (20) Pecora, R.; Berne, B. J. Dynamic Light Scotrering; Wile: New York, 1976. (21) Rigsbee, D. R. Thesis,Purdue University, in preparation. (22) Satori, R.;Sepulveda, L.; Quina, F.; Lissi, E.; Albuin, E. Mucromolecules 1990,23,3878. (23) a n a , R.In Surfuctunt Solutionr; a n a , R., Ed.; Dekker: New York, 1987; Chapter 5.
J. Phys. Chem. 1992, 96,6811-6817 (24) Hill. A. V. J . Physiol. 1910, 40, 190. (25) Brown, W. Macromolecules 1984, 17,66. (26) Wang, L.; Yu, H. Macromolecules 1988, 21, 3498. (27) Akcasu, A. Z.; Han, C. C. Macromolecules 1979, 12, 276.
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(28) Noda, I. M.; Nagasawa. M.; Ota, M. J . Am. Chem. SOC.1964,86, 5075. (29) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J . Phys. Chem. 1991,95, 462.
Ultrasonic Relaxation Studies of Mixed Micelles Formed from AlcohoCDecyItrimethylammonium Bromide- W ater David J. Jobe, R. E.Verrall, Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 0 WO
Bohdan Skalski, Faculty of Chemistry, A . Mickiewicz University, 60- 780, Poznan, Poland
and Emilio Aicart* Departamento de Quimica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense, 28040 Madrid, Spain (Received: January 24, 1992; In Final Form: April 21, 1992)
Ultrasonic relaxation (0.6
