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J. Phys. Chem. B 2001, 105, 8302-8311
Comparison of Original and Cross-linked Wormlike Micelles of Poly(ethylene oxide-b-butadiene) in Water: Rheological Properties and Effects of Poly(ethylene oxide) Addition You-Yeon Won,† Kristofer Paso, H. Ted Davis, and Frank S. Bates* Department of Chemical Engineering and Materials Science, UniVersity of Minnesota, Minneapolis, Minnesota 55455 ReceiVed: NoVember 7, 2000; In Final Form: June 21, 2001
Chemical fixation can convert self-assembled amphiphilic aggregates into covalently bonded giant macromolecules that can have properties that are fundamentally different from the unreacted precursors. Following up our previous report, we here extend the comparison between pristine and cross-linked wormlike micelles prepared from a cross-linkable poly(ethylene oxide-b-butadiene) diblock copolymer. Despite retention of the overall morphology, the cross-linked wormlike micelles exhibit unusual linear and nonlinear flow properties that presumably reflect the micelle stiffening upon cross-linking. Chemical fixation also influences their responses to changes in thermodynamic conditions. To explore this point, we added nonadsorbing homopoly(ethylene oxide) (PEO) into the otherwise stable micelle solutions as a means for creating depletion effects (that is, attractive interactions between the micelles). Experimental studies of the phase behavior and attendant macroscopic properties of the mixtures of the wormlike micelles and PEO in water indicate that, when mixed with homo-PEO, the unreacted micelles phase separate to form hexagonal arrays, due to the depletion interactions. In contrast, the cross-linked analogues, under comparable conditions, remain homogeneously dispersed, and instead form physical gels. Such gels are characterized by time-dependent rheological responses upon large deformation and no flow under small deformations. These results suggest that the addition of PEO produces depletion-induced demixing of the cross-linked wormlike micelles leading to a nonequilibrium physical gel.
Introduction Spontaneous organization of amphiphilic molecules in water leads to a wide range of microstructures: micelles and vesicles in the dilute limit and various ordered mesostructures at high concentrations. The underlying physics that brings about such phenomena involves basic molecular interactions such as hydrophobic-hydrophilic effects, hydrogen bonding, Coulombic interactions, or van der Waals forces.1 The structural and physical properties created in these self-organizing materials are not permanent, but may be influenced by changes in the physical conditions that resulted in the original self-assembly. For example, self-assembled cell membranes can be disrupted by changes in pH or fluid flow. The development of synthetic materials with prescribed microstructural size and shape that are insensitive to environmental perturbation has been a subject of a great deal of research activity for many years. A popular approach to the stabilization of the self-assembled structure consists of the use of amphiphiles that have reactive functional groups. Any of the conventional polymerization chemistries can be utilized to fix the microstructure, provided that the amphiphile has suitable functional groups. Just as in the case of bulk nonlinear polymerizations that lead to branched or networked polymers, the gelation of the cross-linked domain can be defined as the state in which the weight-average size of the constituent molecules diverges, and a threshold conversion for gelation can be given by πgel ) 1/(f - 1) where f is the functionality of the * To whom correspondence should be addressed. † Present address: Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139.
amphiphile.2 This formula implies that the higher the functionality of the amphiphile, the smaller the conversion necessary for complete fixation of the structure, as has been demonstrated by O’Brien and co-workers.3 Recently, we have demonstrated the chemical fixation of structures constructed with macromolecular amphiphiles.4 It has been confirmed that the aggregation structure formed in water can be rationally controlled through the changes in molecular characteristics by using various poly(ethylene oxide)(PEO)based amphiphilic block copolymers.5 Our approach consists of utilizing the cross-linkable macromolecular surfactant of poly(ethylene oxide)-polybutadiene (PEO-PB). We selected 1,2polybutadiene (PB) as the micelle core material, and the double bonds present on each repeat unit are readily coupled through standard cross-linking reactions. With about 45 double bonds per chain, for example, just 3% conversion of the double bonds will likely lead to the gelation of the hydrocarbon domains. The wormlike micelle (shown in Figure 1) has been chosen to illustrate the above concept. This structure has been documented with a wide range of amphiphilic materials, often cationic surfactants (e.g., cetyltrimethylammonium bromide or chloride, CTAB or CTAC) with added salts (e.g., sodium salicylate, NaSal).6,7 The polymer-like configuration of the micelles that closely resembles that of the entangled flexible macromolecules dispersed in solution, but with the capability of reversible breaking and recombination, gives rise to unique rheological properties.8 The micelles, even at small mass fractions of a few thousandths, may completely change the flow properties of the solution from viscous to elastic.9,10 Characterization of the cross-
10.1021/jp004078d CCC: $20.00 © 2001 American Chemical Society Published on Web 08/14/2001
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Figure 1. Sketches illustrating the local aggregation structures of the wormlike micelles with (A) pristine and (B) cross-linked PB cores.
linked wormlike micelles revealed that the structure of the parent micelle was completely preserved, whereas the cross-linking resulted in a remarkable enhancement in elasticity of the system.4 In view of the fact that the cross-linking is accompanied by significant micelle stiffening as anticipated by the transition from liquidlike to rubbery cores, using both pristine and cross-linked wormlike micelles may create a unique opportunity to illustrate the effect of the stiffness of long slender objects on their responses to changes in thermodynamic conditions. We have opted to add nonadsorbing soluble particles of different shape (i.e., homopolymers) into the otherwise stable solution (i.e., the micelle solution) as a means of generating attractive interactions between the dispersed micellar objects. Thus, this paper presents an experimental study of the phase behavior and rheological properties of mixtures of wormlike micelles and PEO in water. The depletion effect has long been useful in many technical applications such as separation of synthetic (e.g., rubber latex)11 or biological (e.g., tobacco-mosaic virus)12 particles. The associated phase separation, aggregation, and gelation phenomena in colloidal mixtures have been subjects of theoretical and experimental activity for decades.13,14 In fact, one of the most ideal model systems for studying this subject is the colloid-polymer mixture. When polymer additives do not adsorb onto the surface of colloidal particles, individual polymer chains assume a configuration of flexible coils whose size is characterized by a radius of gyration Rg. The dispersed polymer chains however cannot approach a region comparable to their size (i.e., Rg) near the colloidal surface without paying an entropic penalty due to chain deformation and, hence, are normally excluded from that region called the depletion layer surrounding each colloidal particle. Concentration gradients across the depletion boundary create an osmotic driving force for colloidal particles to overlap in their depletion layers; see Figure 2 for a schematic representation of this mechanism. The resulting attraction between colloidal particles is considered as weak and short-ranged. The magnitude and range of this interaction are proportional to the concentration and size of the polymer coils, respectively, and therefore are easily tuned. This simple picture of depletion forces, first proposed by Asakura and Oosawa in the early 1950s,15 provides a basis for models describing diverse colloidal mixtures.
J. Phys. Chem. B, Vol. 105, No. 35, 2001 8303
Figure 2. Schematic description of the depletion effect. (A) The polymer coil creates the depletion layer (crosshatched region) around the colloid hard core (dark region) where the entrance of the chain center is prevented. (B) Aggregation of the particles produces overlap of the depletion layers, and increases the free volume available for the polymer.
In this paper, we first characterize the rheological properties of cross-linked wormlike micelle solutions. Subsequently, we compare the consequences of the depletion effects on a homologous pair of pristine and cross-linked wormlike micelles immersed in a suspension of nonadsorbing PEO. We are unaware of previous reports that deal with this type of phase behavior. Estimated size ratios of the cross-sectional radius of the micelles to the radius of gyration of the polymer coils (i.e., R/Rg) of between three and four are employed to produce the depletion forces in the micelle solutions. The phase separation behavior of the mixtures of the non-cross-linked wormlike micelles and homo-PEO in the water-rich limit is investigated by combined experiments of optical turbidity and SAXS. On the other hand, rheological characterization techniques are mainly utilized for the cross-linked wormlike micelles to probe their behavior under comparable conditions. Experimental Section Materials. The poly(ethylene oxide)-polybutadiene (PEOPB) diblock material (abbreviated as OB3) used in this study was prepared by a two-step anionic polymerization. The synthesis and characterization of the copolymer has been described elsewhere.5,16 The molecular weight and the polydispersity index are 4.9 kg/mol and 1.15, respectively. On the basis of the PEO weight fraction of 0.50 determined from the reaction stoichiometry and 1H NMR, the volume fraction of the PEO block was estimated to be 0.45 using the published melt density data of F94%1,2-PB ≈ 0.869 (g/cm3)17 and FPEO ≈ 1.125 (g/cm3)18 at 25 °C. Potassium persulfate (K2S2O8), a water-soluble free radical initiator, obtained from Aldrich was purified by recrystallization from water before use. Redox reagents for initiation of cross-linking, sodium metabisulfite (Na2S2O5) and ferrous sulfate (iron(II) sulfate heptahydrate, FeSO4‚7H2O), were purchased from Fischer Scientific and used as received. Poly(ethylene oxide) (PEO) samples of different number-average molecular weights (i.e., 1,000 g/mol, 8000 g/mol, and 14 000 g/mol) were obtained from Aldrich and will be denoted as PEO1K, PEO8K, and PEO14K, respectively. The polydispersity
8304 J. Phys. Chem. B, Vol. 105, No. 35, 2001 indices M h w/M h n (where M h w and M h n are weight- and numberaverage molecular weights, respectively) of 1.12 (PEO1K), 1.11 (PEO8K), and 1.11 (PEO14K) were determined by gel permeation chromatography (GPC). Chemical Fixation of the Micelles. A weighed amount of potassium persulfate initiator (0.10 g) was dissolved with a premade 1wt % OB3 aqueous micellar solution (10.00 g of the copolymer/water solution). The polymer-initiator solution was then stirred at room temperature for several hours. The crosslinking reaction was initiated at room temperature by injecting weighed quantities of predissolved redox reagents in water (0.17 g of a 30wt % Na2S2O5 solution and 0.07 g of 3wt % FeSO4‚ 7H2O solution) in the sequence of sodium metabisulfite (reductant) and ferrous sulfate (oxidant). The sample was initially agitated with a magnetic stirring bar for minutes and then left quiescent. Upon addition of ferrous sulfate, the solution became brownish and the color disappeared in half an hour with the progress of the reaction. The final cross-linked solution containing the added inorganic compounds appeared homogeneous, clear, and slightly more yellowish than the parent solution. All cross-linking experiments were performed at fixed weight ratios of 1:1:0.5:0.02 between the copolymer, the initiator, the reductant, and the oxidant. Shear Rheometry. Rheological measurements were carried out using a strain-controlled Rheometrics fluid spectrometer (RFS-II) equipped with a force-rebalance transducer whose torque range is 0.002 to 100 g‚cm with 1% accuracy. We used a standard Couette cell that contains the sample in a 1 mm concentric cylindrical gap between a cup (i.e., the outer cylinder) with a diameter of 34 mm and a bob (i.e., the inner cylinder) with a diameter of 32 mm and a length of 33 mm. About 12 mL of the sample is first loaded on the cup and fills the gap as the bob is lowered at a speed of 1 mm/s. The bob has a bottom recess for air entrapment and was normally slightly overflowed with the sample. All measurements were taken at 22 ( 0.5 °C, and the temperature was controlled using a circulating fluid bath. To avoid any water evaporation from the sample, the top airinterface was coated with a thin wetting film of a low viscosity (e.g., 10 cP at room temperature) silicon oil and the whole fixture assembly was covered with water-soaked foam-lined covers. Four types of tests were performed on each sample: linear dynamic (i.e., oscillatory) time sweeps for at least 1 h after sample loading, followed by linear dynamic frequency sweeps from 0.05 to 100 rad/s, dynamic strain-amplitude sweeps from 0.001 to 8.75, and steady strain rate sweeps from 0.02 to 1000 s-1. The order in which these tests were performed was chosen so as to minimize measurement-induced disturbance of the sample itself and the spreading of the silicon oil on the solution. The linear regime (i.e., the region of low deformation where the rheological response is independent of the strain amplitude) determined by the dynamic strain sweep experiment varied depending on the sample concentration; linearity is normally restricted to below a few tenths in strain amplitude. In nonlinear steady shear measurements, data were taken for both clockwise and counterclockwise directions and averaged. Because of the long transient at low shear, a preshearing delay of 120 s prior to an actual measurement was adopted for low shear rates < 10 s-1, and a 10 s delay was found to be enough at higher shear rates. Small-Angle Neutron Scattering (SANS) under Steady Shear Flow. SANS measurements under steady shear flow were performed with the SANS instrument at the DR3 reactor at Risø National Laboratory, Denmark. The sample-detector distance, the neutron wavelength (λ), and the wavelength spread (∆λ/λ)
Won et al.
Figure 3. Experimental geometry for the application of rotational steady shear while conducting SANS measurements (top view).
were 6 m, 5.57 Å, and 0.09, respectively. All measurements were taken at 20 °C. The Couette-type shear device used for these in-situ SANS experiments has been described elsewhere by Mortensen et al.19 Briefly, a shear deformation on the sample confined in the gap between the concentric cylinders was produced by the rotation of the inner cylinder with the stationary outer cylinder, and the neutron beam was directed parallel to the shear gradient direction through the center of the cell; see Figure 3. The SANS intensities were measured on an area detector in the x-y plane, and the isointensity contour maps were obtained from the raw data without correction. Small-Angle X-ray Scattering (SAXS). Small-angle X-ray scattering (SAXS) experiments were performed on a custom built instrument located in the Institute of Technology Characterization Facility at the University of Minnesota. The Cu KR X-ray beam produced by a Rigaku RU-200BVH rotating anode X-ray generator was monochromatized by a nickel foil and focused using Franks mirror optics. The sample contained in an epoxy-sealed quartz capillary was placed in an evacuated chamber with temperature control. Two-dimensional scattering patterns were collected on a multiwire area detector, corrected for detector response characteristics, and converted to a onedimensional format by integrating the data azimuthally over a proper range. The sample-to-detector distance of 2.3 m for an X-ray wavelength (λ) of 1.542 Å was chosen to cover scattering wave vectors 0.01 Å -1 < q < 0.1 Å-1. Here the scattering wave vector (q) is defined as q ) (4π/λ) sin(θ/2) and θ is the scattering angle. All measurements were taken at 20 °C. Typical exposure times ranged from two to 5 h, and the reproducibility of the SAXS data indicates that the measurements did not induce any sample degradation. The liquid-crystalline scattering peak was fit with a Gaussian function to determine the position q* and the corresponding repeat spacing d* was calculated by d* ) 2π/q*. Results and Discussion Rheological Properties of the Cross-linked Micelle Solutions. As has been reported previously,4 the core cross-linking has a remarkable effect on the rheological properties of the wormlike micelles, while the static appearance of the original micelles is completely preserved upon reaction. To begin with, we first note the dramatic modification of the marginal elasticity of the 1% pristine solution with the cross-linking, as displayed in Figure 4; the storage modulus (G′) increased by more than 2 orders of magnitude, and became virtually frequency independent after reaction. This suggests an elastically interacting physical network of the cross-linked wormlike micelles. The rheological properties of the cross-linked solution strongly depends on concentration. Figure 4 presents the frequencydependent linear responses with varying concentrations. The
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Figure 5. Representative log-log plots of the linear storage (G′, b) and loss (G′′, O) moduli vs weight fraction of the cross-linked wormlike micelles (c) at a median measurement frequency of ω ) 1.26 rad/s, extracted from the results shown in Figure 4. The straight lines are the best fits to the experimental data and have slopes of 4.2 and 2.6 for G′ and G′′, respectively.
Figure 4. Frequency sweeps for the cross-linked wormlike micelle solutions, taken at 22 °C at varying concentrations (open symbols). Data for the 1.00 wt % solution of the pristine wormlike micelles of OB3 are also displayed as filled circles. The effects of dilution of the cross-linked micelles (originally reacted at 0.96 wt %) are illustrated by the changes in the frequency (ω) dependences of storage and loss moduli (G′ and G′′, respectively) in the linear regime. The strain amplitudes of the oscillatory shear were γ ) 0.10 (0.28 wt %), 0.03 (0.37 wt % and 0.48 wt %), 0.01 (0.65 wt % and 0.96 wt %) for the cross-linked solutions, and 0.10 for the 1.00 wt % non-cross-linked solution.
gellike linear responses obtained by chemical fixation of the sample at a concentration of 1% faded away with progressive dilution, and at the lowest concentration probed, G′ became slightly greater than G′′. Figure 5 represents the variations of G′ and G′′ as functions of concentration (c) at 1.26 rad/s. By fitting the data with a power-law relation we found G′ ∼ c4.2 and G′′ ∼ c2.6. In fact, there exists some frequency dependence of the exponents; they are decreasing functions of frequency. Over the measurement frequencies, the above introduced procedures yield the values of 4.2 ( 1.0 for G′ and 2.9 ( 1.0 for G′′. Overall, the results indicate a significant departure from any of the theoretical predictions for flexible (G′o ∼ c2.3)20 or semiflexible chains (G′o ∼ c1.4)21 where G′o is the plateau modulus. We suspect that this concentration dependence is comparable to prior results obtained from rigid rod dispersions such as boehmite.22 The cross-linked wormlike micelles exhibit flow behaviors that are fundamentally different from those of the non-crosslinked homologues. As illustrated by the rheological data in Figure 6, the 1% cross-linked solution displayed apparent shear thinning behavior under steady shear, qualitatively resembling the unreacted system. At the bottom Figure 6 also presents the
Figure 6. Comparison of steady shear viscosities (η) for the 1% unreacted and cross-linked wormlike micelle solutions as functions of shear rates (γ˘ ) at 22 °C. Also shown at the bottom are the contour plots of equal intensity in SANS measured with the incident radiation directed parallel to the direction of shear gradient through the center of the Couette cell. The arrows in the η vs γ˘ plots indicate the shear rates at which the scattering data were taken.
two-dimensional through-view scattering patterns obtained with the shear-SANS geometry described in Figure 3. Unlike the pristine wormlike micelles that normally align under shear along the flow direction, the cross-linked micelles retain the orientational isotropy even under higher shear (e.g., ≈ 450 s-1). This implies disparate physical origins for the outwardly similar phenomena of shear thinning between the two homologous systems, and the apparent shear thinning exhibited by the crosslinked solution is therefore better explained by some sample
8306 J. Phys. Chem. B, Vol. 105, No. 35, 2001
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Figure 7. Schematic illustration of the geometry of a cylindrical micelle core of cross-sectional radius Rc bent in a loop of radius Rl.
fracture or wall slip presumably through the creation of a low viscosity shear band within the fluid or near the cylinder surfaces.23 We have not made explicit attempts to determine the true viscosities for the 1% cross-linked solution, and this may well be impossible because the characteristic relaxation time in the cross-linked system is evidently very long and the response will be so highly elastic as to invite artifacts (e.g., instabilities or slip) in almost any scheme to measure steady shear viscosity. Nonetheless, the SANS results clearly indicate severe mechanical strengthening of the micelles associated with the core cross-linking along with the one-100-fold rise in apparent viscosity. Prior experiments with OB3 indicated that the cross-linking leads to a complete fixation of the micelle structure and that all the mass of the core is in the single gel;5 that is, the average molar mass of the resulting molecules is estimated to be ∼2.2 × 109 g/mol on the basis of the measured core radius of 76 Å (via cryogenic transmission electron microscopy or cryo-TEM)24 and micelle contour length of ∼8.8 µm (by means of smallangle neutron scattering or SANS).29 Complete conversion of the primary chains is likely connected with high degree of crosslinking of the core domain, and such effect is in fact implicit in the rheological data. In a randomly percolated network of the cross-linked wormlike micelles, shear stress is likely accommodated by a bending and stretching of the strands.21,25 To better account for the observed macroscopic behavior, we consider the effect of cross-linking on the bending stiffness of the cylindrical structure. When we consider a cross-linked cylinder of cross-sectional radius Rc which has no spontaneous axial curvature and has been deformed into a loop of radius Rl (Figure 7), there will be elastic forces that result in some free energy stored in the curved section (∆Fcore). Assuming that the elastic deformation of the rubbery core is solely responsible for the bending rigidity of the cross-linked micelles, the bending modulus of the micelle (Kb) can be expressed by Kb ) ∆FcoreRl/π for small deformations (that is, for large Rl).26 Here, we note that the free energy change associated with the coronal chain deformation due to the looping is ignored for the sake of simplicity, and also that the interfacial contribution is zero because there is no net change in overall interfacial area with bending. ∆Fcore can be expressed in terms of the energy stored per unit volume of the rubbery core after looping E(R)
∆Fcore )
∫VE(R)dV
(1)
where V is the volume, and R is the displacement gradient. A simple geometric treatment of the integral leads to
∫-RR xRc2 - x2E(R(x))dx
∆Fcore ) 4πRl
c
c
(2)
Figure 8. Experimental phase diagrams for the OB3 wormlike micelle/ PEO/water systems at 18 °C associated with the two different molecular weights of homopolymer PEO (i.e., M h n ) 8000 g/mol for PEO8K, and M h n ) 14 000 g/mol for PEO14K). The open and filled circles represent the minimum amounts of PEO required to induce phase separation determined by optical turbidity measurements to within the accuracies indicated as error bars, and the dotted and solid curves delimit the experimental range covered by the data. The two basic phases introduced as fluid and solid in these figures are defined on the basis of state of long range order of the wormlike micelles; that is, when the concentrations of OB3 and PEO are low enough, the solution is mesoscopically disordered (i.e., fluidlike), whereas the micelle structures, when coacervated, can develop crystalline order to form the solid phase. The solid-phase boundary anticipated at high OB3 concentrations has not been identified explicitly, but the micelle organization behavior in the solid phase separated from dilute micellar solutions will be illustrated in Figures 9 and 10.
where R(x) ) (Rl + x)/Rl. Although we have not determined the exact cross-linking density for the chemically fixed wormlike micelles, micropipette mechanical characterizations of PEOPB diblock vesicles cross-linked by the equivalent procedures indicate that the number of monomers between interchain crosslinks is quite small, perhaps as few as 3.27 On the basis of the known expression for E(R) for uniaxial deformation,28 we calculate a bending stiffness of Kb g ∼95µm‚kBT for the crosslinked micelles using the above equation. Previously, we have reported that the non-cross-linked wormlike micelles of OB3 are characterized by an average persistence length lp of 0.57 µm and an average overall length of 8.8 µm.29 Noting the relationship lp ≈ Kb/kBT,26,30 at the corresponding cross-link densities, we find that the chemically fixed wormlike micelles are stiffer by a factor of at least 170 than their precursors, and are well represented as rigid rods in the sense that the persistence length is even greater than the micelle length. On this ground, it is reasonable to expect that their mechanical properties will be dictated by the rubber elasticity of the core, and in fact, we believe that such micelle stiffening after cross-linking was clearly reflected by the linear and nonlinear rheological properties. Measurements performed on the cross-linked solutions showed a concentration dependence of G′ ∼ c4.2 in the linear regime (Figure 5) and a mechanical yielding under steady flow (Figure 6), consistent with prior results obtained from rigid rod dispersions such as boehmite.22 In connection with this argument, we here note that the considerable curvature of the crosslinked micelles often captured by cryo-TEM (for example, see Figure 2B in Reference 4) does not necessarily signify corresponding flexibility of the structure but has been intrinsically locked in presumably in the act of thermal undulation. This view
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Figure 9. (A) A schematic representation of the macroscopic behavior of a phase separated OB3 wormlike micelle/PEO14K/water mixture. The aqueous solution containing 1.0 wt % micelle and 1.5 wt % PEO14K becomes dehomogenized into two optically distinct layers (i.e., upper cloudy and lower clear) by gravitational creaming of the close-packed micellar domains; (B) A two-dimensional SAXS pattern taken from the cloudy supernatant. Regions of high intensity are shown in white. The three isotropic concentric rings with peak spacing ratios of 1:x3:x4 indicate equal orientation of the crystalline domains and the hexagonal arrangement of the cylindrical micelles therein; (C) GPC chromatograms for OB3 and PEO14K prepared in chloroform through extraction from the upper cloudy and lower clear solutions. The OB3 molecules accumulate in the upper solution, indicating that the hexagonal structure is derived from the wormlike micelles of OB3 that has escaped the PEO solution.
is also reflected in the schematic illustration of the cross-linked system presented later in this paper (Figure 15). Effects of Poly(ethylene oxide) Addition Phase Separation in Wormlike Micelle/PEO Mixtures. Colloidal mixtures of wormlike micelles of a PEO-PB diblock copolymer (OB3) and homopolymer PEO (PEO14K or PEO8K) were studied. Our investigation focused on low concentrations of OB3 (
