Phase Behavior, Microstructure, and Dynamics in a Nonionic

However, there is a possible short cut in this case. Upon bringing a sample into the two phase region (Lα + W), a microscopic phase separation almost...
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Langmuir 1997, 13, 4204-4218

Phase Behavior, Microstructure, and Dynamics in a Nonionic Microemulsion on Addition of Hydrophobically End-Capped Poly(ethylene oxide) H. Bagger-Jo¨rgensen,*,†,| L. Coppola,†,‡ K. Thuresson,† U. Olsson,† and K. Mortensen§ Physical Chemistry 1, Chemical Center, University of Lund, P.O. Box 124 S-221 00 Lund, Sweden, and Physics Department, Risø National Laboratory DK-4000 Roskilde, Denmark Received December 2, 1996. In Final Form: May 16, 1997X We report on the effects on the phase behavior, microstructure, and rheology in the water-rich part of the ternary nonionic surfactant system comprising pentaethylene glycol dodecyl ether (C12E5)-waterdecane, on addition of poly(ethylene oxide) (PEO) and hydrophobically end-capped PEO (HM-PEO). The two polymers destabilize both the micellar and the lamellar phases. With PEO, a segregative phase separation is observed, while with HM-PEO, an associative phase separation is seen. The micellar phase containing HM-PEO was investigated by NMR relaxation and self-diffusion measurements and smallangle neutron scattering as well as low shear viscosity and oscillatory frequency sweep measurements. It was found that the polymer affected the intermicellar interaction, leading to an increased ordering of the micelles, while leaving the micellar size unchanged. Addition of HM-PEO (e2 wt %) led to a drastic decrease of the micellar self-diffusion coefficient and additionally to an increase of the low shear viscosity by several orders of magnitude. The storage and loss moduli were successfully fitted to a single Maxwell element. Analysis of the fitted parameters and comparison with percolation theory yielded the fraction of polymers that interconnected the micelles (thus forming bridges) as well as the fraction of polymers that did not contribute to the connectivity of the network (resulting in loops).

Introduction The basic properties of mixtures between polymers and surfactant-water-oil systems have received much attention recently.1-12 Together with more fundamental interest, these systems also are of great practical importance, for example, in rheology control and colloidal stability. The behavior of these mixed systems depends strongly on the interaction between the polymer and the surfactant film. A first rationalization is to distinguish polymers that adsorb onto the surfactant film from polymers that do not adsorb.7,8 Uncharged homopolymers are normally nonadsorbing and, when mixed with a solution of, for example, surfactant micelles, may induce a phase separation with a polymer-rich phase and a surfactant-rich phase in equilibrium,9 so-called segregative phase separation,4 a behavior that has been described by a depletion-flocculation mechanism.13 A nonadsorb†

University of Lund. Present address: Dipartimento di Chimica, Universita´ della Calabria, 87100 Arcavacata di Rende (CS), Italy. § Risø National Laboratory. | Present address: Astra Draco AB, P.O. Box 34, S-221 00 Lund, Sweden. X Abstract published in Advance ACS Abstracts, July 15, 1997. ‡

(1) Brooks, J. T.; Cates, M. E. J. Chem. Phys. 1993, 99, 5467. (2) Iliopoulos, I.; Olsson, U. J. Phys. Chem. 1994, 98, 1500. (3) Singh, M.; Ober, R.; Kleman, M. J. Phys. Chem. 1993, 97, 11108. (4) Piculell, L.; Lindman, B. Adv. Colloid Interface Sci. 1992, 41, 149. (5) Magny, B.; Iliopoulos, I.; Audebert, R.; Piculell, L.; Lindman, B. Prog. Colloid Polym. Sci. 1992, 89, 118. (6) Kabalnov, A.; Olsson, U.; Wennerstro¨m, H. Langmuir 1994, 10, 2159. (7) Kabalnov, A.; Olsson, U.; Thuresson, K.; Wennerstro¨m, H. Langmuir 1994, 10, 4509. (8) Bagger-Jo¨rgensen, H.; Olsson, U.; Iliopoulos, I. Langmuir 1995, 11, 1934. (9) Clegg, S. M.; Williams, P. A.; Warren, P.; Robb, I. D. Langmuir 1994, 10, 3390. (10) Eicke, H.-F.; Quellet, C.; Xu, G. Surf. Sci. Technol. 1988, 4, 111. (11) Holmberg, A.; Piculell, L.; Wessle´n, B. J. Phys. Chem. 1996, 100, 462. (12) Thalberg, K.; Lindman, B. In Surfactants in Solution; Mittal K. L., Shah, D. O., Eds.; Plenum Press: New York, 1991; Vol. 11.

S0743-7463(96)02054-9 CCC: $14.00

ing, hydrophilic homopolymer may be modified by chemical grafting of strongly hydrophobic side chains and thereby be transformed to an adsorbing polymer.14 These so-called hydrophobically modified (HM) polymers normally show completely different solution properties compared to the homopolymer, even for a very low degree of hydrophobic modification. Addition of HM polymer to a surfactant mixture often has a profound influence on phase equilibria, molecular dynamics, and rheology.15 Contrary to the nonadsorbing case, the attraction between the surfactant film and the hydrophobic side chains in this case leads to associative phase separation,4 where excess water is expelled. Mixtures of end-modified polymers (ABA block copolymers) and micelles have been studied by several groups.10,11,16-23 The present study deals with the effects of an ABA block copolymer on a nonionic oil/water (O/W) microemulsion system. The block copolymer consists of a poly(ethylene oxide) chain, containing ∼250 ethylene oxide units, to which C18 chains have been attached on both ends by ester bonds. As a reference microemulsion system, we have chosen the well-characterized pentaethylene oxide dodecyl (13) Lekkerkerker, H. N. W.; Poon, W. C.-K.; Pusey, P. N.; Stroobants, A.; Warren, P. B. Europhys. Lett. 1992, 20, 559. (14) Wang, T. K.; Iliopoulos, I.; Audebert, R. Polym. Bull. 1988, 20, 577. (15) Nystro¨m, B.; Thuresson, K.; Lindman, B. Langmuir 1995, 11, 1994. (16) Gradzielski, M.; Rauscher, A.; Hoffmann, H. J. Phys IV 1993, 3, 65. (17) Quellet, C.; Eicke, H.-F.; Xu, G.; Hauger, Y. Macromolecules 1990, 23, 3347. (18) Odenwald, M.; Eicke, H.-F.; Friedrich, C. Colloid Polym. Sci. 1996, 274, 1996. (19) Persson, K.; Wang, G.; Olofsson, G. J. Chem. Soc., Faraday Trans. 1994, 90, 3555. (20) Persson, K.; Bales, B. L. J. Chem. Soc., Faraday Trans. 1995, 91, 2863. (21) Odenwald, M.; Eicke, H.-F.; Meier, W. Macromolecules 1995, 28, 5069. (22) Stieber, F.; Eicke, H.-F. Colloid Polym. Sci. 1996, 274, 826. (23) Vollmer, D.; Vollmer, J.; Stu¨hn, B.; Wehrli, E.; Eicke, H.-F. Phys. Rev. E 1995, 52, 5146.

© 1997 American Chemical Society

PEO Effects in a Nonionic Microemulsion

Figure 1. Partial phase diagram of the C12E5-D2O-decane system (redrawn from ref 24) for a constant weight ratio, 52/48, of C12E5-decane. The phase diagram is shown as temperature versus the total weight fraction of surfactant and oil, W(S+O). L1 denotes the microemulsion phase and LR the lamellar liquid crystalline phase. L1 + O is a two-phase area where the microemulsion is in equilibrium with excess oil, L1 + W denotes a two-phase equilibrium between one concentrated and one dilute phase (essentially pure water), and LR + W denotes the lamellar phase in equilibrium with excess water.

ether (C12E5)-water-decane system at a constant surfactant-to-oil weight ratio of 52/48. In the water-rich part (>60 wt % water), a microemulsion phase is stable. Phase equilibria in both the micellar and the lamellar phases upon addition of polymer are reported and compared. As experimental tools for studying microstructure and intermicellar interaction we have chosen NMR techniques (relaxation and self-diffusion), smallangle scattering, and rheology measurements. NMR relaxation measurements on the (R-deuterated) surfactant were performed since this technique is very sensitive to aggregate growth. NMR self-diffusion measurements are powerful since this technique can directly discriminate between discrete micellar aggregates and a bicontinuous structure, and additionally, the magnitude of the diffusion coefficient can indicate network formation. Small-angle scattering allows us to measure the aggregate dimension and also reports on intermicellar interactions. Finally, we have performed low shear viscosity and oscillatory frequency sweep measurements, which also can give information about network formation. The basic principles of the microemulsion and the polymer are described in the following subsections. The Reference Microemulsion System The reference microemulsion system is composed of the nonionic surfactant C12E5, water, and oil at a constant surfactant-to-oil weight ratio of 52/48. For oil-swollen normal micelles, this corresponds to keeping the total interfacial area to enclosed volume ratio constant. A partial schematic phase diagram (omitting some multiphase regions) of the water-rich part (g80 wt % water) is shown in Figure 1 (data taken from ref 24). The phase diagram is plotted as temperature versus the total weight fraction of surfactant and oil, W(S+O). A microemulsion (24) Olsson, U.; Schurtenberger, P. Langmuir 1993, 9, 3389.

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phase (L1) is stable within the temperature interval of ∼24-30 °C. At lower temperatures, the microemulsion coexists with an essentially pure oil phase (L1 + O). The L1 phase terminates at ∼30 °C, where the microemulsion, in a narrow temperature interval, splits into a concentrated phase (with respect to surfactant and oil) and a dilute phase in equilibrium, denoted L1 + W in the phase diagram. This upper phase boundary corresponds to a lower consolute boundary, with a critical point. This lower consolute boundary is an extension of the “clouding” curve of the binary surfactant water system, and is a general property of oligo(ethylene oxide) surfactants. Slightly above the microemulsion phase, a lamellar liquid crystalline phase (LR) is formed. The microstructure of the microemulsion phase depends on the temperature and the surfactant plus oil concentration. The lower phase boundary is, however, of particular significance. On this boundary, which corresponds to the saturation limit of oil solubilization, the microstructure corresponds to well-defined spherical oil droplets, which here have a hydrocarbon radius of ∼75 Å and low polydispersity (∼16%).25 Increasing the temperature away from this boundary results in a slight growth of the micelles into nonspherical shapes.25-27 This growth is concentration dependent. At lower concentrations (W(S+O) e 0.05) there is essentially no growth at all, while the growth becomes more and more pronounced the higher the concentration. The growth is, however, limited. At W(S+O) ) 0.20, the micelles reach a size at higher temperatures which in volume corresponds to approximately twice that of the spheres. At this concentration, an abrupt change in microstructure, from micelles to a bicontinuous network, occurs ∼2 °C below the upper phase boundary. The polar/apolar interface, separating the pentaethylene oxide from the hydrocarbon chain of the surfactant monolayer, has an essentially invariant area per molecule.28-30 The radius of the spherical micelles, related to that interface, can be calculated from

1 Rhc ) 3 Φ0 + Φs ls/Φs 2

(

)

(1)

where we note that the polar/apolar interface encloses the oil and the hydrocarbon tails of the surfactant, which make up approximately half of the surfactant volume, vs. Here, Φo and Φs are the oil and surfactant volume fractions, respectively, and the radius, Rhc, we refer to as the hydrocarbon radius. ls is the surfactant length, defined as ls ) vs/as, where vs ) 702 Å3 29 is the surfactant volume and as is the area per molecule at the polar/apolar interface. The radius Rhc ) 75 Å of the spherical micelles has also been determined by small-angle neutron scattering (SANS).25 From Rhc, the number of surfactant (ns ≈ 1500) and oil (no ≈ 4000) molecules per spherical micelle can be calculated, and hence, the number of micelles per unit volume is accurately known. The “molecular weight” of the spherical micelles is ∼1.2 × 106. Polymer Functionality and Concentration Parameter The block copolymer consists of a water-soluble poly(ethylene oxide) PEO chain with strongly hydrophobic (25) Bagger-Jo¨rgensen, H.; Olsson, U.; Mortensen, K. Langmuir 1997, 13, 1413. (26) Leaver, M. S.; Olsson, U.; Wennerstro¨m, H.; Strey, R. J. Phys. II Fr. 1994, 4, 515. (27) Leaver, M.; Furo´, I.; Olsson, U. Langmuir 1995, 11, 1524. (28) Leaver, M. S.; Olsson, U.; Wennerstro¨m, H.; Strey, R.; Wurz, U. J. Chem. Soc. Faraday Trans. 1994, 91, 4269. (29) Olsson, U.; Wu¨rz, U.; Strey, R. J. Phys. Chem. 1993, 97, 4535. (30) Rajagopalan, V.; Bagger-Jo¨rgensen, H.; Fukuda, K.; Olsson, U.; Jo¨nsson, B. Langmuir 1996, 12, 2939.

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Figure 2. Schematic illustration of what might happen in a microemulsion droplet phase with HM polymer present. The open circles illustrate the droplets. The hydrophobic end groups of the polymer (the black boxes) adsorb onto the droplets. In case a, the polymer forms a bridge between two adjacent droplets, corresponding to a “single bond”. In case b, two polymers form bridges between the same two droplets, resulting in a “double bond”. It may happen that the polymer anchors both end groups in the same droplet as in (c), thus forming a loop. It may also happen that only one or even none of the end groups are anchored, illustrated in (d) and (e), respectively.

stearate end groups. It is expected that the polymer molecules will adsorb onto the surfactant film with their hydrophobic end groups (“stickers”). If added to a micellar phase, the polymer may thus act as a cross-linker between adjacent micelles. The situation can be visualized in terms of “atoms and bond” or “balls and stick” models, where the micelles are the atoms (balls) and the polymer molecules may act as bonds (sticks), linking the micelles together, as schematically illustrated in Figure 2. Depending on the relative “positions” of the two hydrophobic end groups, the polymer can take different configurations. It may form a bridge (a) between two micelles by placing the hydrophobic end groups in different micelles. The bond configuration is characterized by a local coordination number and the relative number of single bonds (a), double bonds (b), triple bonds, etc. There is also a possibility that the polymer end groups are present in the same micelle and that the polymer forms a loop (c). In addition, the polymer can also have a reduced functionality with one (d) or both (e) hydrophobic chains exposed to water. The behavior of the system, for example, the rheology, is expected to depend on the average number of polymer molecules per micelle. As mentioned above, the microemulsion consists of well-defined spherical droplets at lower temperatures, near the emulsification failure boundary. We have therefore in appropriate cases chosen to express the polymer concentration not only in weight fraction but also in terms of the number of polymers per spherical micelle, which we will denote R. This is calculated from

R)

Npol Wpol Mmic ) Nmic Wmic Mpol

(2)

where Npol and Nmic are the number of polymers and micelles, respectively and Wpol and Wmic ) W(S+O) are the weight fractions of polymer and micelles, and finally, Mpol and Mmic are their respective molecular weights. Experimental Section Materials. C12E5 was obtained from Nikko Chemicals Co. Ltd., Tokyo, Japan; decane (>99%) was obtained from Sigma

and D2O (99.8% isotopic purity) from Norsk Hydro. The R-CD2 deuterated surfactant used in NMR relaxation studies was synthesized by Synthelec (Lund, Sweden). Nonmodified poly(ethylene oxide) with a molecular weight of 8000 was obtained from Union Carbide Corp. All these chemicals were used without further purification. The hydrophobically modified polymer used in this study was a poly(ethylene oxide) distearate, C17H35COO(EO)250OCC17H35, with a molecular weight of ∼11 500. It was received as white flakes from Kao Corp., Tokyo, Japan, and before use was purified from nonchemically attached stearate according to the following procedure. The flakes were allowed to swell, or partly dissolve, in acetone for a few hours followed by an addition of hexane. On the hexane addition, the solvent turned less polar and the polymer precipitated as a white powder. This procedure was repeated five times, after which the polymer sample was dried thoroughly. The polymer functionality, i.e., the number of end groups per polymer, was checked with 1H NMR. The ratio of the peak areas of the two different methylene groups, in the octadecyl chain and in the ethylene oxide chain, was found to be very close to 17/250, indicating a functionality very close to 2. It is difficult to estimate the error margin in this experiment, but a deviation of more than 10% seems unlikely. Thus, the majority of the polymer molecules have two end groups, whereas a small fraction of polymers with only one end group cannot be ruled out. The dry powder was stored in a desiccator prior to use. All experiments were performed on freshly prepared samples to prevent any interference from breakdown due to hydrolysis of the polymer molecules. Methods. (a) Phase Diagram Determinations. Samples for the phase diagram studies were prepared by weighing the appropriate amounts of C12E5, decane, water, and polymer into glass ampules, which, after addition of small magnet stirrers, were immediately sealed. The samples were mixed by magnetic stirring and, if necessary, by a vortex mixer for several days to ensure complete homogeneity. The ampules were studied in a thermostated water bath. Phase boundary temperatures were studied by visual inspection of transmitted light, scattered light, and through cross polarizers. The lower phase boundary, L1 + O T L1, needs special experimental caution since the kinetics involved are extremely slow (of the order of days) in both directions. The other phase equilibria are, however, rather fast. The compositions of the phases in two phase regions were determined by 1H NMR. (b) Rheological Measurements. Most rheological measurements were performed both in the flow and in the oscillatory mode on a Carrimed CSL100 rheometer equipped with automatic gap setting. Samples with low viscosity (low polymer content) were only run in the flow mode, since the resolution of the instrument is limited, while the temperature scans, performed on samples with the highest polymer content, were only run in the oscillatory mode. The temperatures in all runs were kept within (0.1 °C of that desired. All the viscosity data are presented at the low shear plateau where the samples display a Newtonian behavior. At the plateau, the runs in the oscillatory and in the flow modes gave equal viscosity values (see Figure 17). In contrast to the NMR and the SANS measurements, which were performed on samples with D2O as solvent, the samples used in the rheological measurements were prepared with protonated water of Millipore quality. Replacing D2O with H2O shifts the phase boundaries ∼2 °C higher,28 but the viscosity is not affected. To prevent phase separation, the temperature scans were performed in two parts, both with starting temperatures in the middle of the L1 phase. In one run the temperature was decreased, and in the other run the temperature was increased. (c) Self-Diffusion Measurements. Fourier transform NMR self-diffusion experiments were performed on a Nicolet instrument with a proton resonance frequency of 360 MHz in a 8.33 T magnetic field. The field homogeneity was maintained by an internal deuterium field frequency lock. Due to the short transverse relaxation times of the microemulsion components, all echo-decay curves were recorded using the stimulated spinecho sequence: (π/2)-τ1-(π/2)-τ2-(π/2)-τ1-echo, in the presence of a pair of short magnetic gradient pulses applied within the τ1 time windows.31 The diffusion probe delivered a field gradient (31) Tanner, J.-E. J. Chem. Phys. 1970, 48, 4938.

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adjusted to 0.8 T/m, calibrated against the value of the surfactant diffusion coefficient in a 10% C12E8-water mixture in the temperature range 25-45 °C, as reported by Nilsson et al.32 The experimental echo attenuation due to molecular diffusion was measured as a function of the width of the field gradient pulse, δ, which was varied in the range from 0.2 to 20 ms. The diffusion time of the experiments, ∆, i.e., the separation between the gradient pulses, was kept constant to 140 ms. Under these conditions, the lowest detectable diffusion coefficient, D, is of the order of 10-14 m2/s. The selection of the time between the first two radio frequency pulses, τ1, deserves to be mentioned particularly. In this pulse sequence, τ1 is the time when the magnetization is in the plane perpendicular to the mean magnetic field and is controlled by the transverse relaxation times. In our experiments, it was kept constant at 30 ms. The polymer transverse relaxation time was much shorter than 30 ms, and hence the polymer did not contribute to the echo nuclear signal. After Fourier transformation, an independent determination of the surfactant and the oil self-diffusion coefficients was achieved by measuring the signal amplitude from the methylene groups in the ethylene oxide and in the hydrocarbon chain, respectively. As, within the experimental accuracy, we always observed a monoexponential echo attenuation for both components, the selfdiffusion coefficients were simply obtained by fitting the experimental echo intensities with Tanner’s equation31

A(τ) ) B exp[-(γδg)2D(∆ - δ/3)]

(3)

where B accounts for spin concentration and relaxation effects, γ is the magnetogyric ratio of protons, g is the field gradient strength, δ and ∆ are the two experimental time constants previously described, and D is the diffusion coefficient. The experimental error in the diffusion coefficient was ∼( 4% and the temperature, which was controlled by an air flow regulator, was stable to within (0.2 °C. (d) Relaxation Measurements. The measurement of the R-deuterated surfactant line width at half-height was performed on the same NMR instrument as described above, but now working at the deuterium resonance frequency of 55.53 MHz. The spectra were each obtained from 200 averaged scans. The line widths were determined using a Lorentzian fit with a minor correction for magnetic field inhomogeneity. In this experiment, as in the rheology measurements, the solvent was H2O and not D2O. The only consequence of this is a 2 °C temperature shift (upwards) in all phase boundaries.28 (e) Small-Angle X-ray Scattering (SAXS). SAXS experiments were performed on a Kratky compact small-angle system equipped with a position-sensitive detector with 1024 channels. The sample-to-detector distance is 277 mm and the wavelength 1.54 Å, allowing measurement down to a scattering vector q ≈ 0.01 Å-1. The slit smeared spectra were desmeared by using the direct method of beam height correction.33 (f) Small-Angle Neutron Scattering. SANS experiments were performed on the small-angle instrument at Risø National Laboratory. Three different detector distances, D, and two different wavelengths, λ, were used. At λ ) 12 Å and D ) 6 m the q-range was 0.002 < q < 0.02 Å-1, for λ ) 5.6 Å and D ) 3 m 0.01 < q < 0.1 Å-1 and for λ ) 5.6 Å, D ) 1 m 0.02 < q < 0.29 Å-1. The wavelength spread, ∆λ/λ, was in all cases 9% (full width at half-maximum). The intensity was recorded on a 128 × 128 pixel 2-D detector. All samples gave azimuthally isotropic scattering patterns, and the data were radially averaged. Transmission measurements were done for all samples, setups, and temperatures. The incoherent scattering of H2O was used for absolute calibration and to take variation in detector response into account. The three absolute scaled parts showed good agreement in overlapping regions (within 10%) and were spliced together with a least-squares fit. At the highest q-values, the incoherent scattering of the sample dominates, giving rise to a q-independent value. This constant term was subtracted.

Phase Behavior The phase behavior of the microemulsion system on addition of unmodified PEO and hydrophobically modified (32) Nilsson, P.-G.; Wennerstro¨m, H.; Lindman, B. J. Phys. Chem. 1983, 87, 1377. (33) Singh, M. A.; Ghosh, S. S., R. F. S., Jr. J. Appl. Crystallogr. 1993, 26, 787.

Figure 3. Addition of PEO to the reference system increases the two-phase area L1 + W. Essentially all polymer is in the water phase. (a) The weight ratio W(PEO)/W(S+O) ) 1/10 is kept constant while the total concentration is varied. (b) The PEO concentration is varied at constant W(S+O) ) 0.20.

PEO (HM-PEO) was studied. The two polymers were chosen to have approximately the same number of monomers (∼180 for PEO and ∼250 for HM-PEO), making a comparison between the two additives meaningful. The effect of PEO on the phase behavior is shown in Figure 3. In Figure 3a, the weight ratio W(PEO)/W(S+O) ) 1/10 is constant, while in Figure 3b we have fixed W(S+O) ) 0.20 and varied only the polymer concentration. Comparing Figure 3a with the reference system (Figure 1), we note a few interesting differences. The LR phase cannot solubilize the PEO but separates into two phases, one PEO-rich, surfactant-poor phase (denoted W) and one surfactant-rich, PEO-poor LR phase, i.e., a segregative phase separation. This equilibrium will be further discussed in the next section. The stability of the L1 phase is also changed on addition of PEO, since both the L1f L1 + W and the L1 + O f L1 equilibrium now occurs at lower temperatures. The phase changes are due to an osmotic effect of the polymer, which effectively decreases

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Figure 4. Addition of HM-PEO to the reference system. (a) The weight ratio W(HM-PEO)/W(S+O) ) 1/100 is kept constant while the total concentration is varied, corresponding to one polymer per micelle; i.e., R ) 1. (b) same as in (a) except that the weight ratio W(HM-PEO)/W(S+O) ) 1/20 or R ) 5. (c) Same as in (a) except that the weight ratio W(HM-PEO)/W(S+O) ) 1/10 or R ) 10. (d) The HM-PEO concentration is varied at constant W(S+O) ) 0.20.

the spontaneous curvature of the surfactant film.34 In the reference system, L1 + W denotes a liquid-liquid equilibrium between one very dilute phase (essentially pure water) and one phase enriched in surfactant. This biphasic area is enlarged upon addition of PEO, since the polymer preferentially dissolves in the aqueous phase, also in this case leading to a segregative phase separation. In Figure 3b, where W(S+O) was fixed and only the PEO concentration was varied, we see the effect of PEO upon the L1 f L1 + W phase boundary more clearly. This is in line with recent studies on polymer-surfactant mixtures, which have shown that PEO-CnEm are segregating solutions.35,36 We now focus on the hydrophobically modified polymer (HM-PEO) to see what impact this polymer has on the (34) Kabalnov, A.; Olsson, U.; Wennerstro¨m, H. J. Phys. Chem. 1995, 99, 6220. (35) Wormuth, K. R. Langmuir 1991, 7, 1622. (36) Piculell, L.; Bergfeldt, K.; Gerdes, S. J. Phys. Chem. 1996, 100, 3675.

phase behavior of the microemulsion system. In Figure 4a-c we have constant weight ratios W(HM-PEO)/W(S+O) ) 1/100, 1/20, and 1/10 (corresponding to R ) 1, 5, and 10, respectively), while in Figure 4d we have fixed W(S+O) ) 0.20 and varied only the HM-PEO concentration. The LR phase is, in all investigated cases, unstable on addition of HM-PEO and separates into two phases. In this case, contrary to PEO addition, one phase is almost pure water, while the other is concentrated in surfactant, oil, and polymer, i.e., an associative phase separation. This will be further discussed in the next section. The L1 phase is also substantially reduced, showing a phase separation (L1 + W) at low W(S+O). The extent of the two-phase area (L1 + W) is strongly dependent on the amount of HM-PEO added. For the lowest polymer content (Figure 4a), the biphasic area is restricted to higher temperatures and the L1 phase has an infinite water swelling, while for higher polymer contents (Figure 4b,c) the L1 phase has a limited water swelling, expelling excess water below

PEO Effects in a Nonionic Microemulsion

approximately W(S+O) ) 0.04 and W(S+O) ) 0.07, respectively. To briefly summarize the phase behavior, we may state that PEO induces a segregative phase separation in the system, while addition of HM-PEO induces an associative phase separation. With segregative phase separation we mean that the two components, the polymers and the surfactant aggregates, go into different phases upon phase separation. This is the normal situation upon mixing PEO with nonionic surfactants of the CnEm type.35 The phenomenon is mainly an effect of excluded volume and may also be described by the depletion flocculation model.13 An associative phase separation means that all macromolecules enrich one phase, expelling excess water as a second phase. This event must be driven by an effective attraction between the macromolecules.4 In our case, this attractive interaction arises from polymer bridging (see Figure 2). The Lr Phase Studied by SAXS The LR phase upon addition of PEO and HM-PEO was investigated by SAXS. As already stated, both polymers induce phase separation in the LR phase. The two phases are unfortunately very difficult to separate macroscopically. For example, centrifugation for several days was not sufficient to obtain complete separation of the phases. This complicates the experimental work. However, there is a possible short cut in this case. Upon bringing a sample into the two phase region (LR + W), a microscopic phase separation almost immediately takes place, resulting in a homogeneously turbid solution. This emulsion consists of microdomains of each phase. Since the microdomains are much larger than macromolecular dimensions, the X-ray scattering pattern will be a superposition of the scattering curves from each of the two phases. In our experiments the samples were loaded into quartz capillaries at ∼25 °C, where all samples were monophasic. The capillaries where then placed in the instrument and heated to the desired temperature, in this case 36 °C, where measurements were performed. Complete microscopic phase separation took place in a few minutes, and after this time, the scattering pattern and intensity was independent of time. The contrast difference between water and PEO (as well as for HM-PEO) is very low due to a similar electron density, and hence the polymer did not contribute significantly to the scattering curve. Hence, the only contribution to the scattering is from the surfactant and oil aggregates. The bilayer repeat distance in the LR phase in the samples containing W(S+O) ) 0.20 and a varying amount of PEO was measured. The result is shown in Figure 5. Addition of PEO monotonically decreases the interbilayer distance, d, and at the highest PEO concentrations produces a LR phase containing W(S+O) ) ∼0.55. The equilibrium may be seen as an interplay between the osmotic pressure of PEO in the water phase and the pressure due to the undulation force37 in the LR phase. It is interesting to compare the size of the polymer coil and the water layer thickness in the LR phase. The radius of gyration of the PEO molecule is ∼33 Å,38,39 corresponding to a mean end-end distance of 80 Å. The bilayer (hydrocarbon plus ethylene oxide layer) thickness, dbil, is ∼80 Å. The water layer thickness, dw, is given by dw ) d - dbil, where d is the repeat distance in the phase. Initially, i.e., without added polymer, dw ≈ 280 Å. As (37) Helfrich, W. Z. Naturforsch. 1978, 33A, 305. (38) Gregory, P.; Huglin, M. B. Makromol. Chem. 1986, 187, 1745. (39) Ke´kicheff, P.; Cabane, B.; Rawiso, M. J. Colloid Interface Sci. 1984, 102, 51.

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Figure 5. Addition of PEO to the LR phase. The repeat distance in the two-phase region, LR + W, was measured at 36 °C. The figure shows the bilayer repeat distance, d, at varying PEO concentrations at constant W(S+O) ) 0.20.

seen in Figure 5, there is first a strong decrease in d for small additions of polymer, followed by a weaker decrease as the polymer concentration is increased further. Extrapolating the d values from the phase-separated lamellar phase to zero polymer concentration, we obtain dw0 ≈ 160 Å, corresponding to dw0 ≈ 80 Å. This value is close to 2Rg, which is what we expect since, in a first approximation, we may consider a depletion zone outside the bilayer of thickness Rg, from which the polymer is excluded. The observation that the lamellar phase deswells even at very low bilayer concentrations, where the water layer thickness is much larger than the PEO coil, has been theoretically explained.1 One might note that, in other systems, where the surfactant was charged, large amounts of PEO with high molecular weight was shown to be soluble in the lamellar phase.39,40 The main difference between these studies and ours is the different type of surfactant. Nonionic LR phases are stabilized by the relatively weak undulation forces,37 while the LR phases formed by ionic surfactants are stabilized by the far stronger electrostatic interaction. Hence, the two opposing observations are not in contradiction.1 If, instead of PEO, we add HM-PEO to the lamellar phase with fixed W(S+O) ) 0.20, we measure the repeat distances shown in Figure 6a. As in the case of unmodified PEO, but for a different reason, there is an initial rapid collapse of the lamellar phase to a water layer thickness corresponding approximately to the size of the polymer coil. However, contrary to the PEO case, a minimum in d is reached after the initial strong decrease, and further HM-PEO addition instead gives a larger repeat distance. This is more clearly seen in the inset, which shows the same data but drawn on a different scale. This behavior can be understood as follows. In addition to the attractive “bridging” force at large separations, there is a shortrange osmotic repulsion which increases with increasing polymer concentration. The separation where the two forces are balanced shifts slightly to higher values when the polymer concentration increases. Keeping the weight ratio W(HM-PEO)/W(S+O) ) 1/10 constant (R ) 10) while varying the total concentration, we get the curve shown in Figure 6b. Within the experimental errors, we measure the same repeat distance at all concentrations. This shows that we are varying the (40) Ficheux, M.-F.; Bellocq, A.-M.; Nallet, F. J. Phys. II Fr. 1995, 5, 823.

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lines the experimental line width, ∆υ1/2, is related to R2 by R2 ) π∆υ1/2. For large aggregates like the ones present here, the dynamics associated with the aggregates are slow compared to the inverse resonance frequency of the deuteron and also the transverse relaxation rate is much faster than the longitudinal one. Under these conditions, R2 is, to a good approximation, given by42,43

R2 = (9π2/40)|χS|2 js(0)

(4)

where χ is the quadrupolar coupling constant and S is the so-called order parameter of the surfactant. The numerical value of |χS| is experimentally found to be essentially independent of the aggregate geometry44 and may in this case be regarded as a constant. The last term in eq 4, js(0), is the spectral density at zero frequency that describes the slow motions of the aggregate. For spherical particles, js(0) ) 2τs, where τs is the correlation time in an exponential time autocorrelation function of the slow motion. τs carries contributions from both the aggregate tumbling (τt) and the surfactant lateral diffusion within the surfactant film (τd), given by

τt ) 4πηR3/3kBT

(5a)

τd ) R2/6Dlat

(5b)

where R is the micellar radius, η is the solvent viscosity, kBT is the thermal energy, and Dlat is the surfactant lateral diffusion coefficient. These two processes may be considered as statistically independent, leading to

τs-1 ) τt-1 + τd-1

Figure 6. Addition of HM-PEO to the LR phase. (a) The figure shows the bilayer repeat distance, d, as function of the HMPEO concentration at fixed W(S+O) ) 0.20. The inset shows the same data drawn in another scale. (b) In this case, the weight ratio W(HM-PEO)/W(S+O) ) 1/10, corresponding to R ) 10, was fixed and the total concentration was varied. Within experimental uncertainty, the measured repeat distance was constant in this case.

concentration along a tie line, and since one of the phases is essentially pure water, the phase separation is totally associative. It is illuminating to compare the impact of polymer on the L1 and the LR phases. Obviously the lamellar phase is much more sensitive to polymeric additive, in all our investigated cases leading to phase separation, where the nature of the equilibrium is dictated by the polymer. Although the L1 phase shows a reduced stability on polymer addition, the effect is only important for the higher polymer concentrations. The Microemulsion Phase Deuterium Relaxation. In the relaxation experiments, the samples were prepared with a selectively R-deuterated C12E5. The actual experiment is described in detail elsewhere,26 as well as the theoretical background for the NMR line width applications. Here we will limit ourselves to observe and perform an intuitive analysis of the observed data. For a 2H nucleus, the quadrupolar mechanism determines the longitudinal (R1) and the transverse (R2) relaxation rates.41 For Lorentzian NMR (41) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, U.K., 1961.

(6)

In all experiments the longitudinal relaxation rate was found to be slow (compared to the transverse relaxation rate) and almost constant as function of temperature and composition of the microemulsion, validating the use of eq 4. The line widths, ∆υ1/2, as a function of temperature for the W(S+O) ) 0.10 and W(S+O) ) 0.20 samples, with W(HM-PEO) ) 0.010 and W(HM-PEO) ) 0.020, respectively (R ) 10 in both cases), are shown in Figure 7. The experiment was carried out upon cooling through the L1 phase. For comparison, the result from the pure microemulsion system, redrawn from ref 26, is also shown as an inset to Figure 7. Comparing the results from the samples with and without polymer shows a qualitative agreement; at low temperatures (∼ Ds. It is notable that even the highest polymer concentration affects the diffusion in the bicontinuous structure to a very limited degree (a factor of ∼3 compared to the micellar case where the difference is at least 1 order of magnitude larger). Summarizing, the diffusion on HM-PEO addition to the microemulsion system is qualitatively similar to the reference system, although with several magnitudes slower diffusion in the micellar case. It seems that the polymer connects, or anchors, the micelles, resulting in large (or even infinite) micelle/polymer aggregates, yielding very slow molecular translation at, and above, length scales comparable to our experimental space scale (∼1 µm). The results also agree with previous diffusion studies.22,51 Rheology. Rheology experiments were performed only in the microemulsion (L1) phase, and in the following discussion we will use the parameter R (defined in eq 2) to express the polymer concentration, as this gives a better intuitive understanding of the system. It is important to keep in mind that a certain R-value corresponds to the double amount of polymer hydrophobic tails per microemulsion droplet, assuming all hydrophobic tails are bound and no dangling ends exist. This is probably a good assumption since the end caps consist of C18 chains and therefore have a considerable hydrophobicity. As an example, R ) 2 corresponds to an average of four active bonds per microemulsion droplet if loops (i.e., one polymer molecule binds twice to the same droplet) and hyperloops (a number of polymers and microemulsion droplets are involved in a loop without any further connection) can be neglected. The former is, as will be shown, important in the W(S+O) ) 0.10 case but almost negligible for W(S+O) ) 0.20, while the latter, which only is possible at low R-values, still contributes to the viscosity but not to the (51) Struis, R. P. W. J.; Eicke, H.-F. J. Phys. Chem. 1991, 95, 5989.

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Figure 14. Newtonian viscosity, η0, in the W(S+O) ) 0.10 (O) and W(S+O) ) 0.20 (b) systems as a function of HM-PEO concentration at T ) 24 °C. The polymer content is expressed in numbers of polymers per micelle, R.

elasticity. Here it is instructive to define a parameter, β, describing the fraction of polymer chains that result in active bonds,

β ) Reff/R

(11)

i.e., the ratio between the effective and the stoichiometric R-values. Before presenting the results, we will compare some typical lengths in the solution. Approximating the droplet structure with a cubic (BCC) lattice, the average dropletdroplet distance is ∼80 Å for W(S+O) ) 0.20 and ∼130 Å for W(S+O) ) 0.10. The unperturbed end-end distance of a corresponding PEO chain, 〈r〉1/2, is 80 Å. This value is, however, not correct if one end of the polymer is adsorbed, or grafted, onto a surface. For a polymer grafted onto a flat surface, the perpendicular distance is a factor x2 larger than the bulk value52 and hence the polymer is somewhat more extended. Since the droplet-droplet distance and polymer size is of comparable length, it suggests that the interdroplet distance can be spanned by the polymer molecules, at least in the W(S+O) ) 0.20 system. The Newtonian viscosity, η0, measured close to the lower phase boundary (at 24 °C), where the microemulsion droplets are spherical, is presented in Figure 14 as a function of polymer content. Important observations are that the viscosity increases rapidly at low R-values and for R g 4 the slope of the viscosity appears to have the same value both for W(S+O) ) 0.10 and W(S+O) ) 0.20 in a semilogarithmic plot. The viscosity increase is substantial, more than 4 orders of magnitude for the highest polymer concentration in both systems. Oscillatory frequency sweep measurements were performed to get further information. Typical results are shown in Figure 15, where we have plotted the storage (G′) and the loss (G′′) modulus as a function of frequency, f, for constant W(S+O) ) 0.20 and different polymer concentrations, R. For each R-value, the measured frequency range data are well described by a single Maxwell element (a spring and a dash dot in a series). G′ and G′′ are in this model given by (52) Eisenriegler, E.; Kremer, K.; Binder, K. J. Phys. Chem. 1982, 77, 6296.

Figure 15. Storage modulus, G′ (×), and loss modulus, G′′, (+), as a function of frequency at W(S+O) ) 0.20 and various R-values. G′ and G′′ have been vertically shifted according to the table. The full lines represent best fits to Maxwell models.

G′ (ω) ) G∞

τ2ω2 1 + τ2ω2

(12)

G′′ (ω) ) G∞

τω 1 + τ2ω2

(13)

where G∞ represents the plateau value of G′ at high frequencies, τ is the specific time of the relaxation process and ω ) 2πf is the angular frequency (rad/s). Discrepancy between the model and experimental points, which is notable for G′′ at high ω, is expected since here the crosslinks can be regarded as permanent on the experimental time scale, and the rheological response therefore approaches that of rubber (with a phase angle independent of frequency), yielding a higher G′′-value than predicted from the Maxwell model. The discrepancy between the model and the experimental G′′-values at small R- and low ω-values is due to the limited resolution of the instrument. G∞, which is proportional to the number density, n, of active, elastic chains53

G∞ = nkBT

(14)

where kB is the Boltzmann factor, and the characteristic lifetime of a cross-link, τ, dependent on the activation energy for the relaxation process, Em, is

τ ) ∝ exp{Em/kBT}

(15)

were extracted from the fits. The fair description given by one Maxwell element implies that mainly one relaxation process is responsible for the viscoelastic properties. In this context, it is interesting to note that all solutions in this investigation are below the polymer overlap concentration, c*, of an unmodified PEG sample of comparable molecular weight (estimated to be ∼4 wt %).38 The highest polymer concentration is found in the sample W(S+O) ) 0.20 with R ) 10 and corresponds to W(HM-PEO) ) 0.02. The contributions to the viscoelasticity by entanglements of polymer chains is therefore small. The ratio of the Newtonian viscosity for the W(S+O) ) 0.20 and W(S+O) ) 0.10 systems as function of R is shown in Figure 16. From the oscillatory measurements at low frequencies, the Newtonian viscosity can be expressed as the product of G∞ and τ,53-56 (53) Green, M. S.; Tobolsky, A. V. J. Chem. Phys. 1946, 14, 80.

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Figure 16. Ratio of the viscosities in the W(S+O) ) 0.20 and the W(S+O) ) 0.10 microemulsion systems, η0.2/η0.1, both from Newtonian viscosity values obtained from low shear experiments (O) and from oscillatory measurements (b), according to eq 16. The ratio of G∞ in the two microemulsions, G∞,0.2/G∞,0.1, as a function of R is also given in the figure ([).

η0 = G∞τ

Figure 17. Illustration of the Cox-Merz rule in W(S+O) ) 0.20 at 24 °C at different R-values. The filled symbols (b) refer to the viscosity measured in continuous shear while the open symbols (O) refer to the complex viscosity, measured in oscillatory shear experiments.

(16)

and this ratio is also shown in Figure 16. The ratio between G∞ in the two systems is also shown. As seen from the figure, this ratio levels out at ∼6 at high R-values. A factor of 2 is trivial and originates from the difference in concentration, while the remaining factor of 3 suggests that only one-third of the polymer molecules that result in active bonds in the W(S+O) ) 0.20 microemulsion give active bonds in the W(S+O) ) 0.10 microemulsion; i.e., β(W(S+O) ) 0.10)/β(W(S+O) ) 0.20) ) 1/3. The remaining two-thirds bind twice to the same droplet or has one or two dangling ends. (The latter case is expected to have a low statistical weight since it is energetically very unfavorable to expose a C18 chain to water). Incidentally, the empirical Cox-Merz rule,57 which suggests that the complex viscosity, η* ) (G′′2 + G′2)1/2/ω, as a function of ω should coincide with the viscosity, η, as a function of the shear rate, γ˘ , seems to be valid for the present system in the ω-regime where the solutions are not shear thinning; see Figure 17. From eq 14 it follows that G∞ should be insensitive to small variations in temperature (around 25 °C), and only a slight increase can be expected, provided that the topology of the system remains unchanged. In Figure 18, we have plotted G∞ as a function of the temperature for the two microemulsions at R ) 10. The microemulsions are metastable below the lower phase boundary (at ∼24 °C), and therefore, it is possible to measure down to lower temperatures. Above 29 °C, G∞ drops rapidly for the W(S+O) ) 0.20 microemulsion as can be expected because the structure of the microemulsion changes from droplets to a bicontinuous structure. The same pattern is seen for G∞ in the W(S+O) ) 0.10 microemulsion with the difference that at temperatures above 29 °C the solution separates into two phases (see Phase Behavior). The ratio of G∞ extracted from the two microemulsions as a function (54) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics, 1st ed.; Oxford University Press: New York, 1986. (55) Ferry, J. D. Viscoelastic Properties of Polymers; John Wiley & Sons: New York, 1980. (56) Lodge, A. S. Rheol. Acta 1968, 7, 379. (57) Cox, W. P.; Merz, E. H. J. Polym. Sci. 1958, 28, 619.

Figure 18. G∞ for W(S+O) ) 0.20, (b) and for W(S+O) ) 0.10 (O) and the ratio of them, G∞,0.2/G∞,0.1 ([), at constant R ) 10 as a function of temperature.

of temperature is also shown in Figure 18, and the rather constant value (∼6) indicates that the topology of the systems is rather unchanged with temperature (or at least that the two systems change in a similar way). Provided that the topology is unchanged in the investigated temperature interval (cf. SANS), an activation energy for the relaxation process can be extracted from eq 15, and indeed ln(τ) as a function of 1/T can be described by a straight line; Figure 19. The slope gives values of Em ) 26kBT and 84kBT at 25 °C for W(S+O) ) 0.10 and W(S+O) ) 0.20, respectively. The value in the W(S+O) ) 0.10 microemulsion corresponds well to that obtained by Annable et al. in a similar system (28kBT at 25 °C with C16 hydrocarbon chains as end caps)58 and is close to the free energy change for transferring an octadecyl chain (58) Annable, T.; Buscall, R.; Ettelaie, R.; Whittlestone, D. J. Rheol. 1993, 37, 695.

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Langmuir, Vol. 13, No. 16, 1997 4217

Figure 19. Arrhenius’ fits to the characteristic times, τ, at R ) 10 for W(S+O) ) 0.10 (O) and W(S+O) ) 0.20 (b).

from hydrocarbon to water.59 The, ∼3 times, larger activation energy in the W(S+O) ) 0.20 system is at present not fully understood. The activation energies together with the G∞ values can be used to create master plots of the viscoelastic response given by oscillatory measurements. The shift factors are given by60

{ (

aT ) exp -

bT )

)}

Em 1 1 kB T0 T

n(T0)kBT0 n(T)kBT

G∞(T0) )

G∞(T)

(17)

(18)

where aT is the frequency (horizontal) shift factor and bT is the modulus (vertical) shift factor. The result of the shift procedure is shown in Figure 20 for W(S+O) ) 0.20 at R ) 10 where viscoelastic measurements in the temperature range 19-27 °C have been condensed into one curve. Recently a statistical mechanical model was developed by Annable et al. for systems containing surfactants and associating polymers, yielding interesting results concerning the fraction of loops and bridges.58,61 Their approach is somewhat different from ours and considers a rather concentrated polymer solution upon adding surfactant. Our system consists of large droplets at relatively high concentrations, and the polymer content is low. We therefore chose to describe the crossover from a viscous to a viscoelastic liquid with increasing R in terms of a percolating network. From percolation theory we expect62

η0 ∝ (Rc - R)-k

(19)

G∞ ∝ (R - Rc)t

(20)

where Rc is the percolation threshold and the two exponents have the values k ≈ 0.7 and t ≈ 1.7. In principle, (59) Tanford, C. The Hydrophobic Effect; Wiley: New York, 1973. (60) Tanaka, F.; Edwards, S. F. J. Non-Newtonian Fluid Mechanics 1992, 43, 273. (61) Annable, T.; Buscall, R.; Ettelaie, R.; Shepherd, P.; Whittlestone, D. Langmuir 1994, 10, 1060.

Figure 20. Storage, G′ (×), and loss, G′′ (+), modules as a function of frequency, f, for the W(S+O) ) 0.20 microemulsion with R ) 10. Measurements at different temperatures (19, 21, 23, 24, 25, and 27 °C) have been condensed into a master plot at 24 °C by using eqs 17 and 18 with T0 ) 24 °C. The full lines represent the best fits to a Maxwell model.

the viscosity has a meaning only for R < Rc, where it is described by a summation of the contributions to the viscosity by all different cluster sizes. In the same manner, the elasticity has a meaning only for R > Rc, where a network of infinite size is formed. Once a bond is formed it is permanent in the treatment in the theory. This is of course not the case here. However, at high frequencies (i.e., at the plateau value in G′) the time set by the experiment is too short for the network to respond with a relaxation to an applied deformation (a redistribution of the bonds). The network can thus be regarded as permanent at short times. In the W(S+O) ) 0.10 microemulsion, where we can expect a higher percolation threshold (due to loops), Rc and t in eqs 19 and 20 were fitted simultaneously to the viscosity, η0, and elasticity, G∞, keeping k ) 0.7 fixed, because the number of points in the viscosity curve (below Rc) is small. From the fit, shown in Figure 21, we obtain t ) 1.5, a value that is in good agreement with what has been reported for other systems treated with percolation theory and from simulations of random bond percolation on a three-dimensional nearest-neighbor lattice62 (t ≈ 1.7). On a Bethe lattice, the Flory-Stockmayer theory predicts a value of the percolation threshold Rc,FS ) 0.6, and a Monte Carlo simulation of the gel point in a simple cubic lattice gave a value Rc,MC ≈ 0.74, if we assume that the coordination number of each microemulsion droplet is 6 (as in a simple cubic lattice).62 In a real system, loops are present (β < 1) and hence the fitted Rc,exp is expected to be somewhat higher than the value predicted from the Flory-Stockmayer theory, Rc,FS. The value found from the fit, Rc,exp ) 2.04, gives a fraction of active bonds, β(W(S+O) ) 0.10) ) Rc,FS/Rc,exp ≈ 1/3, which shows that ∼2/3 of the polymer molecules are inactive and do not contribute to the connectivity. From comparing the values of G∞ for the two systems, it was shown above that the ratio β(W(S+O) ) 0.10)/β(W(S+O) ) 0.20) ) 1/3. This ratio, together with the fitted value of β(W(S+O) ) 0.10), suggests that β(W(S+O) ) 0.20) is close to 1. We note, (62) Stauffer, D.; Coniglio, A.; Adam, M. Adv. Polym. Sci. 1982, 44, 103.

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also in line with earlier reports.58,61 An interesting observation is that G∞ follows the same scaling exponent despite the network being already “saturated” at R ≈ 3. Further addition can be expected to form double and triple bonds between the microemulsion droplets. As the droplets are large, it is likely that double and triple bonds form without any severe obstruction restrictions due to overlap of polymer coils. It can also be noted that following the given assumptions the W(S+O) ) 0.10 system is saturated at R ≈ 9-10. To end this section we also note that in the case of a slightly lower polymer functionality than the ideal value of 2, the analysis is not affected since polymers containing only one end group will not contribute to the network. Since the above analysis shows that, in the W(S+O) ) 0.20 system, almost all polymers contribute to the network, the functionality is probably very close to 2.

Figure 21. Newtonian viscosity, η0 (O), and G∞ (b) as a function of R for W(S+O) ) 0.10. The lines represent fits to eq 19 below the percolation threshold, Rc, and to eq 20 above Rc.

Figure 22. G∞ (b) as a function of R for the W(S+O) ) 0.20 microemulsion. The line represents a fit to eq 20 above the percolation threshold, Rc.

however, that the uncertainty in this value is relatively high, due to the uncertainty in Rc,exp. In Figure 22, G∞ for the W(S+O) ) 0.20 microemulsion is fitted to eq 20 with Rc,exp set to 2.04/3. The fit gives t ) 1.56 which is in good agreement with both the value found in the 10 wt % microemulsion and with the predicted value. This again is consistent with β(W(S+O) ) 0.20)≈1 and that the major part of the polymer molecules form active chains. An increased fraction of bridges at the expense of loop conformations as the crosslinking density is increased is

Conclusions The effects of a water-soluble adsorbing polymer, HMPEO, on the phase equilibria, structure, and rheology of a ternary surfactant-water-oil system has been investigated. In the lamellar phase, the polymer induces a long-range “bridging” attraction leading to a phase separation with excess water. The water layer thickness of the collapsed polymer containing lamellar phase increases slightly with increasing polymer concentration. The L1 phase also shows a reduced stability on HM-PEO addition, for low droplet concentrations and high polymer content leading to the same associative type phase separation as in the lamellar phase. It is illuminating to compare the surface-surface separation in the two phases where phase separation occurs. With HM-PEO present, the lamellar phase cannot swell to a water layer thickness more than dw ≈ 160 Å and the L1 phase expels excess water at approximately W(S+O) ) ∼0.07, where the droplet-droplet distance (assuming a cubic BCC lattice) is ∼170 Å. Unmodified, nonadsorbing, PEO of similar molecular weight also induces phase separation. In this case, however, the attractive force is due to depletion and the polymer is enriched in the excess water phase. In the O/W microemulsion phase HM-PEO form bridges between droplets leading to an infinite transient network for polymer concentrations above a certain percolation threshold. The polymer concentration is much lower than the surfactant concentration, and the microemulsion structure is therefore unaffected by the polymer. The rheological behavior can be understood within a bond percolation model. At a droplet concentration of 20%, essentially all polymer molecules are active in “bond” formation while at 10% the value is lowered to ∼1/3, the remaining 2/3 forming inactive loops. This difference is ascribed to unfavorable polymer stretching when the network is swelling. Acknowledgment. This work was supported by the Swedish Natural Science Research Council (NFR). L.C.’s stay in Lund was supported by a research scholarship from CNR (Consiglio Nazionale delle Ricerche). LA962054L