Effects of an Amphiphilic Graft Copolymer on an Oil-Continuous

J. Phys. Chem. B 2002, 106, 2533-2544

2533

Effects of an Amphiphilic Graft Copolymer on an Oil-Continuous Microemulsion. Molecular Self-Diffusion and Viscosity Anna Holmberg, Lennart Piculell,* and Magnus Nyde´ n† Physical Chemistry 1, Center for Chemistry and Chemical Engineering, UniVersity of Lund, P.O. Box 124, S-221 00 Lund, Sweden ReceiVed: October 23, 2001

Mixtures of an amphiphilic graft copolymer in water/sodium bis(2-ethylhexyl) sulfosuccinate (AOT)/ cyclohexane oil-continuous microemulsions are studied by the PGSE NMR technique and by viscometry. The graft copolymer has an oil-soluble poly(dodecyl methacrylate) backbone and water-soluble poly(ethylene glycol) side chains. Water, surfactant, and polymer self-diffusion coefficients can be measured individually by PGSE NMR. The water and the surfactant self-diffusion coefficients are equal, and both monitor the overall diffusion of the water droplets of the microemulsion. The graft copolymer enhances the microemulsion viscosity (relative increase ) 2000), and large viscosifying effects are promoted by increased degrees of grafting, increased polymer concentration, and large water droplets. Systems with high viscosities always display slow polymer self-diffusion. The droplet diffusion is always much more rapid than the polymer diffusion; thus, the polymer molecules do not immobilize the droplets. The results give the following microscopic picture of the mixtures. Polydisperse, but mostly finite, polymer-droplet aggregates coexist with a large fraction (30%) of “free” droplets. The aggregate size varies strongly with the polymer concentration, but only at the highest polymer concentration investigated (28 g/dm3) is there evidence of a fraction of very large (possibly infinite) aggregates. If the polymer/droplet ratio is increased, or if the mixture is diluted by oil, the system responds by inserting more polymer side chains per bound droplet, thus maintaining a high free-droplet concentration.

Introduction Interactions between amphiphilic polymers and surfactants have been extensively studied. Most of this research has concerned mixtures of water-soluble polymers and surfactants in aqueous solution.1,2 Because of their importance in various industrial applications, one class of amphiphilic polymers that has been widely studied are hydrophobically modified watersoluble polymers (HMWSP).3 An HMWSP consists of a watersoluble backbone modified by hydrophobic units that are attached either as side chains (in a graft copolymer) or as end caps (in an end-modified polymer). Added surfactant typically has a large influence on the rheology and phase behavior of aqueous HMWSP solutions.4-16 In particular, the viscosity of a mixture can - at certain mixing ratios - be enhanced by orders of magnitude compared to the viscosities of solutions of the surfactant or the HMWSP alone. It is notable that published studies concerned with ‘reverse’ amphiphilic polymer/surfactant systems, i.e., mixtures of oilcontinuous surfactant microemulsions with hydrophilically modified oil-soluble polymers (HMOSP), are both comparatively few and limited with regard to the polymer type. It is of fundamental interest to study also the latter type of mixture, and to explore analogies between oil-continuous and watercontinuous surfactant systems mixed with associating polymers. Research in this field will give potentially useful knowledge on how to modify structure and rheology of oil-continuous surfactant systems. * To whom correspondence should be addressed. † Present address: Applied Surface Chemistry, Chalmers University of Technology, S-412 96 Gothenburg, Sweden.

Microemulsions are single-phase mixtures containing at least water, oil, and surfactant.17 They are optically isotropic and thermodynamically stable. An oil-continuous microemulsion consists of water droplets, which are stabilized by surfactant and surrounded by oil. HMOSP can dissolve in oil-continuous microemulsions with the hydrophilic parts immersed in the water droplets and the hydrophobic part in the oil phase. Work by other groups on this type of mixture concerns exclusively block copolymers or telechelic ionomers, i.e., poly(oxyethylene)polyisoprene-poly(oxyethylene) triblock copolymers or endsulfonated polyisoprene telechelical ionomers. These have been mixed in oil-continuous microemulsions formed by sodium bis(2-ethylhexyl) sulfosuccinate (AOT) or pentakis(ethylene glycol)mono(dodecyl ether) (C12E5), water, and oil (mostly isooctane).18-33 Those systems have been studied relatively extensively by a number of different techniques; light scattering, NMR, rheology, freeze fracture electron microscopy, electrical conductivity, and transient electric birefringence. Both the triblock copolymers and the telechelic ionomers generate reversible networks in the oil-continuous microemulsions as a result of the association of the hydrophilic ends with the droplets and the formation of bridges between droplets.18,20,32 The rheological behavior of the mixtures varies from stable gels to fluids depending on the composition of the microemulsion, the polymer concentration, and the sizes of the polymer blocks.19,21 The telechelic ionomers give rise to much weaker associations and much lower relative viscosities, which is a consequence of the hydrophilic end group being located in the surfactant layer and not in the water domain.21,32,33 Candau et al. have studied microemulsions containing an HMOSP of the graft copolymer

10.1021/jp0139235 CCC: $22.00 © 2002 American Chemical Society Published on Web 02/19/2002

2534 J. Phys. Chem. B, Vol. 106, No. 10, 2002

Holmberg et al. TABLE 1: Polymer Characteristics, As Obtained by GPC/Light Scattering and NMR

Figure 1. Structure of hydrophilically modified poly(dodecyl methacrylate). x is the number of PEO chains per 100 monomers.

type, but in their case the system was surfactant-free. In the particular ternary solvent mixture they studied (water/toluene/ 2-propanol), the microemulsions were stabilized by the graft copolymer itself.34,35 We have synthesized an HMOSP of the graft copolymer type by grafting poly(ethylene glycol) (PEO) side chains, with a weight average molecular weight of 2000 g/mol, onto a hydrophobic poly(dodecyl methacrylate) (PDMA) backbone (Figure 1). The nonmodified backbone is soluble in cyclohexane and the side chains are water-soluble. In a series of studies, we are investigating mixtures of this copolymer with oil-continuous microemulsions based on AOT. Polymer-free microemulsions stabilized by AOT are known to contain droplets that are very nearly spherical in shape in the entire stability range of the L2 phase.36 Our previous studies37,38 have shown that the PDMA-g-PEO graft copolymer is not soluble in either cyclohexane or water, but it is very soluble in water/AOT/cyclohexane oil-continuous microemulsions. The nonmodified PDMA backbone is also soluble in the microemulsion at certain compositions, but it causes phase separation into two clear phases at sufficiently high concentrations of droplets or polymer molecules. The graft copolymer gives rise to an increase in the viscosity of the microemulsions. We attributed the enhanced viscosity to the formation of mixed polymer-droplet aggregates, where the backbone of the polymer is dissolved in the oil-continuous phase and the side chains are anchored in the water droplets. The viscosity increase can vary by orders of magnitude depending on the composition of the microemulsion and the polymer concentration. The largest viscosity enhancement is obtained for the largest droplet sizes. A maximum in the viscosity may be obtained when the droplet concentration is increased progressively at a constant polymer concentration. Results from timeresolved fluorescence quenching measurements show that the graft copolymer affects the microemulsion by increasing the size of the water droplets. In the present study, we aim for detailed information on the molecular level on the copolymer/microemulsion system. To that end, we have performed pulsed magnetic field gradient spin-echo (PGSE) NMR self-diffusion experiments, which give direct information on the molecular translation of water, surfactant, and polymer in the mixtures. This information is interesting in its own right, but it also gives indirect structural information on the extent of polymer-droplet aggregation and the aggregate sizes. The self-diffusion measurements have been compared with viscosity measurements. Experimental Section Chemicals. Dodecyl methacrylate (DMA) monomers were purified by passing them through a column of basic alumina (BDH, active basic, Brockman Grade 1). The chemicals 2,2’azobisisobutyronitrile (AIBN, Merck, 97%), potassium methylate (Merck, 97%), isobutyric acid (BDH, 99%), toluene (p.a.),

polymer

Mw (g/mol)

Mw/Mn

rg (nm)

degree of PEO substitution (mol %)

P0 P1 P2

370 000 440 000 610 000

1.9 1.4 1.2

16 (( 3) 24 (( 2) 30 (( 2)

0.9 2.4

poly(ethylene glycol) monomethyl ether (MPEO; Mn ) 2000, Aldrich-Chemie), AOT (Sigma, 99%), and cyclohexane (Merck, p.a) were used as delivered. The hydroscopic AOT was stored in a desiccator. Millipore water was used in the microemulsions. Polystyrene standards (Shodex), tetrahydrofuran (THF; HPLC grade, Fisher) and toluene (HPLC grade FSA) were used for MALLS/GPC measurements. 99.5 atom % deuterated cyclohexane, 99.8 atom % deuterated water, and 99.5 atom % deuterated THF used in the PGSE NMR experiments were obtained from Dr. Glaser AG, Basel. Polymer Synthesis. The synthesis of the graft copolymer (Figure 1) has been described in detail earlier,37 and only a brief description is given here. Poly(docecyl methacrylate) (PDMA) was synthesized by radical polymerization of DMA in toluene with AIBN as the initiator. The polymer was purified by repeated precipitation from toluene/methanol and was subsequently dried in a vacuum. Monofunctional MPEO was grafted onto PDMA as described by Wessleń et al.39 Potassium methylate was added to a toluene solution of MPEO. The mixture was refluxed and methanol was distilled off. The MPEO-alkoxide solution was mixed with a toluene solution of PDMA. The solution was refluxed under nitrogen. Since the grafting was carried out in dilute homogeneous solution the grafts may be assumed to be randomly distributed along the backbone.40 The efficiency of the grafting onto the dodecyl methacrylate backbone was found to be low (approximately 1/10 of the MPEO chains in the reaction bath ended up as grafts), presumably resulting from steric hindrance. The reaction was stopped by neutralizing the reaction mixture with isobutyric acid. The crude polymer was reprecipitated twice from toluene/diethyl ether, dried, redissolved in THF, and precipitated by addition of water. The solution was poured into a dialysis bag and dialyzed against water to remove unreacted MPEO. Polymer Characterization. The results from the characterization of the unsubstituted PDMA (P0) and the two different batches of graft copolymer (P1 and P2), both made by grafting onto P0, are collected in Table 1. The degree of substitution of a graft copolymer (in mol %, i.e., number of PEO grafts per 100 repeating units of PDMA) was calculated from 1H NMR spectra at ambient temperature in CDCl3 by integrating and comparing resonance signals from the methoxy and oxymethylene groups in the PEO grafts with characteristic signals from the PDMA backbone. The weight and number averages of the molecular weight (Mw and Mn, respectively) and the root-mean-square radius of gyration (rg) of each polymer sample were obtained by GPC/ light scattering. Light scattering was measured at 632.8 nm on a Dawn F MALLS photometer (Wyatt Technology, Santa Barbara, CA) equipped with a 5 mW He-Ne linearly polarized laser. The GPC setup included four Waters Styragel HR columns (500 Å, 103 Å, 104 Å mixed bed) coupled in series. A Wyatt/ Optilab 903 interferometric refractometer, working at the same wavelength as the light-scattering laser, was used as a masssensitive detector. The measurements were made at 25 °C with THF as the mobile phase. The molecular weight and the radius of gyration of the eluate from the GPC setup were evaluated

Oil-Continuous Microemulsion

J. Phys. Chem. B, Vol. 106, No. 10, 2002 2535

continuously via a Debye plot of R(Θ)/Kc versus sin2(Θ/2) through an extrapolation to zero concentration and zero angle. Here, R(Θ) is the excess Rayleigh ratio, c is the concentration of the macromolecule, and Θ is the scattering angle. K is an optical constant equal to 2π2no2(dn/dc)22λ0-4NA-1, where n0 is the refractive index of the solvent at the incident wavelength (λ0), dn/dc is the refractive index increment, and NA is Avogadro’s constant. The second virial coefficient was put to zero (the second term in the virial expansion may generally be neglected at the low concentrations used in chromatographic separations), and dn/dc was determined to 0.070 ( 0.002 mL/g using the software DNDC supplied by Wyatt Technology. The same value was used for the graft copolymers, since the limited amounts of these polymer samples precluded a dn/dc determination. However, this value of dn/dc was found to be consistent with the known injected mass. Each reported value of Mw and rg results from three independent GPC/light scattering runs. Viscosity measurements for determination of the intrinsic viscosity of PDMA in cyclohexane were performed on an Ubbelohde Capillary Viscometer (Schott Gera¨te) with a capillary diameter of 0.46 mm. Samples were prepared in cyclohexane in a concentration range from 0.5 to 16 g/dm3. The capillary was placed in a temperature-controlled water bath. Each measurement was made at 20 °C after an equilibration time of 15 min. The measurements were repeated until three values differing less than 0.1% had been obtained. Sample Preparation. Polymer-free microemulsions were first prepared (with deuterated solvents for NMR and normal solvents for viscosity) and stirred for 1 day at room temperature. The desired amount of polymer was then added, and the mixtures were stirred for several days until the dispersions became transparent. All samples used for viscosity and NMR measurements were transparent and homogeneous. Viscosity Measurements. Sample viscosities were measured on a Carri-Med CSL controlled stress rheometer with a cone and plate geometry. A solvent trap filled with microemulsion was used to avoid solvent evaporation, and the temperature was controlled by a Peltier element. The measurements were done in the shear stress sweep mode. PGSE NMR Experiments. Samples were placed in 5-mm NMR tubes, which were flame sealed to prevent solvent evaporation. The self-diffusion coefficients of the polymer, AOT, and water components were measured on a 200 MHz Bruker spectrometer equipped with a field gradient probe. The probe had a capacity to deliver gradient pulses of up to 9 T m-1 at a current of 40 A. The stimulated echo pulse sequence was used.41 In a typical experiment, the gradient pulse duration, δ, and the experimental observation time, ∆, were kept constant at values between 1.5 and 5.0 ms and 100-200 ms, respectively. In an initial experiment on a microemulsion containing graft copolymer, the effect of varying ∆ (in the range 100-400 ms) was investigated and the measured self-diffusion coefficients of all components were found to be unaffected by this variation. The time τ separating the first two 90° pulses was kept short (6 ms or less) in order to eliminate effects from T2 weighting. (The signal line widths were ca. 10 Hz.) The gradient strength, g, was increased in 32 steps of 0.2 Tm-1. Single exponential decays were obtained for water and AOT when the respective signal intensities I(k) were plotted against k in accordance with the Stejskal-Tanner expression for free nonrestricted diffusion42

I(k) ) exp(-kD)

(1)

Here D is the self-diffusion coefficient of a single diffusing

Figure 2. Experimental signal intensity decays (symbols) for polymer P2 in microemulsion B2 at 21 °C together with best fits (lines). Squares (0): cpol) 9.4 g/dm3, eqs 3 and 4. Circles (O): cpol) 23.4 g/dm3, eqs 5 and 4.

component and k is defined as

(

k ) (γgδ)2 ∆ -

δ 3

)

(2)

where γ is the proton magnetogyric ratio (γ ) 2.6752 × 108 rad T-1s-1), δ is the duration of the gradient pulses, and ∆ is the time between the leading edges of the gradient pulses. For the polymer components, plots of the logarithm of the signal intensity against k were always curved. The signal intensity decays were then interpreted in terms of a distribution of diffusing species, according to

I(k) )

∫P(D) exp(-kD)dD ∫P(D)dD

(3)

where P(D) is the normalized distribution of self-diffusion coefficients, D. As in previous similar studies of polydisperse polymers, 43 we have assumed a log-normal distribution function

P(D) )

[(

log (D) - log (DME) 1 exp Dσx2π σx2

)] 2

(4)

Here DME is the mass-weighted median self-diffusion coefficient and σ the width of the distribution. A representative fit is shown in Figure 2. In some cases, good fits could only be obtained if a second diffusing component, in addition to the log-normal distribution, was assumed. This is expressed in eq 5,

I(k) ) f

∫P(D) exp(-kD)dD + (1 - f) exp(-kDS∆) ∫P(D)dD

(5)

where f is the fraction that belongs to the log-normal distribution. Figure 2 shows a fit to eq 5 for 23.4 g/dm3 P2 dissolved in microemulsion B2. Here the additional component corresponds to a slowly diffusing fraction (diffusion coefficient DS) of the polymer.


Holmberg et al.

Figure 3. Compositions of microemulsions investigated by viscometry and PGSE NMR measurements. The fat solid line indicates the phase boundary between the oil-continuous microemulsion phase, L2, and the two-phase area, 2φ, for microemulsions containing 1% graft copolymer.38

In microemulsion samples containing P0, an additional rapidly diffusing component, corresponding to AOT, had to be used in the fits. This is owing to an overlap of the signals from PDMA with signals from AOT. The reliability of the self-diffusion coefficient obtained for P0 became better as the polymer concentration was increased. Experimental uncertainties were estimated by a Monte Carlo procedure, where the fit was performed at least 1000 times in order to obtain a good estimate of the error in the final fit parameters. Typically, the uncertaintes were found to be less than (5% for the diffusion coefficients, (10% for σ, and (10% for f. All measurements were made at 21 °C except for the studies involving microemulsion B1. The latter experiments were performed at 25 °C because samples containing microemulsion B1 (prepared with deuterated solvents) phase separated at 21 °C. Results Strategy. To systematically study the effect of added polymer on the dynamic properties of the microemulsions, we studied the influences of three different variables separately in the mixtures: We varied the graft copolymer concentration at a fixed composition of the microemulsion, the degree of grafting of the polymer at a fixed polymer concentration and microemulsion composition and, lastly, the microemulsion droplet concentration at fixed polymer content and droplet size. Both viscosity and self-diffusion measurements were performed for all series. The specific choice of mixtures was based on the following considerations. We wished to include systems with high viscosities, i.e., with big droplets and large polymer contents.37,38 For comparison, we also wished to study systems with smaller droplets, closer in size to the ones that we were able to access by fluorescence measurements in our previous study.38 To that end, oil-continuous microemulsions of water/AOT/ cyclohexane at five different compositions were chosen for mixing with the graft copolymers. The locations of these mixtures in the ternary water/AOT/cyclohexane phase diagram are indicated in Figure 3. Sample compositions are given in Table 2 together with calculated44 data on the radii, r, the number concentrations, cdrop, and the volume fractions, φd, of

Figure 4. Apparent viscosities of B2 microemulsions containing (from bottom to top) 4.7, 9.4, 14.1, 23.4, or 28.1 g/dm3 of polymer P2 versus shear rate.

TABLE 2: Compositions, Calculated Droplet Characteristics, and Measured Viscosities (in Normal Solvents) of the Microemulsions Used in This Study micro- cAOT cwater emulsion (M) (M) w0

φd

r cdrop temp (number/dm3) (nm)a (°C)

A B1 B2

0.21 0.15 0.21

3.16 15 0.1 4 3.51 23 0.1 2 4.73 23 0.1 7

10.0 × 1020 3.1 × 1020 4.2 × 1020

3.2 4.5 4.5

B3 B4

0.26 5.97 23 0.2 1 0.49 11.2 23 0.3 9

5.3 × 1020 10.0 × 1020

4.5 4.5

21 25 21 25 25 25

viscosity (Pas) 1.5 × 10-3 1.4 × 10-3 1.8 × 10-3 1.6 × 10-3 2.0 × 10-3 6.1 × 10-3

a

The droplet radius,r, is obtained as the radius of the water domain, rw, plus the length of the surfactant tail () 8 Å). Here rw ) 3*w0*Vw/ Na*aAOT, where Vw is the molecular volume of water and aAOT the headgroup area of AOT () 51 Å2).44

the droplets in the polymer-free microemulsions. In the B series of samples, the droplet size (which is controlled by w0, the molar water/surfactant ratio) was kept constant, but the concentration was varied. The compositions of the B microemulsions were close to the phase boundary (cf. Figure 3) in order to obtain the maximum size droplets. The droplet size was smaller in microemulsion A. Microemulsions A and B2 had the same concentration of AOT, whereas A and B4 had the same concentration of droplets. Note that the radii of even the largest droplets were considerably smaller than the radii of gyration of the polymers (Table 1). On the other hand, even the smallest droplets were larger than an unperturbed PEO side chain (rg ≈ 1.5 nm when M ) 2000). For P2, the most highly substituted graft copolymer, the average distance between grafts along the contour of the polymer backbone was 10 nm. Viscosity. The intrinsic viscosity [η] ) 0.048 dm3/g obtained for P0 in cyclohexane is in good agreement with the value in isooctane for the same polymer.45 This corresponds to a hydrodynamic radius of 14 nm and an overlap concentration of 21 g/dm3. The overlap concentration for this simple binary mixture of backbone polymer and solvent is a useful reference point; we will refer to this concentration as c*0. Samples of graft copolymers in microemulsions took a very long time to mix if the graft copolymer concentration was above c*0, and the majority of the data presented below are for lower polymer concentrations.


Figure 5. Newtonian viscosities at 21 °C of B2 microemulsions containing increasing concentrations of graft copolymer P2. The line is a guide for the eye.

Figure 4 shows the shear rate dependence of B2 microemulsions containing the graft copolymer P2. Newtonian viscosities were obtained at all accessible shear rates for samples containing 9.4 g/dm3 (1.1 wt %) of polymer. Samples with higher polymer concentrations were shear thinning (especially above c*0), but the Newtonian plateau was still accessible at low shear rates. The viscosity of the microemulsions increased dramatically when the graft copolymer was added. Figure 5 shows the Newtonian viscosities obtained from the data in Figure 4 and plotted against the polymer concentration. At 28.1 g/dm3 polymer, the viscosity was 2000 times larger than that of the polymer-free microemulsion. This particular sample had the largest viscosity that we have yet observed in this type of mixture. In our previous studies, either the polymer concentration or the droplet size was kept lower, both yielding a lower viscosity.37,38 Samples at still higher polymer concentrations should be difficult to prepare: It took 10 days for the graft copolymer to dissolve at the highest concentration in Figures 4 and 5. The viscosity increased when the number of PEO side chains on the polymer was increased. Measurements (not shown) were made on samples of microemulsion B2 all containing 9.4 g/dm3 of polymer, but with different degrees of substitution (from 0 to 2.4 mol %) with PEO side chains. Over this range, the Newtonian viscosity increased from 2.5 to 8.2 mPas, and the increase was almost linear in the degree of substitution. The volume fraction of droplets also affects the viscosity, as we have demonstrated previously.38 In Figure 6, viscosity data are shown for the B series of microemulsions (increasing φd at constant w0 ) 23). Both the polymer-free microemulsions and the mixtures with 1.1 wt % of P2 show a viscosity increase when the volume fraction of droplets is increased. The figure also shows the relative viscosity, i.e., the viscosity of the polymer/microemulsion mixture divided by the viscosity of the corresponding polymer-free microemulsion. In this particular series, the relative viscosity is nearly constant, but this result is not general for the type of systems studied here. In our previous study on a different batch of the copolymer (which had a slightly higher degree of grafting and a larger viscosifying effect), similar plots showed maxima in the relative viscosity at φd values in


Figure 6. Newtonian viscosities at 25 °C of the B series of microemulsions with (b) and without (O) 1.1 wt % of polymer P2. The relative viscosities (9; right scale) of the polymer-containing samples are also indicated. Lines are guides for the eye.

TABLE 3: PGSE NMR Self-Diffusion Data and Calculated Hydrodynamic Radii for Various Polymer Samples in Simple (Deuterated) Solvents polymer

solvent

temp (°C)

cpol (g/dm3)

Dpol × 1011 (m2/s)

σ

rh (nm)

P0 P1 P2 P2 P2 P0 P0 P0

THF THF THF THF THF cyclohexane cyclohexane cyclohexane

21 21 21 21 21 21 21 21

9.9 9.9 5.0 9.9 14.9 4.4 8.9 13.4

3.3 3.2 3.6 1.8 1.4 1.8 1.7 1.5

0.50 0.78 0.82 0.54 0.55 0.53

14 15 13 26 34 12 13 15

the range 0.11-0.15. These maxima were more or less pronounced, becoming stronger with increasing droplet size and decreasing temperature. Self-Diffusion: General Observations. The proton NMR spectra of microemulsions containing the graft copolymer gave well-resolved peaks for water, AOT (two well-separated peaks), and the EO groups of the copolymer side chains. In addition, there was a large peak due to methylene groups from both AOT and PDMA. Consequently, the system was ideally suited for simultaneous measurements of the self-diffusion coefficients of water, AOT, and graft copolymer by PGSE NMR. Mixtures containing nonmodified PDMA were more difficult, owing to the lack of a separate signal for the polymer. As explained in the Experimental Section, we could extract diffusion data for P0 in the microemulsions by fitting the signal intensities from the methylene peak (resulting from both the P0 and the AOT components) to eq 5. For comparison, we also measured the self-diffusion of the various polymer samples in simple solvents. All measured diffusion data are compiled in Tables 3 and 4. The data for AOT refer to the peak from the single proton on the R carbon; data from the other well resolved AOT peak gave the same results to within 5%. In all samples, the signal intensities for water and AOT displayed single-exponential decays when plotted against k. This means that the exchange rates of water and AOT between different microenvironments were rapid (on the NMR time scale). As has previously been found for polymer-free oilcontinuous microemulsions, the self-diffusion coefficients were


Holmberg et al.

TABLE 4: PGSE NMR Self-Diffusion Data from Microemulsion Samples (in Deuterated Solvents) with and without Polymers microemulsion

polymer

temp (°C)

cpol (g/dm3)

Dw × 1011 (m2/s)

Ddrop × 1011 (m2/s)

DAOT × 1011 (m2/s)

Dpol × 1011 (m2/s)

A A A A A A A B1 B1 B2 B2 B2 B2 B2 B2 B2 B2

P0 P0 P1 P2 P2 P2 P2 P0 P0 P1 P2 P2 P2 P2

21 21 21 21 21 21 21 25 25 21 21 21 21 21 21 21 21

9.3 14.0 9.3 3.7 9.3 14.0 9.3 9.4 14.1 9.4 4.7 9.4 14.1 23.4

5.2 3.5 4.2 3.6 3.6 2.7 2.5 3.9 3.0 3.4 2.8 2.5 2.8 2.4 1.9 1.6 1.5

4.7 3.0 3.7 3.0 3.1 2.2 2.0 3.4 2.5 3.0 2.5 2.2 2.5 2.1 1.5 1.2 1.1

4.5 3.0 3.4 2.8 2.6 2.2 1.9 3.1 1.9 3.0 2.0 2.0 2.2 2.0 1.3 1.0 0.82

B2 B2 B3 B3 B4 B4

P2 P2 P2

25 25 25 25 25 25

9.4 9.5 10.0

3.8 2.4 3.2 1.7 1.2 0.91

3.4 2.0 2.9 1.4 1.1 0.76

3.3 1.5 3.3 1.4 0.92 0.50

2.3 1.5 1.0 0.76 0.33 0.19 0.55 1.0 1.1 0.67 0.62 0.20 0.077 0.29 0.003 0.28 0.21 0.092

σ 0.94 0.78 0.51 0.78 0.72 1.1 0.95 0.31 0.67 0.90 0.81 1.0 1.2 1.3 0.94 1.1 0.85

quite similar for AOT and water (Table 4), although they were slightly - but significantly - larger for water.46,47 This indicates that both self-diffusion coefficients report on the diffusion of closed water droplets in the microemulsions. The slightly more rapid water diffusion may be attributed to a significant contribution from rapidly diffusing water molecules dissolved in the oil.48,47 The measured water self-diffusion coefficient, Dw, may thus be written as

Dw) (1 - pdrop)Dw/o + pdropDdrop

(6)

where pdrop is the fraction of water molecules that are contained in the droplets, Ddrop is the droplet diffusion coefficient, and Dw/o is the diffusion coefficient for water molecules dissolved in cyclohexane. Previously, Angelico et al. estimated Dw/o in cyclohexane to be in the range 3-15 × 10-9 m2 s-1, using measured self-diffusion coefficients for water in lecitin/water/ cyclohexane microemulsions and literature data on the solubility of water in cyclohexane (1.2-4.4 × 10-3 M).48 Adopting the values Dw/o ) 15 × 10-9 m2 s-1 and a solubility of 1.2 × 10-3 M for water in cyclohexane, we calculated Ddrop from Dw, using eq 6. These calculated values, which are included as Ddrop in Table 3b, came quite close to DAOT. We conclude that for all our microemulsions, including those that contained dissolved polymer, both DAOT and Ddrop may be regarded as the overall droplet self-diffusion coefficients. As described in the Experimental Section, the Stejskal-Tanner plots of the echo decays for the polymer components were always curved (cf. Figures 2a and 2b), but we found that a lognormal distribution, eq 4, of polymer diffusion coefficients gave satisfactory fits to the curves. The values quoted here as Dpol (Tables 3 and 4) are the median self-diffusion coefficients obtained assuming such a distribution. A distribution of diffusion coefficients would result from either a polydispersity of the polymer sample itself or from a size-distribution of the polymerdroplet aggregates formed. The parameter, σ, in the log-normal distribution function (eq 4) is a measure of the width of the distribution of diffusion coefficients. Self-Diffusion: Trends. After the above general observations, as regards the measured droplet and polymer self-diffusion

Figure 7. Self-diffusion coefficients at 21 °C for water (triangles pointing up), surfactant (triangles pointing down), and polymer P2 (circles) in microemulsions A (empty symbols) and B2 (filled symbols) versus the polymer concentration. Lines are guides for the eye. Two diffusion coefficients are given for P2 at its highest concentration in B2; these correspond to the two fractions (slow and fast diffusion) of polymer; cf. eq 5.

coefficients, we will now turn to the trends in these diffusion coefficients that were found when the mixture compositions were varied according to the strategy outlined above. Figure 7 illustrates the effects of increasing concentrations of P2 on the self-diffusion coefficients in two different microemulsions, A and B2 (cf. the corresponding viscosity data for microemulsion B2 in Figure 5). In each microemulsion, both the droplet and the polymer diffusion is slowed when the polymer concentration is increased, but the slowing down is much more pronounced for the polymer molecules than for the droplets. An increased water content at constant surfactant concentration (we recall that B2 and A have the same surfactant


Figure 8. Self-diffusion coefficients at 21 °C for water (triangles pointing up), surfactant (triangles pointing down) and polymer (circles) in microemulsion A (empty symbols) and B2 (filled symbols) containing 9.4 g/dm3 polymer at different degrees of PEO substitution. Lines are guides for the eye.

concentration, but B2 contains more water) results in a stronger slowing down of the graft copolymer diffusion. We found, furthermore, that the width of the diffusion coefficient distribution for the graft copolymer increased with increasing cpol in the microemulsions (Table 4). In microemulsion B2 we obtained σ ) 0.81 at 0.5 wt % P2 and σ ) 1.2 at 1.5 wt % of P2. A similar increase in σ has previously and often been seen for associating polymer solutions, 11,43,9,49 as well as for simpler solutions of polydisperse polymers.50 It seems natural, in the present case, to attribute this phenomenon to the formation of polydisperse polymer-droplet aggregates. In microemulsion B2, the measurements were extended to 23.4 g/dm3 P2 (above c*0) where a very slowly diffusing component became evident. In Figure 7, the two values of D, shown for P2 in the latter sample, represent the slowly and rapidly diffusing fractions of the polymer (aggregates). Similar observations have been made for hydophobically modified and nonmodified ethyl hydroxyethyl cellulose in water, and for styrene-methyl methacrylate random copolymers in acetone.43,51,49,50 The effect of an increasing PEO substitution degree on the various diffusion coefficients was measured at constant polymer concentration in micoemulsions A and B2; see Figure 8. The results are those expected from the trends already shown in Figure 7: The introduction of PEO side chains slows down both the polymer and the droplet diffusion in the mixed systems, but the effect is much larger for the polymer than for the droplets. Finally, Figure 9 shows diffusion results for increasing volume fractions of droplets in the B series of microemulsions, both in the absence and in the presence of 1.0 wt % P2 (cf. Figure 6 for viscosity data). All diffusion coefficients (for graft copolymers and of droplets) slowed to a comparable (relative) extent by an increase in φd, although the curves are not exactly parallel. Since the graft copolymer is not soluble in pure cyclohexane, we made some measurements in THF to investigate its diffusion in a neat (droplet-free) solvent. The results (Table 3) show that for low polymer concentrations or low grafting densities, all


Figure 9. Self-diffusion coefficients at 25 °C for water (triangles pointing up), surfactant (triangles pointing down) and polymer (circles) as a function of the volume fraction of droplets in the B series of microemulsions with (filled symbols) and without (empty symbols) 1.0 wt % P2. (1.0 wt % P2 in a microemulsion with deuterated solvents corresponds to 1.1 wt % P2 in a microemulsion with normal solvents.) Lines are guides for the eye.

data converge on the value D ) 3 × 10-11 m2/s, which was found also for the unmodified polymer. At higher concentrations of polymer P2, however, the diffusion was significantly slower. Discussion From the results above it is clear that both the molecular selfdiffusion and the viscosity in polymer/microemulsion mixtures vary with the polymer concentration, the number of PEO substituents on the polymer, and the composition of the microemulsion. Moreover - as expected - an increase in the viscosity is always accompanied by a decreased polymer and droplet self-diffusion. The strongly enhanced viscosity and decreased diffusion in the copolymer/microemulsion samples both indicate the formation of larger aggregates of graft copolymers and droplets. Our objective in this discussion is to exctract as much information as possible about the details of the droplet-copolymer association from the NMR self-diffusion data. We will discuss the droplet and polymer self-diffusion coefficients separately, in each case beginning with the simple reference systems that do not display polymer-droplet association. Droplet Diffusion in Pure Microemulsions. The hydrodynamic radius rh of a spherical particle dispersed in a medium can be obtained from the particle self-diffusion coefficient via the Stokes-Einstein relationship

D0 ) kBT/6πηrh

(7)

where D0 is the particle self-diffusion coefficient resulting from Brownian motion, η the viscosity of the pure dispersion medium, T the absolute temperature, and kB the Boltzmann constant. Equation 7 is only valid in the dilute limit; owing to particleparticle interactions, the self-diffusion coefficient decreases with an increasing volume fraction of the dispersed phase φd. Accordingly, the droplet diffusion data in Figure 9 were fitted to the linear expression


DNMR ) D0(1 - Rφd)

Holmberg et al.

(8)

where DNMR represents the measured droplet self-diffusion coefficient (DAOT). This fit yielded D0 ) 4.7 × 10-11 m2 s-1 and (from eq 7) rh ) 4.5 nm for the B series microemulsions (w0 ) 23), in good agreement with the calculated droplet radius (4.5 nm) in Table 2. The value of R from this fit was 1.9, which agrees with previous theoretical and experimental findings for microemulsions.52,53 No concentration dependence was measured for microemulsion A, but if one makes the reasonable assumption that eq 8 (with R ) 1.9) holds also for the smaller droplets, one obtains (from eq 7) the value rh ) 3.3 nm for their size - again in good agreement with the calculated value in Table 2. Droplet Diffusion in Polymer-Containing Microemulsions. The droplet diffusion was slower with polymer present in the microemulsion. The effect was seen for both the unsubstituted polymer and the graft copolymers, but it was much larger for the graft copolymers. From this we conclude that the droplet diffusion is slowed to some extent by the presence of polymer in the oil-phase (obstruction), but much more by polymer-droplet aggregation. However, in the aggregating mixtures, the droplet diffusion is not reduced as much as the diffusion of the graft copolymer. This could be explained by a large fraction of free droplets, i.e., droplets not connected to the polymer-droplet aggregates. A single self-diffusion coefficient was seen for the droplets, which implies a fast exchange, on the experimental time scale (100 ms) of AOT and water between aggregated and free droplets. Accordingly, we may write the observed droplet self-diffusion coefficient (taken here as DAOT) as

DAOT ) (1-p)Dfreedrop + pDaggdrop

(9)

where p is the fraction of droplets bound in polymer-droplet aggregates, and Dfreedrop and Daggdrop are the respective diffusion coefficients for the two states of the droplets. We have used eq 9 to calculate p for the graft-copolymer containing microemulsions. In these calculations, we have assumed that Daggdrop ) Dpol (i.e., the median polymer selfdiffusion coefficient), and that Dfreedrop is equal to the measured DAOT in the corresponding polymer-free microemulsion. The former assumption implies that movement of bound droplets along the polymers in the aggregates does not contribute to the measured translation. (We will provide some support for this assumption below.) The latter assumption is an approximation, since it implies that the presence of the polymer does not affect the free droplet diffusion. An alternative estimate would be to set Dfreedrop equal to DAOT measured in the corresponding system containing the backbone polymer, P0, rather than a graft copolymer. This yields lower values of Dfreedrop and p, but calculations give only small differences. Thus, the p values we have calculated may be quantitatively inaccurate, but that they should nevertheless be of the correct order of magnitude and show the correct trends. Figure 10 shows the variation of p with increasing concentration of polymer P2 in microemulsions A and B2. In both systems, the fraction of bound droplets is remarkably constant. In particular, p is not proportional to the polymer content but seems to level off at a value far below 1. We have taken the analysis one step further by calculating, for each mixture, the number of PEO side chains per bound droplet. Figure 10 shows that this value clearly increases with increasing polymer concentration. Evidently, even at high concentrations, the graft copolymer does not bind all droplets - presumably because

Figure 10. Number of PEO side chains per bound droplet (circles, left scale) and fraction of droplets bound in polymer-droplet aggregates (squares, left scale) at different concentrations of polymer P2 in microemulsions A (empty symbols) and B2 (filled symbols). Lines are guides for the eye.

the entropic cost is too high. Rather, it buries more than one PEO chain in each droplet. A clearly unrealistic feature in Figure 10 is that the calculated number of PEO side chains per bound droplet becomes less than unity at low polymer concentrations in microemulsion A, the microemulsion with the smallest droplets. It should be noted, however, that the calculated values were obtained under the assumption that the number of droplets do not change in the presence of the polymer. According to our previous fluorescence quenching experiments, the latter is actually not the case, since (at least small) droplets combine into larger droplets when they bind to the graft copolymer.38 In this context, we should also comment on the fact that the previous fluorescence measurements did not reveal any increase in droplet polydispersity in the samples containing the graft copolymer. This would seem to contradict the picture we propose here, with two populations of droplets that differ significantly in size. To check this point we simulated (by calculations) fluorescence quenching results for bimodal distributions containing two Gaussian populations of droplets. The polydispersities obtained from a standard evaluation of these simulated data turned out to be rather similar for the combined bimodal distributions as for the individual Gaussian populations, as long as the average droplet volumes of the two populations differed by a factor < 3 (as suggested by the experimental data in our fluorescence study.38). Figure 11 shows results from a similar analysis as in Figure 10 of the droplet diffusion data for increasing droplet concentrations (in the B series of microemulsions) at a constant concentration of polymer P2. (Here, we have used the linear fit, according to eq 8, of DAOT versus φd in the polymer-free microemulsions to obtain estimates of Dfreedrop.) The results are quite remarkable: The fraction of bound droplets is more-orless constant, but the number of PEO chains per bound droplet decreases considerably when the overall droplet content is increased. The results in Figures 10 and 11 have interesting implications for the solubility of the graft copolymer in the microemulsions. We recall that the graft copolymer is not soluble in cyclohexane;


Figure 11. Number of PEO side chains per bound droplet (circles, left scale) and fraction of droplets bound in polymer-droplet aggregates (squares, right scale) in P2-containing microemulsions of series B versus the volume fraction of droplets. cpol) 1.0 wt % P2 (this corresponds to 1.1 wt % in microemulsions prepared with normal water and cyclohexane). Lines are guides for the eye.

some minimum number of bound droplets per copolymer molecule is required for miscibility. Thus, for a fixed copolymer concentration, a phase separation is expected at sufficiently low droplet concentrations. Indeed, independent measurements showed that a phase separation occurred, under the conditions of Figure 11, when the volume fraction of droplets was lowered below φd ) 0.11 (the dashed line in the figure). Conversely, there must be an upper limit to the concentration of graft copolymer that can be dissolved at a given droplet concentration. The result in Figure 10 suggests that this limit may be reached earlier than one might expect by simply considering the global droplet/side chain ratio: Since the system always maintains a quite high fraction of free droplets, the number of bound droplets per copolymer chain rapidly decreases at increasing concentration of graft copolymer. The large fraction of free droplets in the mixtures also gives a clue to an observation, to which we could not propose a satisfactory interpretation, in our previous study:38 On dilution with cyclohexane at a constant global polymer/droplet ratio, a phase separation occurred. Our present results suggest the following explanation. On dilution, the fraction of bound droplets should decrease, resulting from the increasing entropic cost of binding droplets to the polymer. At some stage, the number of bound droplets per copolymer molecule reaches the minimum value required for solubility, and a further loss of droplets resulting from dilution leads to the precipitation of a fraction of the graft copolymer. We have not succeeded in finding a single model that describes how the fraction of bound droplets varies with the polymer (Figure 10) and with the droplet (Figure 11) concentrations. A Langmuir model for the binding of droplets to “binding sites” on the polymer fails to produce a single binding constant, presumably because there is no single bound state (cf. the large variation in the number of PEO chains per bound droplet in Figures 10 and 11). A very simple description that predicts the constant value of p in Figure 11 would be in terms of a partitioning of droplets between a bound “phase” and a solution

J. Phys. Chem. B, Vol. 106, No. 10, 2002 2541 phase. However, we see no physical justification for this model, which, moreover, fails to describe the data in Figure 10. A quite different approach is to assume that the PEO side chains distribute randomly among the droplets. A Poisson distribution applied to the mixtures in Figures 10 and 11 predicts stronger variations in p than those observed experimentally, although the predicted magnitude of p (0.2-0.8) is reasonable. The model correctly captures the monotonic increase in p with polymer concentration (Figure 10); however, it also predicts a significant decrease in p with an increase in droplet concentration, contrary to the invariance seen in Figure 11. Possible reasons for the failure of this approach are not difficult to find: The side chains cannot distribute randomly in the system since they are connected to other side chains via the backbone polymer. Moreover, nonnegligible interactions between two or more PEO chains within a bound droplet should also affect the distribution. Polymer Diffusion. We will now turn to a major consequence of the association between side chains and droplets, i.e., the formation of larger aggregates, containing more than one polymer chain. To obtain some further information on polymer aggregation and aggregate sizes, we have used the polymer selfdiffusion coefficients in Tables 3 and 4 to calculate apparent hydrodynamic radii via eq 7. The results are given in Figures 12 and 13 and, for the polymers in pure solvents, in Table 3. As “solvent” viscosities in these calculations we have consistently used the viscosities of the corresponding polymer-free systems (pure solvent or microemulsion; measured microemulsion viscosities are given in Table 2). This approach seems warranted, since the sizes of the polymer (aggregates) are significantly larger than the sizes of the microemulsion droplets. However, we have in the calculations again neglected the effects of obstruction resulting from the presence of the polymer (aggregates) themselves as expressed, e.g., by eq 8. This means that the calculated hydrodynamic radii, especially at high polymer concentrations, should represent upper limits to the true radii. Starting with the simplest systems (Figure 12a), we consistently find a hydrodynamic radius around 10 nm for the nonmodified polymer P0, regardless of the medium (microemulsion A or B2, pure cyclohexane, or THF) or the polymer concentration. This agrees with our picture of a nonassociating polymer in a good solvent. The radii of the graft copolymers in a pure solvent (THF) are quite similar at low concentrations. However, rh for the most modified graft copolymer P2 displays a significant increase with increasing polymer concentration in THF. This result implies that some self-association occurs for the graft copolymer in THF. One further observation that points in the same direction is the unexpectedly high Mw value obtained by light scattering for polymer P2 (Table 1). We note also that in a previous study, we found a fraction of graft copolymer aggregates in THF.38 When dissolved in a microemulsion, the graft copolymer P2 shows a fairly modest value of rh (ca. 20 nm) at low polymer concentrations (Figure 12b). In this limit of a large excess of droplets, we may imagine that the graft copolymer molecules are individually dispersed in polymer-droplet aggregates each containing only one polymer molecule. This is consistent with the low ratios of PEO side chains per bound droplet seen in Figure 10. A marked increase in rh occurs, however, as the polymer concentration is increased, especially in microemulsion B2 that contains the larger and less numerous droplets. The hydrodynamic radius has increased to 150 nm at 14.0 g/dm3 of P2 in B2. At 23.4 g/dm3, the two diffusion coefficients observed


Holmberg et al.

Figure 14. Pictorial view of solutions of graft copolymer at two concentrations (below c*) in microemulsions. a) At low polymer concentrations, the graft copolymers are singly dispersed. b) When the polymer concentration is increased, the fraction of free droplets remains high, and the number of side chains per bound droplet increases. Large polymer-droplet aggregates are formed.

Figure 12. (a) Hydrodynamic radii calculated from the polymer selfdiffusion coefficient of polymer P0, P1 and P2 in simple solvents plus polymer P0 in micremulsion A and B2. Key: empty squares, P0 in microemulsion A; filled squares, P0 in microemulsion B2; crosses, P0 in cyclohexane; plus, P0 in THF; triangle pointing down, P1 in THF; triangles pointing up, P2 in THF. (b) Hydrodynamic radii calculated from the self-diffusion coefficients of polymer P1 and P2 in microemulsions A and B2. Key: empty diamonds, P1 in microemulsion A; filled diamonds, P1 in microemulsion B2; empty circles, P2 in microemulsion A; filled circles, P2 in microemulsion B2. Two radii are given for P2 at its highest concentration in B2; these correspond to the two fractions (slow and fast diffusion) of polymer; cf. eq 5 and Figure 7.

Figure 13. Hydrodynamic radius calculated from the self-diffusion coefficient of polymer P2 in the microemulsions of series B versus the volume fraction of droplets.

translate into two fractions of aggregates, one pertaining to a distribution of rather small aggregates with an apparent rh of 42 nm, and one corresponding to a very large apparent radius of several micrometers. The latter may possibly correspond to

to a very slow diffusing polymer network. We recall that the highest polymer concentration studied is above c*0, the overlap concentration for the nonmodified polymer in cyclohexane. When the droplet concentration in the B series of microemulsions is varied at a constant (low) polymer concentration (Figure 13) the aggregates remain comparatively small with apparent hydrodynamic radii in the range 30-50 nm. This rather constant aggregate size is also consistent with the small variation in the relative viscosity of the same mixtures observed in Figure 6 above. Still, the number of PEO side chains per bound droplet varies significantly over this series of mixtures (Figure 11). We can imagine two mechanisms explaining why the aggregates are so small at low droplet concentrations, where the number of side chains per bound droplet is high: The aggregates are expected to be dense, since the system is close to phase separation (Figure 11). Moreover, the cross-linking (through droplets shared by two or more side chains) could occur predominantly within copolymer molecules (rather than between molecules) at this rather low concentration of graft copolymer. In conclusion, the interpretation of polymer diffusion data in terms of apparent hydrodynamic radii supports an overall picture of graft copolymer-droplet aggregates with a variable but finite size, diffusing in a dispersion of free droplets. A schematic illustration is given in Figure 14. Only at the highest polymer concentration studied is there an indication of the formation of a very highly aggregated (possibly infinite) polymer fraction. This picture of finite aggregates also supports the assumption, made in the analysis of the droplet diffusion data above, that the possible diffusion of bound droplets along the polymer chains in an aggregate does not contribute to the translation of droplets over long distances, so that the diffusion coefficient of the aggregated droplets may indeed be assumed to be the same as the diffusion coefficient of the polymer. Conclusions The main conclusions from our study may be summarized as follows. NMR self-diffusion provides quite useful information on the dynamics in complex mixtures of graft-modified poly-

Oil-Continuous Microemulsion mers dissolved in oil-continuous microemulsions. Both the polymer and the droplet diffusion may be accessed by the measurements. As far as we are aware, there is no previous NMR self-diffusion study on amphiphilic polymers in oilcontinuous microemulsions where the individual diffusion coefficients of surfactant, water, and polymer have been measured directly. There is a good correlation between the polymer self-diffusion and the macroscopic viscosity of the system: Systems with high viscosities display slow polymer diffusion, and vice versa. Whereas the polymer component invariably shows a distribution of diffusion coefficients, a single diffusion coefficient is always observed for the droplets. The latter observation shows that there is a rapid (on the experimental time scale, i.e., 100 ms) exchange of water and AOT between free droplets and the various aggregates. Even when the global number of side chains per droplet is larger than one, the fraction of free droplets remains quite high, presumably resulting from the entropy loss associated with the binding of the droplets to the aggregates. The system adjusts to a high side chain/droplet ratio by the insertion of more than one side chain per bound droplet (cf. Figure 14). Owing to the considerable fraction of free droplets (never less than ∼ 30% under the conditions of this study), the droplet diffusion is always much faster than the polymer diffusion. Thus, the amphiphilic polymer is only modestly efficient at slowing down the droplet translation; it cannot “immobilize” the droplets of the microemulsion. The apparent hydrodynamic radii of the polymer-droplet aggregates vary considerably with the system composition. At low polymer concentrations, the experiments indicate individually dispersed polymer molecules, dressed with bound droplets. There is a marked growth in the aggregate size, especially for large microemulsion droplets, when the concentration of the graft copolymer is increased at constant droplet concentration (cf. Figure 14). The wide distribution of aggregate diffusion coefficients indicates that the aggregates are polydisperse, but they seem to be of finite size, except possibly at quite high polymer concentrations (above the overlap concentration of the nonmodified parent polymer), where a very slowly diffusing polymer component appears. The high free droplet concentration implies that the free energy gain associated with polymer-droplet aggregation does not grossly outweigh the loss in translational entropy of the bound droplets. This has implications for the solubility of the graft copolymer in the microemulsions, and probably explains why a precipitation eventually occurs when a single-phase mixture is diluted with oil at a constant polymer/droplet ratio. Acknowledgment. Helpful and stimulating discussions with Ulf Olsson and Per Hansson are gratefully acknowledged. We thank Bjo¨rn Håkansson for help with NMR measurements and for valuable discussions concerning the results. This work was supported by a grant from the Centre for Amphiphilic Polymers from Renewable Resources at Lund University (CAP). The rheometer and the NMR spectrometer were funded by grants from Nils and Dorthi Troe¨dsson’s Research Foundation, and from the Swedish Council for Planning and Coordination of Research, respectively. References and Notes (1) Piculell, L.; Lindman, B.; Karlstro¨m, G. Phase Behavior of PolymerSurfactant Systems. In Polymer-Surfactant Systems; Kwak, J. C. T., Ed.; Marcel Dekker: New York, 1998; pp 65-141.

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Effects of an Amphiphilic Graft Copolymer on an Oil-Continuous

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