J. Phys. Chem. B 2004, 108, 5443-5452
5443
Investigation of the Segregative Phase Separation Induced by Addition of Polystyrene to AOT Oil-Continuous Microemulsions Iseult Lynch,* Sophie Cornen, and Lennart Piculell Physical Chemistry 1, Centre for Chemistry and Chemical Engineering, Lunds UniVersity, P.O. Box 124, 22100 Lund, Sweden ReceiVed: February 11, 2004; In Final Form: February 26, 2004
The effect of different molecular weight polystyrenes (PS) on the phase behavior of sodium 1,4-bis(2-ethylhexyl) sulfosuccinate (AOT)/water/cyclohexane oil-continuous microemulsions was investigated. The surfactantcovered water droplets were treated as a pseudocomponent in the mixture, and ternary polymer/droplet/oil phase diagrams were established as a function of microemulsion droplet radius (2.7 or 3.8 nm), PS molecular weight (18 700, 45 730, and 700 000), and temperature. The different polymer radii of gyration (Rg) and droplet radii (Rd) resulted in a broad range of size ratios (Rg/Rd ) q) being accessible: 0.9 e q e 8.9. The aims of this work were to study polymer-particle segregation in this well-defined system, where both polymer size, particle size, and hence size ratio could be controlled and where polymer-solvent interactions could be varied across the θ temperature, and to compare the fluid-fluid binodal phase diagrams with those predicted theoretically. It turns out that the polystyrene chains in AOT oil-continuous microemulsions behave almost as ideal chains, over all q values and temperatures investigated.
Introduction Segregation is a common phenomenon in mixed solutions of two macromolecular species. The translational entropy of mixing is weak for such mixtures of macromolecular species, and the segregation has two possible driving forces: preferential interactions (enthalpy) or depletion (entropy). In a totally symmetric system composed of two macromolecular solutes, which have equal interactions with the solvent, equal size, and flexibility, segregation can only be driven by unfavorable shortrange macromolecule interactions between the two different macromolecular species.1-3 Thus, in the case of a mixed solution of two flexible polymers, which is treated by the Flory-Huggins (FH) theory, segregation is totally determined by the polymerpolymer χ parameter, which is purely enthalpic (neglecting entropy of solvation).1-3 The phase behavior of asymmetric systems is an active area of research, with much work focusing on the case of large colloids (spheres) and short polymers (the so-called “colloidal limit”). Most studies on nonadsorbing polymer-particle mixtures focus on the depletion interaction.4-8,11 This is a result of the polymers being excluded from the space between two colloids, which leads to an unbalanced osmotic pressure, and an attractive force between the colloids. In this case, the phase separation is entropy driven. Thus, in the two aforementioned cases (two flexible polymers or large colloids and short polymers), the same phenomenon (segregative phase separation) has two entirely different driving forces. More recently, interest in the other asymmetric extreme, small colloids with long polymers, has increased due to its relevance to protein crystallization, giving this limit its title of the “proteinlimit”. Although it is less clear how to treat depletion in the protein limit, where the particles can penetrate into the polymer coils, the fundamental idea remains valid that the perturbation * To whom correspondence may be addressed. E-mail: Iseult.Lynch@ fkem1.lu.se.
of the polymer coils by the particles can be reduced and the polymer conformational entropy enhanced by clustering of the colloid particles.9 This point has been discussed by Fuchs et al. in their recent review of depletion effects9 and by Sear, who recently derived a FH-type theory for the case of mixtures of hard spheres and larger polymers and suggested that the phase separation in such systems should be equivalent to that of a long polymer and a poor solvent.10 The phenomenon of segregative phase separation in mixed polymer-particle solutions is currently of great theoretical interest. There are two main issues being investigated theoretically: (1) variation of the polymer solvency (taking into account “excluded-volume” effects) and (2) variation of the size ratio, q (the radius of gyration of the polymer divided by the radius of the colloid, Rg/Rc), especially to values of q > 1, corresponding to the “protein” limit. Many advances have been made in recent years addressing one or both of these points. Gast et al. developed a hard-sphere perturbation theory on the basis of the AOV model (Asakura and Oosawa model4,5 with modification by Vrij11 to consider the polymers as penetrable hard spheres) which predicts, among other things, fluid-fluid separation for q g 0.3.12 By use of a free volume theory approach, Lekkerkerker et al. were able to take into account polymer partitioning between the colloid-rich and colloid-poor phases, leading to more realistic descriptions of the phase diagrams,13 but this still only applies to θ solvent conditions and to the colloidal limit, where q < 1. The free-volume theory has been further extended to include polymer-polymer interactions (excluded-volume effects).14 Specifically addressing the issue of high q values, PRISM (polymer reference interaction site model) theory,15 a microscopic liquid-state description of structure, thermodynamics, and phase separation, which includes multiple effects not in the classical approaches, was developed to account for more realistic mixtures and is potentially applicable over all size ratio ranges. Actually, PRISM was also shown to be applicable to both athermal and ideal solvent conditions.16 A Gaussian core model was developed by Louis
10.1021/jp0493834 CCC: $27.50 © 2004 American Chemical Society Published on Web 04/02/2004
5444 J. Phys. Chem. B, Vol. 108, No. 17, 2004 et al., where the particles interact via a penetrable repulsive Gaussian potential.17 Phase diagrams have been simulated on a mixture of colloidal spheres and Gaussian core spheres in the colloidal limit18 and using excluded volume chains and hard spheres in the protein limit.19 Both of these simulations gave results in terms of binodal curves, and thus direct comparisons can be made between the predicted phase diagrams and the experimental data determined here. The general trend in all these theories is that the miscibility increases as the size ratio, q, increases (when the polymer concentration is described as the reduced concentration, c/c*), especially in comparison to the results of predictions for ideal polymers and colloidal spheres. Recently, the depletion thickness for the intermediate case of arbitrary solvency was considered.20 Thus the challenge facing experimentalists is to provide experimental data that address these two points. In this work, we introduce a versatile model polymer-particle system composed of polystyrene (PS) and a water-in-oil microemulsion composed of the surfactant AOT (sodium 1,4-bis(2-ethylhexyl) sulfosuccinate), water, and cyclohexane. The versatility of the system lies is the fact that the droplet (particle) size can be easily controlled by the composition term w0 ) [H2O]/[AOT], and well-fractionated PS samples are available, meaning that a range of polymer-particle size ratios, q, can be obtained. Additional advantages to the chosen system are that the phase behavior of the microemulsion is well studied and understood,21,22 the droplets are nearly monodisperse, the polymer is as close as possible to a “model” polymer, it is easy to go through the θ temperature for the polymer, and the polymer/solvent mixtures are also well studied.23,24 Moreover, we can access the interesting region where the polymer/particle size ratio, q, goes from below to above unity. Thus, by use of this model system, we have provided valuable data for future analyses. Microemulsions have been used previously as colloidal particles in the study of the phase behavior of mixtures of colloidal particles and polymers, for example, by Xia et al.,25 who determined the cloud-point curves experimentally and using an attractive interaction potential, which included both polymer-induced depletion and a square-well attraction between the microemulsion droplets. The effect of adding different molecular weight PS to AOT oil-continuous microemulsions with two different molar ratios, w0 ) 10 and w0 ) 17 (corresponding to droplet radii of 2.7 and 3.8 nm, respectively) was investigated. In the determination of the phase diagrams, the microemulsion droplet (at constant size) is treated as a pseudocomponent in the mixture, an approach first used by Xia et al.25 and later by Holmberg et al.26 Ternary polymer/droplet/oil phase diagrams were established at two different droplet sizes (i.e., constant w0 values), three polymer molecular weights (MW), and various temperatures. The experimental results are compared to the binodal curves predicted using the Gaussian core model18,19 and using the free-volume theory for hard spheres and excluded volume chains of Aarts et al.14 Experimental Section Materials. AOT (Sigma, >99% purity) was dried by heating at 50 °C under vacuum. The water loss was estimated to be 1.0 wt %. The hygroscopic AOT was stored in a desiccator and used without further purification. Cyclohexane (Merck) and D12cyclohexane (99.5 atom % D, Dr. Glaser, AG Basel) were used as received. Millipore water or D2-water (99.8 atom % D, Dr. Glaser, AG Basel) was used in the microemulsions. Polystyrenes of different molecular weights from Fluka (MW ) 18 700,
Lynch et al. polydispersity ) 1.07) and from Sigma-Aldrich (MW ) 45 730, polydispersity ) 1.05 and MW ) 700 000, polydispersity ) 1.03) were used as received. Determination of the Droplet Size by NMR Self-Diffusion. The self-diffusion coefficient of AOT was measured on a 200MHz Bruker spectrometer equipped with a field gradient probe. The probe has 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.27 In a typical experiment, the gradient strength, g, was increased in 19 steps of 0.5 T‚m-1. The gradient pulse duration, d, and the experimental observation time, D, were kept constant at values between 0.5-1 ms and 20-50 ms, respectively. Samples were placed in 3-mm NMR tubes which were flame sealed to prevent solvent evaporation. Two series of samples were prepared, corresponding to two different droplet sizes: w0 ) 10 and 17. Deuterated solvents were used in order to get a strong and well-resolved proton signal for AOT. The experiment was performed at three different droplet volume fractions, φc, in the range 5-15%. Measurements were performed at 25 and 40 °C for the w0 ) 10 samples and at 25 °C for the w0 ) 17 samples. All samples were clear (i.e., monophasic) at both temperatures. The diffusion coefficient of AOT was calculated as an average of the peaks at 0.9, 1.3, and 3.1 ppm. Single exponential decays were obtained for all samples when the signal intensity I(k) was plotted against k in accordance to ln(I/Io) ) e-kD, where k ) (γgd)2(D - d/3)D, γ is the magnetogyric ratio of the nuclei being observed (γ ) 2 675 × 108 s-1‚T-1 for the proton), g is the magnitude of the gradient pulse, d the duration of the gradient pulse, and D the time between the leading edges of the gradient pulses. The diffusion coefficient, D, was obtained by regressing ln(I/Io) ) e-kD onto the experimental data. Do was then obtained from D using the linear expression D ) Do(1 - kaφc) where φc was in the range 5-15%. Determination of Polystyrene Radius of Gyration. Static light scattering (SLS) was used to characterize Rg of the PS of MW 700 000 at 40 °C (lower temperatures and MWs were below the resolution of the equipment). Four samples of different concentration (0.01, 0.02, 0.03, and 0.05 wt %) were prepared and stirred at 40 °C until homogeneous. Samples were filtered through 0.45 µm size pores to remove dust particles and transferred into cylindrical tubes with Teflon plugs. Measurements were performed with an ALV-5000 photometer equipped with an Nd:YAG laser (model 532-400 DPSS, λ ) 532 nm), a digital autocorrelator, and a variable-angle detection system.28 SLS measurements were performed at 12 different angles (40 e ϑ e 150°) with toluene as the scattering standard (Rtoluene(ϑ) ) 2.84 × 10-5), and 3 individual measurements of 10 s each were averaged for each angle, thus yielding the intensity 〈I(q)〉. Determination of the Phase Diagrams. Cloud Point CurVes. For the phase-diagram studies, stock solutions of microemulsion and polymer were prepared separately in a first step. The microemulsions were prepared at two different droplet sizes (w0 ) 10 and 17) by mixing AOT, water, and cyclohexane for 24 h at room temperature. The microemulsions were monophasic in the temperature range of interest up to ∼98 wt % cyclohexane for w0 ) 10 and up to ∼95 wt % cyclohexane for w0 ) 17. PS was dissolved in cyclohexane above PS 40 °C to yield clear homogeneous solutions. For a given droplet size and PS MW, a series of samples of increasing PS to droplet ratio was prepared in the two-phase region (turbid samples) by mixing suitable amounts of the two stock solutions in glass tubes. The stock solutions were clear at the studied temperature before being mixed together. After homogenization by vigorous stirring above
Segregative Phase Separation 40 °C, the samples were kept in a thermostat with a temperature stability of (0.1 °C and diluted with small portions of cyclohexane until they reached the one-phase region. A sample was regarded as monophasic when it was completely transparent visually (without stirring). Tie-lines. Polymer-free stock microemulsions were prepared with d12-cyclohexane and D2O and stirred until transparent and homogeneous at room temperature. The desired amount of PS was added, and the mixture was diluted with d12-cyclohexane to the desired final composition. Samples were stirred above 40 °C, transferred into 5-mm NMR tubes with a syringe, flame sealed to prevent solvent evaporation, and shaken above 40 °C (in the one-phase region) to ensure thorough mixing. Phase separation occurred upon standing at the required temperature (controlled by a thermostat with a temperature stability of (0.1 °C). Once phase separation was complete, i.e., both phases were clear, the NMR tube was cut and the top phase was collected with a syringe and transferred into another NMR tube. d12Cyclohexane was added to increase the sample volume when needed. Volumes and weights of the respective phases were accurately noted down at each step. The tubes were flame sealed again, and NMR measurements were performed at a temperature slightly above 40 °C (to ensure that samples were in the onephase region). The composition of the phases was determined from proton and deuterium spectra, as follows. The proton spectra yielded the weight ratio of PS to AOT by integration of the peaks at 6.5-8.5 ppm for PS (benzene ring, 5 protons) and at 3.0-5.0 ppm for AOT (22 protons). The amount of water is related to the amount of AOT through the molar ratio w0, so the weight ratio of PS to droplets could be calculated to yield a first “construction line”. The deuterium spectra yielded the weight ratio of cyclohexane to water by integration of the peaks at -15 to -10 ppm for the cyclohexane (12 deuterons) and at -10 to -5 ppm for water (2 deuterons). Again the weight ratio was related to the ratio of cyclohexane to droplets as explained above. This yielded a second construction line. The intercept of the two construction lines gives the composition of the phase. However, the relative amount of water in most of the polymerrich phases turned out to fall below the resolution of the equipment. Thus the second construction line could not be drawn in such cases, and instead an upper limit to the droplet concentration was determined from the detection limit. Because of difficulties in separating the phases and limits in the resolution, exact tie lines were not possible to determine in every case, although the general direction of the tie lines could be determined. A strong isotope effect on the phase behavior was not considered likely, as deuterium isotope effects on surfactant systems are typically small and have been mainly reported for surfactants containing O-H bonds,29 which AOT does not. Results By use of NMR self-diffusion, the sizes of the droplets at w0 ) 10 and w0 ) 17 were determined. The hydrodynamic radius of the droplets, Rc, was obtained from D0 via the StokesEinstein equation (using the viscosity of d12-cyclohexane) on the basis of two assumptions: that the droplets are spherical30 and that the diffusion coefficient of AOT may be regarded as the effective droplet diffusion coefficient.31 It was not possible to determine the droplet hydrodynamic radii at 40 °C due to convection in the samples. The calculated and experimental droplet radii are compared in Table 1. The radii of gyration Rg for the different PS MWs were calculated using the equation of Sun et al.33 The experimental value determined by Sun et al. for the Rg of PS of MW 2.6 ×
J. Phys. Chem. B, Vol. 108, No. 17, 2004 5445 TABLE 1: Calculated and Experimental Droplet Radii (Rc) T ) 25 °C results
w0 ) 10
w0 ) 17
Rc (exp) Rc (calc)a
3.0 2.7
3.6 3.8
a Calculated using rwatercore (obtained from w0 according to the method of Hilfiker et al.)32 + length of AOT tail (8 Å).
TABLE 2: Values of the Radius of Gyration (Rg) in nm for the Different PS MWs MW T
18 700
24°C 30°C 40°C
3.6 3.7
45 730
700 000
5.7 5.9
20.3 23.9
TABLE 3: Summary of the Different Size Ratios q Studied polymer MW 18 700
45 730
700 000
T
24 °C
40 °C
30 °C
40 °C
30 °C
40 °C
w0 ) 10 w0 ) 17
1.3 0.9
1.4 1.0
2.1
2.2
7.5
8.9
107 (under θ conditions) served as a reference to determine the coefficient of proportionality, A, of the equation Rg ) A(MW)0.5. The Rg of the different MW PS could then be calculated at the θ temperature, and from this at any temperature using the R parameter in the equation
( )
( ) ( ) ( )
14 Rmin 3 θ 2 Rmin 3 1 Rmin 6 (1 - R2) + + )σ -1 3N R 3 R 2 R T
where N is the number of segments of the chain, R ) 〈R2g〉1/2/ 2 1/2 〈Rgθ 〉 is the expansion factor and Rgθ the radius of gyration under θ conditions, Rmin is the expansion factor for the totally collapsed state, σ ) 1 - ∆S/kB, T is the temperature, θ is the θ temperature, and kB is the Boltzmann constant. From their experimental study, Sun et al. found that the following parameters gave a satisfactory fit: N ) 9.6 × 10-4(MW), Rmin ) 2.41(MW)-1/6, σ ) 4, and θ ) 35.4 °C. Table 2 summarizes the Rg results for the three PS MWs used in this study. Critical temperatures were calculated for the three PS MWs using Flory’s equation.1 The values were 12.1 °C for MW 18 700, 20.2 °C for MW 45 730, and 31.4 °C for MW 700 000. Experimentally, however, the critical temperature was below 30 °C for the latter sample, as samples were clear at this temperature in the concentration range (2-10 wt % PS) studied. The Rg of the PS 700 000 was also determined experimentally by static light scattering. The value of Rg was taken as that at infinite dilution, i.e., at the intercept with the y axis of a plot of Rg vs the polymer concentration, and was 25 nm, in good agreement with the theoretical value of 23.9 nm at 40 °C. Thus the theoretical values of Rg were used as estimates of Rg of the lower MW PS samples, which could not be studied by SLS, due to their molecular weights being below the limit of resolution of the instrument. The range of q values accessible in the investigated systems are presented in Table 3. The values of both Rc and Rg used were those calculated. The majority of the mixtures are clearly in the protein limit, with values of q well above 1, and there are also some mixtures with values around 1 and even slightly below 1, giving a good span of size asymmetry. The empty cells in the table correspond to cases not studied.
5446 J. Phys. Chem. B, Vol. 108, No. 17, 2004
Figure 1. Phase diagram for PS of MW 18 700 and microemulsion with w0 ) 1 0.
Figure 2. Phase diagram for PS of MW 18 700 and microemulsion with w0 ) 17.
Phase-Separation Kinetics. As all of the samples were prepared in the two-phase region, macroscopic phase separation into two distinct phases was always observed upon standing. The macroscopic phase separation was reversible and reproducible for all samples. When a sample was shaken, a homogeneously turbid solution was obtained. Upon standing, the onset of the phase separation first manifested itself as an increase in the turbidity, followed by a decrease in the turbidity to yield translucent grains in the solution. The phase separation into a droplet-rich amorphous phase and a polymer-rich amorphous phase occurred over time scales varying from hours to days, depending on the sample composition. The interface between the two phases was sharp and fluid, indicating a fluid-fluid phase separation. Two effects seemed to govern the kinetics of the phase separation: the concentration and the MW of the PS, both of which affected the viscosity of the system. The interface between the two phases was always quick to form, but the more viscous polymer-rich phase remained translucent for several days for the highest MW PS. For the highest concentration of the lowest MW PS (18 700) the phase separation was completed within a couple of hours, as was also reported for Xanthan-colloid mixtures by Koenderink et al., who found that phase separation was fastest for the highest polymer and colloid concentrations.8
Lynch et al.
Figure 3. Phase diagram of PS of MW 45 730 and microemulsion with w0 ) 10.
Figure 4. Phase diagram for PS of MW 700 000 and microemulsion with w0 ) 10.
Phase Diagrams. Figures 1-4 show the phase diagrams (cloud-point curves) for the four different PS MW and dropletsize combinations studied (PS 18 700 w0 ) 10, PS 18 700 w0 ) 17, PS 45 730 w0 ) 10, and PS 700 000 w0 ) 10). All concentrations are in weight percentages (wt %). All mixtures displayed a segregative phase separation; the samples separated into two phases, with each phase being enriched in one of the cosolutes. Above the binodals, the mixtures were completely clear and monophasic, whereas below the binodals, samples were turbid and eventually phase separated into two clear phases. The macroscopic phase separation occurred over varying time scales for the different samples, as described above. Each of Figures 1-4 shows the effect of temperature on the phase behavior of a given polymer-particle combination. In each case, the system showed a decrease of the two-phase area (increased miscibility) when the temperature was increased. The magnitude of the decrease of the two-phase area was small, since even at the lower temperatures the PS fractions used here were completely miscible with cyclohexane due to their low molecular weights, but it increased with increasing PS MW. The effect of the droplet size was studied for the lowest MW (18 700) only and is shown by comparing Figures 1 and 2. The
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Figure 5. Plots of the tie lines determined for PS of MW 18 700 with (a) w0 ) 10 and (b) w0 ) 17.
Figure 6. Tie line at 40 °C for PS of MW 700 000 in microemulsion with w0 ) 10.
droplet size appeared to have almost no effect on the phase behavior of the studied mixtures. The phase boundary at 40 °C was shifted to slightly higher cyclohexane concentrations for the biggest droplet size (w0 ) 17, Rd ) 3.8) (indicating decreased miscibility with increasing droplet size), whereas the boundary at 24 °C did not shift at all. The phase diagram of the highest MW PS (700 000) with the biggest droplet size (w0 ) 17) could not be investigated due to the fact that the microemulsion itself proved to be turbid at such high dilutions as were required for polymer-droplet miscibility. The effect of polymer MW on the phase behavior can be seen by comparing Figures 1, 3, and 4, and clearly the two-phase area significantly expands as the polystyrene chain length increases. Tie Lines. Few tie lines were obtained due to difficulties in resolving the NMR data. However the direction of the tie line could be determined for all systems and are shown in Figures 5 and 6. The directions of the tie lies show that the phase separation is clearly segregative. Discussion Nature of the Phase Separation. All mixtures displayed a very uneven partitioning of the solvent, as indicated by the steep slope of the tie lines. The tie-line determination was not accurate enough to draw any conclusions relating to the effect of the different parameters, except the effect of the polymer MW, and by comparison to work on polymers and nonionic surfactants,
the effect of droplet size, as discussed below. On the basis of the directions of the tie lines, the PS-induced phase separation of AOT oil-continuous microemulsions is clearly segregative. With the low MW PS samples, the droplet phase is more pure and contains only droplets with no polymer. The phase diagrams obtained show striking similarities to those of Piculell et al. for aqueous mixtures of polymers and nonionic surfactants.34 This and other studies on polymer/surfactant systems have shown that the segregative two-phase area increases with increasing polymer MW35,36 or with increasing size of the surfactant micelle.34-38 A strong partitioning of the solvent to the polymer-rich phase in a segregating mixture of spherical particles and polymer in a common solvent is expected and is in fact typically observed in aqueous polymer/surfactant and polymer/protein mixtures.34,39 This effect can be traced to the fact that the osmotic pressure of a flexible polymer solution is larger than that of a solution of compact particles, if the solutes have the same molar mass and the solutions are compared at the same mass concentration of solutes. The osmotic pressure of hard spheres derives solely from the translational entropy of the particles. By contrast, the osmotic pressure of a flexible polymer in a good solvent is dominated by an additional contribution, which is due to the internal degrees of freedom of the polymer molecule. This contribution corresponds to the molecular-weight-independent term in the Flory-Huggins entropy of mixing. Physically, this contribution is due to the increase in the number of allowed bond configurations of a flexible chain molecule in a dilute solution, as compared to the polymer melt. The tie lines for the mixtures containing the two PS samples with the lowest MW agree with the trends just described. Surprisingly, however, the slope of the tie-line for the highest PS MW is in the opposite direction. While a decrease in the osmotic pressure of the polymer-rich phase is expected as the molecular weight of the polymer increases, it is not obvious that this effect should be strong enough to shift the direction of the tie line. It is probable that the marginal quality of the solvent, the PS/cyclohexane system is close to θ conditions, is responsible for the comparatively low osmotic pressure. Size Effects: Increasing PS MW or Decreasing the Droplet Radius. From an examination of the data in Table 3, it is clear that there are three main ways to increase the q value: increase the PS molecular weight, decrease the droplet size, or increase the temperature (which increases the PS Rg). In this section, we focus on the first two ways to increase the
5448 J. Phys. Chem. B, Vol. 108, No. 17, 2004
Figure 7. Phase diagram for PS of MW 18 700, 45 730, and 70 0000 at 40 °C with w0 ) 10.
q value. The effect of increasing the PS MW is clear: the twophase area significantly expands as the polystyrene chain length increases, as can be seen by comparing the phase diagrams in Figures 1, 3, and 4. To further illustrate this point, the miscibility curves for the three different PS MWs are plotted on the same phase diagram at 40 °C and w0 ) 10 in Figure 7, where the two-phase region (immiscibility) can be clearly seen to increase with increasing PS MW. The experimental data observed in Figure 7 is easily understood: If the degree of polymerization of one of the components is increased at constant mass fraction, the number of particles decreases. Consequently, the translational contribution to the entropy of mixing, and the miscibility, decrease. Experimental studies on model athermal silica-polystyrenetoluene suspensions also showed a miscibility decrease with increased polymer molecular weight.6 Similarly, the miscibility should decrease with increasing droplet size. However, the droplet size appeared to have almost no effect on the phase behavior of the mixtures studied here. The phase boundary at 40 °C was shifted to slightly higher cyclohexane concentrations for the biggest droplet size (indicating decreased miscibility with increasing droplet size), whereas the boundary at 24 °C did not shift at all. These results are replotted in Figure 8, for clarity. It should be noted that the
Lynch et al. change in Rc at 40 °C is just 40%, which is not a very considerable change. For comparison, the change in Rg from the PS of MW 18 700 to that of PS of MW 45 700 is 60%, and the difference in the phase boundary there (Figure 7) is not much larger than that shown here (Figure 8) for the change in droplet size at 40 °C. Thus it would seem that the lack of change in the phase boundary observed here was a result of the small change in the droplet size on going from w0 ) 10 to w0 ) 17 (i.e., from 2.7 to 3.8 nm). An earlier onset of demixing with increasing colloidal particle size has been shown experimentally by de Hek et al.,40 although the colloidal particle radii in that work were significantly larger than ours (21 and 46 nm compared to our 2.7 and 3.8 nm droplets) and the relative size change was also significantly larger (2.2 compared to 1.4 in our case). Comparisons with Previous Investigations of Depletion. Existing depletion theories consider two distinct limits: the “ideal-chain” limit, where the repulsive forces due to the excluded volume are exactly balanced by preferential polymerpolymer or solvent-solvent interactions, or the “repulsivechain” limit, where all binary interactions are equal and thus the excluded-volume effect causes the polymer to adopt an expanded coil configuration. The ideal limit corresponds to the θ condition, where χ ) 0.5. Above the θ temperature, χ < 0.5 and the repulsive-chain limit corresponds to χ ) 0, i.e., an athermal solvent. From a theoretical point of view, one of the simplest systems to consider is hard spheres and flexible polymers under athermal solvent conditions, which is characterized solely by hard-core repulsive interactions between all the species. The theoretical advances using this type of system have recently been reviewed by Fuchs and Schweizer.9 The role of polymer-polymer interaction has been investigated theoretically by considering the “ideal” solvent case where the polymers are treated as noninteracting Gaussian random coils, as is the case with the recently developed PRISM model which has been applied to ideal solvent conditions.16 The phantom-sphere free-volume (PSFV) approach of Lekkerkerker et al. replaces the polymers by spheres with no internal (conformational) degrees of freedom that can pass freely through each other (“ideal”) but act as hard spheres of radius Rg when interacting with colloids.13 The PSFV theory predicts fluid-fluid spinodal (and binodal) boundaries to shift monotonically to smaller reduced polymer concentration, c/c* as q increases (indicating reduced miscibility). This trend
Figure 8. (a) Phase diagram for PS of MW 18 700 in microemulsions with w0 ) 10 and w0 ) 17 at 24.3 °C. (b) Phase diagram for PS of MW 18 700 in microemulsions with w0 ) 10 and w0 ) 17 at 40 °C.
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Figure 9. Data from Figures 1, 3, and 4 replotted to show fluid-fluid binodal curves. (a) PS of MW 18 700 (with q ) 1.3 and 1.4 at 30 and 40 °C respectively); (b) 43 730 (with q ) 2.1 and 2.2 at 30 and 40 °C respectively); and (c) 700 000 (with q ) 7.5 and 8.9 at 30 and 40 °C respectively) showing the effect of increasing temperature on the fluid-fluid phase separation. (O) T ) 30 °C; (0) T ) 40 °C. (d) For comparison, the phase diagram of Ramakrishnan et al. (redrawn with permission from Figure 2a in Ramakrishnan et al.)43 of silica particles of Rc ) 50 nm in cyclohexane (O) and toluene (0) in the presence of PS of MW 1.88 × 106. The Rg of the PS is larger in toluene (a good solvent) than in cyclohexane, leading to q values of 1.39 and 0.84, respectively.
is opposite to the trend observed for athermal solvent experiments.13 The phase separation behavior predicted by integral equation theory for ideal polymers is also quite different than the athermal case for all size asymmetries and particle volume fractions.16 For large polymers or small colloids under ideal solvent conditions, the suspension miscibility worsens with increasing size asymmetry, opposite to the case for athermal solvent behavior. Theories using the simplest hard-sphere approach and athermal solvent conditions for dilute and semidilute polymer concentrations involve only three fundamental dimensionless variables: (1) the colloid packing fraction, φc; (2) the size asymmetry, q; and (3) the polymer concentration reduced by its value at the dilute-semidilute crossover (where polymerpolymer interactions in a particle-free solution become important), c/c*. Theories such as the Gaussian core model of Bolhuis et al. and the free-volume theory of Aarts et al. use the effective volume fraction of polymer, defined as φp ) Fp4/3πR3g ≈ c/c*, where Fp is the number density of polymer molecules. Thus the polymer volume fraction can be higher than 1. Since we
are interested in comparing our experimental phase diagrams directly with the theoretical phase diagrams, it was necessary to recalculate the experimental phase diagrams from the conventional experimental units of wt % to the volume fraction units described above. The total volume was obtained as Vt ) Vcyclohexane + VPS + Vdroplets, where Vdroplets ) Vwater + VAOT with the approximation that the density of AOT is 1 g/cm3. The PS partial specific volume in cyclohexane was taken as 0.93 cm3/ g,41 and the density of cyclohexane was 0.779 g/ cm3.42 φp ) Fp4/3πR3g with Fp ) Np/Vliq, where Vliq ) Vtotal - Vdroplets, since the PS is considered to be only in the oil fraction. Finally, the volume fraction of droplets (colloids), φc ) Vdroplet/Vtotal. Effect of Temperature. As mentioned above, the third way to change the size ratio, q, is by increasing the temperature (increasing the solvent quality for the PS). For each polymer, the phase boundary was determined at different temperatures above and below the θ temperature in order to determine the effect of improving the solvent quality (changing from ideal to repulsive (excluded-volume) conditions) on the phase behavior. As shown in Figures 1-4, all systems showed a decrease of
5450 J. Phys. Chem. B, Vol. 108, No. 17, 2004
Figure 10. Comparison of experimental data at q ) 1 (PS of MW 18 700, w0 ) 17, T ) 40 °C) (O) with theoretical predictions by Tuinier45 from the free-volume theory for ideal chains + colloids at q ) 1 (0) and repulsive (excluded-volume) polymers at q ) 1 (4), as well as with theoretical predictions from Bolhuis et al.19 for ideal polymers and hard-sphere colloids at q ) 1.03 (+).
the two-phase area (increased miscibility) when the temperature was increased. The temperature effect was small, except for the PS of highest MW. An increase in temperature results in an improved solvent quality for the PS, changing from below to above the θ temperature. Thus the PS chains adopt a more extended conformation with a larger radius of gyration Rg at higher temperatures. The effect of temperature on the phase diagrams expressed in reduced polymer concentration can be seen in the recalculated phase diagrams in parts a-c of Figure 9. The binodals shift to higher-volume fractions with increasing temperature, indicating increased miscibility with increasing solvent quality. The
Lynch et al. influence of temperature on the binodals increases with increasing PS molecular weight, due to both the larger effect of temperature on an absolute scale (Figures 1-4) and the larger effect on the coil dimensions of the higher MW PS and thus on the reduced volume fraction, φp. Thus, for PS of 18 700 and 43 730, the relative change in Rg is only 1.04, whereas for the 700 000 PS, the relative change is 1.2 (see Table 3). For comparison, the results of Ramakrishnan et al. on the phasebehavior silica particles of radius 50 nm in the presence of PS of MW 1.88 × 106 in toluene and cyclohexane are shown in Figure 9d. Here the relative change in Rg is 1.65 on going from cyclohexane to toluene, and again the miscibility increases with increasing solvent quality. The data of Ramakrishnan et al. are qualitatively similar to our data, indicating good agreement between our experimental data and that of other experimental systems. Quantitative Comparisons with Depletion Models. As mentioned above, the two main areas of theoretical investigation of the depletion effect are the effect of solvent quality and extending the applicable range of the theories to include systems where q . 1. Since our experimental system enabled us to investigate both of these conditions, we now proceed to make direct comparisons between our experimental data and the predictions of some of the most recent theories. The first comparison we make is at low q values and at 40 °C, which is above the θ temperature of PS, to determine which theory (ideal or repulsive chains) gives the best description of the experimentally observed fluid-fluid binodal. The comparison is made in Figure 10 between PS of MW 18 700 at 40 °C in microemulsion with w0 ) 17 (Rg ) 3.8), which has q ) 1, and the theoretical predictions of Tuinier et al.,44 which were recalculated for q ) 1 in a personal communication from Tuinier,45 using both the free-volume theory for ideal chains with colloids (which was first published by Aarts et al.)14 and repulsive (excluded-volume) polymers with colloids, as well as with theoretical predictions from Bolhuis et al. for ideal polymers and hard-sphere colloids at q ) 1.03. The plot shows clearly that, even at 40 °C, the behavior of the PS chains is close to the ideal chain limit, as would be expected, since despite
Figure 11. (a) Data from Figure 7 replotted in terms of the volume fractions of PS and droplets. The data are the fluid-fluid binodals for the polymers of different MW in microemulsions with w0 ) 10 and T ) 40 °C. (O) PS of MW 18 700, corresponding to q ) 1.4; (0) PS of MW 43 730, corresponding to q ) 2.2; and (q) PS of MW 700 000 corresponding to q ) 8.9. (b) Data from Figure 1 in Bolhuis et al.19 reproduced with permission, showing fluid-fluid binodals for a mixture of ideal chains and hard-sphere colloids with different size ratio q. (O) simulation at q ) 1.03; (0) simulation at q ) 1.45; (q) simulation at q ) 2.05; (×) simulation at q ) 3.20. In both plots, solid lines are guides to the eye.
Segregative Phase Separation
Figure 12. Comparison of theory and experiment at high q values. (O) Experimental results at q ) 8.9 (PS of MW 700 000; w0 ) 10; T ) 40 °C). (0) Theoretical prediction at q ) 7.78 for repulsive chains, reproduced from Figure 2 in Bolhuis et al.19 Solid lines are a guide to the eye.
the temperature being above the θ temperature of PS in cyclohexane, χ ) 0.49, and thus much closer to the ideal limit than to the athermal limit. To address the effect of increasing the q value, the data from Figure 7 (increasing PS MW at w0 ) 10 and T ) 40 °C) is replotted as fluid-fluid binodal curves in Figure 11a. As can be seen from Table 3, increasing the PS MW results in q values ranging from 1.4 to 2.2 to 8.9. In Figure 11b, the simulation results of Bolhuis et al. for ideal polymers and Gaussian hard spheres in the range 1.03 < q < 3.20 are plotted for comparison. Qualitatively similar patterns can be seen in the two plots, particularly the crossover of the binodals for the PS MW 18 700 and 43 730 at low φc. Finally, a comparison is made between the theory of Bolhuis et al.19 for repulsive chains (at high q values) and the experimental data on PS in oil-continuous microemulsions at high q values, as shown in Figure 12. Bolhuis et al.19 found that for repulsive chains the phase separation occurs well into the semidilute region (the crossover from dilute to semidilute solution occurs at φp ≈1). However, we found experimentally that even at high q values (up to q ) 8.9) phase separation occurred in the dilute solution region, and in fact, the experimental fluid-fluid binodal curve is displaced by almost an order of magnitude from the predicted one (in terms of both φp and φc). Thus the behavior of PS in oil-continuous microemulsions did not resemble the behavior of repulsive (excluded volume) chains at high q values, as can be seen from Figure 12. In fact, at all q values, the behavior of the PS chains in microemulsions resembles that of ideal chains. Conclusions The phase behavior of PS in AOT/water/cyclohexane oilcontinuous microemulsions has been studied as a function of temperature, microemulsion droplet size, and PS MW over size ratios q ) Rg/Rd ranging from slightly below to far above unity (0.9 < q < 8.9). The miscibility of the mixtures was found to increase with increasing temperature (i.e., solvent quality) but to decrease with increasing PS MW. The effect of changing
J. Phys. Chem. B, Vol. 108, No. 17, 2004 5451 the microemulsion droplet size was very small, presumably due to the small size difference between the droplets. These trends agreed with the behavior of aqueous polymer and nonionic micellar systems.34 To make direct comparisons with theoretically predicted (or simulated) fluid-fluid binodals, the experimental data were replotted in terms of the volume fractions of polymer and droplets, φp and φc. Increasing the solvent quality, by increasing the temperature, resulted in increased miscibility, as observed by the shift of the fluid-fluid binodals to higher-volume fractions. Comparison of the experimental data at q ) 1 with ideal and repulsive chain calculations of Tuinier et al. showed that even at high temperature (40 °C, above the θ temperature of PS in cyclohexane) the behavior of the polystyrene chains was much closer to that of the ideal chains than that of repulsive chains. Comparison was also made with the simulations of Bolhuis et al. for ideal chains with increasing q, and qualitatively similar trends were observed experimentally; in particular, the predicted crossover of the binodals was observed experimentally. However, the predictions for high q values considering the polymers as repulsive chains were quantitatively different from the experimental results at high q, and again the PS chains appeared to behave more like ideal chains even at high q values. Thus, in summary, the PS/AOT oil-continuous microemulsion system in an elegant model system for the study of segregative phase behavior, offering the possibility to study the effect of both increasing q (by changing either the PS MW or the droplet radius) and of changing the solvent quality. From the experimental results, it is clear that PS chains in oil-continuous microemulsions behave more like ideal chains than repulsive chains, even at the higher temperatures studied, where the polymer is considered to be in a good solvent. The behavior at high q values is significantly different from that predicted theoretically based on repulsive chains, again suggesting that PS chains behave essentially as ideal chains in AOT oilcontinuous microemulsions, over all q values. Acknowledgment. This research has been supported by a Marie Curie Fellowship of the European Community program Improving Human Potential under contract number HPMF-CT2001-01239 (I.L.) and by a grant from the Swedish Research Council (L.P.). The authors thank the reviewers for very valuable comments and suggestions. References and Notes (1) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. (2) Sieglaff, C. L. J. Polym. Sci. 1959, 41, 319. (3) Bergfeldt, K.; Piculell, L.; Linse, P. J. Phys. Chem. 1996, 100, 3680. (4) Asakura, S.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255. (5) Asakura, S.; Oosawa, F. J. Polym. Sci. 1958, 33, 183. (6) Ramakrishnan, S.; Fuchs, M.; Schweizer, K. S.; Zukoski, C. F. Langmuir 2002, 18, 1082. (7) Tuinier, R.; Rieger, J.; de Kruif, C. G. AdV. Colloid Interface Sci. 2003, 103, 1. (8) Koenderink, G. H.; Aarts, D. G. A. L.; De Villeneuve, V. W. A.; Phillips, A. P.; Tuinier, R.; Lekkerkerker, H. N. W. Biomacromolecules 2003, 4, 129. (9) Fuchs, M.; Schweizer, K. S. J. Phys.: Condens. Matter 2002, 14, R239. (10) Sear, R. P. Phys. ReV. E 2002, 66, 051401. (11) Agterof, W. G. M.; Vanzomeren, J. A. J.; Vrij, A. Chem. Phys. Lett. 1976, 43, 363. (12) Gast, A. P.; Hall, C. K.; Russell, W. B. J. Colloid Interface Sci. 1986, 96, 251. (13) Lekkerkerker, H. N. W.; Poon, W. C.; Pusey, P. N.; Stroobants, A.; Warren, P. B. Europhys. Lett. 1992, 20, 559. (14) Aarts, D. G. A. L.; Tuinier, R.; Lekkerkerker, H. N. W. J. Phys.: Condens. Matter 2002, 14, 7551. (15) Chatterjee, A. P.; Schweizer, K. S. J. Chem. Phys. 1998, 109, 10464.
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