Bicontinuous Polymeric Microemulsions from Polydisperse Diblock

Dec 16, 2008 - Lithium Salt-Induced Microstructure and Ordering in Diblock Copolymer/Homopolymer Blends. Matthew T. Irwin , Robert J. Hickey , Shuyi X...
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J. Phys. Chem. B 2009, 113, 3726–3737

Bicontinuous Polymeric Microemulsions from Polydisperse Diblock Copolymers† Christopher J. Ellison, Adam J. Meuler, Jian Qin, Christopher M. Evans, Lynn M. Wolf, and Frank S. Bates* Department of Chemical Engineering and Materials Science, UniVersity of Minnesota, Minneapolis, Minnesota 55455 ReceiVed: August 16, 2008; ReVised Manuscript ReceiVed: October 14, 2008

Polymeric bicontinuous microemulsions are thermodynamically stable structures typically formed by ternary blends of immiscible A and B homopolymers and a macromolecular surfactant such as an AB diblock copolymer. Investigations of these bicontinuous morphologies have largely focused on model systems in which all components have narrow molecular weight distributions. Here we probe the effects of AB diblock polydispersity in ternary blends of polystyrene (PS), polyisoprene (PI), and poly(styrene-b-isoprene) (PS-PI). Three series of blends were prepared using the same PS and PI homopolymers; two of them contain nearly monodisperse components while the third includes a polydisperse PS-PI diblock. The PS and PI homopolymers and two of the PS-PI diblocks were prepared by anionic polymerization using sec-butyllithium and have narrow molecular weight distributions. The polydisperse PS-PI diblock was prepared by anionic polymerization using the functional organolithium 3-tert-butyldimethylsilyloxy-1-propyllithium; this diblock has a polydisperse PS block (Mw/Mn ) 1.57) and a nearly monodisperse PI block (Mw/Mn < 1.1). The phase behavior of the three series of blends was probed using a combination of dynamic mechanical spectroscopy, small-angle X-ray scattering, and cloud point measurements, and a bicontinuous microemulsion channel was identified in each system. These results prove that monodisperse components are not required to form bicontinuous microemulsions and highlight the utility of polydispersity as a tool to tune polymer blend phase behavior. The random-phase approximation, originally advanced by de Gennes, and self-consistent field theory are used to provide a theoretical supplement to the experimental work. These theories are able to predict the directions of the polydispersity-driven shifts in domain spacing, order-disorder transition temperatures, and the location of the microemulsion channel. Self-consistent field theory is also used in conjunction with the experimental data from a series of nearly monodisperse blends to probe the variations of χ with temperature. A single linear relation of the form χ ) R/T + β does not describe χ at all blend compositions. Rather, two separate relations describe χ as a function of temperature; one is obtained from data on the diblock-rich side of the bicontinuous microemulsion channel while the other is obtained from data on the homopolymer-rich side of the channel. The blend morphology, rather than the composition (homopolymer fraction), apparently dictates whether the system is in the “diblock χ” or “homopolymer χ” regime. These results reinforce the notion that a true understanding of χ still eludes the polymer science community. Introduction If oil, water, and a suitable surfactant are combined in appropriate proportions, a bicontinuous microemulsion (BµE) can be formed.1-6 The BµE structure is thermodynamically stable and can be described topologically as interweaving continuous domains of oil and water. These continuous domains traverse the entire sample and are typically 10-100 nanometers in size with the oil and water channels separated by a selfassembled monolayer of surfactant. On the micron length scale, the bicontinuous structure lacks translational order and has a spongelike appearance. The BµE structure differs from the more common micellar or droplet microemulsions that contain swollen micelles of oil or water dispersed in a continuous domain of the opposing component. More recently, polymeric analogs to the small molecule BµEs described above have been discovered and studied.7-40 The polymeric BµE is also a ternary system but does not contain oil and water. Rather, it is comprised of two thermodynamically * To whom correspondence should be addressed. E-mail: bates@ cems.umn.edu. † Part of the “PGG (Pierre-Gilles de Gennes) Memorial Issue”.

incompatible homopolymers (A and B) and a complementary macromolecular surfactant such as an AB diblock copolymer. It is important to note that the polymeric BµE differs significantly from the polymer mixtures termed cocontinuous blends. Cocontinuous polymer blends are kinetically trapped structures made by melt processing/mixing a blend of several different homopolymers using a combination of high intensity shear and extensional flow.41 Since the processing-induced structure is not thermodynamically stable, the cocontinuity is often destroyed following subsequent high temperature annealing or melt processing. Destruction of domain continuity is common for multiply continuous polymeric structures prepared by locking in a kinetically trapped state through solvent casting, reactioninduced phase separation, or other processing strategies.42-47 This feature limits the utility of these kinetically trapped structures in materials applications.41 In addition to differences in thermodynamic stability, BµEs and cocontinuous blends often have differing domain sizes; the domains in cocontinuous blends vary from many tens of nanometers48 to several hundred microns49 while BµE domains almost exclusively contain a 10-100 nanometer periodicity.16

10.1021/jp807343b CCC: $40.75  2009 American Chemical Society Published on Web 12/16/2008

Bicontinuous Polymeric Microemulsions

Figure 1. Schematic of the ternary phase portrait at equal volume fractions of A and B homopolymer (ΦhA ) ΦhB). The abscissa is the overall volume fraction of homopolymer (Φh ) ΦhA + ΦhB).

BµE phases have been reported in many different A/B/AB ternary systems, including polystyrene (PS)/polyisoprene (PI),13,16,17,23 polystyrene/polybutadiene,17 poly(ethylene-alt-propylene)/poly(butylene oxide),24 poly(ethyl ethylene)/poly(dimethyl siloxane),10,12,15,20,22 poly(ethylene-alt-propylene)/poly(ethylene oxide),10,11 polyethylene/poly(ethylene-alt-propylene),8,9,12 polyethylene/poly(ethylene oxide)12 and polyethylene/polypropylene.25,26 A few additional studies18,27-30,34,40 have focused on A/B/AC blends. A number of theoretical reports concerning polymeric bicontinuous microemulsions have also contributed significantly to the understanding of the physics and phase behavior of these ternary polymeric materials.7,14,19,21,31-33,35-40 At constant pressure, the phase space of an A/B/AB ternary blend system can be visualized as a ternary prism with the blend composition plane at the base and temperature as the vertical axis. As in previous work,9,12,23,24 here we have chosen to focus on a vertical slice of the prism where the volume fractions of the two homopolymers PS and PI are equal, but the block copolymer content and temperature are varied. The basic layout of this phase portrait is shown in Figure 1. At the leftmost portion of the phase diagram (Φh ) 0) is pure diblock that adopts a lamellar microstructure at low temperatures; this morphology is expected50 for the roughly symmetric (i.e., equal volume fractions of PI and PS) poly(styreneb-isoprene) (PS-PI) diblock copolymers employed in this study. When the diblock is heated above the order-disorder transition temperature (TODT), the A and B blocks become miscible and form a disordered homogeneous melt. The lamellar microstructure persists (below TODT) as homopolymer is added to the pure diblock (Φh > 0) provided that the ratio (R) of the degree of polymerization of the homopolymer (Nh) to that of the entire diblock copolymer (Ncp) is less than ∼1 (R ≡ Nh/Ncp < 1).51-55 (In this manuscript, the degrees of polymerization of all polymers are calculated with respect to a reference volume of 118 Å3.) If R > 1, the homopolymer will not swell the lamellae but will be expelled from between the monolayers, leading to macrophase separation into homopolymer-rich and diblock-rich domains. There are two primary free energy contributions that determine whether the homopolymer swells the diblock lamellae or is expelled into homopolymer-rich domains.51,54,56 The translational entropy of the system increases when homopolymers are not localized in homopolymer-rich grains, but are free to penetrate into and swell the lamellar domains of the diblock mesostructure.14,54 The system’s conformational entropy, on the other hand, decreases if homopolymer chains are confined between lamellar domains where they cannot maintain relaxed

J. Phys. Chem. B, Vol. 113, No. 12, 2009 3727 Gaussian configurations, but are forced to stretch to adopt conformations that allow them to fit within the lamellae.14,54 When R > 1, the homopolymers are large relative to the lamellar domains and the chains must significantly alter their conformations to fit within the lamellae. As a result, the conformational entropic free energy cost associated with penetrating the lamellae is too high and the homopolymers are expelled into homopolymer-rich grains. From the standpoint of the diblock monolayers, the introduction of long homopolymer chains into the system results in an apparent attraction of adjacent monolayers.54 When R < 1, the homopolymer chains are relatively short and do not have to adjust their conformations as much to fit within the lamellar domains, leaving the homopolymer conformational entropy relatively unaltered. As a result, the translational entropic free energy contribution to the system free energy dominates and the homopolymers penetrate and swell the lamellar microdomains. Because of the translational entropy gains of the added short homopolymers, the adjacent diblock copolymer monolayers experience an apparent net repulsion.54 On the basis of the entropic arguments presented above, macrophase separation could be prevented by selecting R such that the diblock copolymer is significantly longer than the homopolymers (R f 0). This selection of R would seemingly serve to maintain repulsive monolayers and promote the formation of a stable BµE. However, this argument overlooks the critical requirement of a highly flexible monolayer. Monolayers comprised of low molecular weight (MW) diblock copolymers possess more flexibility, as measured by the bending modulus, than those containing high MW diblocks.5,19,57 Thompson and Matsen54 described the details of the important compromise driving the choice of R; the entropic effects discussed above suggest R approaching zero while monolayer modulus/flexibility considerations suggest R approaching one. By using self-consistent field theory (SCFT), Thompson and Matsen54 predicted that R e 0.8 is required for the monolayers to remain repulsive and maintain the flexibility required to form a stable BµE.58 However, an R slightly less than 0.8 was found to be optimal for both maximizing homopolymer molecular weight (to provide mechanically tough materials) and achieving reasonable domain sizes.57 While most experimental studies have identified polymeric BµEs at much lower values of R (R < 0.2), Messe et al.13 recently pushed toward the R ) 0.8 threshold and reported BµEs formed at R ) 0.74 and R ) 0.38. Besides the appropriate choice of R, de Gennes and Taupin5 and Strey4 pointed out two other criteria must be met to form a stable BµE: interfacial tension must be ultralow and the spontaneous curvature of the interface must be near-zero. These features are required to accommodate the large interfacial area of a BµE and inhibit the block copolymer from disengaging from the monolayers to form micelles.19 Following a careful choice of R and the addition of a sufficient amount of homopolymer, the blend approaches the BµE channel, as shown in Figure 1. The location of the BµE channel in the phase portrait can be determined both theoretically and experimentally. From theory, the location of the channel is commensurate with the Lifshitz point. For R < 1, the location of the Lifshitz point is readily predicted from mean-field theory. The abscissa coordinate is given by ΦL ) 1/(1 + 2R2) while the ordinate position is given by (χNcp)L ) 2 (1 + 2R2)/R, where χ is the Flory-Huggins segment-segment interaction parameter between components A and B (χ is inversely proportional to temperature and its magnitude in this manuscript is provided with respect to a reference volume of 118 Å3).7,33 Physically, it has been hypothesized9 that the position of the left edge of the

3728 J. Phys. Chem. B, Vol. 113, No. 12, 2009 BµE channel in Figure 1 is related to the composition at which the monolayer flexibility is sufficiently high to allow thermal fluctuations to stabilize the BµE and render it an equilibrium structure (i.e., monolayer bending modulus e kBT 5,14,57). An increasingly defective lamellar microstructure has been observed by transmission electron microscopy9,20 and by modeling38,39 for blend compositions near the left edge of the channel, supporting this hypothesis. As more homopolymer is added to the blend, the interfacial coverage of the diblock copolymer decreases until it is no longer sufficient to sustain the high surface area of the BµE structure, leading to macrophase separation. The right edge of the BµE channel corresponds to the incidence of macrophase separation. The overall BµE channel width has typically been observed experimentally to be several percent wide in terms of the homopolymer volume fraction.11,12,22,24,48,59 Unfortunately, there has been very little research focused on BµEs derived from polymers that have unique architectures (e.g., miktoarm star or graft copolymers) or broad MW distributions. Most research has involved homopolymers and diblock copolymers synthesized by anionic polymerization that have narrow MW distributions with polydispersity indices (PDI) < 1.1 (PDI is defined as weight-average MW divided by number-average MW or PDI ) Mw/Mn). As a result, the notion has emerged59 that “...the Achilles heel of co-continuous microemulsions is that they require polymers with similar lengths and sizes (low polydispersity) that are expensive to synthesize...” However, a previous SCFT report14 suggested that polydisperse diblock copolymers may in fact be beneficial for BµE formation. Thompson and Matsen14 predicted diblock polydispersity can both improve monolayer flexibility and lead to stable BµEs for systems with R > 0.8. The increased flexibility of polydisperse monolayers also reportedly stabilizes poorly ordered cocontinuous structures formed by graft copolymers.48 Pernot et al. prepared a polymeric mixture containing polyethylene and polyamide homopolymers (∼55 wt %) and graft copolymers comprised of a polyethylene backbone and polyamide side chains (∼45 wt %) by reactive blending. This material formed a cocontinuous structure that persisted following three weeks of melt-phase annealing, and the stability of this structure was attributed to the significant polydispersity present in the backbone, the side chains, and the length between grafting sites.48 Furthermore, given recent reports60 (and references therein) highlighting the use of polydispersity as a tool to control block copolymer phase behavior, there is reason to expect that polydispersity could be equally useful for BµEs given that its impact on the underlying physics (i.e., entropic and enthalpic contributions to free energy) is similar. Block copolymers are the most costly component in polymeric BµEs because they are made by anionic polymerization that is widely known to be expensive to implement commercially due to the necessary feedstock purification and other required reaction conditions.61 Furthermore, only a limited number of monomer chemistries are compatible with living anionic methods.61 Researchers have developed a number of alternative synthetic methodologies to overcome these limitations. Advances in controlled radical polymerizations (CRP)62-66 and metathesis polymerizations67 have greatly expanded the palette of monomers that are readily incorporated into block copolymers. These protocols are typically more tolerant of impurities in solvent, monomer, etc., than living anionic polymerizations and their deployment in large scale production environments is expected to provide materials with controlled architectures (e.g., block copolymers) in large quantities and at relatively low costs. However, polymers made by CRP often contain MW distribu-

Ellison et al. tions that are significantly broader than polymers made using living anionic techniques; PDIs greater than 1.2 are commonly obtained in the laboratory using CRP.64-66 Understanding the impact of polydispersity in self-assembling materials, such as pure block copolymers and BµEs, should facilitate the development of lower cost, thermodynamically stable, multiply continuous materials.68 In this manuscript, we experimentally interrogate polydispersity effects in ternary blends of PS, PI, and PS-PI. Three series of blends are prepared using the same nearly monodisperse PS and PI homopolymers; two series contain nearly monodisperse PS-PI diblocks (R ) 0.12 and 0.15) while the third has a polydisperse (PDI ) 1.57) PS block (R ) 0.15). The blend phase behavior is characterized using a combination of dynamic mechanical spectroscopy (DMS), small-angle X-ray scattering (SAXS), and cloud point measurements; BµEs are identified in all three series. Random-phase approximation (RPA) and self-consistent field theory (SCFT) calculations augment the experimental work and are used to explain the shifts in TODT, domain spacing, and BµE channel location due to differences in molecular weight and polydispersity. These results demonstrate that narrow MW distributions are not required for BµE formation and that polydispersity is an additional tuning parameter that can be used to control the phase behavior of ternary polymeric blends. Experimental Methods Polymer Synthesis. All polymers were prepared by anionic polymerizations conducted in cyclohexane (purified using activated alumina columns69) using standard inert atmosphere techniques and appropriately purified monomers.70 All polymers were ultimately recovered from cyclohexane solutions by precipitation in methanol and were dried under dynamic vacuum at room temperature until the pressure reached the baseline value. PS and PI homopolymers and PS-PI diblock copolymers with narrow MW distributions (PDI values 0, and c2 ≈ 0. Furthermore, the domain periodicity d can be extracted using eq 279

[( )

d ) 2π

1 a2 2 c2

1/2

-

1 c1 4 c2

]

-1/2

(2)

The parameters that result from fitting eq 1 to the SAXS profiles for the BµE samples shown in Figures 3 and 4 (and Figures 6 and 7 to be discussed later) are listed in Table 2. The parameters presented in Table 2 confirm that the samples designated as BµEs exhibit SAXS profiles that are expected for this structure. When combined with the observations from DMS and optical microscopy, these data provide definitive evidence for the formation of BµEs.

3732 J. Phys. Chem. B, Vol. 113, No. 12, 2009

Ellison et al. TABLE 2: Parameters Resulting from Fitting the Teubner-Strey Equation (Equation 1) to the SAXS Profiles for Ternary Samples Exhibiting a BµE Structure diblock copolymer

Φh

a2

c1 (nm2)

c2 (nm4)

PS(1.07)-PI-16

0.89 0.90 0.91 0.915 0.83 0.84 0.85 0.86 0.88 0.90 0.91 0.92 0.925 0.93

0.66 0.48 0.35 0.35 0.24 0.20 0.40 0.26 0.26 0.24 0.24 0.24 0.24 0.24

-146 -124 -102 -102 -83 -74 -118 -96 -160 -72 -78 -81 -91 -95

11540 11540 11450 11450 11450 11450 11540 11450 11290 11450 11450 11450 11450 11450

PS(1.57)-PI-17

PS(1.05)-PI-21 Figure 5. Inverse domain spacings of ternary blends at 100 °C containing PS(1.07)-PI-16 (circles) and PS(1.57)-PI-17 (squares) diblock copolymers. Solid symbols indicate lamellar samples. Open diamonds at Φh ) 0.89, 0.90, 0.91, and 0.915 and open triangles at Φh ) 0.83, 0.84, 0.85, and 0.86 indicate compositions where BµEs have been identified for samples containing PS(1.07)-PI-16 and PS(1.57)-PI-17, respectively. Inverse domain spacings are expressed as q* taken from the q values of the primary peaks in the SAXS profiles for lamellar samples. For BµEs, d* was calculated from eq 2 using the fitting parameters from Table 2 and then converted to q* by using q* ) 2π/d*.

Figure 6. Phase portraits constructed with either PS(1.05)-PI-21 (circles) or PS(1.57)-PI-17 (squares) diblock copolymers. Solid squares and circles denote the location of TODT while open squares and circles denote the macrophase separation temperature. Open diamonds at Φh ) 0.88, 0.90, 0.91, 0.92, 0.925, and 0.93 and open triangles at Φh ) 0.83, 0.84, 0.85, and 0.86 indicate compositions where BµEs have been identified in the respective phase portraits. These data points are approximately 5 °C tall in the Figure and include the (2 °C uncertainty (based upon measurement reproducibility) in the transition temperature measurements. The location of the BµEs data points on the temperature axis has been chosen arbitrarily for ease of viewing. Solid and dotted lines are intended only as guides to the eye.

Interestingly, the data presented in Figure 3 also demonstrate that exchanging the monodisperse diblock copolymer with the polydisperse analog does not substantially alter the width of the BµE channel but does significantly shift its location toward lower Φh. In other words, more diblock copolymer is required to generate a BµE with polydisperse diblock copolymer. We believe that the origin of this effect is related to the flexibility of the diblock copolymer monolayer at the interface between the two continuous domains. Regardless of the diblock polydispersity, the addition of homopolymer to blends on the left side of the channel decreases the interfacial coverage of the diblock copolymer and, consequently, increases the monolayer flexibility because the monolayer is more loosely packed.14 After sufficient homopolymer is added to the blend, the monolayer flexibility exceeds a threshold value (i.e., monolayer bending modulus e kBT) and the blend adopts a BµE.5,14,57 In the polydisperse system, it is reasonable to expect that, on average, shorter blocks will adopt relaxed conformations near the inter-

face while longer blocks will occupy space further into the domain.80,81 This staggered packing presumably14enhances the flexibility of the monolayer and shifts the BµE channel to lower homopolymer volume fractions. This argument explaining the impact of polydispersity on monolayer flexibility is consistent with Matsen and Thompson’s mean field theory results14 for ternary blends containing bidisperse diblock copolymers. Matsen and Thompson predicted14 that mixing diblock copolymers (i.e., a bidisperse system) would enhance monolayer flexibility and stabilize the BµE structure for R values higher than 0.8 in a polydisperse system. While our results support their prediction regarding monolayer flexibility, exploring the limiting upper value of R for stable microemulsions is outside the scope of the present manuscript. The fact that more diblock copolymer is required to stabilize microemulsions when the diblock contains a polydisperse block than when it has blocks with narrow MW distributions may at first appear to be counterproductive. In the past, diblock copolymers have been considered to be very expensive components and, as a result, some research has been focused on reducing the amount of block copolymer used in polymeric microemulsions.27 However, recent developments in controlled radical polymerizations62-66 are expected to significantly reduce the cost of manufacturing diblock copolymers. As noted earlier, these techniques typically yield block PDIs that are greater than 1.264–66 while anionic polymerizations (previously the mainstay for block copolymer synthesis) often yield block PDIs < 1.1. We expect that the cost differential between these two synthetic strategies may outweigh the need for additional polydisperse block copolymer. The inverse domain spacings (q* ) 2π/d*) of the PS(1.07)PI-16 and PS(1.57)-PI-17 samples that adopt lamellar and BµE structures are provided in Figure 5. The dependence of q* on Φh for the blends containing monodisperse (PS(1.07)-PI-16) and polydisperse (PS(1.57)-PI17) diblock copolymers is qualitatively similar. At low Φh, there is little change in the value of q* as homopolymer is added into the blend. However, q* decreases rapidly upon approaching the BµE channel. For samples inside the channel, q* again is relatively unchanged with Φh. Overall, this picture of the Φh dependence of q* is consistent with previous reports,9,12,17 and it provides additional evidence that the introduction of polydispersity into the diblock copolymer does not perturb the ternary blend behavior in an adverse manner. There is a notable quantitative difference in the value of q* between the two blend series. The difference is largest for the

Bicontinuous Polymeric Microemulsions

Figure 7. Representative synchrotron SAXS data acquired at 100 °C for BµE samples containing the PS(1.05)-PI-21 diblock copolymer (see Figure 6). These SAXS data were collected from samples with Φh ) 0.92 (squares) and Φh ) 0.925 (circles). Solid lines are fits to the Teubner-Strey equation shown in the text as eq 1. SAXS data are not shown below q ) 0.05 nm-1 because parasitic scattering was significant at lower q values.

pure diblock copolymer where the value of q* for the monodisperse diblock copolymer is nearly twice that of the polydisperse diblock copolymer (PS(1.57)-PI-17 has a 75% higher d* than PS(1.07)-PI-16). However, the difference decreases following the addition of homopolymer and is smallest for samples in the BµE channels. The decrease in q* upon introducing polydispersity into the diblock copolymers and ternary blends on the left side of the BµE channel is qualitatively consistent with recent literature concerning polydispersity in pure diblock copolymers.77,80,82 The origin of this effect is related to the reduction in the entropic penalty associated with stretching a polydisperse ensemble of chains compared to its monodisperse analog. This decrease results in a larger domain spacing for pure polydisperse diblock copolymers and, we believe, for ternary blends containing polydisperse diblock copolymers. Quantitatively, however, our 75% increase in d* for the PS-PI diblocks is larger than the polydispersity-driven increases reported in the literature. We used SCFT to compute (see Theoretical Results and Discussion for details) the ratio of d* values for two model systems designed to mimic the PS(1.07)-PI-16 and PS(1.57)PI-17 diblocks. The χ value used in the calculations was obtained at 100 °C from the “diblock-side” fit in Figure 10 and the model polymers had the molecular weights reported in Table 1, the PS molecular weight distributions measured by SEC, and monodisperse PI blocks. The predicted increase in d* with this broadening of the PS molecular weight distribution is only 19%, below the 75% measured by SAXS. We do not have a definitive explanation for this quantitative discrepancy, but note that reported theoretical predictions are not typically in quantitative agreement with experimental reports. For instance, while theoretical studies suggest the sensitivity of domain periodicity to changes in PDI should decrease with increasing χN,77,80 Lynd and Hillmyer82 reported the opposite trend in polydisperse poly((ethylene-alt-propylene)-b-lactide) diblock copolymers. Our results represent another quantitative disagreement between experiment and theory. We speculate that some of these quantitative differences may be related to the reported composition-dependence of χ in polymer blends.83 The computed ratio of domain spacings is very sensitive to the input χ values and the composition distribution inherent in polydisperse diblock copolymers could effectively change the χ parameter from the monodisperse analog, leading to discrepancies between experiment and theory. The phase portraits constructed with the PS(1.05)-PI-21 and PS(1.57)-PI-17 diblocks are presented in Figure 6. As shown

J. Phys. Chem. B, Vol. 113, No. 12, 2009 3733

Figure 8. Inverse domain spacings of ternary blends at 100 °C containing PS(1.05)-PI-21 (circles) and PS(1.57)-PI-17 (squares) diblock copolymers. Solid symbols indicate lamellar samples. Open diamonds at Φh ) 0.88, 0.90, 0.91, 0.92, 0.925, and 0.93 and open triangles at Φh ) 0.83, 0.84, 0.85 and 0.86 indicate compositions where BµEs have been identified for samples containing PS(1.05)-PI-21 and PS(1.57)PI-17, respectively. Inverse domain spacings are expressed as q* taken from the q value of the primary peaks in the SAXS profiles for lamellar samples. For BµEs, d* was calculated from eq 2 using the fitting parameters from Table 2 and then converted to q* using q* ) 2π/d*.

in Table 1, these diblock copolymers differ in both overall MW and in the PDI of the PS block. Representative SAXS profiles used to locate the BµE channel in the blends containing PS(1.05)-PI-21 diblock copolymer are provided in Figure 7; the Teubner-Strey model (eq 1) is fit to both SAXS curves, indicating the presence of a microemulsion in this ternary system. As in the other two phase portraits presented in this manuscript (Figure 3), DMS, optical microscopy and SAXS provided conclusive evidence for the presence of microemulsions (see Table 2 for the Teubner-Strey parameters). The high MW diblock copolymer (PS(1.05)-PI-21) was chosen for comparison because its TODT nearly matches that of the lower MW diblock copolymer with the polydisperse PS block (PS(1.57)-PI-17). The near equivalence of TODT at Φh ) 0 for (PS(1.05)-PI-21 and PS(1.57)-PI-17) allows a direct comparison between the merits of tuning the phase behavior by adjusting the molecular weight of the diblock copolymer (and the segregation strength of the pure diblock copolymer as measured by χN) or the polydispersity of the diblock copolymer. On the left side of the microemulsion channel shown in Figure 6, the dependence of TODT on Φh is nearly identical, although there is slightly more curvature in the blend containing the polydisperse diblock. In contrast, the homopolymer-rich right side of the phase diagram is substantially different. In this region, the macrophase separation temperature is higher at all values of Φh for the blend containing the polydisperse diblock. The locations of the BµE channels are also different in Figure 6 with the channel in the PS(1.05)-PI-21 series not shifting significantly from the PS(1.07)-PI-16 channel depicted in Figure 3. Unlike broadening the MW distribution of the PS block increasing the MW of the diblock copolymer from 16.4 to 20.8 kDa (increase in R from 0.12 to 0.15) does not significantly change the location of the microemulsion channel. The middle of the channel in terms of composition (identified by taking a mean of the microemulsion samples shown in Table 2) is roughly 0.904 for PS(1.07)-PI-16, 0.911 for PS(1.05)-PI-21 and 0.845 for PS(1.57)-PI-17. These results suggest that modest levels of polydispersity in the diblock copolymer may be particularly useful for both shifting the location of the microemulsion channel and increasing the temperature at which a microemulsion is first identified upon cooling.

3734 J. Phys. Chem. B, Vol. 113, No. 12, 2009

Ellison et al.

Figure 9. The RPA predictions for q* (left panel) and 1/(χN)spinodal (right panel) as functions of the overall homopolymer volume fraction for PI/PS/PS-PI ternary blends. Note that the ordinate in the plot on the right is quantified using the N of the homopolymer (Nh); substituting the N of the diblock would not change any qualitative features of this plot, but would simply scale the values on the ordinate by the ratio of the two chain lengths. The Lifshitz points are denoted by b. The polydisperse PS block in the diblock copolymer has either the experimentally measured distibution (exp-distribution, PS PDI ) 1.57 by SEC) or model Schulz-Zimm distributions (various PDIs). These RPA results are in qualitative agreement with the experimental data provided in Figures 3 and 5; both q* and χspinodal decrease with increasing PS PDI (note that 1/(χN)spinodal scales with TODT) and the Lifshitz point shifts toward lower homopolymer concentrations as PS PDI is increased.

The monomer-monomer density correlation function may be represented by a single quantity for any multicomponent polymer blend containing only two chemically distinct monomers (A and B)86

S(q) ) S(q b) ) 〈δfA(q b)δfA(- b q )〉 ) -〈δfA(q b)δfB(- b q )〉

Figure 10. Comparison of the χODT values computed using SCFT (“diblock-side”) and the χspinodal values calculated using RPA (“homopolymer-side”); both data sets are plotted as a function of the experimentally measured phase separation temperatures. The data clearly fall into two regimes; a straight line is fit to each data set and extrapolated to T ) 100 °C (open symbols) to obtain the χ values used to generate Figure 11.

The inverse domain spacings for the samples from Figure 6 that adopt lamellar and BµE structures are shown in Figure 8. Increasing the MW of the diblock increases the domain periodicity of the lamellar mesostructures. This increase is not as significant as that obtained by increasing the PS block polydispersity; the domain sizes of the neat diblocks are 15.6 nm for PS(1.07)-PI-16, 19.4 nm for PS(1.05)-PI-21, and 27.2 nm for PS(1.57)-PI-17. This trend in domain size is sustained in ternary blends forming lamellar morphologies, but not for blends adopting the BµE. All three ternary blends exhibit slightly different BµE domain sizes; the average domain size of BµE samples is roughly 83.7 nm for blends containing PS(1.07)-PI16, 98.1 nm for blends containing PS(1.05)-PI-21, and 92.0 nm for blends containing PS(1.57)-PI-17. We do not have a complete explanation for this observation and further investigations of the impact of polydispersity and MW on the domain size of BµEs are needed to elucidate the mechanisms at work. Theoretical Results and Discussion The RPA concept originally advanced by de Gennes84,85 is used to calculate the monomer-monomer density correlation functions and the stability limits (spinodals) of the homogeneous melts. Our computational approach is similar to that described by Fredrickson and co-workers;7,33 here we merely introduce the relevant quantities pertaining to our discussion.

where fi is the volume fraction of component i and q is the scattering wave-vector modulus. Here δfA ) fA - 〈fA〉 and δfB ) fB - 〈fB〉 represent the density fluctuations about the average component densities; the periodicity of these density fluctuations is characterized by q-1. The inverse of S(q) is related to the free energy cost associated with the density fluctuations87 and for these binary systems, regardless of the polydispersity, adopts a particularly compact form

S-1(q) ) F(q) - 2χ where F(q) is related to intramolecular correlations of Gaussian chains and also depends on N, and fi of each component, the statistical segment lengths of both monomer units, and the overall fi. The segment-segment interaction between the two monomers is incorporated in the -2χ term. For the ternary A/B/AB systems investigated in this work (fA ≈ fB), F(q) reaches a minimum at a finite q value (q ) q*) that characterizes the periodicity of the density fluctuations. q* decreases as the homopolymer volume fraction increases and drops to 0 at the so-called Lifshitz point; a minimum in F(q) at q* ) 0 corresponds to a macrophase separation. Beyond the Lifshitz point, the minimum of F(q) is always obtained at q* ) 0. The stability limit of the homogeneous phase is computed within the RPA framework by setting S1-(q) ) 0 (χspinodal ) F(q*)/2). For a completely symmetric system (equal block statistical segment lengths, equal homopolymer chain lengths, and a symmetric diblock copolymer), χspinodal is the value of χ (χODT) at the lamellar-disorder transition (or the value of χ at the macrophase separation point for the homopolymer-rich blends). χspinodal does not rigorously correlate with χODT for asymmetric systems, although the values are typically close.88 As the first step to understand the polydispersity effects in the PI/PS/PS-PI ternary system, the RPA formalism is used to calculate the q* and χspinodal values for a variety of homopolymer volume fractions (all with fA ) fB). PS and PI statistical segment length values reported in the literature are used in this computation.74 Both experimentally measured and model molecular weight distributions are incorporated into the RPA calculations. The molecular weight distribution of the polydisperse PS block

Bicontinuous Polymeric Microemulsions

Figure 11. q* as a function of overall homopolymer volume fraction for the monodisperse system. The data points were obtained experimentally at 100 °C using SAXS. The three theoretical curves are obtained using the equilibrated lamellar domain spacings computed using SCFT (q* ) 2π/d*) with three different χ values at 100 °C: (1) the “homopolymer-side fit” uses the χ obtained from the macrophase separation data (see Figure 10), (2) the “diblock-side fit” uses the χ obtained from the lamellae-to-disorder transition temperatures (see Figure 10), and (3) the domain fit uses the χ computed by requiring SCFT to accurately predict the lamellar domain periodicity of the neat diblock at 100 °C.

Figure 12. Normalized q* as a function of normalized homopolymer volume fraction. q* is normalized by dividing it by the q* obtained for the neat diblock copolymer while Φ is normalized by dividing it by Φ at the Lifshitz point. Three sets of data are reproduced from ref 12: PE/PEP/PE-PEP, PE/PEO/PE-PEO, and PEE/PDMS/PEE-PDMS. The monodisperse and polydisperse data reported in Figures 3 (“monodisperse” and “polydisperse”) and 8 (“monodisperse (high Mw)”) are also included, along with the RPA results for our monodisperse system. All of these data seem to collapse onto the same underlying curve, suggesting some sort of universal behavior in ternary A/B/AB systems that does not depend strongly on the system χ parameters or the diblock polydispersity.

in diblock PS(1.57)-PI-17 was measured using SEC; this distribution was an input for the RPA calculation, and the results are presented in Figure 9 (labeled “exp-distribution”). The Schulz-Zimm distribution (SZD)89,90 is employed here to generate curves with a variety of PDI values; this distribution has been widely used in theoretical investigations of polydispersity effects in block copolymers due to its simplicity.77,78,80,91,92 Results for SZD PS PDI values of 1, 1.2, 1.57, and 2 are provided in Figure 9 alongside the exp-distribution. These RPA calculations are in qualitative agreement with the experimental data presented in Figures 3 and 5; both q* and χspinodal decrease with increasing PS PDI (note that 1/(χN)spinodal scales with TODT) and the (mean field) Lifshitz point shifts toward lower homopolymer concentrations as PS PDI is increased. These results are also in general agreement with previous literature reports on polydisperse diblock copolymer melts. Both domain

J. Phys. Chem. B, Vol. 113, No. 12, 2009 3735 periodicities77,80,82,91,93 and, for materials with fA ≈ fB, TODT’s76,78 have been reported to increase with block PDI. The results presented in Figure 9 for a PS PDI ) 1.57 also reinforce the notion that the shape of the MW distribution, and not just the PDI, influences phase behavior; the slight variations in q* and 1/(χN)spinodal for different MW distributions with PS PDI ) 1.57 are generally consistent with those reported for polydisperse diblocks.91 To quantitatively compare the theoretical predictions and the experimental data, a reliable relation between the χ parameter and temperature T is required. We attempt to extract χ(T) from the experimental data for the monodisperse system using two different strategies. Both approaches employ the literature values of the statistical segment lengths,74 the experimentally measured (with SEC) MW distribution for the PS block, and perfectly monodisperse PI and PS homopolymers and PI blocks. The first method utilizes SCFT and the data to the left of the BµE channel. SCFT is a standard theoretical tool for studying the phase behavior of polymeric systems; Matsen authored an excellent review describing the details of this theory.94 In our implementation, the free energies of lamellae and a disordered state are computed and the configuration with the lowest free energy is considered the equilibrium morphology. Since all of our experimental data are consistent with the lamellar mesostructure, other ordered morphologies are not considered in SCFT. The values of χODT were computed at four of the experimental blend compositions to the left of the BµE channel using SCFT. These computed χODT values are plotted as a function of the experimentally measured 1/TODT in Figure 10, and a straight line is fit to the data (diblock-side). The second approach utilizes the data measured at compositions to the right of the BµE channel. The RPA is used to compute χspinodal for three of these compositions; these data are plotted versus 1/TMS (where TMS is the experimentally measured macrophase separation temperature) in Figure 10 (homopolymer-side). The data obtained from the two approaches follow two distinct lines, a clear indication that a single χ relation cannot explain the thermodynamics of blends on both sides of the BµE channel. Maurer and co-workers previously reported that a single χ(T) relation did not describe the phase behavior of both pure AB diblock copolymers and blends comprised of A and B homopolymers.95 Our data include these two extremes investigated by Maurer et al., but also contain ternary A/B/AB blends with varying amounts of homopolymers. These ternary data do not connect the two extremes with a smooth curve, but fall into one of two regimes: a diblock-side that involves lamellae-to-disorder transitions and a homopolymer-side that involves the homogenization of A-rich and B-rich domains. The regime is apparently determined by the morphology of the system and not the homopolymer composition; even the lamellae-forming blend that contains 80% homopolymer seems to have the diblock χ and not the homopolymer χ. These two χ fits are extrapolated to 100 °C to obtain χ values that can be used to quantitatively predict q* as a function of the homopolymer concentration using SCFT. The calculated q* values and the experimental data are plotted as a function of homopolymer volume fraction in Figure 11. Note that the two χ fits in Figure 10 happen to provide comparable χ values at 100 °C, resulting in nearly coincident curves in Figure 11; this coincidence would not occur at most temperatures. The predicted q* values qualitatively follow the experimental data obtained at 100 °C, but are initially offset because the χ values obtained from the transition temperatures (i.e., those in Figure 10) do

3736 J. Phys. Chem. B, Vol. 113, No. 12, 2009 not accurately predict q* for the neat diblock. This discrepancy can be corrected by computing a third value of χ at 100 °C from the experimental data. Here χ is calculated by requiring the SCFT results to match the experimentally measured q* for the neat diblock; the χ value that does this at 100 °C is 0.077. The q* values predicted using SCFT and this χ value are plotted in Figure 11 and labeled “domain fit.” The quantitative agreement between SCFT and experiment is much better when this χ value is employed in the theory. These results further highlight the need for an improved understanding of the χ parameter. Hillmyer and co-workers normalized q* and Φ data obtained from three different series of ternary blends by using q*/ [q*(Φ ) 0)] as the ordinate and Φ/[Φ(Lifshitz)] as the abscissa.12 When plotted in this manner, these data essentially collapsed onto the same curve. Our data are plotted alongside those obtained by Hillmyer et al.12 in Figure 12. The RPA results obtained for a monodisperse system are also included in Figure 12 for comparison. All of these data collapse onto essentially the same underlying curve, indicating that this normalized relationship does not depend strongly on the values of χ in the system or on the polydispersity of the diblock. These data further support the notion that A/B/AB blends exhibit some universal behavior,12 although there currently is not any theoretical justification for this data normalization scheme. Conclusions In this manuscript, we have presented an experimental and theoretical analysis of the impact of block copolymer polydispersity on BµE-forming ternary blends of A and B homopolymers and the corresponding AB diblock copolymers. The experimental and theoretical approaches are found to be in excellent qualitative agreement in their description of the impact of polydispersity on the phase portrait and domain spacing. The most important finding of this research is that polydispersity does not adversely impact the formation of the thermodynamically stable bicontinuous microemulsion. This work supports the notion that polydispersity provides an additional avenue for uniquely tuning phase behavior in ternary blends. Lastly, there are parallels between the polydispersity work presented here for ternary polymeric systems containing block copolymer “surfactants” and analogous low MW surfactant/oil/ water systems. In surfactant/oil/water microemulsions containing nonionic surfactants, the impact of the chain length distribution has been studied96-100 in nonionic surfactants. Significant improvements in the emulsification capacity and the ability to lower surface tension were reported for surfactants with broad chain length distributions. This effect has been attributed to differences in packing polydisperse and monodisperse surfactants at the interface. Others101-109 have broadened chain length distributions by mixing amphiphilic diblock copolymers with low MW surfactants and found block copolymers serve as “efficiency boosters” that enhance the solubilization capacity of oil-in-water microemulsions (i.e., less surfactant is required to form a microemulsion). This effect has been attributed to an increase in the effective bending modulus6 when diblock copolymer is added. Since fundamental issues of bending modulus and packing of amphiphilic molecules at an interface are common to both the ternary polymeric blends and oil/water/ surfactant systems, future studies comparing the impact of polydispersity/chain length distribution in these two systems could be instructive for developing universal understanding. Acknowledgment. The authors gratefully acknowledge financial support from the Department of Energy through Grant

Ellison et al. 5-35908. We also acknowledge support from the National Science Foundation (NSF DMR-0220460). Graduate fellowships to A.J.M. from the Department of Homeland Security and the Department of Defense are gratefully acknowledged. Portions of this work were performed at the DuPont-Northwestern-Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the Advanced Photon Source (APS). DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company, and the State of Illinois. Use of the Advanced Photon Source (APS) was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. Parts of this work were carried out in the University of Minnesota Institute of Technology Characterization Facility, which receives partial support from NSF through the NNIN program. We thank Professor Thomas R. Hoye for the use of his laboratory’s ozonolysis equipment and Professor David C. Morse for helpful discussions. References and Notes (1) Schwuger, M. J.; Stickdorn, K.; Schomacker, R. Chem. ReV. 1995, 95, 849. (2) Clausse, M.; Peyrelasse, J.; Heil, J.; Boned, C.; Lagourette, B. Nature 1981, 293, 636. (3) Scriven, L. E. Nature 1976, 263, 123. (4) Strey, R. Colloid Polym. Sci. 1994, 272, 1005. (5) de Gennes, P. G.; Taupin, C. J. Phys. Chem. 1982, 86, 2294. (6) Komura, S. J. Phys.: Condens. Matter 2007, 19, 463101. (7) Fredrickson, G. H.; Bates, F. S. J. Polym. Sci. Part B: Polym. Phys. 1997, 35, 2775. (8) Bates, F. S.; Maurer, W.; Lodge, T. P.; Schulz, M. F.; Matsen, M. W.; Almdal, K.; Mortensen, K. Phys. ReV. Lett. 1995, 75, 4429. (9) Bates, F. S.; Maurer, W. W.; Lipic, P. M.; Hillmyer, M. A.; Almdal, K.; Mortensen, K.; Fredrickson, G. H.; Lodge, T. P. Phys. ReV. Lett. 1997, 79, 849. (10) Morkved, T. L.; Stepanek, P.; Krishnan, K.; Bates, F. S.; Lodge, T. P. J. Chem. Phys. 2001, 114, 7247. (11) Washburn, N. R.; Lodge, T. P.; Bates, F. S. J. Phys. Chem. B 2000, 104, 6987. (12) Hillmyer, M. A.; Maurer, W. W.; Lodge, T. P.; Bates, F. S.; Almdal, K. J. Phys. Chem. B 1999, 103, 4814. (13) Messe, L.; Corvazier, L.; Ryan, A. J. Polymer 2003, 44, 7397. (14) Thompson, R. B.; Matsen, M. W. Phys. ReV. Lett. 2000, 85, 670. (15) Burghardt, W. R.; Krishnan, K.; Bates, F. S.; Lodge, T. P. Macromolecules 2002, 35, 4210. (16) Brinker, K. L.; Mochrie, S. G. J.; Burghardt, W. R. Macromolecules 2007, 40, 5150. (17) Corvazier, L.; Messe, L.; Salou, C. L. O.; Young, R. N.; Fairclough, J. P. A.; Ryan, A. J. J. Mater. Chem. 2001, 11, 2864. (18) Lee, J. H.; Balsara, N. P.; Krishnamoorti, R.; Jeon, H. S.; Hammouda, B. Macromolecules 2001, 34, 6557. (19) Matsen, M. W. J. Chem. Phys. 1999, 110, 4658. (20) Morkved, T. L.; Chapman, B. R.; Bates, F. S.; Lodge, T. P.; Stepanek, P.; Almdal, K. Faraday Discuss. 1999, 112, 335. (21) Schwahn, D.; Mortensen, K.; Frielinghaus, H.; Almdal, K. Phys. ReV. Lett. 1999, 82, 5056. (22) Schwahn, D.; Mortensen, K.; Frielinghaus, H.; Almdal, K.; Kielhorn, L. J. Chem. Phys. 2000, 112, 5454. (23) Zhou, N.; Bates, F. S.; Lodge, T. P. Nano Lett. 2006, 6, 2354. (24) Zhou, N.; Lodge, T. P.; Bates, F. S. J. Phys. Chem. B 2006, 110, 3979. (25) Lee, J. H.; Jeon, H. S.; Balsara, N. P.; Newstein, M. C. J. Chem. Phys. 1998, 108, 5173. (26) Jeon, H. S.; Lee, J. H.; Balsara, N. P.; Newstein, M. C. Macromolecules 1998, 31, 3340. (27) Ruegg, M. L.; Reynolds, B. J.; Lin, M. Y.; Lohse, D. J.; Balsara, N. P. Macromolecules 2007, 40, 1207. (28) Ruegg, M. L.; Reynolds, B. J.; Lin, M. Y.; Lohse, D. J.; Balsara, N. P. Macromolecules 2006, 39, 1125. (29) Reynolds, B. J.; Ruegg, M. L.; Balsara, N. P.; Radke, C. J.; Shaffer, T. D.; Lin, M. Y.; Shull, K. R.; Lohse, D. J. Macromolecules 2004, 37, 7401. (30) Lee, J. H.; Ruegg, M. L.; Balsara, N. P.; Zhu, Y. Q.; Gido, S. P.; Krishnamoorti, R.; Kim, M. H. Macromolecules 2003, 36, 6537. (31) Holyst, R.; Schick, M. J. Chem. Phys. 1992, 96, 7728. (32) Müller, M.; Schick, M. J. Chem. Phys. 1996, 105, 8885. (33) Broseta, D.; Fredrickson, G. H. J. Chem. Phys. 1990, 93, 2927.

Bicontinuous Polymeric Microemulsions (34) Wanakule, N. S.; Nedoma, A. J.; Robertson, M. L.; Fang, Z.; Jackson, A.; Garetz, B. A.; Balsara, N. P. Macromolecules 2008, 41, 471. (35) Nunalee, M. L.; Guo, H. X.; de la Cruz, M. O.; Shull, K. R. Macromolecules 2007, 40, 4721. (36) Duchs, D.; Ganesan, V.; Fredrickson, G. H.; Schmid, F. Macromolecules 2003, 36, 9237. (37) Ganesan, V.; Fredrickson, G. H. J. Chem. Phys. 2000, 113, 2901. (38) Kodama, H.; Komura, S.; Tamura, K. Europhys. Lett. 2001, 53, 46. (39) Komura, S.; Kodama, H.; Tamura, K. J. Chem. Phys. 2002, 117, 9903. (40) Denesyuk, N. A.; Gompper, G. Macromolecules 2006, 39, 5497. (41) Potschke, P.; Paul, D. R. J. Macromol. Sci., Polym. ReV. 2003, C43, 87. (42) Girard-Reydet, E.; Pascault, J. P.; Brown, H. R. Macromolecules 2001, 34, 5349. (43) Kim, B. S.; Chiba, T.; Inoue, T. Polymer 1995, 36, 43. (44) Yu, G.; Gao, J.; Hummelen, J. C.; Wudl, F.; Heeger, A. J. Science 1995, 270, 1789. (45) Xu, Z.; Jandt, K. D.; Kramer, E. J.; Edgecombe, B. D.; Frechet, J. M. J. J. Polym. Sci., Part B: Polym. Phys. 1995, 33, 2351. (46) Halls, J. J. M.; Walsh, C. A.; Greenham, N. C.; Marseglia, E. A.; Friend, R. H.; Moratti, S. C.; Holmes, A. B. Nature 1995, 376, 498. (47) Harrats, C.; Blacher, S.; Fayt, R.; Jerome, R.; Teyssie, P. J. Polym. Sci., Part B: Polym. Phys. 1995, 33, 801. (48) Pernot, H.; Baumert, M.; Court, F.; Leibler, L. Nat. Mater. 2002, 1, 54. (49) Sarazin, P.; Roy, X.; Favis, B. D. Biomaterials 2004, 25, 5965. (50) Bates, F. S.; Fredrickson, G. H. Phys. Today 1999, 52, 32. (51) Semenov, A. N. Macromolecules 1993, 26, 2273. (52) Shull, K. R.; Winey, K. I. Macromolecules 1992, 25, 2637. (53) Janert, P. K.; Schick, M. Macromolecules 1997, 30, 137. (54) Thompson, R. B.; Matsen, M. W. J. Chem. Phys. 2000, 112, 6863. (55) Mayes, A. M.; Russell, T. P.; Satija, S. K.; Majkrzak, C. F. Macromolecules 1992, 25, 6523. (56) Shull, K. R. J. Chem. Phys. 1991, 94, 5723. (57) Morse, D. C. Curr. Opin. Colloid Interface Sci. 1997, 2, 365. (58) Morse, D. C. Phys. ReV. E 1994, 50, R2423. (59) Ryan, A. J. Nat. Mater. 2002, 1, 8. (60) Lynd, N. A.; Meuler, A. J.; Hillmyer, M. A. Prog. Polym. Sci. 2008, 33, 875. (61) Perrier, S.; Wang, X. S. Nature 2007, 445, 271. (62) Matyjaszewski, K.; Xia, J. H. Chem. ReV. 2001, 101, 2921. (63) Hawker, C. J.; Bosman, A. W.; Harth, E. Chem. ReV. 2001, 101, 3661. (64) Chiefari, J.; Chong, Y. K.; Ercole, F.; Krstina, J.; Jeffery, J.; Le, T. P. T.; Mayadunne, R. T. A.; Meijs, G. F.; Moad, C. L.; Moad, G.; Rizzardo, E.; Thang, S. H. Macromolecules 1998, 31, 5559. (65) Chong, Y. K.; Le, T. P. T.; Moad, G.; Rizzardo, E.; Thang, S. H. Macromolecules 1999, 32, 2071. (66) Braunecker, W. A.; Matyjaszewski, K. Prog. Polym. Sci. 2007, 32, 93. (67) Bielawski, C. W.; Grubbs, R. H. Prog. Polym. Sci. 2007, 32, 1. (68) Ruzette, A. V.; Leibler, L. Nat. Mater. 2005, 4, 19. (69) Pangborn, A. B.; Giardello, M. A.; Grubbs, R. H.; Rosen, R. K.; Timmers, F. J. Organometallics 1996, 15, 1518. (70) Ndoni, S.; Papadakis, C. M.; Bates, F. S.; Almdal, K. ReV. Sci. Instrum. 1995, 66, 1090. (71) Meuler, A. J.; Mahanthappa, M. K.; Hillmyer, M. A.; Bates, F. S. Macromolecules 2007, 40, 760. (72) Quirk, R. P.; Jang, S. H.; Han, K.; Yang, H.; Rix, B.; Lee, Y. ACS Symp. Ser. 1998, 704, 71.

J. Phys. Chem. B, Vol. 113, No. 12, 2009 3737 (73) Quirk, R. P.; You, F. X.; Wesdemiotis, C.; Arnould, M. A. Macromolecules 2004, 37, 1234. (74) Fetters, L. J.; Lohse, D. J.; Richter, D.; Witten, T. A.; Zirkel, A. Macromolecules 1994, 27, 4639. (75) Rosedale, J. H.; Bates, F. S. Macromolecules 1990, 23, 2329. (76) Lynd, N. A.; Hillmyer, M. A. Macromolecules 2007, 40, 8050. (77) Cooke, D. M.; Shi, A. C. Macromolecules 2006, 39, 6661. (78) Matsen, M. W. Phys. ReV. Lett. 2007, 99, 148304. (79) Teubner, M.; Strey, R. J. Chem. Phys. 1987, 87, 3195. (80) Matsen, M. W. Eur. Phys. J. E 2006, 21, 199. (81) Noro, A.; Okuda, M.; Odamaki, F.; Kawaguchi, D.; Torikai, N.; Takano, A.; Matsushita, Y. Macromolecules 2006, 39, 7654. (82) Lynd, N. A.; Hillmyer, M. A. Macromolecules 2005, 38, 8803. (83) Krishnamoorti, R.; Graessley, W. W.; Balsara, N. P.; Lohse, D. J. J. Chem. Phys. 1994, 100, 3894. (84) Jannink, G.; de Gennes, P. G. J. Chem. Phys. 1968, 48, 2260. (85) de Gennes, P. G. J. Phys. (Paris) 1970, 31, 235. (86) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (87) Leibler, L. Macromolecules 1980, 13, 1602. (88) Cochran, E. W.; Morse, D. C.; Bates, F. S. Macromolecules 2003, 36, 782. (89) Schulz, G. V. Physik Chem. 1939, B43, 25. (90) Zimm, B. H. J. Chem. Phys. 1948, 16, 1099. (91) Lynd, N. A.; Hillmyer, M. A.; Matsen, M. W. Macromolecules 2008, 41, 4531. (92) Sides, S. W.; Fredrickson, G. H. J. Chem. Phys. 2004, 121, 4974. (93) Matsushita, Y.; Noro, A.; Iinuma, M.; Suzuki, J.; Ohtani, H.; Takano, A. Macromolecules 2003, 36, 8074. (94) Matsen, M. W. J. Phys.: Condens. Matter 2002, 14, R21. (95) Maurer, W. W.; Bates, F. S.; Lodge, T. P.; Almdal, K.; Mortensen, K.; Fredrickson, G. H. J. Chem. Phys. 1998, 108, 2989. (96) Ishitobi, M.; Kunieda, H. Colloid Polym. Sci. 2000, 278, 899. (97) Huibers, P. D. T.; Shah, D. O. Langmuir 1997, 13, 5762. (98) Shinoda, K.; Saito, H.; Arai, H. J. Colloid Interface Sci. 1971, 35, 624. (99) Crook, E. H.; Fordyce, D. B.; Trebbi, G. F. J. Am. Oil Chem. Soc. 1963, 41, 231. (100) Crook, E. H.; Fordyce, D. B.; Trebbi, G. F. J. Phys. Chem. 1963, 67, 1987. (101) Jakobs, B.; Sottmann, T.; Strey, R.; Allgaier, J.; Willner, L.; Richter, D. Langmuir 1999, 15, 6707. (102) Endo, H.; Allgaier, J.; Gompper, G.; Jakobs, B.; Monkenbusch, M.; Richter, D.; Sottmann, T.; Strey, R. Phys. ReV. Lett. 2000, 85, 102. (103) Endo, H.; Allgaier, J.; Mihailescu, M.; Monkenbusch, M.; Gompper, G.; Richter, D.; Jakobs, B.; Sottmann, T.; Strey, R. Appl. Phys. A 2002, 74, S392. (104) Endo, H.; Mihailescu, M.; Monkenbusch, M.; Allgaier, J.; Gompper, G.; Richter, D.; Jakobs, B.; Sottmann, T.; Strey, R.; Grillo, I. J. Chem. Phys. 2001, 115, 580. (105) Gompper, G.; Endo, H.; Mihailescu, M.; Allgaier, J.; Monkenbusch, M.; Richter, D.; Jakobs, B.; Sottmann, T.; Strey, R. Europhys. Lett. 2001, 56, 683. (106) Gompper, G.; Richter, D.; Strey, R. J. Phys.: Condens. Matter 2001, 13, 9055. (107) Hiergeist, C.; Lipowsky, R. J. Phys. II 1996, 6, 1465. (108) Komura, S.; Safran, S. A. Eur. Phys. J. E 2001, 5, 337. (109) Mihailescu, M.; Monkenbusch, M.; Endo, H.; Allgaier, J.; Gompper, G.; Stellbrink, J.; Richter, D.; Jakobs, B.; Sottmann, T.; Farago, B. J. Chem. Phys. 2001, 115, 9563.

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