Article pubs.acs.org/Macromolecules
Exploring Lateral Microphase Separation in Mixed Polymer Brushes by Experiment and Self-Consistent Field Theory Simulations Andrew D. Price,† Su-Mi Hur,‡,§ Glenn H. Fredrickson,‡,§,∥ Amalie L. Frischknecht,† and Dale L. Huber*,† †
Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States Department of Chemical Engineering, §Materials Research Laboratory, and ∥Department of Materials, University of California, Santa Barbara, Santa Barbara, California 93106, United States
‡
S Supporting Information *
ABSTRACT: Similar to block copolymers, mixed polymer brushes are physically constrained and, upon annealing, microphase separate into nanodomains with morphologies largely dependent on the volume fractions of the polymers. A combination of experimental analysis of polystyrene (PS)/ poly(methyl methacrylate) (PMMA) brushes and selfconsistent field theory (SCFT) simulations is employed to determine the phases of annealed binary brushes. By annealing the brushes under conditions that maximize lateral versus vertical separation, a rich array of phases are observed with general agreement to predictions by SCFT simulations. The incorporation of random perturbations to the grafting density in SCFT simulations accounts for disorder in the arrangement of the polymer domains for the PS/PMMA brushes. Additionally, autocorrelation of the polymer domains yields an experimental domain spacing that is nearly 2 times greater than SCFT predictions, which is hypothesized to result from polydispersity in the PS/PMMA brushes. These findings should provide a basis for the improved fabrication of nanopatterned mixed polymer brushes with implications for the enhancement of biological surfaces, membranes, and nanolithography.
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system.8 A complementary patterning technique that does not rely on the physical deposition of block copolymers has the potential to overcome such drawbacks. As an alternative to block copolymers, the microphase separation of binary polymer brushes has been investigated.21−26 Similar to block copolymers, immiscible polymers are limited to microphase separation by covalent linkages, in this instance by their attachment to the substrate surface. As polymer brushes can create dense and stable polymer coatings, they have been frequently investigated for surface modification of nanoparticles and planar substrates for use in biological systems, membranes, chromatography supports, and antifriction surfaces.27−29 When applied as mixed brushes, they may become environmentally responsive whereby one polymer is attracted to the free surface while the other collapses away from it.23,30−32 Properties including wettability, adhesion, and biocompatibility are largely dependent upon the polymer component at the free surface. On the other hand, lateral phase separation of mixed polymer brushes may occur when the surface is not selective for either polymer during annealing.21,25,26 A number of theoretical and computational studies have predicted the equilibrium structure of phase-separated mixed polymer brushes as a function of factors such as grafting density, solvent selectivity, and polymer volume fraction, yet
INTRODUCTION Patterning surfaces by the self-assembly of polymers allows a high-throughput and inexpensive means for creating feature sizes below those easily accomplished by conventional photolithography.1−10 Such nanoscale patterning can be achieved by spatially limited phase separation of two or more immiscible polymers. When macroscopic phase separation is prevented through the connectivity of the polymer molecules, the system compensates by arranging the polymers into ordered nanodomains to minimize the energy of the system.11,12 This “microphase separation” has been definitively demonstrated with block copolymer systems by experiment, analytical theory, and simulation.1,2,5,6,8−10,12−16 Selective deposition of materials into block copolymer patterns creates nanopatterned surfaces with electronic, biological, and membrane applications and is even being applied to the manufacture of computer chips. 2,10,17−20 The research possibilities and commercial promise of block copolymer lithography is substantial, but the need to coat surfaces with the copolymers using physical means (typically spin-coating) creates limitations. For example, block copolymers can be problematic when patterning nonplanar surfaces or creating composites where the polymer layer is a component of the final, permanent structure. Additionally, the directed assembly of block copolymers into complex geometries, such as sharp bends, is limited by energetically unfavorable polymer stretching except with the added complexity of a ternary © 2011 American Chemical Society
Received: November 21, 2011 Published: December 12, 2011 510
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used to grow the polymer brushes with the polymer volume fraction systematically varied by manipulation of the grafting density of the constituent polymers. The observed phases are compared with those predicted by full three-dimensional SCFT calculations assuming melt conditions. With a careful approach to brush preparation and annealing, we demonstrate that, similar to block copolymers, binary polymer brushes may selfassemble into different phases.
scant evidence in the literature demonstrates experimental agreement with simulation.24,26,32,33 Here, we aim to explore the phases in laterally segregated mixed brushes by minimizing polymer selectivity under annealing conditions, i.e., by minimizing the tendency for vertical segregation. A combination of both vertical and lateral phase separation in binary polymer brushes occurs in response to solvent selectivity and is mediated by asymmetry in polymer chain lengths and grafting densities. Binary brushes of poly(methyl acrylate) (PMA) and poly(styrene-co-2,3,4,5,6-pentafluorostyrene) (PSF) vertically segregate in response to selective solvents with notable lateral segregation of PMA into depressions when PSF is selected for.21 Nanomechanical mapping of the surfaces confirmed lateral segregation of the two polymers. A subsequent study by Minko and co-workers demonstrated the appearance of a ripple phase when polystyrene (PS)/poly(methyl methacrylate) (PMMA) brushes were exposed to a nonselective solvent.34 Plasma etching of the PMMA component confirmed that the lateral segregation remained well into the polymer layer. Rühe and co-workers also examined PS/PMMA brushes showing laterally segregated domains when exposed to a nonselective solvent.25 The proportion of PMMA vs PS measured at the top surface by AFM roughly corresponds to volume fractions of the polymers when the molecular weight and grafting density of the PMMA fraction are varied. The polymer domains exhibited a “memory” due to local fluctuations in brush composition with domain switching being harnessed to induce nanomotion in nanoobjects.35−37 Similar responsive surfaces were prepared by Zhao and co-workers with a narrow polydispersity by growing polymers from the surface via living radicals.38 Despite addressing polydispersity, such brushes were typically thin and composed of low-molecular-weight polymers perhaps limiting their segregation potential. These studies give glimpses into the domain structure of mixed polymer brushes, but as discussed by Zhao and Zhu, the challenges of sample preparation and analysis have left the phase morphologies of mixed polymer brushes largely unexplored experimentally.39 Both theory and simulation have been used to study phase separation in grafted binary brushes. The behavior of ideal binary brushes with uniform grafting densities has been fairly comprehensively explored using field theoretic models and in particular self-consistent field theory (SCFT).22,24,23,26 The most recent of these studies include calculations of the phase behavior of mixed brushes in both nonselective24 and selective solvents23,26 and a recent calculation for the phase behavior of a mixed brush in the melt state with no solvent.40 In the melt or in nonselective solvent, a symmetric 50−50 mixture of two grafted homopolymers of equal molecular weight results in lateral phase separation of the brush into a “ripple” phase, with domains of each polymer extending in one lateral direction. More asymmetric compositions lead to various hexagonally packed or checkerboard phases. The SCFT results for brushes with uniform grafting density all exhibit a high degree of longrange order, similar to that seen in block copolymer thin films but not seen to date in mixed polymer brushes. Monte Carlo41,42 and single-chain-in-mean-field36,43 simulations have demonstrated that fluctuations in grafting density lead to a loss of long-range order in the laterally phase-separated morphologies. Here, we explore the phase morphologies of PS/PMMA binary brushes when annealed under nonselective conditions using experiment and simulation. A free radical approach is
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MATERIALS AND METHODS
Materials. Silicon wafers (Silicon Quest International) were test grade P-type, CZ silicon doped with boron. 2,2′-Azobis(2-methylpropionitrile) (AIBN, Aldrich, 98%) and 4,4′-azobis(4-cyanovaleric acid) (ACVA, Aldrich, ≥98%) were recrystallized twice from methanol. Methyl methacrylate (Aldrich, 99%) and styrene (Aldrich, ≥99%) were distilled under reduced pressure to remove inhibitor. Methylene chloride (Fisher, Certified ACS) and triethylamine (Alfa Aesar, ≥99%) were distilled from calcium hydride and stored over 3 Å molecular sieves. 1,4-Dioxane (Acros, 99.8%, extra dry), chloroform (Fisher, Certified ACS), thionyl chloride (Aldrich, 99.5%), tetrahydrofuran (THF, Fisher, HPLC), toluene (Fisher, Optima), heptane (Aldrich, 99.8%) benzene (Aldrich, 99.8%), and 3-aminopropylmethyldiethoxysilane (APMDES, Gelest) were used as received. Deionized water had a resistivity of greater than 18.2 MΩ·cm. Methods. IR data were obtained using a Bruker IFS 66v/S FTIR in KBr. Growth from the surface was measured using a Nanofilm EP3 imaging ellipsometer operating with an internal solid-state laser at 532 nm and angle of incidence of 70°. Results were obtained from three different spots on the wafer with four measurements per spot. The refractive index was taken as 1.49 for PMMA and 1.59 for PS with the number varied according to the composition of the mixed polymer brush. The refractive indices for APMDES and ACVA were taken as 1.43 and 1.45, respectively. A liquid cell attachment was used for measuring the polymer brush swelling to THF vapor. The cell was used with an angle of incidence of 60° and attached to a temperaturecontrolled reservoir of THF and an empty syringe for drawing the vapor into the flow cell. The phase and height morphologies of the polymer brushes were characterized by an Asylum MFP3D atomic force microscope (AFM). Tapping mode images were acquired with a silicon cantilever (Nanosensors) with a resonance frequency of ∼330 kHz, a force constant of ∼42 N/m, and a tip radius of less than 7 nm. All measurements were taken in the repulsive region of the Lennard-Jones interaction force curve (phase THF > benzene, while the inverse holds for PMMA. Figure 6 demonstrates the phase morphologies of similar samples annealed in different solvent vapors. Samples J, K, and I are annealed in THF vapor and imaged by AFM and shown in
Table 2. Hildebrand Solubility Parameters of Polymers and Solvents54 solubility parameter (MPa1/2) polymer PS PMMA solvent toluene THF benzene a
17.5−19.1a 18.5−19.5a 18.2 18.6 18.8
Range due to method of measurement.
parts a, c, and e of Figure 6, respectively. Following, the samples are washed with chloroform to mix the brushes, and sample J is reannealed in toluene vapor (Figure 6b) and samples K and I are reannealed in benzene vapor (parts d and f in Figure 6, respectively). Changing the annealing solvent from THF to toluene vapor has a similar effect to increasing the fraction of PS, and as a consequence, the PS domains in Figure 6a substantially elongate (Figure 6b). The AFM phase images are analyzed to quantify the extent of each polymer on the brush surface with the areal PS percentage of sample J increasing from 46% to 55%. Conversely, changing the annealing solvent from THF to benzene is analogous to increasing the fraction of PMMA, and as a consequence, the elongated PS domains in Figure 6c substantially shorten (Figure 6d). The areal percentage of PS presented on the brush surface of sample K decreases from 51% PS to 44% PS. Even more dramatic is when solvent annealing appears to drive a phase transition. In Figure 6e, sample I appears largely in a cylindrical phase when annealed in THF but clearly is in the ripple phase when annealed in benzene (Figure 6f). The areal percentage of PS at the brush surface dramatically decreases from 68% PS to 55% PS. While there is a clear trend between polymer fractions and annealing solvent, the polymer areal percentages of PS and PMMA measured do not always match overall volume fractions of the brush. We speculate that the solvents have a tendency to change the partitioning of the polymers, thereby altering the composition of polymer domains. In other words, the amount of minority polymer comprising a domain changes with the annealing solvent. It is also possible that the phase morphology presented on the top surface changes with depth; however, a previous study which etched into the polymer brush showed the composition changed little with depth.34 Large Cell SCFT Morphologies. The lowest free energy morphologies predicted by the unit cell SCFT calculations exhibit perfect long-range order, while as is clear from this work and previous experimental work, long-range order has not been observed to date in mixed polymer brushes. Perfect long-range 519
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Figure 6. AFM phase images of (a, b) sample J, (c, d) sample K and (e, f) sample I annealed for 24 h in THF vapor (a, c, e), toluene vapor (b), and benzene vapor (d, f). Phase range = 6°.
order is difficult to achieve even in diblock copolymer thin films, which exhibit various defects unless efforts are made to align the domains. However, mixed brushes typically do not show as much order as copolymer films. Previous computational and experimental work proposed that the lack of long-
range order in mixed brushes is due to heterogeneities in the grafting densities of the two polymers.36,42,43 To explore this possibility, we performed large cell SCFT calculations in which the composition of the grafting density was not uniform. Instead, the grafting density of A polymers was generated using 520
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correlated Gaussian random fields
⎡ |x − x′ |2 ⎤ ⟨φA (x⊥)φA (x′⊥ )⟩ = λ exp⎢ − ⊥ 2 ⊥ ⎥ ⎢⎣ ⎥⎦ 2σ with an average lateral A grafting density (normalized by the total grafting density) of ⟨φA(x⊥)⟩ = fA. The total grafting density of A and B polymers is kept fixed, so grafted B chains compensate accordingly for fluctuations in the A grafting density. Calculations are performed at χN = 16 for mixed brushes of height 3Rg as before, with lateral dimensions of 50Rg. The amplitude of the correlations was fairly low, λ = 0.02, and the length scale (standard deviation) of the correlations in the grafting density was taken to be σ = 0.5Rg. Since the distance between grafting points is on the order of 2.5−3 nm, or around (0.25−0.3)Rg (see Table 1), it seems reasonable to assume that experimental variations in grafting density would be at least this large but probably not much larger than Rg. We found that varying the length scale σ of the grafting density correlations between 0.35Rg and 0.7Rg resulted in very similar morphologies, so here we present results for σ = 0.5Rg. The simulated morphologies of the brush with grafting density fluctuations are shown in Figure 7 for various values of fA along with the corresponding morphologies assuming uniform grafting of both polymers. In these calculations, the SCFT fields W− and W+ are given random initial values, and the free energy is relaxed to its stationary value at χN = 16 using a steepest descent search method. This corresponds to a fairly rapid quenching of the brush from the disordered to an ordered state. For the cases with uniform grafting, the mixed brush forms well-ordered domains of the appropriate phase (as determined by the phase diagram), but there are still some defects present. The hemispherical and cylindrical phases display hexagonal ordering, and the ripple phases show the distinctive “fingerprint” texture commonly observed in lamellarforming block copolymer thin films as we noted previously.40 If the value of χN is slowly increased (annealed), the systems with uniform grafting will eventually converge to states with few or no defects. Introducing fluctuations in the relative grafting density of the two species has a significant effect on the morphologies. As shown in Figure 7, all the morphologies show considerably less order. There are some elongated domains in the cylindrical phase at fA = 0.3, and in all cases there is more variation in domain size than for the uniformly grafted brushes. The simulated morphologies appear qualitatively very similar to the AFM images in Figure 4. We note that for the cases with fluctuations in the grafting density annealing the systems slowly instead of quenching does not lead to significant differences in the morphologies of Figure 7. Autocorrelation of Polymer Domains. An ideal binary brush is formed when the following are true: (1) monodisperse polymers, (2) linear polymers, and (3) uniform grafting density. When annealed in a melt, these ideal brushes are predicted to assemble into the phases of the left-hand column of Figure 7. Even minor variations in polymer grafting density disrupts the long- and short-range ordering predicted to form in melts from ideal binary brushes. It is certain that our experimental PS/PMMA brushes contain a combination of nonidealities that generate phase morphologies qualitatively similar to predicted SCFT simulations of binary brushes incorporating fluctuations in grafting density (Figure 7, righthand column). Additionally, solvent annealing evidently does
Figure 7. SCFT phase images (top surface) of a mixed polymer brush of height 3Rg and lateral dimensions of (50 × 50)Rg at χN = 16 for various fA: (a, b) fA = 0.1, (c, d) fA = 0.3, (e, f) fA = 0.4, and (g, h) fA = 0.5. While (a, c, e, g) have uniform grafting density distributions, the normalized grafting density distributions of A chains in (b, d, f, h) are generated using correlated Gaussian random fields with a mean value of fA. In all cases the total grafting density is uniform over the domain.
not create a fully equilibrated melt adding further deviation of our experiments from SCFT predictions. To gain a quantitative measurement of order and domain spacing in both our experiments and simulations, the autocorrelation of polymer domains was calculated as a function of radial distance, as shown in Figure 8. The autocorrelations in the experimental systems are significant and qualitatively similar to those predicted by the SCFT simulations. This is particularly true for the SCFT results with fluctuating grafting density. In that case, for both cylindrical and ripple phases, the amount of correlation among domains as measured by the magnitudes of the first trough and subsequent peak is similar in the experiments and the SCFT results, indicating a similar degree of order. From Figure 8a we can discern five positive peaks beyond the radial center indicating at least a measurable long-range correlation distance of ∼480 nm. Additionally, we can obtain a nearest-neighbor distance of PS domains of 109 nm or 521
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Figure 8. Radial autocorrelation functions calculated for the cylindrical morphology (a, c, e) and ripple morphology (b, d, f). Experimental samples: (a) sample E (PS fraction = 0.38) and (b) sample H (PS fraction = 0.58). SCFT Simulations with uniform grafting density distributions: (c) fA = 0.3 and (d) fA = 0.5. SCFT simulations with fluctuating grafting density distributions (λ = 0.02): (e) fA = 0.3 and (f) fA = 0.5.
∼11.5Rg for sample E. Comparing to SCFT simulations with fA = 0.3, we find nearest-neighbor distances of polymer A cylindrical domains to be 5.3Rg for uniform grafting density distributions and 6.15Rg for fluctuating grafting density distributions (Figure 8, parts c and e, respectively). The slightly greater Rg distances of nearest-neighbor cylindrical domains with fluctuating grafting density is a result of the disruption of domain packing. However, this small increase does not account for the almost 2 times increase in nearestneighbor spacing measured for the experiments when compared to the SCFT simulations. The ripple morphology yields similar results. We can discern from Figure 8b four positive peaks beyond the radial center, indicating at least a measurable long-range correlation distance of ∼450 nm. Additionally, we can obtain a nearest-neighbor distance of 112 nm or ∼12.5Rg for sample H. Comparing to SCFT simulations with fA = 0.5, we find nearest-neighbor distances of polymer A ripple domains to be 5.7Rg for uniform grafting
density distributions and 6.0Rg for fluctuating grafting density distributions (Figure 8, parts d and f, respectively). There are several likely contributions to the discrepancy in domain spacing. The experimental systems are at higher χN values than the simulations, and we expect the domain spacing to increase with increasing χN. However, on the basis of the domain spacing for the hexagonal phases for 10 < χN < 20,40 we estimate the domain spacing at χN = 35 to be larger by only about 5%. The experimental systems are annealed in solvent vapor, which could lead to larger domain sizes than the SCFT results due to swelling in the solvent. Solvent could affect the various phases differently due to small differences in selectivity of the solvent for the PS as compared to the PMMA domains. Preliminary results indicate that the domain spacing also increases with increasing values of both λ and σ. In particular, increasing the amplitude of the grafting density correlations from λ = 0.02 to λ = 0.1 for the ripple phase leads to an increase in the domain spacing from 6.00Rg to 6.35Rg. Details of the 522
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twice that predicted by SCFT simulations even with a fluctuating grafting density accounted for. As the simulations do not account for the full complexity of the experimentally generated brushes, it is reasonable to expect there to be this difference. Future experiments will seek to improve the convergence of experimentally observed phases with theoretical predictions. We anticipate the advancements presented here to provide a basis for improving both the physical fabrication and computational predictions of nanopatterned mixed polymer brushes. Like nanopatterned block copolymer surfaces which are coming into their own, this complementary technique has enormous potential to transition from a laboratory curiosity into a driver for technological innovation.
grafting density fluctuations are difficult to measure experimentally. We could in principle adjust λ and σ so that the SCFT calculations would fit the measured domain spacing, but this would lead to morphologies that look qualitatively different than the experimental morphologies. A detailed SCFT study of the effects of varying the grafting density fluctuations with a range of λ and σ values will be presented in a future manuscript. Finally, unlike the simulations, the PS/PMMA brushes contain significant polydispersity in both polymers, and the average molecular weights of PS and PMMA are not exactly the same (see Table 1). Previous studies of microphase-separated block copolymer systems have observed similar increases in domain spacing with polydispersity for both lamellar and cylindrical structures.64−67 In polydisperse systems, it is speculated that the overall stretching energy is reduced by recruiting larger polymers into the center of domain structures to minimize the stretching of the smaller ones. To the best of our knowledge, no study has characterized the influence of polydispersity on domain spacing in laterally separated binary polymer brushes, but on the basis of the results here, it is reasonable to anticipate a similar trend.
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ASSOCIATED CONTENT
S Supporting Information *
AFM height and phase images of chloroform solvent annealed PS/PMMA brushes (Figure S1); AFM phase images of PS/ PMMA brushes annealed from a melt (Figure S2). This material is available free of charge via the Internet at http:// pubs.acs.org.
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CONCLUSIONS The phase morphologies of binary brushes annealed under nonselective conditions were explored by a combination of experiment and SCFT simulations. The phase morphologies were determined by varying the grafting density of one polymer while keeping the overall grafting density constant. To grow mixed polymer brushes of PS and PMMA, free radical initiators were immobilized on a surface and successively initiated in the presence of styrene followed by methyl methacrylate to form a series of samples with PS volume fractions ranging from 0.00 to 0.68. Careful attention was paid to the surface chemistry to create a uniform initiator layer and minimize heterogeneities in the final mixed brush. Additionally, the experimental setup was designed to minimize the effect of molecular weight differences on the equilibrium melt morphology. SCFT simulations of a binary polymer brush annealed under melt conditions predicted disordered, hexagonal, and ripple phases above a critical χN value. At high χN values the phase transition boundaries change little with χN and provide guidance to the phase transition boundaries in our PS/ PMMA brushes. Indeed, PS/PMMA brushes annealed under nonselective solvent vapor exhibited the domain structures predicted by SCFT. Our ability to achieve lateral versus vertical separation of the polymers allowed unambiguous visualization of the polymer phases as a function of polymer fraction. Observed were ripple and circular domains with the further subdivision of the circular domains into cylinders and hemispheres. The lack of long-range hexagonal packing by the circular domains, along with distortions in shape, suggests nonidealities in brush structure and annealing conditions. To create an improved approximation of the experimental system through SCFT simulations, fluctuations in the grafting density of polymers were introduced which disrupted the hexagonal order of the circular domains. Visualizations of the polymer domains calculated using SCFT showed a qualitative similarity to our experiments. The calculated autocorrelation functions for the domain structures showed a similar degree of order in both the experiments and the SCFT simulations for systems with grafting density fluctuations. However, the experimental nearest-neighbor spacing of the polymer domains in both the cylindrical and ripple phases was approximately
AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected]. ACKNOWLEDGMENTS This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under Contract DEAC04-94AL85000. Partial support was also provided from the MARCO Center on Functional Engineered Nano Architectonics (FENA) and the Sandia National Laboratories LDRD program.
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dx.doi.org/10.1021/ma202542u | Macromolecules 2012, 45, 510−524
