Article pubs.acs.org/Macromolecules
Time Evolution of the Topography of Structured Hybrid Polymer/ Nanoparticle Systems Jenny Kim† and Peter F. Green*,†,‡ †
Department of Materials Science and Engineering and ‡Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States ABSTRACT: An important class of functional hard/soft hybrid nanocomposites is formed when nanoparticles (NPs) are induced to self-assemble within the structures of ordered A-b-B diblock copolymers (BCPs). Based on their size, NPs will preferentially reside within edge dislocations, defects, which enable the formation of surface structures, islands or holes, in BCP thin films. The islands (and holes), ubiquitous in BCP thin films, coarsen in a manner reminiscent of 2-dimensional phase ordering systems of binary alloys, where the growth is self-similar, governed by classical capillarity driven Ostwald ripening and coalescence mechanisms. In the pure BCP thin films, coarsening initially occurs via coalescence and at later times via Ostwald ripening. In BCP/nanoparticle systems, the dynamics are considerably slower, and throughout similar time scales, the mechanism of coarsening occurs predominantly via coalescence. Contributions to the structural evolution due to Ostwald ripening are comparatively small over these time scales. Our assessments are based on an analysis of the power law growth exponents and of probability density distribution functions of data obtained from samples using microscopy.
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INTRODUCTION Control of the structure and properties of materials at the nanoscale is a key challenge associated with the development of nanostructured materials for many technological applications. Hybrid soft material/nanoparticle (NP) systems are viable for a wide range of applications, from biosensors and batteries to optoelectronic devices.1−11 Macromolecules such as conjugated polymers, block copolymers, liquid crystals, and proteins exhibit an ability to self-assemble over various length sales.12−18 Lithographic processes may be exploited to create templates on which the chemistry and topography may be tailored; such engineered substrates enable additional control over the structure and long-range order of these soft materials that possess an intrinsic ability to self-assemble.6,15,19−23 Of interest in this study are A-b-B diblock copolymers, which self-assemble into different geometrical structures (spherical, hexagonal, lamellar), possessing long-range order. When mixed with nanoparticles, the A/B domains act as scaffolds, directing the self-assembly of nanoparticles, provided the nanoparticles are sufficiently smaller than the A- or B-rich domain dimensions. Defects such as dislocations and grain boundaries are ubiquitous within the structure of these materials.24,25 These structural disruptions occur randomly during the assembly process often during solvent evaporation; consequently, internal stresses develop and disorientations of ordered domains occur.26 Controlling the defect formation and distribution in these systems during processing is a major challenge. With regard to thin A-b-B diblock copolymer systems, it is well-known that when the A and B bocks are comparable in size, the material forms a lamellar structure; the lower surface © 2012 American Chemical Society
energy component resides at the free, air/vacuum, interface. Specific chemical interactions determine whether the A or B component resides at a substrate.28,29 The topography of a thin film A-b-B copolymer is composed of islands or holes, provided the film thickness, h, does not meet certain selection criteria.28−30 For the case of symmetric wetting, where the same component resides at both external interfaces, the topographical features, islands or holes, develop when h ≠ 2nL, where n is an integer. In the asymmetric wetting case the topographies develop when h ≠ (2n + 1)L. Line defects, specifically edge dislocations, surround and facilitate the existence of islands.31 For A-b-B diblock/nanoparticle systems, the nanoparticles reside at the boundaries of islands, i.e., within the edge dislocation cores that enable formation of islands.31 We recently showed that when the size of the nanoparticles approaches that of the domain dimensions it becomes energetically more favorable for the nanoparticles to reside within the defect structures.27 A scanning transmission electron microscopy (STEM) image of the organization of the nanoparticles around an island is shown in Figure 1a. An atomic force microscopy (AFM) image of a typical island is shown in Figure 1c, and a schematic of the nanoparticles in the vicinity of an island is shown in Figure 1b. This article reports a study of the 2-dimensional structural and temporal evolution of the topography of a symmetrically wetting A-b-B diblock thin film of thickness of h < 2L. The islands in this film are shown to increase in size, with a growth Received: February 3, 2012 Revised: March 18, 2012 Published: April 4, 2012 3496
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Figure 1. Local structure, island, of a PS-b-PnBMA diblock copolymer film containing 3 wt % AuPS10. (a) Plan-view of island, imaged using HAADFSTEM, revealing NP clusters at its perimeter (b) schematic of the edge of an islands showing the location of NPs; (c) AFM topographical image of island. The films were annealed under supercritical CO2 (scCO2) conditions at a temperature of T = 60 °C and a pressure of P = 2000 psi for durations that ranged from t = 150 to 12 000 min. ScCO2 is a poor solvent that plasticizes the samples, thereby enabling the structure to get to equilibrium. A judicious choice of temperature and pressure enables control of the time scale and thermodynamics of the process. This particular choice of T and P for our experiments created a benign environment for processing of this system. We note that we annealed the pure diblock at 150 °C for long periods of time under vacuum and carefully examined the coarsening of the topography. We obtained identical results as we did in scCO2; i.e., the mechanisms that characterize the structural evolution were identical to those that occurred in the high-temperature vacuum environment under which the samples were processed. The low-temperature scCO2 environment was chosen to avoid detachment of the ligands from the nanoparticles, which occurs at high temperatures. The two sets of samples, pure PS-b-PnBMA and 5 wt % AuPS10/PSb-PnBMA, were processed simultaneously. The AuPS10/PS-b-PnBMA samples that were analyzed using STEM were fabricated by spincasting solutions onto glass substrates, from which they were floated onto a bath of distilled water. They were then picked up onto silicon nitride windows (TEM grid (SPI Supplies)). Images were taken using high annular angle dark field (HAADF) detector (Z-contrast) applying an accelerating voltage of 200 kV.
rate that exhibits a power law dependence; this behavior is selfsimilar. The classical coarsening mechanism, coalescence, is shown to dominate the growth of the islands of the pure BCP during the early stage; Ostwald ripening, where the larger islands grow at the expense of the smaller ones, became the dominant mechanism at later times.32 In the hybrid system, however, islands grew at a considerably smaller rate, primarily via coalescence, throughout the same duration. The coarsening of the islands is reminiscent of that of 2-dimensional phase ordering systems, including binary alloys, magnetic systems, and others.33,34
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EXPERIMENTAL SECTION
We begin by discussing the materials. The PS-b-PnBMA diblock copolymers of number-average molecular weight, Mn = 93 000 g/mol (Mw/Mn = 1.08), were purchased from Polymer Source, Inc. The molecular weights of PS and PnBMA blocks were Mn = 45 000 and 48 000 g/mol respectively, and the volume fraction of polystyrene was f ps = 0.56 (this system forms a lamellar structure). The nanoparticles were synthesized using the two-phase arrested precipitation method reported by Brust et al.35 Thiol-terminated polystyrene molecules (PS-SH) of number-average molecular weight Mn = 1000 g/mol (Mw/ Mn = 1.4), purchased from Polymer Source, Inc., were then grafted onto the surface of nanoparticles. The resulting brush-coated NPs were characterized by scanning transmission electron microscopy (STEM) to determine the average NP core diameter Dcore = 5.1 ± 1.2 nm and the overall diameter of the nanoparticle and the brush layer thickness DNP = 8.9 ± 1.1 nm. The grafting density of σ = 2.1 chains/ nm2 was determined based on thermal gravimetric analysis experiments. Thin films of a poly(styrene-b-n-butyl methacrylate) (PS-bPnBMA) diblock copolymer mixed with PS-ligand-coated gold nanoparticles (Au NPs) were prepared on silicon substrates; a native oxide layer, 1.5 nm thick, resided on each substrate. While the preparation methods have previously been described,27 we mention briefly that solutions containing 5 wt % Au nanoparticles, prepared using toluene as the solvent, were spin-cast onto SiOx substrates to create films of average thickness 53 nm. These films corresponded to thicknesses of h = 1.4L. For the pure BCP, the interlamellar spacing L = 35 nm, whereas L = 37 nm for the BCP/NP mixtures. The time evolution of the topographies of the films was examined using atomic force microscopy (AFM), optical microscopy (OM), and scanning transmission electron microscopy (STEM). The AFM measurements were performed using the MFP-3D Asylum Research, Inc., atomic force microscope. Silicon cantilevers (Olympus, Inc.), each with a spring constant of 42 N/m and resonant frequency of 300 kHz, were used. The OM studies were performed using an Eclipse LV 150, Nikon, optical microscope. The topographical features, island sizes and shapes, of the images were analyzed by using Image J, Igor Pro (Asylum Research, Inc.), and WSXM software.
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RESULTS AND DISCUSSION In-situ images of the topographies, specifically islands, of a pure BCP film and of a BCP/NP film were taken at various times, throughout the interval from 150 minutes 12 000 minutes, using optical microscopy (Figure 2). It is clear from the images of both systems that as the number of islands, N(t), decreases, the average area per island, ⟨S(t)⟩, increases, and the average distance between the islands increases, with increasing time t. The rate of evolution of the structure of the pure BCP sample is more rapid than that of the BCP/NP system. The islands in the images, encircled by the broken lines (Figure 1a,c,e), of the pure BCP film, gradually disappear with time; they are no longer visible after 12 000 min. In the BCP/NP system, however, small islands, enclosed within the broken line circles, still exist after 12 000 min. The process responsible for the gradual disappearance of these islands is believed to be Ostwald ripening, a capillarity driven process, wherein islands of average radius R less than a critical radius, Rc, increase in size and those of R < Rc decrease in size and eventually disappear. This phenomenon is wellknown in phase separated two-phase mixtures;33,34,36,37 we will revisit this question in further detail later. The solid circles in the images show evidence of structural evolution occurring via coalescence. The three islands initially 3497
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period of observation. This latter point is important because the coarsening theories we use to describe our observations are based on the conversation of mass. Classical coarsening theories suggest that the structure may be characterized by a single length scale. Such a length-scale should exhibit a power law dependence on time.33,34,36,38−40 The average area and number of islands, ⟨S(t)⟩ (Figure 3a) and N(t) (Figure 3b), exhibited a power law dependence on time. The behavior of the pure BCP sample is well described by ⟨Spure(t)⟩ ∼ t0.70±0.03 and Npure(t) > ∼t−0.64. In the case of the BCP/NP system, ⟨SBCP/NP(t)⟩ ∼ t0.48±0.02 and Npure(t) > ∼t−0.47. It is known that the values of the exponent, β, provide information not only about the relative rates of growth but also about differences between the physics that govern the mechanisms of growth. The most well-known studies of coarsening have been performed on binary alloy systems that have undergone phase separation. The classical theories, Ostwald ripening as well as static and dynamic coalescence, have successfully been used to describe the late-stage, coarsening, evolution of the structure of these materials.33,34,36,38−41 Parenthetically, an initially homogeneous A/B mixture, when quenched below a critical temperature, would phase separate into A-rich and B-rich phases; over time the domains increase in size. The late-stage coarsening behavior of a system in 3-dimensions, or in 2dimensions, may be described within the framework of the classical coarsening mechanisms: Ostwald Ripening or coalescence. In Ostwald ripening the growth of domains larger than a critical radius, Rc, occurs when entities (atoms or molecules) detach and diffuse from the smaller domains to the larger domains. This process is driven by differences between the local chemical potentials, determined by the local radii of curvature, of the larger and smaller domains. Atoms, or molecules, move from the smaller domains to the larger domains, both of which remain stationary. Theories34,36 based on the earlier work of Lifshitz and Slyozov (LS)38 showed that late-stage coarsening of a binary phase-separated solution, in the limit of dilute volume fraction of minority phase, where the volume fraction of domains remain constant and where the domain locations are static, ⟨R⟩ ∼tβ. When the rate-limiting step for growth is determined by the detachment of an entity
Figure 2. Time evolution of islands on pure thin film PS-b-PnBMA (a, c, e), and on PS-b-PnBMA containing 5 wt % Au nanoparticles (b, d, f) at times t = 2490 min (a, b), 5335 min (c, d), and 12 000 min (e, f). Total surface area of island for both samples remained at 22−23% throughout the annealing period. The islands enclosed by the solid circles undergo coarsening via a coalescence mechanism. The process associated with the reduction in size of the islands enclosed within the circles denoted by the broken lines present Ostwald ripening. Scale bar corresponds to 5 μm.
enclosed within the solid line circle in Figure 2a (t = 150 min) completely coalesced and reshaped, approaching a circular shape, by time t = 12 000 min (Figure 2e). This coalescence process is much slower in the BCP/NP system than in the pure copolymer. Additionally, we note that the average area occupied by the islands remain constant throughout the entire
Figure 3. Log−log plots of the time dependencies of average surface area per island, ⟨S(t)⟩, and number of islands, N(t), for pure BCP (circle) and 5 wt % NP/BCP (square) samples are plotted in (a) and (b), respectively. The data (pure: solid; 5 wt %: dashed) fitted to power law functions. Error bar is from the area analysis of islands from 4 to 5 AFM images (20 × 20 and 30 × 30 μm2) of similar areas. 3498
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Figure 4. Probability distributions of the island sizes (areas) for pure (a) and 5 wt % (b) samples for annealing times t = 970 and 6575 min.
(atom or molecule) from one domain to another, the growth exponent is β = 1/2. Alternatively, when domain growth is determined by a diffusion-limited process, the exponent was β = 1/3. These exponents are valid in 2- and 3-dimensions for the OR mechanism. Further, if the mechanism of growth occurs via dynamic coalescence, then a value of β = 1/3 is possible if the dynamics of the islands are uncorrelated. The exponent of β = 1/3, determined from the data in Figure 2 describing dynamics in the pure BCP film, appears to be consistent with that expected for both mechanisms. The exponent associated with island coarsening in the BCP/ NP system is however smaller than that of the pure BCP film; the former is β = 0.24. It is not immediately clear how to reconcile this apparent discrepancy between the exponents and the relation to the actual coarsening mechanisms. To this end, we note that in general the power law analysis may provide only limited insight into the actual mechanism of coarsening. If, for example, two mechanisms are operational simultaneously, or a different mechanism becomes dominant during different stages of coarsening, then assessments based on the magnitude of the exponent are uncertain.37,39,40 Therefore, a thorough analysis involving the use of the distribution functions, combined with a careful analysis of the images, would reveal additional insight into details regarding the structural evolution of the system. The island size distribution function F(r,t) is described in a scale invariant form F(R′=R/Rc) by theories based on Ostwald ripening and coalescence.34,38,41,42 As mentioned above, when the rate-limiting step for island growth is determined by the detachment of an entity from an island, the exponent β = 1/2. The associated time invariant distribution function is represented by
F(R′) =
4 ⎛ 2R′ ⎞ R′ ⎛⎜ 2 ⎞⎟ ⎟ exp⎜ − ⎝ ⎠ ⎝ 2 − R⎠ 2 2 − R′
(1)
where F(R′) = 0, when R′ > 2. However, for the diffusionlimited process, the growth exponent is β = 1/3, and the distribution function is shown to yield
(
CR′ 2 exp F(R′) =
28/9
( 23 − R′)
−1 3/2 − R′
)
(3 + R′)17/9
(2)
where C is a normalization constant and F(R′) = 0 for R′ > 3/2. While dynamic coalescence involves diffusion and subsequent merging of islands, static coalescence occurs due to the fluctuation of the shapes of the islands (their centers of mass remain stationary). In the case of dynamic coalescence, Smoluchowski41 suggested that R ∼ tβ, where β = 1/d(α +1) and d is dimension (d = 2 for islands on flat surface). The associated distribution function of dynamic coalescence is predicted to be F(R′) =
dW (WR′)d(α+ 1 − (1/ d)) exp( −WR′)d Γ(α + 1)
(3)
where W = Γ (α + 1 + 1/d)/Γ(α + 1) and Γ is the gamma function. Thus, the parameter α is related to details of the coarsening behavior during dynamic coalescence: for periphery diffusion α = 3/2 and so β = 1/5; for terrace diffusion (correlated) α =1 and β = 1/4; for uncorrelated diffusion α = 1/2 and β = 1/3. While the Smoluchowski equation strictly applies to dynamic (Brownian) coalescence, numerical simulations have nevertheless indicated that predictions from static coalescence (islands interact by shape fluctuation) 3499
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In the pure BCP film, the coarsening mechanism occurred primarily by coalescence during the initial stages, as shown in Figure 5b, where the Smoluchowski equation is shown to describe the data quite well (R2 ∼ 0.91). The growth exponent, β, deduced from the single fitting parameter α = 1/2 in Smoluchowski equation turns out to be 1/3, which corresponds well to the experimentally determined exponent (β ∼ 0.35). Notably, for longer time t > 3710 min, the data becomes more skewed toward higher values of S/⟨S⟩. The Smoluchowski equation no longer describes the data as well as it did during the earlier stages (R2 ∼ 0.85). In fact, these data are now described comparably using the detachment (interface)-limited Ostwald ripening equation (R2 ∼ 0.86). This suggests that the Ostwald ripening mechanism becomes more important at later time scales. The images in Figure 2 also confirm the importance of the Ostwald ripening mechanism. The importance of the Ostwald ripening mechanism should not be unexpected: as the distances between the islands increase, it would become increasingly more difficult for a coalescence mechanism to remain operational. A process involving the detachment of chains form the edge of an island, diffusion and attachment to another island, would eventually become energetically more favorable. The transition from coalescence (early growth stage) to Ostwald ripening (later stage) has been observed in other systems such as Cu on Cu(100).33,34 The foregoing analysis indicates that the late-stage coarsening of the pure BCP film initially occurs primarily via a coalescence mechanism, but at longer times, as the islands become more separated, the Ostwald ripening mechanism becomes important. The images in Figure 2 are consistent with this assessment. We now return to the BCP/NP system, whose behavior was characterized by a much smaller power law exponent. As shown in Figure 5c, the probability distributions are well described by the Smoluchowski equation for all times, with R2 > 0.9; the fitting parameters were α = 1/2 and β = 1/3. The coarsening rates are clearly much slower than that of the pure BCP film. It follows that because the coalescence process is comparatively fast in the pure BCP system, ⟨SBCP(t)⟩ = t0.2⟨SBCP/NP(t)⟩, the average distance between the islands increases more rapidly. Consequently, at later times the coarsening mechanism in the pure BCP proceeds via Ostwald ripening, since long-range mass transport between the islands becomes more favorable. In the BCP/NP system, the islands remain in proximity throughout the same time scales, so coarsening continues to evolve via coalescence. We found it instructive to examine STEM images of regions of the BCP/NP samples at two very different times (Figure 6) to gain further insight into the details of the coarsening mechanisms, first described in Figure 2. Information in Figures 2 and 6 together provide useful insight into the coalescence processes. The islands labeled 1 and 2, in both Figures 6a and 6b, are typical of islands that have coalesced. The arrows denote the direction of motion of the boundaries. In part b, the coalescence process is more advanced, and the average local curvature is reduced, thereby decreasing the surface area. Examples of this process are shown in Figure 2. The island labeled 3 has decreased in size due to the transfer of chains from its boundaries; this is expected of samples that have undergone Ostwald ripening. The groups of nanoparticles labeled 4 are remnants of islands that have disappeared. The process in the BCP/NP system is very slow due to the larger activation barrier associated with removal of chains from the islands whose cores contain nanoparticles.
theories do not provide additional length scales that would describe the behavior of the system.27 The experimental distributions, plotted in Figure 4, were determined from measurements of the number of islands within a specific area, normalized by the total number of islands. The data describing the island size distributions in the BCP film are plotted in Figure 4a; those for the BCP/NP film are plotted in Figure 4b. The distributions are plotted for two different times, 970 min and 6600 min. We computed probability densities from the data in Figure 4 for the pure BCP and the BCP/NP samples and compared them with the theoretical probability density distribution functions for coarsening. Shown in Figure 5a are the theoretical probability density distribution functions (F(R/⟨R⟩) vs R/⟨R⟩) that account for Ostwald ripening (detachment-limited, eq 1, and diffusion-limited, eq 2) and for coalescence (eq 3).34,37,39,40,43
Figure 5. (a) Theoretical probability density distribution functions, F(R/⟨R⟩) vs R/⟨R⟩, describing Ostwald ripening (detachment-limited and diffusion-limited) and coalescence respectively are plotted. Normalized size distribution of islands (S/⟨S⟩) for pure (part b) and for 5 wt % NP/BCP (part c) samples are shown at different times: t = 150 min (red circles), 3710 min (blue squares), and 6575 min (green triangles). In part b (t = 150 min) the data are best described by the Smoluchowski distribution. At longer times the data are fit by both the Smoluchowski and the detachment-limited OR distributions, in order to illustrate the change in distribution at long times. Note that the peak is shifted slightly to the right, as the positive tail disappeared, when the time increased from 150 to 3710 min. In part c (BCP/NP), the data are well described by the Smoluchowski equation throughout the same time interval. 3500
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potential) becomes increasingly important. In the hybrid system, the rate of coarsening decreases appreciably and occurs primarily via coalescence. Ostwald ripening also occurs in the BCP/NP system, as shown by the images in Figures 2 and 6, but it makes only a small contribution to the structural evolution, compared to the pure BCP system. We anticipate that Ostwald ripening will have an increasingly important contribution to the structural evolution of the BCP/NP system at much longer times, when the separation distance between island increases. Finally, we note that our data are well described by distribution functions predicted by the classical theories. These theories assume that the structure may be characterized by a single length-scale, an average domain radius ⟨R⟩, and that the dynamics are self-similar. In this regard the coarsening dynamics in the system is akin to the behavior of a large class of systems, from alloys to magnetic systems that undergo coarsening.
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was supported by the DOE office of Science, Basic Energy Sciences (BES), Synthesis and Processing Program, DOE no. DE-FG02-07ER46412.
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Figure 6. STEM images of PS-b-PnBMA with 3 wt % AuPS10, annealed for times: t = 2340 min (part a) and 12 000 min (part b). The symbols 1 and 2 in the images denote two typical islands that have undergone coalescence; the process is more complete in part b. The island (encircled) labeled 3 has reduced in size considerably from a much larger size, due to OR (see inset and text). On the other hand, the groups of nanoparticles denoted by 4 are remnants of islands that shrunk and disappeared due to OR.
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