Retardation of Grain Growth and Grain Boundary Pinning in Athermal

Feb 4, 2014 - Filler addition is shown to reduce the rate of grain growth and to induce grain size distributions that deviate from the log-normal type...
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Retardation of Grain Growth and Grain Boundary Pinning in Athermal Block Copolymer Blend Systems Hyung Ju Ryu,† Jane Sun,† Apostolos Avgeropoulos,‡ and Michael R. Bockstaller*,† †

Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, Pennsylvania 15213, United States ‡ Department of Materials Science and Engineering, University of Ioannina, University Campus - Dourouti, 45110 Ioannina, Greece S Supporting Information *

ABSTRACT: The effect of filler addition on the grain coarsening characteristics of block copolymer materials is analyzed for the particular case of a lamellar poly(styrene-b-isoprene)-type block copolymer and polystyrene as well as polystyrene-grafted nanoparticle fillers. Filler addition is shown to reduce the rate of grain growth and to induce grain size distributions that deviate from the log-normal type that is characteristic for pristine block copolymer systems. The retardation of grain growth is shown to be associated with the segregation of filler additives into high energy grain boundary defectsa process that bears similarities to the segregation of impurity atoms within grain boundary structures in ceramics or metals. The analysis of grain boundary energy, grain size distribution, and grain coarsening kinetics suggests two major mechanisms for the interference of filler additives with grain coarsening: First, the segregation of fillers into boundary regions lowers the relative grain boundary energy and hence the driving pressure for grain growth. Second, the formation of particle aggregates along grain boundaries gives rise to a “pinning pressure” that counteracts grain growth and that limits the ultimate grain size during thermal annealing. This is in contrast to pristine block copolymer systems in which continuous grain growth is observed during thermal annealing. The results highlight the fundamental differences between structure evolution in pristine and mixed block copolymer systems and suggest that thermal annealing (in the absence of structure-guiding fields) is an inefficient path to facilitate the controlled growth of large grains in athermal block copolymer blend materials.

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INTRODUCTION

requisite for the exploitation of BCPs as novel functional materials. In a previous paper (that we will refer to in the following as “Grain Coarsening-I”) we analyzed the role of GB defects on the coarsening characteristics of a one-component (i.e., pristine) near-symmetric poly(styrene-b-isoprene) (PS−PI) copolymer.15 Grain coarsening in this lamellar BCP model system was found to proceed via the initial relaxation of “frozen-in” kink boundary defects (that arise as a consequence of mechanical stresses during film formation) and the subsequent continuous grain growth by relaxation of symmetric tilt GBs.16 The grain growth exponent n (relating the average radius of grain ⟨R(t)⟩ to the time of thermal annealing via ⟨R(t)⟩ ∼ t1/n) was found to be n ≅ 1.8, consistent with normal grain growth kinetics that is commonly observed in periodically ordered materials such as metals or ceramics, thus suggesting that the reduction of GB energy plays a major role as driving force for grain coarsening.15,17−20 However, it is important to note that the grain coarsening characteristics of pristine

Block copolymer (BCP)-based materials have been widely proposed as a platform for innovative material technologies in areas ranging from dynamic photonic sensors to solid state ion conductors or bulk heterojunction materials for polymer photovoltaics.1−12 A common thread among many of these proposed applications is that the copolymer presents a template for “functional fillers” and that the material performance depends on the transport characteristics of the filler within the copolymer host. Examples encompass the use of BCPs as solid state ion conductors where electrolytes are being added to facilitate ion transport or the application of BCPs as tunable photonic crystals in which reversible solvent swelling enables the dynamic modulation of domain thickness and associated optical properties.3,13,14 Because transport is intimately related to the tortuosity of diffusion pathways within a material, the performance of BCPs in applications such as the ones described above is expected to strongly depend on the presence of grain boundary (GB) defects as they disrupt the long-range periodicity within the material. Understanding of the parameters that govern the formation and annealing of GB defects in BCP microstructures is therefore an important © 2014 American Chemical Society

Received: October 22, 2013 Revised: January 28, 2014 Published: February 4, 2014 1419

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120 °C), where χ is the Flory−Huggins parameter.28 Polystyrene homopolymer (hPS) with molecular weight Mw = 35 kg/mol and molecular weight dispersity index Mw/Mn = 1.18 was obtained from Polymer Source Inc. and used without further purification. PS−PI films with a homopolymer weight fraction of 1, 3, and 10 wt % were prepared by dissolution of appropriate amounts of homo- and copolymer in toluene (concentration 5 wt %). Films of 1 mm thickness were cast from toluene solution at T = 23 °C at a partial pressure of toluene of p = 80 mbar (pressure was controlled using a modified Buchi Rotavapor R-200); the time for solvent evaporation was 8 h. Samples were thermally annealed in vacuum at 120 °C for 0, 3, and 7 days. Prior to electron imaging films were microsectioned at −120 °C using a LEICA EM FCS cryo-ultramicrotome and stained with OsO4 (selective staining of PI domains) that was obtained from EM Sciences. PS-grafted gold nanocrystals (AuPS) were synthesized following previously published procedures.29,30 Mercapto-functionalized PS (Mw = 2.5 kg/mol, Mw/Mn = 1.05) was purchased from Polymer Source and used without further purification. The particle core diameter of AuPS particles was determined as dAu = 3.5 ± 2.5 nm by electron microscopy; the grafting density was determined by thermogravimetry to be σPS = 0.6 nm−2. PS−PI/AuPS as well as PS− PI/hPS blends were prepared by mixing of appropriate amounts of material in toluene solution and subsequent solvent evaporation at 80 mbar (see above). Transmission Electron Microscopy (TEM). Electron imaging of BCP microstructures was performed using a JEOL 2000 FX electron microscope operated at 200 kV. Imaging was based on the amplitude and phase contrast, and images were recorded by a Gatan Orius SC600 high-resolution camera. Thermogravimetry (TGA). The inorganic content of AuPS was determined using a TA Instruments thermogravimeter model SDT 2960. Microstructure Analysis. Analysis of the grain characteristics as well as type and frequency of grain boundary defects was performed by image analysis following a procedure that has been described in detail in “Grain Coarsening-I”.15 Analysis of the relative energies of boundary defects in block copolymers and their blends was performed by analysis of dihedral angles as described previously.31 Small-Angle X-ray Scattering (SAXS). SAXS was performed using a Rigaku S-Max3000 with a 2D multiwire detector. Data were acquired at room temperature under vacuum. Two-dimensional SAXS patterns were azimuthally integrated to obtain plots of scattered intensity vs the modulus of the momentum transfer vector, q = (4π/λ) sin(ϑ/2), where ϑ is the scattering angle and λ = 1.54 Å (Cu Kα).

materials do rarely translate to blend systems. This is because filler species (such as additives or impurities) can interact with GB defects and alter both the energetics and kinetics of structure evolution. The effect of additives on microstructure evolution has been particularly well studied for the case of metals where alloy atoms or second-phase particle inclusions have been shown to significantly alter the evolution of grain size and shape during annealing or recrystallization.20,21 Recent research has provided evidence in support of the hypothesis that filler−GB interactions in BCP-based blend materials give rise to segregation processes that resemble the aggregation of alloy atoms within defect regions in metal alloys. For example, by using polymer-modified nanoparticles as “tracer inclusions”, Listak et al. demonstrated the segregation of particle fillers within high energy tilt and twist GB structures during thermal annealing of BCP/nanoparticle blend systems.22 The segregation of particle fillers within GB regions was argued to be driven by the associated relaxation of chains within the GB region to their equilibrium conformation and the resulting reduction of stored elastic energy.22 Support for the proposed energetic stabilization of GB defects by means of particle segregation was provided by Thompson, who analyzed the formation of symmetric tilt GB structures in BCP/nanoparticle blend systems using a hybrid self-consistent field/density functional theory.23 The segregation of particles within GB regions in BCP materials also confirmed earlier reports by Gido and coworkers, who noted a distinctive change of the morphology of high energy tilt GB structures in a lamellar BCP/homopolymer blend system as compared to the pristine BCP system.24 In summary, previous research provides ample evidence for the interaction of filler species with GB defects. Understanding of the implications of these interactions on the structure evolution in BCP blend materials therefore presents an important requisite for the development and processing of multicomponent BCP-based functional materials. The objective of this contribution is to elucidate the effect of additives on the grain coarsening process in athermal BCP/ homopolymer blend systemsthat is, blends in which there are no specific interactions (attractive or repulsive) between the filler and copolymer host domain. The material system in our study consists of the near-symmetric poly(styrene-b-isoprene) copolymer (PS−PI) of which the grain coarsening characteristics have already been established in a previous study (see “Grain Coarsening-I”) as well as polystyrene homopolymer (hPS) and PS-grafted gold nanoparticles (AuPS) as athermal additives to the copolymer.25 We demonstrate that the addition of moderate amounts of homopolymer results in the significant retardation of grain growth and alteration of the grain size distribution. The “retardation effect” is interpreted as consequence of the segregation of filler into high energy GBs, thus resulting in a reduction of the driving pressure for grain coarsening along with the pinning of GB defects. Our results therefore suggest that thermal annealing (in the absence of structure-guiding fields) is an inefficient path to facilitate formation of large-grained microstructures in (athermal) BCP blend materials.

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RESULTS AND DISCUSSION The equilibrium microstructure of PS−PI/hPS blend systems was evaluated after 7 days of thermal annealing at T = 120 °C using small-angle X-ray scattering (SAXS) as shown in Figure 1. For the neat PS−PI copolymer (see black line in Figure 1) scattering peaks are observed at odd multiples of q* ≅ 0.011 Å−1, thus confirming a symmetric lamellar microstructure in agreement with the near-symmetric composition of the copolymer. Comparison of the scattering curves of pristine PS−PI with those of the PS−PI/hPS blend systems reveals that the lamellar microstructure is retained for all blend compositions. While the position of the first-order peak in Figure 1 is found to remain approximately constant for all PS−PI/hPS systems (indicating a near-constant lamellar period), the intensity ratio of even- and odd-order peaks progressively increases with increasing hPS content. This supports the conclusion that the hPS additive is about uniformly distributed within the PSdomain of the copolymer, thus resulting in the concurrent swelling of the PS domains and contraction of the adjacent PI domains (the latter is a consequence of the constraint of equal area per junction that applies to both blocks across the domain

MATERIALS AND METHODS

Materials. Poly(styrene-b-isoprene) (PS−PI) copolymer with molecular weight Mw = 79.6 kg/mol, molecular weight dispersity index Mw/Mn = 1.05, and volume fraction of styrene component ϕPS = 0.48 was synthesized as described previously.26,27 The degree of segregation is estimated to χN ≅ 58 at the annealing temperature (T = 1420

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systems after 0, 3, and 7 days of thermal annealing is presented in Figures S1−S11 (see Supporting Information). The results presented below are based on the analysis of total reconstructed contiguous areas corresponding to 351.92 μm2 (as-cast, 0 wt % hPS), 411.78 μm2 (3 TA, 0 wt % hPS), 504.81 μm2 (7 TA, 0 wt % hPS), 443.45 μm2 (as-cast, 1 wt % hPS), 501.16 μm2 (3 TA, 1 wt % hPS), 439.53 μm2 (7 TA, 1 wt % hPS), 478.26 μm2 (as-cast, 3 wt % hPS), 465.18 μm2 (3 TA, 3 wt % hPS), 472.35 μm2 (as-cast, 10 wt % hPS), 436.58 μm2 (3 TA, 10 wt % hPS), and 511.25 μm2 (7 TA, 10 wt % hPS) where “x TA” is short for “x days of thermal annealing at T = 120 °C”. The probability plots of grain size distributions for ϕhPS = 0, 0.01, and 0.1 blend systems are depicted in Figure 3 for 0 (“ascast”), 3 (“3 TA”), and 7 (“7 TA”) days of thermal annealing along with the respective fit (solid line) and 95% confidence intervals (dotted lines) corresponding to log-normal distributions (a summary of all grain size distributions is shown in Figure S12 of the Supporting Information). The agreement between the experimental and calculated distributions for “ascast” conditions (left column in Figure 3) that is within the confidence range confirms that the initial distribution of grain dimensions in PS−PI/hPS blend systems is of log-normal-type similar to the pristine PS−PI (top row in Figure 3). Two important conclusions regarding the effect of hPS addition on the microstructure evolution process can be deduced from Figure 3: First, with increasing time of thermal annealing the distributions of PS−PI/hPS blend systems increasingly deviate from the log-normal reference distribution. Second, for a given duration of thermal annealing, the deviation increases with hPS filler content. In contrast to the blend systems, the grain size distribution of the pristine PS−PI system retains its log-normal character during the course of thermal annealing. Note that in all blend systems the deviation from log-normal behavior follows a common trend; i.e., a larger (smaller) number of small (large) grains are observed as compared to the reference distribution. This suggests that the presence of the filler exerts a “stabilizing effect” on small grains, thus retarding the coarsening process. The effect of hPS addition on the evolution of the (number) averaged grain area ⟨A(t)⟩ in PS−PI/hPS blend systems is summarized in Figure 4a. The figure reveals that the addition of very small amounts of hPS (ϕhPS = 0.01) exerts only a minor influence on grain coarsening. This is in contrast to the ϕhPS = 0.1 blend system (blue bars in Figure 4a) that depicts two significant deviations of the grain size evolution as compared to the pristine PS−PI system. First, the initial grain size in as-cast films is significantly increased in the presence of hPS with ⟨A(t=0)ϕ=0.1⟩ ≅ 2⟨A(t=0)ϕ=0⟩. This confirms previous reports by Hasegawa and co-workers, who reported the grain size in ascast films to increase with homopolymer addition.36 We interpret the increase of initial grain size after film casting to be a consequence of a reduced melt (and solution) viscosity of the blend systems that should accelerate grain growth during the nucleation and growth process of the microstructure.37,38 However, although the initial grain size in PS−PI/hPS (ϕhPS = 0.1) is increased, the rate of grain growth is significantly reduced. This is revealed in Figure 4b that depicts the grain size disparity Δ⟨A(t)⟩ = ⟨A(t)⟩ − ⟨A(t)ϕ=0⟩ in blend and pristine BCP systems during thermal annealing. The decrease of Δ⟨A(t)⟩ with increasing annealing time confirms the conclusion that the grain growth kinetics is reduced in the PS−PI/hPS blend system. Similarly, the analysis of ⟨R(t)⟩ = ⟨A(t)⟩1/2 ∼ t1/n (see inset of Figure 4b) reveals that

Figure 1. SAXS intensity profiles of PS−PI/hPS blend systems with 0, 1, 3, 10 wt % of added homopolystyrene. All samples were thermally annealed at 120 °C for 7 days. First peaks of each pattern are indicated with arrows. The beamstop position is indicated with a gray block, and patterns are offset vertically for clarity.

interface; see also refs 32 and 33).34,35 We note that the mutual offset of domain swelling and contraction and the resulting (approximately) constant lamellar thickness is consistent with previous reports on the structure formation in PS−PI/hPS blend compositions similar to the systems used in the present study.32,33 Grain Size Evolution. To elucidate the effect of hPS addition on microstructure evolution during thermal annealing, the grain structure of PS−PI/hPS blend systems was analyzed after t = 0, 3, and 7 days of thermal annealing. The upper limit of annealing time was chosen as compromise to allow for significant “domain reorganization” while preventing degradation of the polymer during annealing at elevated temperatures (the latter was tested by dissolution of samples after annealing). The grain structure analysis process was performed analogous to the procedures described in “Grain Coarsening-I”, and we refer to this previous article regarding the technical details of the grain mapping process.15 Figure 2 depicts an exemplary grain map representing the as-cast PS−PI/hPS (ϕhPS = 3 wt %). A complete account of grain maps for all PS−PI/hPS blend

Figure 2. Grain map representing microstructure of the as-cast PS− PI/hPS (3 wt %). Colors distinguish adjacent grains with misorientation exceeding θ = 15° (color selection is random); xand y-axis indicate the in-plane orientation of the film (for more details the reader is referred to ref 15). A comprehensive summary of grain maps representing other compositions is presented in the Supporting Information. 1421

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Figure 3. Log-normal probability plots representing grain size distributions after t = 0 days (“as-cast”), 3 days (“3 TA”), and 7 days (“7 TA”) of thermal annealing. The distinct concentrations of polystyrene are represented by black (ϕhPS = 0 wt %), red (ϕhPS = 1 wt %), and blue (ϕhPS = 10 wt %) symbols, respectively. The middle lines of each corresponding color indicate log-normal distribution; the two dotted lines represent the 95% confidence intervals. All grain size distributions in as-cast systems follow a log-normal distribution while PS−PI/hPS blend systems increasingly deviate from the log-normal type with increasing time of thermal annealing. The gray shaded area delineates the range of grain sizes that was considered for grain structure analysis (see ref 15).

grain growth exponent n of the ϕhPS = 0.1 system is significantly increased as compared to the pristine PS−PI system that follows normal grain growth with n = 1.8. Note that the retardation of grain growth is most pronounced during the early stage of film annealing as evidenced by the strong decrease of Δ⟨A(t)⟩ = ⟨A(t)ϕ=0.1⟩ − ⟨A(t)ϕ=0⟩ after 3 days of thermal annealing. Below this trend will be rationalized as a consequence of the stabilization of high-energy kink boundaries by filler additives and the subsequent slowdown of the early stage coarsening process that is dominated by the annealing of high-energy kink-boundary defects. To elucidate the mechanism of the interference of the hPS additive with the grain coarsening process, reference experiments were performed with PS-grafted gold nanocrystal fillers (AuPS; dAu = 3.5 ± 2.5 nm, σPS = 0.6 nm−2, Mw,PS = 2.5 kg/mol, with σPS denoting the grafting density of surface-bound PS chains) at a gold volume fraction of ϕAu = 0.02. PS-grafted gold nanoparticles were chosen for two reasons: First, the high electron density of gold results in pronounced contrast of AuPS nanoparticles within polymer matrices, thus rendering gold particles ideal “tracer inclusions” to track the segregation of filler particles. Second, established techniques (see Materials and Methods section) facilitate the synthesis of small diameter nanocrystals, such that the total effective size of AuPS filler particles approximately equals the radius of gyration of hPS (RG,hPS ≅ 5 nm). It should be noted that while the abovementioned characteristics benefit the role of AuPS as “tracer inclusions” in PS−PI blend systems, several aspects limit the scope of the conclusions that can be drawn from annealing

experiments of PS−PI/AuPS blend systems. In particular, the limited thermal stability of the Au−S bond along with the large surface energy of metals renders Au nanoparticles sensitive to Ostwald ripening and coalescence.39 Particle size and particle− matrix interactions hence become a function of thermal annealing time and render detailed comparisons with homopolymer fillers difficult. Furthermore, the contrast associated with the high electron density gold core introduces artifacts in the image analysis procedure used to determine the coarsening characteristics of the BCP microstructuresmicrographs thus need to be interpreted by manual analysis. For the reasons mentioned above we will focus in the following only on direct observations of the particle distribution along grain boundary defects rather than presenting a quantitative analysis of the evolution of microstructure in PS−PI/AuPS blend systems. Figure 5 depicts electron micrographs of high-angle tilt GBs of PS−PI/AuPS (ϕAu = 0.02) after as-cast (Figure 5a), 3 days(Figure 5b), and 7 days (Figure 5c) of thermal annealing at T = 120 °C. Whereas for as-cast conditions particles appear uniformly dispersed within the host PS domain, the formation of aggregate structures along the boundary region is observed after thermal annealing. Here we note thatconsistent with previous reports on particle segregation within GB defectsthe formation of aggregates was observed for all GB types; however, only symmetric tilt GBs will be considered in the following due to their particular significance to the graincoarsening process.15,23 1422

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perturbation of chain conformations within the boundary increases with grain misorientation, the aggregation of particle fillers is expected to depend on the tilt angle between adjacent grains. This is indeed confirmed by the data shown in Figure 6

Figure 6. Dependence of the particle aggregate diameter as a function of thermal annealing time and tilt angle in BCP/AuNP blends (for symmetric tilt GB defects). Blue squares and brown circles correspond to 3 and 7 days of thermal annealing, respectively. The lines are introduced to guide the eye. Aggregate formation is observed for tilt angles exceeding a threshold value, i.e., θ > 45°; aggregate size increases with annealing time. The inset depicts the distribution of aggregate sizes after 3 and 7 days of thermal annealing, respectively.

Figure 4. Evolution of grain characteristics during thermal annealing. (a) Evolution of number-averaged grain cross-sectional area ⟨A(t)⟩ for pristine (black) as well as PS−PS/hPS blend systems with ϕhPS = 0.01 (red) and ϕhPS = 0.1 (blue), respectively. Initial grain size in as-cast systems increases with hPS content. (b) Plot of the grain size disparity Δ⟨A(t)⟩ = ⟨A(t)⟩ − ⟨A(t)ϕ=0⟩ in blend and pristine BCP systems during thermal annealing. The disparities of the average grain size of “1 wt %” and “10 wt %” as compared to “0 wt %” are indicated with red squares and purple triangles, respectively. The grain size disparity between blend and neat systems rapidly decreases during thermal annealing. Inset shows difference in grain growth characteristics between pristine and blend systems. Black line corresponds to grain growth exponent n = 1.8.

that reveals the rapid increase of aggregate size (measured in terms of the number of particles per aggregate) at tilt angles θ > 45° and the leveling-off of aggregate size at θ > 100°.40 We note that this trend mirrors the corresponding dependence of the GB energy on grain misorientation (see Figure 7) that depicts a rapid increase of GB energy in the low-angle region and a leveling-off for tilt angles θ > 90°. We hypothesize that the threshold angle for particle aggregation that is revealed in Figure 6 is determined by the competition between the release of stored elastic energy and the loss of particle placement entropy that is associated with the confinement of particles within the narrow GB regions. A further important conclusion from Figure 6 is that distinctive aggregate structures can be observed already after only 3 days of thermal annealing. Although minor differences between the kinetics of segregation of particle and homopolymer fillers are likely, it is plausible that hPS additives will exhibit a segregation behavior

With increasing annealing time the size of the aggregates increases, thus indicating a diffusion-based segregation process (the latter is superimposed to the process of particle coarsening that is evidenced by the increase of the size of “individual” particles during thermal annealing). We interpret the segregation of particle fillers as being driven by the release of stored elastic energy that results from the relaxation of perturbed chain conformations along the boundary. Since the

Figure 5. Representative transmission electron micrographs of tilt GBs in BCP/AuNP blends after 0 days (panel a), 3 days (panel b), and 7 days (panel c) of thermal annealing at T = 120 °C. Particle aggregate formation is observed in thermal annealed systems; the aggregate size increases with thermal annealing time. Scale bars correspond to 100 nm. 1423

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Solute Effect on GB Energy and Coarsening Kinetics. The results presented above suggest that the retardation of grain growth is related to the segregation of fillers into highangle tilt GBs (that play a dominant role during the early stage of grain coarsening, see also “Grain Coarsening I”). This implies two possible pathways for the interference of fillers with the grain coarsening process, i.e., the retardation of grain growth as the consequence of the thermodynamic stabilization of GB defects or due to the “immobilization” of GB defects within the microstructure. To assess the effect of hPS segregation on the energy of GB defects, the relative energy of symmetric tilt GBs was determined as a function of grain misorientation (i.e., tilt angle) by triple-junction analysis following analogous procedures as described in ref 31. Figure 7 presents the relative boundary energy γrel. for the pristine PI−PS as well as the PS− PI/hPS (ϕhPS = 0.1) blend system after 7 days of thermal annealing. Note that in Figure 7 the relative GB energies for both systems are normalized with respect to the corresponding energies at θ = 15° to allow for the quantitative evaluation of the effect of filler addition on the relative GB energy. The tilt angle θ = 15°i.e., the smallest experimentally accessible angle for triple-junction analysiswas chosen as a reference value because the absence of filler segregation in the low-angle range (as determined from Figure 6) should render GB energy approximately independent of the presence of filler additives. This assumption allows for the direct comparison between γrel.(θ) in pristine and blend systems.41 Similar to the pristine PS−PI system (black circles), the GB energy is found to strongly increase in the low-angle region and to level off at intermediate tilt-angles (θtrans ≅ 78°). In agreement with the pristine system, the transition between the two GB energy regimes was found to be related to the reconstruction of the boundary structure from Chevron (Ch) to Omega (Ω) type (results not shown here).42,43 Interestingly, Figure 7 reveals that although the overall trend of GB energy is similar in the pristine and BCP blend systems, γrel.(θ) is consistently reduced in the presence of homopolymer additivethe maximum reduction corresponds to approximately 25% and is observed at tilt angles θ > 70°. This is in agreement with the expectation that filler segregation into GBs should reduce the energy penalty of GB formation. The observed reduction of GB energy in the presence of homopolymer filler supports prior predictions by Schick and co-workers, who analyzed GB formation in pure and mixed lamellar BCP systems using self-consistent field simulations.44 For example, a volume fraction ϕ = 0.3 of added homopolymer component to a symmetric BCP in the weak segregation limit

Figure 7. Plot of relative GB tensions as a function of tilt angle after 7 days of thermal annealing in pristine PS−PI as well as PS−PI/hPS (10 wt %). Grain boundary energy is normalized to respective values at θ = 15° (see text for more details). Relative GB energy in the PS−PI/hPS blend system is reduced by approximately 25% as compared to pristine PS−PI. The transition of Chevron to Omega structure is observed at the threshold angle θtrans ≅ 78° for PS−PI/hPS as compared to θtrans ≅ 85° for the pristine PS−PI. Inset shows dependence of frequency of GB defects on GB energy. Note that GB frequency in pristine PS−PI follows approximately a Boltzmann-type distribution while the PS−PI/ hPS (ϕhPS = 0.1) system shows pronounced deviation from the linear Boltzmann trend.

similar to AuPS filler particles. (We note that the radius of gyration of the added polymer equals about the total estimated size of AuPS particle fillers, i.e., 2RG,hPS ≅ dAuPS, and thus the diffusion kinetics of both filler systems should be comparable.) This proposition is also supported by recent numerical simulations by Thompson, who predicted the segregation of athermal nanoparticle fillers within the defect regions of lamellar BCPs. In fact, the observed dependence of AuPS aggregate size on the tilt angle (see Figure 6) qualitatively agrees with the simulated morphologies of homopolymer aggregates in symmetric tilt boundary defects (compare, for example, Figure 2 in ref 23). In this context it is interesting to note that the trend of grain size evolution in PS−PI/AuPS blend systems was found to be similar to the PS−PI/hPS system (based on manual analysis, see Figures S13−S15 in Supporting Information). We therefore conclude that the trend toward segregation of dispersed fillers into high-energy GB regions is a general property of athermal small filler species. Scheme 1 illustrates the proposed correspondence between hPS and AuPS segregation for the case of high-angle symmetric tilt boundaries.

Scheme 1. Illustration of Filler Aggregation within High-Angle Symmetric Tilt Grain Boundaries

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Scheme 2. Illustration of the Restraining Force That Is Exerted by a Spherical Second Phase Particle Inclusion Located on a Grain Boundary That Is Moving under the Driving Pressure P (Adopted from Ref 20)

structures depicted in Figure 5)the total pinning pressure acting on a boundary is given as PZ ≈ f vγR/r2, where f v denotes the aggregate volume fraction, R ≅ ⟨A⟩1/2 is the average grain radius, and r is the radius of the second-phase particle (here: the aggregate).49 Note that the above relation suggests that the drag that will be exerted by the aggregates on the boundary will increase with grain size and boundary tension as well as decreasing aggregate size. Thus, the formation of even small AuPS (or hPS) aggregates along kink grain boundaries during the early annealing state will be effective in restraining grain growth. An important conclusion from the above discussion is that growth of a grain is expected to cease when a critical grain size is reached such that the net driving pressure (P − PZ) vanishes. This is indeed supported by the experimental data shown in Figure 3 that suggest larger grains to stagnate in PS− PI/hPS (ϕhPS = 0.1) blend systems even during prolonged thermal annealing.

was predicted to reduce the energy of tilt GBs by about 50% as compared to the pristine copolymer systemalthough filler segregation was not mentioned as a possible cause for GB energy reduction.44 A second notable difference between pristine and blend systems is in the relation between the frequency νrel and the relative energy γrel of GB defects that is depicted for “7 TA” samples in the inset of Figure 7. While the frequency of tilt GBs follows a Boltzmann-type distribution (i.e., νrel ∼ exp[−γrel]) for large relative GB energies in the pristine PS−PI, a distinct deviation of νrel from the Boltzmanntype trend is observed in case of the PS−PI/hPS (ϕhPS = 0.1). Below we will rationalize the non-Boltzmann-type trend as a consequence of the pinning of high-angle tilt GB defects by particle aggregates that form along the boundaries. The reduction of GB energy in the presence of hPS filler that is revealed in Figure 7 provides a rationale for the reduced grain growth kinetics in PS−PI/hPS blend systems (see Figure 4). According to reaction rate theory (that has been successfully applied to describe the migration of GBs in a wide range of materials), the velocity u of a boundary is assumed to be proportional to the mobility M of the boundary (that depends on the diffusivity and structural characteristics of the material) as well as the driving pressure P.21 Following to the grain growth theory by Burke and Turnbull, the driving pressure for grain growth is proportional to the mean grain curvature ⟨A⟩−1/2 and given by P = βγ⟨A⟩−1/2 where β is a geometrydependent numerical constant of the order unity and γ is the surface tension.20,21,45−47 Thus, the reduction of the relative GB energy γrel in PS−PI/hPS blend systems is expected to reduce the driving pressure for grain growth and hence the kinetics of grain coarsening. However, while the reduction of the driving pressure is consistent with the reduced grain growth kinetics it cannot explain the observed stabilization of small grain sizes and the associated deviation from the log-normal type grain size distribution in PS−PI/hPS blend systems that is observed in Figure 3. We therefore propose a second mechanism for the interference of additives with the grain-coarsening process, i.e., the pinning of high-angle GB defects by aggregate structures. Boundary pinning was first analyzed for metal alloys by Zener, who proposed that in the presence of second-phase particles the velocity of a moving boundary is given by u = M(P − PZ), where PZ denotes the pinning pressure.48 The latter can be estimated as PZ = NAFZ, where NA denotes the number of aggregates per GB unit area and FZ the restraining force of one aggregate. For a spherical aggregate structure the boundary restraining force can be estimated from the geometry depicted in Scheme 2 as FZ = rπγ cos α sin α, where r is the aggregate radius and γ the boundary tension. Hutchinson improved on Zener’s theory and demonstrated thatfor the case of boundaries decorated with a regular array of second-phase particles (as is the case for the aggregate

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CONCLUSIONS Our results demonstrate that the presence of athermal particle or homopolymer additives significantly alters the graincoarsening characteristics of BCP materials. In particular, we find that increasing filler content results in the retardation of grain growth and the deviation of the grain size distribution from the log-normal type that is characteristic to pristine BCP materials. The pronounced slowdown of the grain growth kinetics in BCP blend systems is rationalized as a consequence of the segregation of filler species within high-energy GB regions, thus resulting in the stabilization and pinning of GB defects and the overall reduction of the driving pressure for grain growth. The results highlight the fundamental differences between structure evolution in pristine and athermal BCP blend systems. The pinning of grain boundary defects suggests the existence of a limiting grain size (that is determined by the balance of driving and pinning pressure) that constrains grain growth in athermal BCP blend systems. This is in contrast to pristine BCP systems in which grain growth is found to be continuous, and hence grain size continuously increases with thermal annealing time (within a limit that is determined by the frequency of slow-moving boundaries; see ref 15). This fundamental difference between the coarsening characteristics in pristine BCPs and BCP blend systems should be of relevance to a wide range of BCP-based material applications that encompass the blending of BCPs with additives. The processing of these blend materials, for example, with the aim to engineer particular microstructure or texture characteristics, will have to account for filler segregation and pinning effects that can result in the stagnation of grain size and more heterogeneous morphologies.50 Tailoring the interactions 1425

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between boundary and filler could provide opportunities to further modulate the effect of filler addition and realize novel processing pathways of BCP blend materials with controlled microstructure. Finally, we want to emphasize that structure coarsening in block copolymers (as in other materials) is a complex processthe details of which are expected to depend on a range of parameters such as chemical composition, interactions, melt viscosity, or chain asymmetry.51 More research will be necessary to better understand the relative relevance of the various governing parameters on microstructure coarsening.

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(14) Singh, M.; Odusanya, O.; Wilmes, G. M.; Eitouni, H. B.; Gomez, E. D.; Patel, A. J.; Chen, V. L.; Park, M. J.; Fragouli, P.; Iatrou, H.; Hadjichristidis, N.; Cookson, D.; Balsara, N. P. Macromolecules 2007, 40 (13), 4578−4585. (15) Ryu, H. J.; Fortner, D. B.; Lee, S.; Ferebee, R.; De Graef, M.; Misichronis, K.; Avgeropoulos, A.; Bockstaller, M. R. Macromolecules 2013, 46 (1), 204−215. (16) The particular relevance of symmetric tilt GBs for grain coarsening was interpreted as the consequence of favorable kinetic pathways (such as GB splitting) to facilitate the transformation process. (17) We note that the present article focuses on the microstructure evolution in bulk BCP systems. It will be interesting to compare the role of grain boundary defects in 3D materials to the role of 1D defects (dislocations and disclinations) that has been previously evaluated in thin film (2D) geometries. For related work on thin film materials the reader is referred to refs 18 and 19 and citations therein. (18) Harrison, C.; Adamson, D. H.; Cheng, Z.; Sebastian, J. M.; Sethuraman, S.; Huse, D. A.; Register, R. A.; Chaikin, P. M. Science 2000, 290, 1558−1561. (19) Hahm, J.; Sibener, S. J. J. Chem. Phys. 2001, 114, 4730−4740. (20) Humphreys, F. J.; Hatherly, M. Recrystallization and Related Annealing Phenomena, 2nd ed.; Elsevier: Oxford, UK, 2004. (21) Gottstein, G.; Shvindlerman, L. S. Grain Boundary Migration in Metals: Thermodynamics, Kinetics, Applications; CRC Press: Boca Raton, FL, 2000. (22) Listak, J.; Bockstaller, M. R. Macromolecules 2006, 39 (17), 5820−5825. (23) Thompson, R. B. J. Chem. Phys. 2010, 133 (14), 144902-1− 144902-5. (24) Burgaz, E.; Gido, S. P. Macromolecules 2000, 33 (23), 8739− 8745. (25) The choice of filler species is motivated as follows: homopolymer additives present a model for athermal impurities such as residual macroinitiator that are ubiquitous side products of many industrial-scale synthetic procedures. PS-grafted gold particles present tracer inclusions that interact similarly with the BCP host domain as hPS additive. (26) Hadjichristidis, N.; Iatrou, H.; Pispas, S.; Pitsikalis, M. J. Polym. Sci., Part A: Polym. Chem. 2000, 38 (18), 3211−3234. (27) Iatrou, H.; Avgeropoulos, A.; Hadjichristidis, N. Macromolecules 1994, 27 (21), 6232−6233. (28) Balsara, N. P. Thermodynamics of Polymer Blends. In Physical Properties of Polymer Handbook; Mark, J. E., Ed.; AIP: New York, 1996. (29) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. J. Chem. Soc., Chem. Commun. 1994, 7, 801−802. (30) Hui, C. M.; Pietrasik, J.; Schmitt, M.; Mahoney, C.; Choi, J.; Bockstaller, M. R.; Matyjaszewski, K. Chem. Mater. 2014, 26 (1), 745− 762. (31) Ryu, H. J.; Fortner, D. B.; Rohrer, G. S.; Bockstaller, M. R. Phys. Rev. Lett. 2012, 108 (10), 107801-1−107801-5. (32) Winey, K. I.; Thomas, E. L.; Fetters, L. J. Macromolecules 1991, 24 (23), 6182−6188. (33) Hashimoto, T.; Tanaka, H.; Hasegawa, H. Macromolecules 1990, 23 (20), 4378−4386. (34) We note that several features of the SAXS data presented in Figure 1 merit further explanation. First, the increase of intensity of the second-order peak in case of the ϕhPS = 0.01 system is surprising (since the overall composition is more symmetric, a decrease would be expected). We rationalize the observed trend as being caused by a minor error in the reported composition of the PS−PI block copolymer that likely is more symmetric than determined form 1H NMR analysis. Second, a minor shift to larger q of the higher order peaks is observed with increasing hPS content. We rationalize this shift as a consequence of minor fluctuations of the domain thickness that could be induced by local fluctuations of the density of the hPS between the domains (see also ref 35). Both phase separation and order−order transitions were ruled out as a potential cause of the above-mentioned trends on the basis of extensive TEM analysis

ASSOCIATED CONTENT

* Supporting Information S

Grain maps used for analysis of film microstructures; complete set of grain size distributions as well as characterization data of block copolymer/nanoparticle blend systems. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (M.R.B.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was primarily supported by the National Science Foundation via Grants DMR-1006473, EEC-0836633, and DMR-0804770. H.J.R. acknowledges Bertucci Graduate Fellowship support. Furthermore, the authors thank the members of the Mesoscale Interphase Mapping Project (MIMP) at Carnegie Mellon for helpful discussions. David Fortner is acknowledged for help with image analysis.

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REFERENCES

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including multiple large-area electron micrographs representing different sections across the film volume. (35) Roe, R.-J. Methods of X-ray and Neutron Scattering in Polymer Science; Oxford University Press: New York, 2000. (36) Yamauchi, K.; Akasaka, S.; Hasegawa, H.; Iatrou, H.; Hadjichristidis, N. Macromolecules 2005, 38 (19), 8022−8027. (37) We note that the melt viscosity of the present materials was not determined in the present case; however, the effect of homopolymer addition to reduce the viscosity of BCP melts has been demonstrated before. For example, Toy et al. investigated the effect of polybutadiene homopolymer addition on the melt viscosity of poly(styrene-bbutadiene-b-styrene) systems and reported a plasticization effect of homopolymer addition (see ref 38). Since in the present case the additive is the high-Tg polymer component, this issue cannot be fully resolved in the present work. (38) Toy, L.; Niinomi, M.; Shen, M. J. Macromol. Sci., Phys. 1975, 11 (3), 281−299. (39) Jia, X. L.; Listak, J.; Witherspoon, V.; Kalu, E. E.; Yang, X. P.; Bockstaller, M. R. Langmuir 2010, 26 (14), 12190−12197. (40) The “number of particles per aggregate” shown in Figure 6 was determined from electron micrographs as the ratio between the crosssectional area of the aggregate and individual particles, respectively, and does therefore not represent the true aggregation number (that would be difficult to determine due to the 3D nature of the aggregates). (41) A comment should be made regarding the unphysical “fluctuations” of the relative GB energy despite the apparent small experimental error of the technique used to determine γrel(θ). The error bars shown in Figure 7 were determined using a quantitative statistical method that is detailed in ref 31. However, it is important to point out that while our technique is precise, its accuracy depends on the statistics of the GB distribution across the available sample area. The latter is subject to uncertainty due to sampling errors that gives rise to the fluctuations of γrel.(θ) in the low angle range. (42) The transition from Chevron to Omega-type boundary morphologies was found to occur at somewhat smaller misorientations in the presence of hPS. However, since the difference between the critical misorientations was judged to be within the error margin of the present analysis, the results are not further discussed. (43) Note that Figure 7 depicts the relative GB energy, and thus a conclusion regarding the effect of filler on the absolute GB energy is not possible. (44) Duque, D.; Katsov, K.; Schick, M. J. Chem. Phys. 2002, 117 (22), 10315−10320. (45) Since boundary mobility is associated with diffusive processes on the molecular level, filler addition is expected to exert only a minor effect on the intrinsic boundary mobility via the reduction of the melt viscosity. (46) The grain growth model by Burke and Turnbull model assumes isotropic GB energy. In a more general treatment the dependence of the driving pressure on the misorientation between adjacent grains would need to be considered, i.e., P = P(θij). (47) Ryu, H. J.; Tong, Q.; Sibener, S. J. J. Phys. Chem. Lett. 2013, 4 (17), 2890−2895. (48) Humphreys, F. J.; Ardakani, M. G. Acta Mater. 1996, 44 (7), 2717−2727. (49) Hutchinson, W. B.; Duggan, B. J. Metal Sci. 1978, 12 (8), 372− 380. (50) Process-induced alignment could be achieved, for example, by the application of external mechanical, electrical, or magnetic fields. (51) Campbell, I. P.; He, C.; Stoykovich, M. P. ACS Macro Lett. 2013, 2 (10), 918−923.

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