NANO LETTERS
Rapid Transitions between Defect Configurations in a Block Copolymer Melt
2006 Vol. 6, No. 7 1574-1577
Larisa Tsarkova,* Armin Knoll,† and Robert Magerle‡ Physikalische Chemie II, UniVersita¨t Bayreuth, 95444 Bayreuth, Germany Received April 12, 2006; Revised Manuscript Received May 18, 2006
ABSTRACT With in situ scanning force microscopy, we image the ordering of cylindrical microdomains in a thin film of a diblock copolymer melt. Tracking the evolution of individual defects reveals elementary steps of defect motion via interfacial undulations and repetitive transitions between distinct defect configurations on a time scale of tens of seconds. The velocity of these transitions suggests a cooperative movement of clusters of chains. The activation energy for the opening/closing of a connection between two cylinders is estimated.
Block copolymer melts are fluid materials that microphase separate into periodic nanostructures.1 Common features for these structures are point and line defects, grain boundaries, metastable phases, as well as distortions in microdomain orientation, although defects are undesired for many applications.2,3 Modern theories and simulation methods4 have made recent advances in predicting the structure and dynamics of defects and the arrangement of microdomains at interfaces and grain boundaries. Interesting similarities have been proposed between the defect dynamics in lamella forming block copolymers and the fusion of biomembranes.5,6 In experiments, the development of defects in a monolayer of well-ordered cylindrical7-10 and spherical microdomains11,12 has been monitored by cyclic annealing and snapshot imaging with scanning force microscopy (SFM). These studies have focused on long-range interactions between paired defects and revealed similarities with defect interactions in smectic liquid crystals and crystalline solids. The reported time scales of the defects’ interaction and propagation were on the order of hours.10 In this Communication, we report on the fast dynamics of individual defects in a thin film of a cylinder forming a diblock copolymer melt that was directly imaged in the fluid state with unprecedented time resolution. The SFM movie (Supporting Information) depicts processes that have not been considered before, such as fast and repetitive transitions between distinct defect configurations and their spatiotemporal correlations on a time scale of tens of seconds. We * To whom correspondence should be addressed. E-mail:
[email protected]. † Present address: IBM Research GmbH, Sa ¨ umerstrasse 4, CH-8803 Ru¨schlikon, Switzerland. ‡ Present address: Technische Universita ¨ t Chemnitz, Chemische Physik, D-09107 Chemnitz, Germany. 10.1021/nl060825s CCC: $33.50 Published on Web 06/06/2006
© 2006 American Chemical Society
compare the time needed for the opening and closing of a connection between cylinders with the self-diffusion coefficients and propose possible molecular mechanisms that may account for this fast defect dynamics. The material was polystyrene-block-polybutadiene copolymer (SB) (Polymer Source Inc.) with the molecular weights of the polystyrene (PS) and polybutadiene (PB) blocks as 13.6 and 33.7 kg/mol, respectively, and a PS volume fraction of 26.1%. A 50-nm-thick film was prepared by spin-coating a 1.2 wt % solution in toluene on carboncoated silicon wafers. The sample was first annealed at 140 °C for 40 min to induce terrace formation and lateral ordering of the microdomains and then quenched to 105 °C for SFM imaging. Upon long-term annealing (∼20 h) at the above temperatures, the SB film splits into coexisting terraces with thicknesses corresponding to one and two layers of lying cylinders all supported by a layer of half-cylinders at the substrate.13 At these temperatures, the combined FloryHuggins parameter χN is about 30-35, which corresponds to the intermediate segregation regime.14,15 We study the microdomain dynamics at the surface of a two-cylinder-layerthick SB film on carbon coating. Under these experimental conditions, the cylinder morphology is reliably formed in thin films, and the effect of the solid substrate on the microdomain dynamics is minimized.13 In situ annealing and imaging were performed in the hot stage of a MultiMode SFM (Veeco Metrology Group) under a flow of dry nitrogen with a scanning velocity of 11 lines/s for an 1 × 1 µm2 image (with 512 × 512 pixels). Under a relative set point of ∼0.96, no measurable effect of the tip on the structure development was detected.16,17 The best scanning conditions (minimum noise at maximum phase contrast of approximately 5°) were achieved in the temper-
Figure 1. Tapping-mode SFM phase images (the phase scale is 5°). Two snapshots of the SFM movie (Supporting Information) are shown with the corresponding frame number and elapsed time. White corresponds to PS domains below a ∼10-nm-thick PB layer.13,16 The black arrow in frame 056 points to a microdomain with undulations along the cylinder axis. White arrows indicate correlated undulations in neighboring cylinders. The white square in frame 156 highlights the area displayed in Figure 2. In frame 156, characteristic defects are marked as in Figure 2.
ature range of 90-110 °C. We note that changing the scanning parameters from the optimized values to a higher scanning rate or a different amplitude set-point introduces instabilities that make imaging unsuccessful. Throughout the in situ measurements, the phase contrast between PS and PB was still a few degrees. We believe that this is due to the different viscoelastic properties of the two components at 105 °C, which is only slightly above the glass transition temperature of PS (80-100 °C) and well above that of PB (-60 °C). With custom-built software,17 the 257 SFM phase images were flattened, registered, and compiled into a SFM movie (Supporting Information). This movie starts 1 h after the quench to 105 °C and covers 4 h of annealing at this temperature. The SFM movie shows the surface structures of the fluid SB film where it is two cylinder layers thick. Continuous imaging reveals an extremely flexible behavior of microdomains, which allow for local undulations of interfacial walls, distortion of spacings, and elastic deformation of the domains. An example of the microdomains’ shape undulations can be seen in the left image of Figure 1, where we have marked the alternating dark and light regions along a PS cylinder. In some cases, these undulations appear to propagate along the cylinder axis and then vanish. In other instances, they resolve into new microdomain configurations (SFM movie). The characteristic lifetime of such undulations is greater than 1.5 s, which is the time needed to scan a single microdomain along the slow scanning axis (Figure 1). Often the undulations of a cylinder differ from frame to frame. This suggests a typical undulation period of 45 s (1 frame) and a typical propagation velocity along the cylinder axis V ≈ 1 nm/s (one microdomain spacing per frame). The undulations are often correlated within neighboring microdomains. The arrows in Figure 1 (frame 056) point to the synchronized shape undulations in an array of cylinders on a scale of about three microdomain spacings (∼100 nm). This area was scanned within 10 s, which gives a lower limit of the lifetime of these correlations. Interestingly, fast shape fluctuations with a bcc-like correlation order were observed Nano Lett., Vol. 6, No. 7, 2006
near the cylinder-to-sphere phase transition in bulk block copolymer samples.20 In addition, with dynamic light scattering a slow diffusive mode was detected and attributed to long-range density fluctuations with a correlation length of 100 nm.18,19 We note that the microdomain undulations that are visible in the SFM movie fit the above time and length scales. One of the most striking observations is the rapid opening and closing of a connection between cylindrical domains in the area marked by the white square in Figure 1 (frame 156). Examples of these oscillations are visible in frames 156-227 of the SFM movie and cover a time period of about 1 h. Figure 2 shows crops of selected frames from the abovementioned sequence. The structure marked with . fluctuates mainly between the configuration with three “open ends” (frame 166) and the configuration with two “open ends” (frame 167). The latter configuration (2) can be considered as a nucleus for a close pair of +1/2 and -1/2 disclinations, whereas the three “open ends” configuration (1) can evolve into a dislocation. To analyze the temporal evolution of the microdomain oscillations, we associate the configurational energy with the number of open ends in the structure (Figure 3a, upper curve). The plot suggests that there are periods of prevailing appearance of each of the above configurations. Within each of these periods, there are short-time transitions into other configurations, sometimes intermediate between 1 and 2, or different as in frame 169. We applied the same approach to analyze the evolution of the neighboring defect (at a distance about three microdomains) marked by X in Figure 1 (frame 156) and Figure 2. This structure originated from a three “open ends” defect (SFM movie) by fast evolution into a dot-like defect. Before this defect is annihilated, it switches between several configurations with one “open end” (A and F) and several with two “open ends” (B, C, and D); however, each configuration differs in the position of the junctions between the cylinders (Figure 2). The temporal evolution of this structure is shown in Figure 3a (lower plot). The comparison with the upper plot suggests that the events at the two neighboring sites are correlated on the scale of at least several domain spacings and on a time scale of seconds. In 65% of the frames, there are either no changes to defects or transitions occur collectively on both sites within the same frame (or within two consecutive frames). Figure 3a demonstrates the concept to treat the dynamic information that contains a high-temporal-resolution scanning of the same spot. Accumulation of statistical data sets as in Figure 3a and applying time-correlation analysis allow us to obtain quantitative information on the correlations in microdomain dynamics. From the two time series shown in Figure 3a, we have constructed the histogram of a time between two successive transitions into another defect configuration (Figure 3b). The solid line is an exponential fit with a decay of 60 ( 10 s, which is an average lifetime of a defect configuration. In other words, t ) 60 ( 10 s is the typical time between the consecutive opening and closing of a cylinder connection. 1575
Figure 2. Crops (250 × 250 nm2) from selected frames of the SFM movie showing the oscillations between distinct defect configurations. . and X mark the open ends of the cylinders. The structure marked with . fluctuates mainly between the configuration with three “open ends” (1) and the configuration with two “open ends” (2). The structure marked with X fluctuates between configurations with one (A, F) or two “open ends” (B, C, D).
Figure 3. (a) Temporal evolution of the defect configurations displayed in Figure 2. The configurations are sorted and grouped along the configuration coordinate according to their number of “open ends”. (b) The histogram of the time between two successive transitions shown in a. The solid line is a fit with an exponential decay.
Although this value is similar to the frame rate, it differs significantly from the lower bound (1.5 s) of the time resolution limit of the SFM movie. A simple estimate of diffusion using the Einstein relation a ) (Dt)1/2 with a ≈ 30 nm (the width of the gap between two cylinders) and t ≈ 60 s (the average time to close this gap) results in the diffusion constant D ≈ 10-13 cm2/s. We can identify the undulation frequency evaluated earlier as (∼1/45 s-1) with an attempt frequency, f0, for the formation (or break up) of a connection between cylinders. If we further assume a thermally activated process with a 1576
probability p ) tf0 exp(-EA/kBT) and a typical time between transitions t ≈ 60 s (Figure 3b) for which p ) 1, then we get an activation energy of EA ≈ 0.4 kBT. This value is in agreement with the predicted energy barrier of ∼0.2-0.6 kBT for one rupture of a cylinder during the cylinder-tosphere transition.21 Next we estimate the mean driving force for a closing connection FD ≈ EA/a ≈ 0.4 kBT/20 nm and compare it with the viscous force due to friction FF ) VkBT/D according to the Stokes-Einstein relation, where V ≈ 1 nm/s is the velocity of an undulation along the cylinder axis (Figure 1). The resulting diffusion constant D ≈ 10-12 cm2/s is consistent with the above estimate. It has been shown that the diffusivity of block copolymer chains in the cylinder phase is suppressed exponentially with χNPS relative to the diffusion, Do, in the absence of any interactions22,23 (with χNPS ≈ 6, where NPS refers to the core PS block, and Do is similar to the self-diffusion coefficient of PB (∼10-10 cm2/s) at relevant conditions24). In the SB melt, the diffusion of the chains across the interface is additionally hindered due to entanglements in the PB block and is described as D⊥ ≈ Do exp(-R NPB/Ne,PB) with NPB/Ne,PB ≈ 16, where Ne,PB is an entanglement length of PB,25,26 and R depends on the degree of the blocks’ interpenetration and is ∼1/3.27 In this case, the motion of chains proceeds via block retraction with a hindered diffusion coefficient of about 10-15 cm2/s (we note that the self-diffusion coefficient in entangled star PB molecules, diffusing via arm retraction, is of the same order28). The discrepancy between the observed and expected diffusivity in the PB melt could be an indication of enhanced diffusion in the regions with defects in the microdomain structure. Another possibility is that the transport during the closing/opening of a connection between the cylinders is not diffusive. It might be either hydrodynamic flow or a cooperative motion of clusters of polymer chains enhanced by defect strain fields. In recent studies of block copolymer dynamics,7-10,17 these processes have not been considered. Nano Lett., Vol. 6, No. 7, 2006
In summary, with high temporal resolution we reveal elementary steps of fast defect dynamics such as microdomain undulations and repetitive transitions between distinct defect configurations. From kinetic measurements, we determine the activation energy for the opening/closing of a connection between two cylinders. Its high velocity speaks for an enhanced diffusion in defect-rich areas or suggests processes other than diffusion transport mechanisms, such as hydrodynamic flow or correlated movement of clusters of chains. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft (SFB 481). R.M. acknowledges the support of the VolkswagenStiftung. L.T. thanks the support of the State of Bavaria (HWP-Program). We thank G. Krausch for fruitful discussions. Supporting Information Available: Tapping-mode scanning force microscopy movie of the surface structures in a fluid SB film at 105 °C. Bright color corresponds to PS microdomains. The size of the area is 580 × 580 nm2. The frame rate is 46 s/frame, and the total imaging time is 3 h 55 min. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Hamley, I. W. The Physics of Block Copolymers; Oxford University Press: Oxford, 1998. (2) Park, M.; Harrison, C.; Chaikin, P. M.; Register, R. A.; Adamson, D. H. Science 1997, 276, 1401-1404. (3) Segalman, R. A. Mater. Sci. Eng., R 2005, 48, 191-226. (4) Fredrickson, G. H.; Ganesan, V.; Drolet, F. Macromolecules 2002, 35, 16-39. (5) Katsov, K.; Mu¨ller, M.; Schick, M. Biophys. J. 2004, 87, 3277. (6) Katsov, K.; Mu¨ller, M.; Schick, M. Biophys. J. 2006, 90, 915.
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