Defect Evolution in Block Copolymer Thin Films via Temporal Phase

We study the details of the defect dynamics in thin films of a cylinder-forming ... defects are annihilated by short-term phase transitions into what ...
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Langmuir 2006, 22, 8089-8095

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Defect Evolution in Block Copolymer Thin Films via Temporal Phase Transitions Larisa Tsarkova,*,† Andriana Horvat,† Georg Krausch,† Andrei V. Zvelindovsky,‡ G. J. Agur Sevink,§ and Robert Magerle†,| Physikalische Chemie II, UniVersita¨t Bayreuth, D-95440 Bayreuth, Germany, Department of Physics, Astronomy and Mathematics, UniVersity of Central Lancashire, Preston, PR1 2HE, United Kingdom, and Leiden Institute of Chemistry, Leiden UniVersity, P.O. Box 9502, 2300 RA Leiden, The Netherlands ReceiVed May 12, 2006. In Final Form: June 19, 2006 We study the details of the defect dynamics in thin films of a cylinder-forming polystyrene-block-polybutadiene (SB) diblock copolymer melt. The high temporal resolution of in-situ scanning force microscopy (SFM) uncovers elementary dynamic processes of structural rearrangements on time scales not accessible so far. Short-term interfacial undulations and the formation of transient phases (spheres, perforated lamellae, and lamellae) are observed. We demonstrate that the well-known structural defects are annihilated by short-term phase transitions into what may be considered excited states. These temporary phase transitions are reproduced in simulations based on dynamic selfconsistent field theory. We discuss the role of the observed structural evolution in the context of the equilibrium phase behavior in SB thin films.

Introduction Block copolymers are complex materials that self-assemble into periodic nanostructures.1 The growing number of applications of such systems in nanotechnology2 is a strong incentive to develop an improved understanding of the ordering process aimed at controlling the resulting nanopatterned surfaces. The key role of the generation and annihilation of topological defects in block copolymer systems has been emphasized in studies of structural phase transitions,3,4 transport mechanisms,5 long-range alignment,6-12 and reorientation of microdomains under shear13 and in electric fields.14 * To whom correspondence should be addressed. E-mail: larisa.tsarkova@ uni-bayreuth.de. † Universita ¨ t Bayreuth. ‡ University of Central Lancashire. § Leiden University. | Present address: Technische Universita ¨ t Chemnitz, Chemische Physik, D-09107 Chemnitz, Germany. (1) Hamley, I. W. The Physics of Block Copolymers; Oxford University Press: Oxford, England, 1998. (2) Park, M.; Harrison, C.; Chaikin, P. M.; Register, R. A.; Adamson, D. H. Science (Washington, D.C.) 1997, 276, 1401-1404. Thurn-Albrecht, T.; Schotter, J.; Kastle, G. A.; Emley, N.; Shibauchi, T.; Krusin-Elbaum, L.; Guarini, K.; Black, C. T.; Tuominen, M. T.; Russell, T. P. Science (Washington, D.C.) 2000, 290, 2126-2129; Park, C.; Yoon, J.; Thomas, E. L. Polymer 2003, 44, 67256760. (3) Sakurai, S.; Momii, T.; Taie, K.; Shibayama, M.; Nomura, S.; Hashimoto, T. Macromolecules 1993, 26, 485-491. Hajduk, D. A.; Ho, R.-M.; Hillmyer, M. A.; Bates, F. S.; Almdal, K. J. Phys. Chem. B 1998, 102, 1356-1363. Sota, N.; Sakamoto, N.; Saijo, K.; Hashimoto, T. Macromolecules 2003, 36, 4534-4543. Kimishima, K.; Koga, T.; Hashimoto, T. Macromolecules 2000, 33, 968-977. (4) Ryu, C. Y.; Vigild, M. E.; Lodge, T. P. Phys. ReV. Lett. 1998, 81, 53545357. (5) Cavicchi, K. A.; Lodge, T. P. Macromolecules 2004, 37, 6004-6012. (6) Harkless, C. R.; Singh, M. A.; Nagler, S. E.; Stephenson, G. B.; JordanSweet, J. L. Phys. ReV. Lett. 1990, 64, 2285-2288. Edwards, E. W.; Stoykovich, M. P.; Mueller, M.; Solak, H. H.; J.de Pablo, J.; Nealey, P. F. J. Polym. Sci., Part B: Polym. Phys. 2005, 43, 3444-3459. (7) 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. (8) Hahm, J.; Sibener, S. J. J. Chem. Phys. 2001, 114, 4730-4740. (9) Harrison, C.; Angelescu, D. E.; Trawick, M.; Cheng, Z.; Huse, D. A.; Chaikin, P. M.; Vega, D. A.; Sebastian, J. M.; Register, R. A.; Adamson, D. H. Europhys. Lett. 2004, 67, 800-806. (10) Harrison, C.; Cheng, Z.; Sethuraman, S.; Huse, D. A.; Chaikin, P. M.; Vega, D. A.; Sebastian, J. M.; Register, R. A.; Adamson, D. H. Phys. ReV. E 2002, 66, 011706-011706. (11) Segalman, R.; Hexemer, A.; Kramer, E. Phys. ReV. Lett. 2003, 91, 196101.

During the past decade, studies of the dynamics in thin block copolymer films focused on well-defined defects in highly ordered layers of cylindrical7,8,10,15,16 or spherical microdomains.9,11,17 These studies demonstrated strong similarities between the ordering of block copolymer microdomains and the ordering of 2D smectic systems7,10-12,17 or even solid crystalline materials.18 However, cyclic annealing and snapshot imaging of the same spot were utilized in this kind of experiment and limited the time scales of dynamic observations to tens of minutes or even to hours.7,15 Whereas topological defects in polymer thin films indeed resemble those commonly observed in other forms of ordered matter, block copolymers exhibit morphological and dynamic properties that are specific to their polymeric nature. It is well established that cylinder-forming block copolymers in confined geometries frequently exhibit nonbulk structures or hybrid morphologies in response to thickness constraints and surface fields (e.g., refs 19-22). Recently, in-situ scanning force microscopy (SFM) was used to image the phase transition from the cylinder to the perforated lamella (PL) phases in thin films (12) Hammond, M. R.; Cochran, E.; Fredrickson, G. H.; Kramer, E. J. Macromolecules 2005, 38, 6575-6585. (13) Albalak, R. J.; Thomas, E. L.; Capel, M. S. Polymer 1997, 38, 38193825. Laurer, J. H.; Pinheiro, B. S.; Polis, D. L.; Winey, K. I. Macromolecules 1999, 32, 4999-5003. Honeker, C. C.; Thomas, E. L. Macromolecules 2000, 33, 9407-9417. (14) Amundson, K.; Helfand, E.; Quan, X.; Hudson, S. D.; Smith, S. D. Macromolecules 1994, 27, 6559-6570. Zvelindovsky, A. V.; Sevink, G. J. A. Phys. ReV. Lett. 2003, 90, 049601. (15) Hahm, J.; Lopes, W. A.; Jaeger, H. M.; Sibener, S. J. J. Chem. Phys. 1998, 109, 10111. (16) Hammond, M. R.; Sides, S. W.; Fredrickson, G. H.; Kramer, E. J.; Ruokolainen, J.; Hahn, S. F. Macromolecules 2003, 36, 8712-8716. (17) Segalman, R. A.; Hexemer, A.; Hayward, R. C.; Kramer, E. J. Macromolecules 2003, 36, 3272-3288. (18) Rehse, N.; Knoll, A.; Konrad, M.; Magerle, R.; Krausch, G. Phys. ReV. Lett. 2001, 87, 035505-035504. (19) Knoll, A.; Horvat, A.; Lyakhova, K. S.; Krausch, G.; Sevink, G. J. A.; Zvelindovsky, A. V.; Magerle, R. Phys. ReV. Lett. 2002, 89, 035501-035501/ 035504. (20) Knoll, A.; Magerle, R.; Krausch, G. J. Chem. Phys. 2004, 120, 11051116. (21) Park, I.; Park, S.; Park, H.-W.; Chang, T.; Yang, H.; Ryu, C. Y. Macromolecules 2006, 39, 315-318. (22) Tsarkova, L.; Knoll, A.; Krausch, G.; Magerle, R. Macromolecules 2006, 39, 3608-3615.

10.1021/la0613530 CCC: $33.50 © 2006 American Chemical Society Published on Web 08/16/2006

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Figure 1. Fourier-filtered tapping mode SFM phase images of the surface structures in a fluid SB film at 105 °C. The scale is 5°, and bright regions correspond to PS microdomains below an ∼10-nm-thick PB layer.38 The images are frames from an SFM movie,29 and the corresponding frame numbers and the elapsed time are shown. The white square highlights the area that has been cut out for the movie. The arrows in the leftmost image indicate the fast scanning axis along which the tip moves with a velocity of 20 µm/s and the slow scanning axis, along which the image is completed within ∼46 s. The areas surrounded by the dotted and solid ovals in frame 146 are presented in Figures 4-6, 8, and 7, respectively. The elongated grain marked with a dashed oval in frame 257 is discussed in Figure 5.

of concentrated block copolymer solutions.23 It has been shown that the microdomain dynamics on long time scales can be described in great detail with a mean-field approach and dynamic self-consistent field theory (DSCFT). Furthermore, quantitative analysis of defect motion led to an estimate of the interfacial energy between the cylinder and the perforated lamella (PL) phases. Recently we have reported on the fast defect dynamics via repetitive transitions between distinct defect configurations24 and compared the velocity of the observed fast transitions with that of a diffusion-driven transport process. Because the two time scales differ by several orders of magnitude, we concluded that diffusion is not the dominant transport process during the opening and closing of a connection between two cylinders. Alternative transport mechanisms might be either hydrodynamic flow or a correlated movement of clusters of chains. Here we extend our investigation of defect evolution in a block copolymer melt. The time resolution of in-situ SFM allows the observation of elementary processes of defect motion over a large range of time scales: density undulations on a time scale below a second, collective deformation of microdomains on a time scale of tens of seconds, and temporal morphological structures with lifetimes ranging from a minute to hours. Computer simulations based on DSCFT reproduce the observed temporal phase transitions as a pathway of structural evolution. Materials and Methods Polymer. The material under study was a polystyrene (PS)-blockpolybutadiene (PB) diblock copolymer (SB) with weight-averaged molecular weights of the PS and PB blocks of 13.6 and 33.7 kg/mol, respectively, and a polydispersity of 1.02. The volume fraction of the PS (26.1%) results in bulk morphology of hexagonally ordered PS cylinders embedded within a PB matrix. This structure was confirmed by small-angle X-ray scattering (SAXS) measurements on a bulk specimen that have shown a characteristic distance of 32.9 ( 0.3 nm between the next-nearest PS cylinders (at 105 °C). The glass-transition temperatures of the respective homopolymers range from -83 to -107 °C for PB and from 80 to 100 °C for PS.25 The surface tension of PB, γPB ) 31 mN/m, is considerably smaller than the surface tension of PS, γPS ) 41 mN/m.2 (23) Knoll, A.; Lyakhova, K. S.; Horvat, A.; Krausch, G.; Sevink, G. J. A.; Zvelindovsky, A. V.; Magerle, R. Nat. Mater. 2004, 3, 886-891. (24) Tsarkova, L. A.; Knoll, A.; Magerle, R. Nano Lett. 2006, 6, 1574-1577. (25) Brandrup, J., Immergut, E. H., Grulke, E. A., Eds. Polymer Handbook, 4th ed.; John Wiley & Sons: New York, 1999.

Scanning Force Microscopy (SFM). In-situ thermal annealing and scanning were performed under a flow of dry nitrogen in a recently developed SFM heating stage (MultiMode, DI/Veeco Metrology Group), enabling precise control of both the sample and the tip temperature. Standard silicon cantilevers (with a resonance frequency in the range of 200-300 kHz) have been used in the tapping mode at an amplitude setpoint of ∼0.96. No measurable effect of the tip on the structural evolution has been detected. The best scanning conditions (minimum noise at maximum phase contrast of approximately 5°) were achieved in the temperature range of 90-110 °C with a scanning velocity of ∼10-12 lines/s for a 1 × 1 µm2 image (with 512 × 512 pixels). This corresponds to a tip velocity of ∼20 µm/s and an acquisition time of 46 s/image. Experimental Conditions. A 6 ( 1 nm thick carbon layer was evaporated onto a silicon wafer using a Cressington 208HR sputter coater. An SB film with a thickness of about 50 nm was prepared by spin coating a 1.2 wt % SB solution in toluene onto the carboncoated substrate. Stabilizer was added (0.03% of the polymer weight) to prevent cross linking of the PB block during thermal annealing. The sample was mounted into the MultiMode heating stage, annealed at 140 °C for 40 min, and then quenched to 105 °C for SFM imaging. At these temperatures, the combined Flory-Huggins parameter χN is about 30-35,26 which corresponds to the intermediate segregation regime.27 SFM Movie. SFM images (257) were taken successively. With custom-built software,28 the SFM phase images were flattened, registered, and compiled into a movie by cutting the same area (580 × 580 nm2) from the raw phase images. Figure 1 shows the first image, an intermediate image, and the last image from this series. During the long-term in-situ measurements, the scanning area is steadily moving as a result of thermal drifts. The same area (highlighted by the white square in Figure 1) was used for the SFM movie. Whenever the quality of the raw SFM phase images was satisfactory, the raw data was used in the Figures to present the microdomain dynamics. Scanning artifacts such as noise and image distortions were reduced in the SFM movie by averaging successive frames.29 This improves the visibility of the collective rearrangements in the microdomain structure occurring on a longer time scale. The series of images presented as the SFM movie starts 1 h after the quench to 105 °C and covers 4 h of annealing at this temperature. (26) Owens, J. N.; Gancarz, I. S.; Koberstein, J. T.; Russell, T. P. Macromolecules 1989, 22, 3380-3387. Sakurai, S.; Mori, K.; Okawara, A.; Kimishima, K.; Hashimoto, T. Macromolecules 1992, 25, 2679-2691. (27) Fredrickson, G. H.; Bates, F. S. Annu. ReV. Mater. Sci. 1996, 26, 501550. (28) Knoll, A. Ph.D. Thesis, Universita¨t Bayreuth, Bayreuth, Germany, 2003. (29) Movie. Supporting Information is available via the Internet at http:// pubs.acs.org.

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Figure 2. (a) SFM height (upper panel) and phase images (bottom panel) of a 50-nm-thick SB film that was annealed under vacuum at 105 °C for 50 h and measured at room temperature. The images display coexisting terraces of one and two layers of cylinders (both supported by a layer of half-cylinders) with a step height of 28 ( 2 nm. In the phase image, contour lines taken from the height images are shown as white lines. (b) SFM images measured in situ at 105 °C at the start of continuous scanning. The phase image shows defect-rich cylindrical structures with low translational order. The topography image indicates the degree of terrace development. The height of the step between the terraces is 21 ( 2 nm. The white squares highlight the area captured in the SFM movie. Throughout the article, all images have labels corresponding to the frame number and the elapsed time of the movie. Simulations. We have modeled the thin film behavior of cylinderforming block copolymer using the MesoDyn code, which is based on DSCFT developed by Fraaije.30 As a model, a melt of A3B12A3 Gaussian chains was used. A and B correspond to PS and PB in experiments, respectively. For the bead-bead interaction potential, a Gaussian kernel is used, which is characterized by εAB and related to Flory-Huggins parameter χ. The value of εAB was set to 6.5 kJ/mol in order to have cylinders as the bulk structure.31 It corresponds to χN ≈ 35, analogous to the experiment (see above). A substratesupported thin film (with one free surface) was modeled as in ref 32. Here, the interaction with the hard wall (substrate) was set at 7.5 kJ/mol. The interactions with the void component were set to εVA ) 16 kJ/mol and εVB ) 10 kJ/mol. It is possible for the film to change its height. All other parameters are the same as in ref 31. Experiments19,20,22 and computer simulations19,31,33 have shown that the structure formation and the phase behavior in thin films of cylinder-forming triblock copolymers are conceptually very similar to those of diblock copolymers.34

Results and Discussion Surface Structures at Thermal Equilibrium. The phase behavior of SB melts in thin films has recently been investigated as a function of the surface fields and the film thickness.22 On weakly interacting substrates such as carbon-coated silicon, asymmetric wetting conditions prevail. Typically, upon suffici(30) Fraaije, J. G. E. M. J. Chem. Phys. 1993, 99, 9202. (31) Horvat, A.; Lyakhova, K. S.; Sevink, G. J. A.; Zvelindovsky, A. V.; Magerle, R. J. Chem. Phys. 2004, 120, 1117-1126. (32) Lyakhova, K. S.; Horvat, A.; Zvelindovsky, A. V.; Sevink, G. J. A. Langmuir 2006, 22, 5848-5855. (33) Huinink, H. P.; Brokken-Zijp, J. C. M.; van Dijk, M. A.; Sevink, G. J. A. J. Chem. Phys. 2000, 112, 2452-2462. Lyakhova, K. S.; Sevink, G. J. A.; Zvelindovsky, A. V.; Horvat, A.; Magerle, R. J. Chem. Phys. 2004, 120, 11271137. (34) Tsarkova, L. In Nanostructured Soft Matter: Experiment, Theory, Simulation, and PerspectiVes; Zvelindovsky, A. V., Ed.; Springer-Verlag: Heidelberg, Germany, 2006.

ently long annealing above the glass transition of PS, coexisting terraces of a single layer and two layers of cylinders are formed. At the substrate, the films are supported by a wetting layer of half-cylinders. Additionally, a perforated lamella (PL) phase appears within the first layer of structures at intermediate film thicknesses. Figure 2a presents SFM images of a 50-nm-thick film that was equilibrated under vacuum at 105 °C for 50 h. It provides information on the degree of ordering, on the defect density after long-term annealing, and on the stable defect configurations. As seen in the phase image in Figure 2a, along with typical defects such as disclinations and dislocations, small patches of the PL phase are stabilized at the boundaries between the grains of cylindrical domains. Prior to the measurements reported here, the film was first annealed at 140 °C for 40 min to induce microdomain alignment and ordering. Macroscopic terrace formation was followed by optical microscopy. It started after 15 min of annealing at 140 °C. Figure 2b shows SFM height and phase images measured in situ at 105 °C shortly after the quench from 140 °C. The microdomains in both terraces show a pronounced orientation parallel to the plane of the film but low translational and orientational order within each layer. The step height between the terraces is about 21 ( 2 nm, which is some 20% smaller compared to the equilibrium step height.22 The white contour lines in the phase images in Figure 2 are taken from the height images and superimposed onto the phase images. They mark the borders of regions with transition film thickness between the terraces. The step width between the terraces in Figure 2b is significantly extended compared to that of the film that was equilibrated on a much longer time scale (Figure 2a). This observation points to the considerable transport of material between the terraces during the annealing that follows. A comparison of the surface structures in Figure 2a and b suggests that the orientational correlation length and defect density are

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Figure 3. Selected frames taken from the SFM movie29 (unfiltered phase images) showing (a) undulations along the PS cylinder axes, which are highlighted by the white curve in frame 210. The dashed lines in frames 211 and 212 are copied from frame 211 and are shown as a guide to the eye to illustrate the propagation of the undulations. The arrows in frames 210 and 211 indicate correlated undulations of the white and gray colors, respectively. (b) Correlated waviness in the neighboring domains (indicated by arrows in frame 152) induced by the development of a dotlike defect. The waviness is slightly decreased in frame 153.

Figure 4. Successive frames taken from the SFM movie29 (unfiltered phase images) with corresponding schematics showing the annihilation of a small elongated grain (marked by the dashed oval in frame 125) via collective tilt (frame 126) and the formation of transient spherical structures (indicated by arrows in frame 127).

only slightly improved upon long-term annealing. We believe that the poor structural order in Figure 2a results primarily from the kinetic limitations due to the proximity of the annealing temperature to the Tg of the PS block and the finite annealing time. Microdomain Shape Undulations. In-situ SFM imaging reveals the extremely flexible behavior of the microdomains, which allows for local undulations of interfacial walls, distortion of spacings, elastic deformation of the domains, and the formation of energetically exited states. In Figure 3a, the alternating dark and light regions along the PS cylinder are indicated. In some cases, these undulations appear to propagate or oscillate along the cylinder and then vanish (Figure 3a). In other instances, they resolve into new structures (e.g., transient globules, as shown Figures 4 and 5). These structural modulations indicate the presence of strong concentration fluctuations with a characteristic length of about one unit of microdomain spacing. The characteristic lifetime of such undulations is larger than 1.5 s, which is the interval of scanning of a single microdomain along the slow scanning axis (Figure 1). The undulations are often correlated within neighboring microdomains. The array of shape undulations

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Figure 5. Selected frames taken from the SFM movie29 (unfiltered phase images) showing the annihilation of a small elongated grain (marked with a dotted oval in frame 152), which is replaced by another small grain with perpendicular orientation (marked in frame 240) on a time scale of ∼70 min. The transient dots, which are presumable spherical microdomains, are indicated by arrows in frame 162. The transient PL phase (marked by a circle in frame 161) with a lifetime of ∼60 min can be seen in the following frames with shape undulations (frames 163 and 166) or different numbers of connected cylinders (frames 163 and 189).

marked in frames 210 and 211 (Figure 3) was scanned within 10 s, which gives a lower limit of the lifetime of these correlations. Another example of fast correlation microdomain dynamics is shown in Figure 3b. Initially, a nucleating defect appears between parallel cylinders (frame 151). In the next frame, the cylinders in the vicinity of the developing dotlike defect bend collectively and form a wavelike (meandering) structure (frame 152). The related strain field is transmitted to at least three neighboring cylinders on a time scale of ∼10 s and is slightly released in the next ∼40 s (frame 153). Interestingly, with dynamic light scattering a slow diffusive mode was detected in bulk block copolymer systems and was attributed to long-range density fluctuations with a correlation length of 100 nm.35 We note that the microdomain undulations visible in the SFM movie fit the above time and length scales. The described microdomain undulations are an example of an elementary mechanism of microdomain dynamics by which the annihilation of particular defects proceeds on a larger scale. Transient Phases as Pathways of Structural and Orientational Rearrangements. (a) Grain Annihilation. Figure 4 shows another type of cooperative motion of microdomains. In frames 125-130, the local configuration of cylinders in the marked spot changes markedly from frame to frame. The initial disclinationlike defect (frame 125) diverges first into an array of short cylinders with three open ends facing one direction, which then tilt collectively by a few degrees (frame 126). As seen later, in frame 127, the stripes break up into smaller pieces. In frame 128, they rejoin to form a cylinder with perpendicular orientation, which is now connected to the neighboring grain. As a visual guide, a schematic of this process is included in Figure 4. Initially, several differently oriented grains surround a small elongated pattern (frame 125). This middle grain finally transforms into a dislocation in the upper grain (frame 128). We conclude that fast rearrangements of cylinders, which take less than 2 min, are not random but cooperative. The cylinders are rearranged so that the extra grain pattern associated with higher interfacial energy is (35) Stepanek, P.; Lodge, T. P. Macromolecules 1996, 29, 1244-1251. Papadakis, C. M.; Brown, W.; Johnsen, R. M.; Posselt, D.; Almdal, K. J. Chem. Phys. 1996, 104, 1611-1625.

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Figure 6. Selected frames taken from the SFM movie29 showing the transient PL structure that is formed next to an open cylinder end (frame 3). The single PL ring appears to serve as a nucleus of a more extended PL phase, which would include three PL rings (frames 39 and 82). On a time scale of ∼90 min, the defect is finally resolved into a combination of a dislocation and a +1/2 disclination (frame 93).

annihilated, thereby improving the long-range microdomain orientational order. Another example of annihilation of a small elongated grain is presented in Figure 5. The array of short cylinders (highlighted in frame 152) disappears via the formation of transient dot-like defects (presumably spherical microdomains, frame 162) and fast disconnections of cylinders and their reconnections into cylinders that are oriented perpendicular to the initial direction (frames 165-166). On a longer time scale of ∼70 min, the small elongated grain (frame 152) is replaced by another grain with the opposite orientation (frame 240). Such elongated grains appear and annihilate in a few other instances of the SFM movie and in data not shown here. This mechanism could be a common pathway of grain growth at the expense of smaller grains. Interestingly, grain elongation perpendicular to the cylinder or lamella axis has been previously reported36 and attributed to the orientational dependence of the grain surface energy. Our results suggest that in addition to thermodynamic reasons, the elongated grain shape facilitates a fast collective reorientation of short cylindrical domains. (b) Transient Perforated Lamella Phase (Experiment). In addition to the short cylinders and spheres described above, small patches of the PL phase appear during structural rearrangements.22 A few examples of transient PL structures with different lifetimes and different cluster sizes are presented in Figures 5-8. Often we observe structural defects in the cylinder phase such as a single PL ring (e.g., frame 161 of Figure 5). Such single PL rings generally originate from three-arm connections between cylinders and can be considered to be a minimum nucleus of the PL phase during the cylinder to PL phase transition.23 In our case, the formation of the single PL ring appears to be an elementary process of annihilation of the small elongated grain (shown in frame 152 of Figure 5). This individual PL ring exists over a time period of ∼60 min, however with different numbers of connected cylinders (three in frames 161 and two in frame 189) and repeated

Figure 7. Selected frames taken from the SFM movie29 showing the transient PL phase at the boundary between the cylinder grains. In frame 48, an array of PL rings is aligned along the grain boundary and grouped around a horseshoe defect (marked with an arrow). In frame 249, the transient phase is annihilated into the +1/2 disclination. The total evolution of the PL phase lasts about 4 h.

temporary breaks in its structure prior to the annihilation of this defect (SFM movie). Another transient PL phase is visible in Figure 6 next to a short cylinder end. It seemed to serve as a nucleus for a more extended PL phase that would include three PL rings and separate cylinders with different orientations (frame 39). This configuration was quite stable (compare frames 39 and 82) until it resolved into a combination of a dislocation and -1/2 disclination. The lifetime of this PL ring is ∼90 min. Figure 7 presents the evolution of a cluster of PL rings at the boundary between the cylinder grains (lasting some 4 h). Initially, an array of PL rings was aligned along the grain boundary and grouped around a “horseshoe” defect (frame 48). The elementary processes of the PL phase evolution, such as additional connections between cylinders (frame 137) and the movement of kinks parallel to the cylinder/PL border (frame 233), are very similar to that observed earlier during the cylinder to PL phase transition in a swollen film of a triblock copolymer.23 The final annihilation into the +1/2 disclination (frame 249) proceeded in less than 5 min, which is much faster compared to the lifetime of this temporal phase. A transient PL phase with a significantly shorter lifetime of only some 40 s is presented in Figure 8. Although it is not feasible to catalog the defects uniquely in such a defect-rich structure, the complex defect in frame 152 can be schematically described as a pair of oppositely charged disclinations that are separated by a distance of two microdomains. The -1/2 disclination is rather coupled with “open-end” defects (marked by colored circles

Figure 8. Successive frames taken from the SFM movie29 (unfiltered phase images) showing fast structural rearrangements via the formation of a transient PL structure with a lifetime of ∼40 s. The defect-rich structure in frame 152 is schematically described as a pair of oppositely charged disclinations (marked by blue circles). The -1/2 disclination is associated with open-end defects (marked by colored circles in frame 152). The patch of the PL phase (marked by a dashed circle in frame 153) vanishes in the next frame. The newly formed elementary dislocation and localized open-end defects are marked by yellow and red circles, respectively.

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Figure 9. Snapshots of the MesoDyn simulations, which model a thin supported film of an A3B12A3 cylinder-forming block copolymer in a 128 × 32 × 20 grid units large simulation box. Crops of the lower terrace, showing the reorientation of cylinders via the transient PL phase, are shown after (a) 24 000, (b) 30 000, (c) 36 000, (d) 42 000, (e) 46 000, and (f) 48 000 time steps. The thin film morphology is shown via the isodensity surface of the A component for the threshold value FA ) 0.33.

in frame 152). In the next instance, a patch of the PL phase appears between the paired disclinations (frame 153) and vanishes in the next frame. As a result, an elementary dislocation (marked by yellow circles in frames 153-159) is formed, and the openend defects are grouped in a small area (frame 159). As can be followed in the SFM movie, the clustering of short cylinders facilitates fast reconnections that result in a new orientation of cylindrical domains. (c) Transient Perforated Lamella Phase (Simulations). Figure 9 captures the reorientation of a cylindrical grain via the formation and annihilation of the PL phase. The initial film thickness was chosen to be 11/2 microdomain spacings in order to accelerate terrace formation in a natural way similar to the experiment. In the simulation, the initially flat film shows perpendicular cylinders and cylinders with necks. After 8000 time steps, the film starts to roughen. Simultaneously, in the lower terrace the structures transform into lying cylinders. After 24 000 simulation steps, the film shows a well-developed terrace with one layer of cylinders (Figure 9a) that form grains of different orientation. The T-like defects at the grain boundaries serve as nucleation centers for the PL domains (Figure 9c). The PL patch grows along the grain boundaries via the undulations in cylindrical domains, which eventually connect to form the PL lattice sites (Figure 9d). Finally, the microdomains reorganize into defect-free cylinders (Figure 9f). The transition to defect-free cylinders is accompanied by a thinning of the polymer film. From earlier in-situ experiments in swollen SBS films, we know that the real experimental time of ∼1 s can be identified with a single simulation step.23 Because the annealing times to achieve the thermal equilibrium in SBS swollen films and SB melts are comparable (10-20 h), a time calibration factor of the same order could be used for a qualitative comparison. This estimate suggests that in the particular simulation (Figure 9) the reorganization of cylinders proceeds on a time scale of tens of minutes (4000 time steps), which is in good agreement with our experimental observations. (d) Transient Lamella State. A pathway of structural ordering through the formation of a transient lamella phase is shown in Figure 10. Selected frames illustrate the annihilation of the horseshoe defect. This defect is also observed in DDFT simulations that reveal the connection of this defect to the bottom layer of microdomains.37 In frame 051, the open short end appears to connect to the neighboring cylinder to form a PL-like ring. However, in the following few minutes, the “seven neighbors” (36) Balsara, N. P.; Garetz, B. A.; Chang, M. Y.; Dai, H. J.; Newstein, M. C.; Goveas, J. L.; Krishnamoorti, R.; Rai, S. Macromolecules 1998, 31, 5309-5315. Sakamoto, N.; Hashimoto, T. Macromolecules 1998, 31, 3292-3302. Chastek, T. Q.; Lodge, T. P. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 481-491. (37) Magerle, R. Unpublished work.

TsarkoVa et al.

Figure 10. Details (250 × 250 nm2) taken from selected frames of the SFM movie29 illustrating the annihilation of a horseshoe defect (marked by dashed lines in frame 47). Solid lines and filled symbols mark lattice sites that remain unchanged during the transformation. Empty symbols indicate lattice sites at the boundary of the transient lamella phase. The previous position of moving lattice sites is shown by dashed symbols. The evolution of lattice site configurations is shown in the schematics below with the white area corresponding to the lamella phase. In frame 123, dashed lines mark lattice sites that replaced the horseshoe defect in frame 47.

pattern of PL transforms into a small lamella-phase patch (frame 056). The following frames and corresponding sketches depict the shape oscillations of this small domain (frames 056-106). We note that the transient lamella domain is altered through very similar shapes (compare frames 092 and 056; 097 and 065; 106 and 075). Later, the lamella transforms into a PL (frame 109), and finally the initial horseshoe defect is annihilated. Presumably, the formation of the transient lamella phase is caused by the strong packing frustration induced by the horseshoe defect (frame 047), which seems to be incommensurate with the cylinder and PL lattices. It is likely that in this small lamella domain the in-plane mobility of the chains is larger than in the PL phase and the cylinder phase. Moreover, the phase transition from the cylinder structures to the lamella phase was observed in SB films in the case of a strongly interacting substrate.22 The dynamic measurements indicate that in defect-rich structures such patches appear as transient exited states with a lifetime of about 1 h (at 105 °C). This local lamella patch is easily neglected in snapshot experiments because of its relatively short lifetime.

Conclusions With high temporal and spatial resolution, we image the dynamics of cylindrical microdomains in a block copolymer melt and follow the development of well-known structural defects such as disclinations, dislocations, and grain boundaries. We show that along with the previously studied lateral movement of defects the annihilation frequently proceeds through local structural transitions on short time scales that have not been accessed in earlier experiments. We identify interfacial undulations and the formation of local transient phases such as spherical domains, perforated lamella, and lamella patches as short-term pathways facilitating long-term behavior. The observed structural evolution is closely related to the equilibrium phase behavior in SB films. The nonbulk structures that are found as temporary transition states in the present work have been observed upon long-term equilibration of SB films under variation of the film thickness or surface fields, and the corresponding phase diagram of surface structures has been reported.22 Our earlier studies demonstrated that in SB films on carbon-coated substrates the cylinder phase is a dominant structure; the PL phase is stabilized in the first layer at transition

Defect EVolution in Block Copolymer Thin Films

film thickness either at the bottom of a step or in areas with minor thickness variation.22 The characteristic thickness of one layer of the PL phase was shown to be ∼10% larger compared to a single layer of the cylinder phase. Thus, upon long-term equilibration, the morphological phase transition from the cylinder to the PL phase provides a local adjustment of the microdomain structures to the thickness constraint. On the other side, the measured value of the interfacial tension between the cylinder and the PL phase is quite low (∼2.5 µNm-1);23 therefore, it likely accounts for an energetically favorable pathway of structural rearrangements via temporal phase transitions. The length scales and the time scales at which the temporal transitions take place are quite different, ranging from minutes to hours and from a single unit cell to a cluster size of several domain spacings, respectively. We believe that in each case the annihilation scenario is dictated by the energy of a particular defect and by the strain field of the surrounding structures. For example, structurally similar horseshoe defects displayed in Figure 7 (frame 48) and in Figure 10 (frame 47), both appearing in the early stages of annealing, undergo different annihilation pathways because of the differences in the neighboring structures. Also, as seen in Figure 2a, in highly defective areas of the cylinder phase, the PL patches appear to be stabilized even under long-term annealing. The accumulation of statistical data on the evolution of particular defect configurations may initiate theoretical studies on the quantitative evaluation of the energy associated with defect formation and propagation and the onset of the phase transition. We remark that phase transitions from metastable morphologies to equilibrium morphologies as well as thermally reversible order-order transitions have been extensively studied before.3 Here, however, we describe local exited states in the equilibrium phase induced by an energetically unfavorable defect configuration. The simulations based on DSCFT conceptually match the experimentally observed ordering of cylindrical microdomains via temporal phase transitions. We emphasize that the simulation method is not biased to any particular microdomain structure

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and has no a priori knowledge of the macroscopic mechanisms of structural transitions. All structures form spontaneously from an initially homogeneous polymer mixture, and the structural evolution proceeds through the pathways determined by its natural diffusion dynamics. In conclusion, we demonstrate that the microscopic structural details and the short- to medium-term dynamics of defect annihilation in block copolymer thin films are considerably more complex than anticipated so far. As has been revealed in earlier studies, the defect annihilation processes on longer time scales indeed resemble what is known from other forms of ordered matter (inorganic crystals, liquid crystals, etc.) and may be described by the concepts developed in this context. The shortterm dynamics described here, however, seems to be intimately connected to the long-chain nature of the block copolymer material and may therefore not find a simple analogy to other systems. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft (SFB 481). R.M. acknowledges support from the VolkswagenStiftung. L.T. and A.H. acknowledge the support of the State of Bavaria (HWP program). A. Knoll is acknowledged for providing the software for SFM image processing. Supporting Information Available: Movie of tapping mode scanning force microscopy phase images of the surface structures in a fluid SB film at 105 °C. Bright colors correspond to PS microdomains below an ∼10-nm-thick PB layer.38 The size of the area is 580 × 580 nm2. The total imaging time is 3 h 55 min. Scanning artifacts such as noise and image distortions are reduced by averaging successive frames. With VirtualDub (from www.virtualdub.org), raw images were convoluted with a one-pixel-wide Gaussian using the blur filter. Successive frames have been averaged along the time axis by applying the motion blur filter two times. Such processing improves the visibility of the collective rearrangements in the microdomain structure occurring on a longer time scale. This material is available free of charge via the Internet at http://pubs.acs.org LA0613530 (38) Knoll, A.; Magerle, R.; Krausch, G. Macromolecules 2001, 34, 41594165.