Investigation of Molecular Chain Orientation Change of Polymer

Nov 8, 2006 - anisotropy measured by lateral-modulation friction force microscopy (LM-FFM). This technique made possible our investigation of molecula...
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Langmuir 2007, 23, 4740-4745

Investigation of Molecular Chain Orientation Change of Polymer Crystals in Phase Transitions by Friction Anisotropy Measurement Kuniko Kimura,*,†,‡ Kei Kobayashi,§ Hirofumi Yamada,† and Kazumi Matsushige† Department of Electronic Science and Engineering, Kyoto UniVersity, Katsura, Nishikyo, Kyoto 615-8510, Japan, and InnoVation Cluster Creation Project and International InnoVation Center, Kyoto UniVersity, Katsura, Nishikyo, Kyoto 615-8520, Japan ReceiVed NoVember 8, 2006. In Final Form: February 10, 2007 Direct observation of the molecular orientation change in polymer crystals provides us visible information for understanding their structural phase-transition mechanisms. In this letter, we successfully identified the main-chain orientation of poly(vinylidenefluoride-trifluoroethylene) (P(VDF-TrFE)) crystals over all directions using friction anisotropy measured by lateral-modulation friction force microscopy (LM-FFM). This technique made possible our investigation of molecular orientation changes caused by a ferroelectric phase transition and also a fabrication process for artificial nanometer-scale structures. These results give us visual information that is directly connected to the transition mechanisms.

Introduction Molecular-scale investigations of polymer thin films during structural transitions are essential in both scientific and technical aspects. The phenomena caused by phase transitions have been studied mainly in the spectroscopic domain using methods such as X-ray and IR (infrared) analyses, whereas the direct observation of molecular orientation change will provide us visible information for understanding phase-transition mechanisms. Surface friction information focused in a nanometer-scale area is valuable for analyzing molecular orientations. Friction force microscopy (FFM) has been a powerful tool for visualizing the molecular orientation of organic thin films with respect to surface friction. Friction anisotropies on self-assembled monolayers1-3 were suggested to originate from the side-chain orientation perpendicular to the surfaces. Studies on friction anisotropies of a polyethylene single crystal4 or highly oriented polymer layers5 revealed that their anisotropies were possibly caused by the mainchain orientations. In this letter, we investigate orientation change of polymer molecules followed by structural transitions by collecting surface friction information. As a good example, we visualize here the main-chain orientation change of poly(vinylidenefluoride-trifluoroethylene) (P(VDF-TrFE)) caused by its ferroelectric phase transitions, which is quite essential for studying its phase-transition mechanism. Poly(vinylidenefluoride) (PVDF)6-10 and P(VDF-TrFE), which is a copolymer of vinylidenefluoride and trifluoroethylene, are well-known ferroelectric crystalline polymers with a -C-Cmain chain having spontaneous C-F dipoles. Ferroelectric-to* Corresponding author. E-mail: [email protected]. † Department of Electronic Science and Engineering, Kyoto University. ‡ Innovation Cluster Creation Project, Kyoto University. § International Innovation Center, Kyoto University. (1) Overney, R. M.; Takano, H.; Fujihira, M.; Paulus, W.; Ringsdorf, H. Phys. ReV. Lett. 1994, 72, 3546. (2) Liley, M.; Gourdon, D.; Stamou, D.; Meseth, U.; Fisher, T. M.; Lautz, C.; Stahlberg, H.; Vogel, H.; Burnham, N. A.; Duschl, C. Science 1998, 280, 273. (3) Carpick, R. W.; Sasaki, D. Y.; Burns, A. R. Tribol. Lett. 1999, 7, 79. (4) Ryousho, Y.; Sasaki, S.; Nagamura, T.; Takahara, A.; Kajiyama, T. Macromolecules 2004, 37, 5115. (5) Scho¨nherr, H.; Vancso, G. J. Macromolecules 1997, 30, 6391. (6) Land, J. B.; Olf, H. G.; Peterlin, A. J. Polym. Sci., Part A-1, 1966, 4, 941. (7) Kepler, R. G.; Anderson, R. A. J. Appl. Phys. 1978, 49, 1232. (8) Naegele, D.; Yoon, D. Y. Appl. Phys. Lett., 1978, 32, 132. (9) Davis, G. T.; McKinney, J. E.; Broadhurst, M. G.; Roth, S. C. J. Appl. Phys. 1978, 49, 4998. (10) Furukawa, T.; Johnson, G. E. Appl. Phys. Lett. 1981, 38, 1027.

paraelectric phase transition of PVDF cannot be observed under ambient pressure because its Curie point (Tc) is higher than its melting point (Tm).11 However, the Tc of P(VDF-TrFE) is lower than its Tm at ambient pressure; therefore, its ferroelectric phasetransition phenomena have been actively investigated by means of X-ray analysis,12-17 and IR,18 Raman,19 nuclear magnetic resonance (NMR),20 and Brillouin spectroscopy.21 P(VDF-TrFE), whose VDF/TrFE molar content ratio is 75/25, has remarkable ferroelectricity22 and a large piezoelectric constant, d33.11 Recently, ferroelectric switching of several monolayers of this copolymer formed by the Langmuir-Blodgett technique23 and molecularscale images of the layers using scanning tunneling microscopy24 were obtained. The ferroelectric-to-paraelectric phase transition during the heating process (Tc-heat) of the copolymer with this content ratio and the paraelectric-to-ferroelectric one during the cooling process (Tc-cool) are observed at 123 and 70 °C, respectively.11,22 The molecular chain conformation and chain packing in the crystal lattice of this copolymer change with these phase transitions.13,14,17,25 A well-crystallized P(VDF-TrFE) film can be obtained by annealing at a temperature between Tc-heat and its Tm () 147 °C11), which is constructed by many randomly oriented rodlike grains. These grains are considered to be edge-on lamellae.26 At first, we tried to identify the molecular orientation of these grains using conventional FFM, which was used in refs 1-5; however, (11) Koga, K.; Ohigashi, H. J. Appl. Phys. 1986, 59, 2142. (12) Tajitu, Y.; Chiba, A.; Furukawa, T.; Fukada, E. Appl. Phys. Lett. 1980, 36, 286. (13) Lovinger, A. J.; Furukawa, T.; Davis, G. T.; Broadhurst, M. G. Polymer 1983, 24, 1233. (14) Horiuchi, T.; Matsushige, K.; Takemura, T. Jpn. J. Appl. Phys. 1986, 25, L465. (15) Fernandez, M. V.; Suzuki, A.; Chiba, A. Macromolecules 1987, 20, 1806. (16) Takahashi, Y; Nakagawa, Y.; Miyaji, H.; Asai, K. J. Polym. Sci., Part C 1987, 25, 153. (17) Day, J. A.; Lewis, E. L. V.; Davis, G. R. Polymer 1992, 33, 1571. (18) Tashiro,K.;Takano,K.;Kobayashi,M.;Chatani,Y.;Tadokoro,H.Polymer1984,25,195. (19) Tashiro, K.; Kobayashi, M. Polymer 1988, 29, 426. (20) Ishii, F.; Odajima, A. Polym. J. 1986, 18, 539. (21) Kru¨ger, J. K.; Petzett, J.; Legrand, J. F. Colloid Polym. Sci. 1986, 264, 791. (22) Kimura, K.; Ohigashi, H. Appl. Phys. Lett. 1983, 43, 834. (23) Bune, A.; Ducharme, S.; Fridkin, V.; Blinov, L.; Palto, S.; Petukhova, N.; Yudin, S. Appl. Phys. Lett. 1995, 67, 3975. (24) Qu, H.; Yao, W.; Garcia, T.; Zhang, J.; Sorokin, A. V.; Ducharme, S.; Dowben, P. A.; Fridkin, V. M. Appl. Phys. Lett. 2003, 82, 4322. (25) Tashiro, K.; Kobayashi, M. Phase Transitions 1989, 18, 213. (26) Kimura, K.; Ohigashi, H. Jpn. J. Appl. Phys. 1986, 25, 383.

10.1021/la063270p CCC: $37.00 © 2007 American Chemical Society Published on Web 03/28/2007

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we could hardly discriminate the differences in their molecular orientations. In this letter, we investigate the friction anisotropy on randomly oriented grains by using lateral-modulation friction force microscopy (LM-FFM), which is a method for mapping the friction force between a sample surface and the cantilever tip in atomic force microscope (AFM) by measuring the torsional bending vibration of the cantilever caused by horizontal oscillation of the sample (lateral modulation) thorough a lock-in amplifier.27,28 The amplitude of cantilever bending in LM-FFM is proportional to the dynamic friction force between the tip and surface when the lateral modulation has a sufficiently large peak amplitude. This method has some advantages in comparison with conventional FFM, such as high sensitivity for detecting small differences in frictional information, reduction of dc offset, and reduction of topographic influences.28 LM-FFM brought us success in the precise identification of polymer main-chain orientation over all directions on the film surface. Utilizing this result, we investigated the molecular orientation change before and after the paraelectric-to-ferroelectric phase transition of P(VDF-TrFE). AFM has also been a useful tool for the fabrication of nanometer-scale structures on polymer surfaces by mechanical indentation and/or scratching;29-34 one possible application of such structures is a liquid-crystal device.33,34 We have recently developed a novel technique to control the molecular orientation of polymers, which can facilitate the artificial creation of nanometer-scale anisotropies in material properties such as the elasticity, the reflective index, and even the conductivity in conductive polymers. We controlled the molecular orientation of P(VDF-TrFE) or some other polymer films by scanning an AFM cantilever tip in contact with the film surfaces while applying a suitable tip load at temperatures just below the Tm of the films.35-38 This technique brought about well-aligned rodlike grains that look like edge-on lamellae, whose size and regularity of alignment strongly depended on the temperature at which the tip scan was performed.38 The results of this technique have been identified only by topographic images in previous papers.35-38 As another example of the visualization of molecular orientation change in this letter, we cited this orientation control process that can be considered to be an artificially created phase transition. We revealed here the precise molecular orientation in the area applied to its control process. Experimental Section A 200-nm-thick P(VDF-TrFE) film (VDF/TrFE molar content ratio of 75:25 provided by Daikin Industries Ltd.) was obtained by spin-coating a P(VDF-TrFE)-methylethylketone solution on graphite. The film was annealed for 1 h to improve its crystallinity at 140 °C and cooled naturally to room temperature under ambient conditions. (27) Yamanaka, K.; Tomita, E. Jpn. J. Appl. Phys. 1995, 34, 2879. (28) Krotil, H.-U.; Weilandt, E.; Stifter, Th.; Marti, O.; Hild, S. Surf. Interface Anal. 1999, 27, 341. (29) Jin, X.; Unertl, W. N. Appl. Phys. Lett. 1992, 61, 657. (30) Iwata, F., Matsumoto, T.; Ogawa, R.; Sasaki, A. Jpn. J. Appl. Phys. 1999, 38, 3936. (31) Leach, R. N.; Stevens, F.; Seiler, C.; Langford, S. C.; Dickinson, J. T. Langmuir 2003, 19, 10225. (32) Gotsmann, B.; Du¨rig, U. Langmuir 2004, 20, 1495. (33) Ru¨etschi, M.; Gru¨tter, P.; Fu¨nfschilling, J.; Gu¨ntherodt, H.-J. Science 1994, 265, 512. (34) Kim, J.-H.; Yoneya, M.; Yokoyama, H. Nature 2002, 420, 159. (35) Kimura, K.; Kobayashi, K.; Yamada, H.; Horiuchi, T.; Ishida, K.; Matsushige, K. Appl. Phys. Lett. 2003, 82, 4050. (36) Kimura, K.; Kobayashi, K.; Yamada, H.; Horiuchi, T.; Ishida, K.; Matsushige, K. Jpn. J. Appl. Phys. 2004, 43, 4575. (37) Kimura, K.; Kobayashi, K.; Yamada, H.; Horiuchi, T.; Ishida, K.; Matsushige, K. Jpn. J. Appl. Phys. 2004, 43, L1390. (38) Kimura, K.; Kobayashi, K.; Yamada, H.; Horiuchi, T.; Ishida, K.; Matsushige, K. Appl. Surf. Sci. 2006, 252, 5489.

After crystallization, the friction force between the film surface and an AFM cantilever tip was measured at various temperatures by LM-FFM using an AFM instrument (JEOL 4200). All experiments were carried out at ambient pressure. The measurement procedure is shown below. While a Si cantilever tip with a nominal spring constant of 0.2 N/m (Nanosensors CONT) was in contact with the film surface with a tip load of about 1 nN, the film oscillated horizontally at 9 kHz or 500 Hz in the direction perpendicular to the longer axis of the cantilever rectangle (lateral modulation). The peak-to-peak amplitude of the lateral modulation was several nanometers, which is large enough to start tip slip in the lateral modulation direction against the static friction force. (This condition is necessary for measuring dynamic friction force using LM-FFM.28) The torsional bending vibration amplitude of the cantilever, which is proportional to the friction force, was detected using a lock-in amplifier by a laser beam deflection measurement. The amplitude image of surface friction (friction image) was obtained by scanning the tip on the surface with feedback control of constant tip load perpendicular to the film surface. The fast scan direction was parallel to the longer axis of the cantilever rectangle. The molecular orientation of a P(VDF-TrFE) film was controlled as follows. The same cantilever tip used for the friction measurement was scanned in contact with the film surface by applying a tip load of 3 nN while the film temperature was 142 °C, which is just below Tm (which we refer to as a modification scan). The scan direction was perpendicular to the longer axis of the cantilever rectangle. The scan line spacing was 8 nm. After the modification scan, the film was cooled naturally to room temperature.

Results and Discussion After annealing a P(VDF-TrFE) film at 140 °C for crystallization, we observed the film surface at the temperature in its paraelectric phase (125 °C). Randomly oriented rodlike grains, which are considered to be edge-on lamellae, were recognized in a topographic image as shown in Figure 1b. In an edge-on lamella, molecular chains align parallel to the film surface and perpendicular to the lamellar plane with folding turns as illustrated in Figure 1a. We investigated the chain orientation of these crystals using LM-FFM. Figure 1c shows a friction image at 125 °C of the same area as shown in Figure 1b obtained by LM-FFM. The measured LM-FFM signal V is proportional to the value f /kt; where f is the dynamic friction force with respect to the direction of film oscillation and kt is the spring constant of the cantilever for the torsional bending motion.28 We can clearly observe in Figure 1c that the friction anisotropy depends on the crystal orientation but that inside each crystal the friction force was almost uniform. The friction force was the smallest on the crystal whose molecular chain direction (shorter axis of the rodlike grain) was parallel to the lateral modulation of LM-FFM, whereas it was the largest on the crystal whose molecular direction was perpendicular to the lateral modulation. This means that the friction force along the molecular chain is minimum and that perpendicular to the chain is maximum. This friction anisotropy is considered to originate from higher rigidity and less height variation along the -C-C- main chain than from along the perpendicular direction. These results reveal that each crystal has a typical edge-on lamellar structure having good regularity in molecular alignment at a temperature above Tc-heat (paraelectric phase). Thanks to the regularity of the molecular orientation inside each lamella, an angle φ between the direction of the molecular chains and that of the lateral modulation can be defined for each edge-on lamella. Angle φ was determined from Figure 1c as follows. Because molecular chains in edge-on lamella align parallel to the shorter axis of a lamellar grain, the chain direction can be determined from the orientation of a grain. In practice, we obtained geometrically the direction of the longer axis of

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Figure 1. Topographic and frictional observations on randomly oriented P(VDF-TrFE) crystals on graphite at 125 °C, which is higher than its ferroelectric-to-paraelectric phase transition temperature (Tc-heat). (a) Schematic illustration of edge-on lamellae (top view), where molecular chains are aligned on the film surface perpendicular to their lamellar planes with folding turns. (b) Contact-mode topograph (1.5 µm × 1.5 µm). (c) Friction image (1.5 µm × 1.5 µm) obtained by LM-FFM when the sample oscillated at 9 kHz (lateral modulation) in the direction indicated by the arrow. (d) Plot of the friction signal (V(φ)) against the angle φ between the directions of the molecular chains and lateral modulation. Solid squares show the arithmetic mean value µ(φ) of the measured friction signal V(φ) inside each crystal. The mean deviation δV(φ) calculated from eq 1 for several numbered grains in part c are indicated in part d by error bars. The length of the error bar from the corresponding symbol (mean value) to the top or the bottom represents δV(φ). The theoretical V(φ) (solid line) was calculated for the following conditions: Sff0|/kt ) 0.75, Sff0⊥/kt ) 4.95, δ| ) 0.83π, and δ⊥ ) 0 using eq 2.

each grain in Figure 1c, and after that we calculated φ, which is the angle between the lateral modulation direction (white arrow indicated in Figure 1c) and the molecular chain orientation. The arithmetic mean µ(φ) of the LM-FFM signal (V(φ)) inside a grain, whose orientation is represented by φ, was calculated for each lamella. Also, the mean deviation δV(φ) of V(φ) from its mean value inside each lamella was calculated from eq 1

δV(φ) )

1

np

∑ |V(φ) - µ(φ)|

np K)1

(1)

where np is the number of pixels inside each grain. µ(φ), which is obtained from each grain in Figure 1c, is represented in Figure 1d by solid squares. The value of δV(φ) for several numbered grains in Figure 1c is indicated by error bars in Figure 1d that are labeled with the same numbers. The length of the error bar from the corresponding symbol (mean value) to the top or the bottom represents δV(φ). In Figure 1d, µ(φ) varies smoothly with angle φ, and it is the minimum on the crystals whose φ is approximately 0 or 180° and becomes the maximum on those whose φ is approximately 90°. In the case of edge-on lamellae, we calculated the friction force theoretically (Appendix). Equation 2 is a theoretical expression of V(φ) for the anisotropic friction force, which can be directly compared with the measured friction data obtained by LM-FFM. In this equation, f 0| and f 0⊥ are the friction force amplitudes parallel and perpendicular to the molecular chain, respectively, δ| and δ⊥ are the phase delays depending on these directions. The solid line in Figure 1d is the theoretical

one calculated from eq 2 (see Appendix) under the conditions of Sff0|/kt ) 0.75, Sff0⊥/kt ) 4.95, δ| ) 0.83π, and δ⊥ ) 0. Thus, the friction force strongly depends on the angle φ, and it agrees well with the theoretical one. The results shown in Figure 1a-d indicate that each crystal has a typical edge-on lamellar structure having good regularity in molecular alignment in its paraelectric phase. Moreover, the result proves that the molecular chain orientation is identified by the friction force measurement. Next, we discuss the molecular orientation change accompanying the paraelectric-to-ferroelectric and ferroelectricto-paraelectric phase transitions, which were studied by the LMFFM technique. P(VDF-TrFE) crystals showed highly regular molecular orientation above Tc-heat (paraerroelectric phase), whose friction force was almost uniform inside each crystal. However, the molecular orientation changed with decreasing temperature below Tc-cool (ferroelectric phase). Figure 2a,b shows friction images at 125 °C (above Tc-heat) and at 60 °C (below Tc-cool), respectively. These images were obtained in different but not special areas on the same film. To avoid the influences of tip scanning at high temperature, we chose different areas for observation. The contrast of the friction force inside each crystal was not uniform at temperatures below Tc-cool, which may give the impression that the image resolution of Figure 2b is higher than that of Figure 2a. However, the image resolution scarcely changed at these two temperatures because the contrast on grain boundaries in Figure 2a is as sharp as those in Figure 2b. Moreover, the topographic images shown in Figure 2c,d, which were simultaneously obtained with Figure 2a,b, respectively, have

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Figure 2. Molecular orientation change accompanied by the paraelectric-to-ferroelectric phase transition detected by LM-FFM at 9 kHz. Friction images (1 µm × 1 µm) of randomly oriented P(VDF-TrFE) crystals on graphite observed at 125 °C, which is a temperature in the paraelectric phase (a); the observation made at 60 °C is in the ferroelectric phase (b). The direction of lateral modulation is indicated by the arrow. These images were obtained over different areas of the same sample. (c) Contact-mode topograph simultaneously obtained with the image in part a (125 °C). (d) Contact-mode topograph simultaneously obtained with the image in part b (60 °C).

Figure 3. Topographic and frictional observations of a P(VDF-TrFE) film whose molecular chain orientation was controlled at 142 °C (just below Tm) using an AFM cantilever tip. (a) Contact-mode topograph (3 µm × 3 µm) observed at 50 °C. A modification scan was applied to the central part at 142 °C in the direction indicated by the arrow. (b) Friction image (3 µm × 3 µm) of the same area as shown in part a, observed at 50 °C using LM-FFM at 500 Hz. The direction of lateral modulation is indicated by the arrow.

almost the same image resolution. Therefore, we believe that this drastic change originates in the molecular orientation change accompanied by the paraelectric-to-ferroelectric phase transition. The mechanism can be explained as follows. In the paraelectric phase, P(VDF-TrFE) molecular chains containing trans-gauchetrans-gauche′ sequences packed in a hexagonal lattice undergo a flip-flop motion around the chain axis, whereas in its ferroelectric phase, they stop the motion and change the structure to an alltrans conformation with orthorhombic packing.13,14,17,18 After the phase transition, some molecules containing a gauche conformation still remain, which induces irregularity in the chain alignment inside each crystal.25 Moreover, the structural change from a hexagonal lattice to an orthorhombic one, which includes a lattice constant change, also induces disorder in the molecular alignment. These disturbances divided the molecular alignment inside each edge-on lamella into domains. These domains are still orthorhombic, but their molecular orientations are not exactly

the same. After the observation at 60 °C, we increased the film temperature to 115 °C (below Tc-heat). The features of the friction image were basically the same. However, they changed again to the image shown in Figure 2a when the film temperature was increased above Tc-heat. Next, we visualize an artificially created molecular orientation change on the nanometer scale by its direct control process using AFM. Topographic and friction images after the control process that were observed at 50 °C (below Tc-cool) are shown in Figure 3a,b, respectively. We first modified the P(VDF-TrFE) molecular orientation at 142 °C by the modification scan in the direction indicated by an arrow in Figure 3a. After the modification, we evaluated the molecular orientation of the modified area by topographic imaging and LM-FFM. LM-FFM was measured with horizontal film oscillation in the direction indicated by an arrow shown in Figure 3b. The topographic image in the modified area (center part of the image) is not very clear; however, the

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Figure 4. (a) Magnified topograph (1 µm × 1 µm) (at 50 °C) of the dotted area shown in Figure 3a. (b) Friction image (1 µm × 1 µm) (at 50 °C) of the same area as shown in part a, observed by LM-FFM at 500 Hz. The direction of lateral modulation is indicated by the arrow. (c) Schematic illustration of main-chain alignment in a P(VDF-TrFE) film before the modification scan (left), during the modification at 142 °C (middle), and upon cooling down to 50 °C after modification (right) (top view). The area inside the square corresponds to parts a and b.

polymer film, of course, existed in the modified area in Figure 3a,b because randomly oriented edge-on lamellae were reconstructed if the modified film was annealed at a temperature around Tm.38 The friction signal shown in Figure 3b was uniformly small in the modified area, which means that molecular chains are oriented parallel to the modification scan direction. Magnified images (topographic and friction images) of the dotted area in Figure 3a are shown in Figure 4a,b, respectively. We can recognize from Figure 4a that new rodlike grains were formed by the modification scan, whose longer axes were well aligned perpendicular to the scan direction. Figure 4b shows that the molecular chains on the aligned grains are oriented exactly parallel to the modification scan, except for the grain boundaries. This phenomenon can be explained by the schematic illustrations for molecular orientation change shown in Figure 4c. The area inside a square in Figure 4c shows that the molecular orientation corresponds to Figure 4b. Before the modification scan, molecular chains were aligned with folding turns in randomly oriented edge-on lamellae. The molecular orientation at this stage was perpendicular to the lamellar plane of each edge-on lamella. Molecular chains were stretched and aligned parallel to the tip scan direction during the modification scan at 142 °C. After the modification, stretched molecules again formed edge-on lamellae with folding turns in the cooling process while they maintained their orientation in the modification scan direction. Consequently, well-aligned edge-on lamellae were formed. At crystal boundaries, the molecular alignment was disordered with their folding turns. The illustration on the right side of Figure 4c shows the resultant molecular orientation after the modification. Thus, these images give us precise information about the molecular orientation change in the modified area, which proves the effectiveness of our molecular orientation control technique. These structures may look like ridges on polymer films created by continuous tip scan using AFM,28-32 whose topographic images were similar to Figure 4a, but their origin was completely different from that of the phenomenon shown here.35-38 Ridges were observed only on amorphous or partially crystallized

polymer films and were almost independent of the processing temperature.32 However, the phenomenon shown here are highly dependent on the temperature of the modification scan.35,38 The rodlike grains were obtained only by the modification scan at temperatures just below Tm. These results strongly suggest that this phenomenon consists of the stretching of molecular chains in nanometer-scale areas, and newly obtained rodlike grains are aligned edge-on lamellae. This speculation was proven to be correct by the molecular orientation study using LM-FFM. The crystal size in the modified area was smaller than that in unmodified area, as observed in Figure 4a-c. In the modified area, new crystals were formed from the nuclei as brought about by the modification scan. Therefore, the condition between the tip and the sample surface should have a strong influence on the resultant crystals. Actually, the crystal size in the modified area was not always smaller than that in the unmodified area, but sometimes that was as large as or even larger than the crystal size in the unmodified area. Detail parameters that influence the resultant crystal size in this technique are still unknown.

Conclusions We precisely identified the molecular orientation of P(VDFTrFE) crystals by surface friction anisotropy. Using this technique, we visualized the molecular orientation change caused by the paraelectric-to-ferroelectric phase transition of this copolymer. We also evaluated the artificially created molecular orientation change over a nanometer-scale area using this technique. Thus, the surface friction between molecules and an AFM tip brings us essential information about various nanometer-scale phenomena such as phase transitions, crystallization, and even a control process of molecular alignment. The results will direct our interest toward the molecular-scale investigation of various transition phenomena. Acknowledgment. We thank Daikin Industries Ltd. for providing the P(VDF-TrFE). This work was supported by an Innovative Cluster Creation Project and a Grant-in-Aid for

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Scientific Research from the Ministry of Education, Culture, Sport, Science and Technology of Japan.

Appendix Theoretical Calculation of Friction Force. Here, we describe a theoretical expression of the anisotropic friction function f (φ) (in which φ is the angle between the lateral modulation direction and the molecular chain orientation). The lateral mechanical modulation of the sample base causes the friction force acting on the cantilever tip through the anisotropic polymer crystal. Because of this large structural anisotropy with respect to the molecular chain direction, it is more convenient to describe the friction force in terms of two force components: friction parallel ( f | ) and perpendicular ( f ⊥ ) to the molecular chain. When the modulation is sinusoidal at a frequency ω, the two friction terms are expressed as

f | ) f 0| cos(ωt + δ|) f ⊥ ) f 0⊥ cos(ωt + δ⊥)

(a)

where f0| and f0⊥ are the friction force amplitudes for the two components, respectively, and δ| and δ⊥ are the phase delays depending on the crystal directions, in connection with a possible large difference in the viscoelastic response of the sample. Because the cantilever torsional motion for the friction measurement is restricted (actually set) to that in the modulation direction (x axis, shorter axis of the cantilever rectangle), the cantilever lateral movement x(t) (torsional vibration) is expressed by the sum of the x-axis projection of the motion caused by both friction terms, which is given by

x(t) )

f| f⊥ cos φ + sin φ kt kt

(b)

Equations a and b lead to

x(t) )

f (φ) cos(ωt + θ) kt

where f (φ) and θ are represented by f (φ) )

x

f 0|2 cos2 φ + f 0⊥2 sin2 φ + 2 f 0| f 0⊥ cos φ sin φ cos(δ| - δ⊥)

(2) tan θ )

f 0| sin δ| cos φ + f 0⊥ sin δ⊥ sin φ f 0| cos δ| cosφ + f 0⊥ cosδ⊥ sin φ

Thus, we have a theoretical expression, f (φ), for the anisotropic friction force. However, the measured friction signal V(φ) using LM-FFM contains several factors in addition to f (φ), such as the sensitivity of the lock-in amplifier and that of laser beam measurement system and also the effect of the approximation that the torsional bending response of the cantilever for the film oscillation is exactly sinusoidal.28 We included these factors in Sf. Then, the measured friction signal V(φ) can be represented as Sf f (φ)/kt, which is directly compared with the measured friction signal obtained by LM-FFM. The solid line in Figure 1c was calculated from eq 2 under the conditions of Sff0|/kt ) 0.75, Sff0⊥/kt ) 4.95, δ| ) 0.83π, and δ⊥ ) 0. LA063270P