Langmuir 2008, 24, 7793-7796
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Low-Dimensionality Effects in the Melting of a Langmuir-Blodgett Multilayer Ajay Gupta,*,† Parasmani Rajput,† Sigrid Bernstorff,‡ and Heinz Amenitsch§ UGC-DAE Consortium for Scientific Research, UniVersity Campus, Khandwa Road, Indore 452017, India, Sincrotrone Trieste, SS 14, Km 163.5, I-34012 BasoVizza, Trieste, Italy, and Institute of Biophysics and Nanosystems Research, Austrian Academy of Sciences, Schmiedlstr. 6, 8042 Graz, Austria ReceiVed March 23, 2008. ReVised Manuscript ReceiVed May 4, 2008 Low-dimensionality effects in the melting behavior of a cadmium arachidate Langmuir-Blodgett multilayer have been studied. Depth resolved information about structural changes occurring with temperature is obtained using in-plane X-ray diffraction under standing wave conditions. The surface region exhibits a distinctly different melting behavior as compared to the bulk of the film. While in the bulk of a 13-monolayer cadmium arachidate multilayer, the crystalline phase directly transforms to a tilted hexaticlike phase at 360 K, in the near surface region transformation occurs via an intermediate smectic phase. This behavior of the surface region is similar to that observed in twodimensional crystals. Thus even in a thick Langmuir-Blodgett multilayer, the surface region exhibits low-dimensionality effects.
I. Introduction The melting behavior of two-dimensional (2D) crystals is considered a major intellectual challenge, and has been a subject of continuous debate over several decades.1–13 Theory predicts the existence of a hexatic phase, intermediate between solid and liquid phases, which retain the orientational order of the crystal without long-range translational order.14–17 The existence of a hexatic phase in a verity of systems including Langmuir monolayer8 and Langmuir-Blodgett (LB) multilayer9 has been observed. Further, Ostlund and Halperin predicted that, in the case where the local symmetry is distorted from a hexagonal one, an additional smectic or nematic phase is inserted between solid and hexatic phase.17 Existence of such a sequence of phase transitions in a cadmium arachidate trilayer was first observed by Sikes et al.10 Atomic force microscopy (AFM) was used to determine the atomic structure at the surface as a function of temperature. Melting of LB films and the effect of film thickness there upon has been extensively studied in the literature.7–13 Fontana et al.11 performed an interesting study on the dependence * Corresponding author. E-mail:
[email protected]. † UGC-DAE Consortium for Scientific Research. ‡ Sincrotrone Trieste. § Austrian Academy of Sciences.
(1) Kramer, E. J. Nature 2005, 437, 824. (2) Angelescu, D. E.; Harrison, C. K.; Trawick, M. L.; Register, R. A.; Chaikin, P. M. Phys. ReV. Lett. 2005, 95, 025702. (3) Segalman, R. A.; Hexemer, A.; Kramer, E. J. Phys. ReV. Lett. 2003, 91, 196101. (4) Pang, H.; Pan, Q.; Song, P. H. Phys. ReV. B 2007, 76, 064109. (5) Zheng, X. H.; Grieve, R. Phys. ReV. B 2006, 73, 064205. (6) Chou, C.; Jin, A. J.; Hui, S. W.; Huang, C. C.; Ho, J. T. Science 1998, 280, 1424. (7) Igne´s-Mullol, J.; Schwartz, D. K. Nature (London) 2001, 410, 348. (8) Knobler, C. M.; Desai, R. C. Anuu. ReV. Phys. Chem. 1992, 43, 207. (9) Viswanathan, R.; Madsen, L. L.; Zasadzinski, J. A.; Schwartz, D. K. Science 1995, 269, 51. (10) Sikes, H. D.; Schwartz, D. K. Science 1997, 278, 1604. (11) Fontana, M. P.; Facci, P. J. Chem. Phys. 1999, 111, 5562. (12) Mukhopadhyay, M. K.; Sanyal, M. K.; Datta, A.; Mukherjee, M.; Geue, Th.; Grenzer, J.; Pietsch, U. Phys. ReV. B 2004, 70, 245408. (13) Tippmann-Krayer, P.; Kenn, R. M.; Mo¨hwald, H. Thin Solid Films 1992, 210/211, 577. (14) Nelson, D. R. Phys. ReV. B 1978, 18, 2318. (15) Halperin, B. I.; Nelson, D. R. Phys. ReV. Lett. 1978, 41, 121. (16) Nelson, D. R.; Halperin, B. I. Phys. ReV. B 1979, 19, 2457. (17) Ostlund, S.; Halperin, B. I. Phys. ReV. B 1981, 23, 335.
of the nature of melting of fatty acid LB films on thickness, and hence dimensionality, using a quartz crystal microbalance and Fourier transform infrared dichroism. It was found that samples with number of layers, n, more than 12 melt as a normal threedimensional (3D) bulk solid, independent of the sample history, defect content, morphology, and/or structure. Films with n < 8 melt continuously, as is expected for 2D systems. For films with 8 < n < 12, the nature of melting seems to be dependent on sample history. More recently, Mukhopadhaya et al. have observed a transition from 2D to 3D melting as a function of the thickness of the LB multilayer.12 It may be noted that, even in thick films, low-dimensionality effects should be observable in the layers near the surface and would provide information complementary to that obtained using ultrathin films. Therefore, in order to develop a detailed understanding of the melting process in LB films, it is necessary to get information about the temperature-dependent changes in the in-plane structure as a function of depth (for a fixed film thickness). To the best of our knowledge, no such study exists in the literature. In the present work, we study the depth-dependent melting behavior of a cadmium arachidate (CdA) LB film using in-plane diffraction measurements. Depth selectivity is achieved using X-ray standing waves (XSW).18–21 Selective information about the center of the multilayer or the surface regions is obtained by aligning the position of an antinode of XSW either with the center or with the surface region. Present results distinctly show a different behavior of the surface region as compared to the bulk of the film. These results are complementary to the thicknessdependent studies. A different behavior of the surface region relative to the bulk has earlier been observed in polymer films with regard to structural relaxation.22 (18) Bedzyk, M. J.; Bommarito, G. M.; Schildkraut, J. S. Phys. ReV. Lett. 1989, 62, 1376. (19) Bedzyk, M. J.; Cheng, L. ReV. Mineral. Geochem. 2002, 49, 221. (20) Gupta, A.; Rajput, P.; Saraiya, A.; Reddy, V. R.; Gupta, M.; Bernstorff, S.; Amenitsch, H. Phys. ReV. B 2005, 72, 075436. (21) Gupta, A.; Rajput, P.; Meneghini, C. Phys. ReV. B 2007, 76, 195401. (22) Priestley, R. D.; Ellison, C. J.; Broadbelt, L. J.; Torkelson, J. M. Science 2005, 309, 456.
10.1021/la8009018 CCC: $40.75 2008 American Chemical Society Published on Web 06/21/2008
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II. Experimental Section Thirteen monolayers of CdA were deposited on a Si substrate coated with a buffer layer of 70 nm Ni, using a KSV 3000 LB trough. The Ni buffer layer is deposited in order to generate XSW. When the X-ray beam falls on the film at an angle below the critical angle for total reflection for Ni, XSW are formed above the surface of the Ni layer due to interference between the incident and reflected wavefronts.18,19 With increasing angle of incidence, the position of nodes and antinodes of the standing wave shift downward, with separation of successive nodes or antinodes given by D ) λ/(2 sin R), R being the angle of incidence and λ being the wavelength of the X-rays. Depth selective information can be obtained by doing in-plane diffraction measurements at different values of R, which correspond to different positions of the antinodes along the depth of the film. In-plane diffraction measurements were done using the SAXS beam line of an Elettra synchrotron at an X-ray energy of 8 keV. A CCD camera (Photonic Science type X-ray L.A. 1024/12) was kept in the film plane, making an angle of about 22° from the beam direction. The sample to CCD distance was 300 mm, which allowed us to cover an angular range of 12° in both horizontal and vertical directions. A one-dimensional (1D) detector kept in the forward direction at a distance of 1520 mm from the sample was used to measure the scattering in the forward direction. During the measurements as a function of temperature, the alignment of the sample was continuously controlled by monitoring the position of the specular spot on the 1D detector. This ensured the constancy of the angle of incidence of X-rays with an accuracy of (0.003°. During heating, the sample was kept in a protective atmosphere of argon gas. The incident beam had a cross-section of 1.7 mm (h) × 100 µm (V). The intensity of incident beam was attenuated by putting about 1 mm of aluminum in the beam path, and an exposure time of 100 s was used for taking one diffraction pattern. In a control experiment, it was found that no significant radiation damage in the LB film occurred even after an exposure time of 90 min at room temperature. Further, in order to avoid any influence of radiation damage during the measurements, after every 20-30 min of measurement the sample was shifted across the beam by 2 mm so that a fresh area of the film was exposed to the X-rays.
Figure 1. (a) CCD diffraction pattern of a CdA LB multilayer taken at room temperature with the angle of incidence R ) R2. (b) In-plane diffraction profile (at qz ) 0) and (c) out-of-plane diffraction profile at qxy )15.6 nm-1 [corresponding to the (01 + 11j) peak], as extracted from CCD data.
III. Results and Discussions Figure 1a shows a typical 2D CCD diffraction pattern taken at 300 K. The corresponding in-plane diffraction profile (Figure 1b) shows two strong peaks at qxy ) 15.6 and 16.8 nm-1, corresponding to (01 + 11j) and (10) reflections. This suggests that, in conformity with earlier works,12 the in-plane structure is a distorted hexagon. The distortion of the lattice from regular hexagon can be quantified in terms of parameter ∆γ ) 60° γ, where γ ) cos-1(q2/2q1), q1 and q2 being the positions of (01 + 11j) and (10) reflections, respectively. Figure 1c gives the out-of-plane [(01l) + (11l)] diffraction profile. The positions of peaks as a function of qz can be used to obtain the bilayer periodicity in the vertical direction, which in turn can be used to get the vertical tilt angle.23,24 At room temperature, the bilayer periodicity comes out to be 5.23 nm. The bilayer thickness of the CdA multilayer with untilted molecules is 5.54 nm.25 This gives a tilt angle of 19° for the molecular chains with respect to the surface normal in the present case. Figure 2 gives the intensity of the in-plane diffraction peaks as a function of the angle of incidence. Two maxima in the intensity correspond to the resonance enhancement of X-rays inside the LB multilayer corresponding to TE0 and TE1 modes (when, respectively, the first or the second node coincides with (23) Peng, J. B.; Foran, G. J.; Barnes, G. T.; Gentle, I. R. J. Chem. Phys. 2005, 123, 214705. (24) Weissbuch, I.; Popovitz-Biro, R.; Lahav, M.; Leisrowitz, L.; Kjaer, K.; Als-Nielsen, J. AdV. Chem. Phys. 1997, 102, 39. (25) Vitta, S.; Metzger, T. H.; Major, S. S. J. Chem. Phys. 1999, 111, 11088.
Figure 2. Area of the (01 + 11j) and (10) peaks as a function of the angle of incidence of the X-rays. The inset shows a contour plot of the X-ray intensity distribution inside the film as a function of the angle of incidence.
the surface of the multilayer).20,21,26 Two angles of incidence, namely R1 ) 0.14° and R2 ) 0.18°, were used for detailed temperature-dependent measurements. For R ) R1, the position of the first antinode of the standing wave coincides with the surface of the LB film, while at R ) R2, which corresponds to the first resonance enhancement, the first antinode coincides with center of the multilayer (inset of Figure 2). Thus, at R ) R1 the diffraction measurement will give preferential information from the surface region, while at R ) R2 information from the center of the multilayer will be obtained. Figure 3 gives temperature-dependent in-plane diffraction patterns corresponding to the two angles of incidence. Figure (26) Wang, J.; Bedzyk, M. J.; Caffrey, M. Science 1992, 258, 775.
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Figure 3. In-plane diffraction pattern as a function of temperature for (a) R ) R1 and (b) R ) R2.
Figure 5. Tilt angle of the molecular chains as a function of temperature, as calculated from the out-of-plane diffraction profile taken at grazing incidence angles of R1 and R2.
Figure 4. (a) ∆γ as a function of temperature, as calculated from the fitting of in-plane diffraction patterns. (b) Temperature dependence of the width of the (01 + 11j) and (10) peaks.
4a,b summarize the results of the fitting of in-plane diffraction data. From Figure 4a, one may note that, around a temperature of 360 K, ∆γ exhibits a sharp decrease to a value of ∼1°, indicating a decrease in the distortion from regular hexagonal structure. This corresponding to the transition to tilted hexaticlike phase.12,27,28 Further confirmation of this phase being tilted hexaticlike comes from the temperature dependence of the tilt angle as obtained from the analysis of diffraction pattern along qz, shown in Figure 5. For R ) R2 the tilt angle exhibits a sharp transition to a value of 28° at 360 K, confirming transformation to the tilted hexaticlike phase at this temperature. At R ) R1, the error bar in the value of tilt angle is quit large because of poor X-ray intensity at this angle. However, one may note that, in this case also, up to 357 K the tilt angle does not change substantially. Beyond 357 K, the diffracted intensity in the vertical direction became too weak to be analyzed. (27) Kaganer, V. M.; Mo¨hwald, H.; Dutta, P. ReV. Mod. Phys. 1999, 71, 779. (28) Peng, J. B.; Barnes, G. T.; Gentle, I. R. AdV. Colloid Interface Sci. 2001, 91, 163.
Figure 4b gives the width of in-plane diffraction peaks corresponding to the two angles of incidence, as a function of temperature. The width of various peaks is related to the coherence length along that direction. One may note that, while the width of the (01 + 11j) reflection remains almost constant, that of the (10) reflection exhibits substantial variation with temperature. Further, at the incidence angle R1, at which information is preferentially obtained from the surface region, the width of the (10) peak increases at a much faster rate as compared to that at angle R2, at which information is preferentially obtained from the center of the multilayer. The fact that with increasing temperature the (10) peak gets broadened preferentially is consistent with the observation of Sikes et al.,10 who found that intermediate between crystal and hexatic phases, a 2D smectic phase occurs, in which only a short-range 1D periodicity remain. Line broadening is an indication of a decrease in the coherence length ξ that can be calculated using the relation ξ ) 2/∆(qxy),13 where
∆ ) √∆m2 - ∆ins2
(1)
is the full width at half-maximum of the diffraction peak corrected for instrumental broadening, ∆ins () 0.25 nm-1), and ∆m is the experimentally measured width. In the present case, at 357 K, at which the maximum broadening of (10) peak is observed, the
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Figure 6. Schematic diagram of the distorted hexagonal 2D lattice of CdA in real space. The (10) and (01) lines as well as the set of six elementary Burgers vectors grouped into types I and II have been labeled.
Figure 7. Depth distribution of X-ray field intensity inside the CdA multilayer corresponding to the grazing incidence angles R1 and R2. Depth is measured from the surface of the multilayer.
coherence length ξ along the (10) direction in the surface region (corresponding to angle R1) comes out to be 1.4 nm, while that along the (01 + 11j) direction comes out to be 11.4 nm. This is a clear signature of formation of smectic phase prior to the transition to hexaticlike phase. Ostlund et al.17 considered dislocation-mediated melting of 2D crystals. Following them, in a 2D crystal with symmetry lower than hexagonal, six elementary dislocations would not be equivalent (Figure 6). Two equivalent dislocations (type I) have their Burgers vector along a reflection symmetry axis, while the other four dislocations (type II) lie at an angle of ((60 - ∆γ) from the reflection axis. Ostlund et al. predicted that if the type I dislocations unbind first, a 2D smectic phase would be inserted into the phase diagram between the crystalline and hexatic phases. The observed broadening of the (10) peak (Figure 4b) suggests that indeed the type I dislocations unbind first, leading to formation of the smectic phase. It may be noted that at incidence angle R2, for which the information is preferentially obtained from the center of the multilayer, the broadening of the (10) peak is significantly less as compare to that of at the angle R1. Figure 7 gives the depth distribution of X-ray field intensity at the incidence angles R1 and R2. Even at angle R2, although the information is coming preferentially from the center of the multilayer, there is a finite contribution of the surface layers. The small broadening of the (10) peak with temperature may be due to this finite contribution of surface
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layers. Thus, the present results strongly suggest that the melting behavior of surface region is very different from that of the bulk of the multilayer. It may be noted that, in some earlier works, an in-plane X-ray diffraction technique also has been used to study melting behavior of LB films.12,13 However, in both of these works, the incidenceangle of X-rays has been taken to be just below the critical angle of the Si substrate (∼3.5 mrad). Though in their geometry standing waves are also formed above the surface of the Si substrate, due to the significantly large angle of incidence, the antinode of the standing wave lies deep inside the bulk of the LB multilayer, and thus the information obtained pertains to the bulk. On the contrary in the present work, by appropriately choosing two values of incidence angle, an antinode of XSW was made to coincide either with the surface or with the center of the LB multilayer, thus enabling one to separate out the behavior of the surface region from that of the buried layers of the film. In fact, at angle R2, at which the information is obtained from the bulk of multilayer, the melting behavior is very similar to that observed by Mukhopadhaya et al. in 13-monolayer CdA, in the sense that the crystalline phase directly transforms to hexaticlike phase. However, the melting behavior of the surface layers of the film (as observed at incidence angle R1) is very different from that of the bulk. In the surface region, the transition from crystal to hexaticlike phase occurs via an intermediate smectic phase, in conformity with the prediction of theory based on dislocationmediated melting of 2D crystals17 and experimental observation of Sikes et al. in a CdA trilayer.10 Thus, the low-dimensionality effects that have been observed in ultrathin (two-dimensional) LB multilayers are also observed in the surface region of thick LB multilayers.
IV. Conclusions In conclusion, the melting behavior of a 13-monolayer CdA multilayer has been studied as a function of depth. Depth selective information has been obtained by making use of X-ray standing waves. By making in-plane diffraction measurements at two distinct angles of incidence, selective information about the center of the layer or the near surface region has been obtained. It is found that at 360 K the system transforms to a tilted hexaticlike phase. This transition temperature is the same for both the surface region and the center of the layer. However, in the near surface region, transformation to hexaticlike phase takes place via an intermediate smectic phase. This behavior is very similar to that observed in 2D anisotropic crystals. On the other hand, the bulk of the multilayer transforms from crystal to hexaticlike phase directly. Thus, even in thick films, the surface region exhibits low dimensionality effects. Acknowledgment. One of the authors (P.R.) is a senior research fellow of CSIR, India. Travel support for performing the experiment at Elettra, Trieste was provided by the International Center for Theoretical Physics, Trieste. LA8009018
