pubs.acs.org/Langmuir © 2009 American Chemical Society
Polarity Effect near the Surface and Interface of Thin Supported Polymer Films: X-ray Reflectivity Study Sung Il Ahn,† Jung-Hoon Kim,† Jae Hyun Kim,§ Jin Chul Jung,† Taihyun Chang,‡ Moonhor Ree,‡ and Wang-Cheol Zin*,† † Department of Materials Science and Engineering and ‡Department of Chemistry, POSTECH, Pohang-city, Korea, and §Memory Division, Samsung Electronics Co. Ltd., Hwasung-city, Kyonggi-do, Korea
Received December 25, 2008. Revised Manuscript Received February 13, 2009 Four homopolymer films (poly(methyl methacrylate) (PMMA), poly(4-vinylpyridine) (P4VP), polystyrene (PS), and poly(R-methyl styrene) (PAMS)) with different interactions with native Si oxide on Si wafers and three random copolymer films (PS-ran-PMMA) with different mole fractions were investigated with the X-ray reflectivity (XRR) method. The electron density profile of each film was obtained by fitting the results of the XRR measurements. A new data correction technique that uses the vertical real beam profile and a fitting method that uses the distorted wave Born approximation were combined to overcome the sensitivity limitations of XRR analysis. The results show that the chemical structures of polymer pendant groups and the interactions between the polymer films and the native Si oxide layer are strongly correlated with the density profiles of the films near the surfaces and interfaces. Two general types of electron density profiles were found that are characterized by the polarity of the pendant group of the polymer. The reproducibility and credibility of the fitting technique were also thoroughly tested.
Introduction The properties of thin polymer films have been extensively studied with X-ray and neutron reflectivity analysis over the last few decades.1-6 These analyses have focused on the surface and interface properties of polymer thin films on solid substrates,7,8 the detection of specific layers inside thin films,4,9-11 and the measurement of the exact thicknesses of films under various external conditions.6,12-14 The primary use of X-ray and neutron reflectivity analysis is to determine the electron density profile normal to the film surface, so there have also been many attempts to determine the density profiles of polymer thin films. In the widely used Parratt method, the densities of thin polymer films are assumed to be uniform with respect to the *To whom correspondence should be addressed. Telephone: +81-54279-2136. E-mail:
[email protected]. (1) Roe, R. J. Methods of X-ray and Neutron Scattering in Polymer Science; Oxford: 2000; p 236. (2) Tolan, M. X-ray Scattering from Soft Matter Thin Films; SpringerVerlag; 1999, . (3) Holy, V. In High-resolution X-ray Scattering from Thin Films and Multilayers; Pietsch, U., Baumbach, T., Eds.; Springer-Verlag: 1999. (4) Smith, G. S.; Skidmore, C. B.; Howe, P. M.; Majewski, J. J. Polym. Sci., Part B: Polym. Phys. 2004, 42, 3258. (5) Tasaki, S.; Yamaoka, H.; Yoshida, F. Phys. B 1992, 180, 480. (6) Tsui, O. K. C.; Russell, T. P.; Hawker, C. J. Macromolecules 2001, 34, 5535. (7) Sinha, S. K.; Sirota, E. B.; Garoff, S. Phys. Rev. B 1988, 38, 2297. (8) Lin, E. K.; Wu, W.; Satija, S. K. Macromolecules 1997, 30, 7224. (9) Vogt, B. D.; Soles, C. L.; Jones, R. L.; Wang, C.-Y.; Lin, E. K.; Wu, W.; Satija, S. K. Langmuir 2004, 20, 5285–5290. (10) Sirard, S. M.; Gupta, R. R.; Russell, T. P.; Watkins, J. J.; Green, P. F.; Johnston, K. P. Macromolecules 2003, 36, 3365. (11) Russell, T. P. Phys. B 1996, 221, 267. (12) Singh, A.; Mukherjee, M. Macromolecules 2003, 36, 8728–8731. (13) Vogt, B. D.; Soles, C. L.; Lee, H.-J.; Lin, E. K.; Wu, W. Langmuir 2004, 20, 1453–1458. (14) Bhattacharya, M.; Sanyal, M. K.; Geue, Th.; Pietsch, U. Phys. Rev. E 2005, 71, 041801. (15) Parratt, L. G. Phys. Rev. 1954, 95, 359.
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film depth.15-18 The surfaces and interfaces of films can be characterized with the convolution of a Gaussian function and a step function, which describe the diffuse interface and the density, respectively.19 However, in this approach, the density profile of the film is flat within each layer. This model of the density profile is adequate for thick or multilayer films, but for thinner films the density inside the film is affected by several factors such as the interaction between the film and the substrate or the chain conformation of the polymers. There have been some attempts to describe a specific part inside polymer films such as interfaces more carefully in order to take into account the interactions between films and substrates.20 It has been found that the film density near the interface differs from the mean density of the film when certain interactions between the film and the substrate are present. For example, the interfacial density of P4VP (poly-4-vinylpyridine), which has a strong interaction with SiO2, is slightly higher than its mean density. However, the author of this study also indicated that the sensitivity limitations of X-ray reflectivity (XRR) mean that some of these results are unclear. In all these cases, the density profiles were obtained with various kinds of fitting procedures, which are the most troublesome aspect of reflectivity analyses. Both the low intensity of the beam source and the complexity of the fitting procedure contribute to the sensitivity limitations of XRR analyses, so it is important to improve the data processing and fitting techniques. (16) Born, M.; Wolf, E. Principles of Optics, 6th ed.; Pergamon: London, 1980, (17) Vidal, B.; Vincent, P. Appl. Opt. 1984, 23, 1794. (18) Gibaud, A. In X-ray and Neutron Reflectivity: Principles and applications; Daillant, J., Giband, A., Eds.; Springer-Verlag: Berlin, 1999; p 87. (19) Kulasekere, R.; Kaiser, H.; Ankner, J. F.; Russell, T. P.; Brown, H. R.; Hawker, C. J.; Mayes, A. M. Macromolecules 1996, 29, 5493. (20) Bollinne, C.; Stone, V. W.; Carlier, V.; Jonas, A. M. Macromolecules 1999, 32, 4719.
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In this study, four homopolymer thin films and three random copolymers were investigated with XRR. The goal of the study was to obtain the in-depth density profiles of the thin films in more detail that reflect the chemical structures of polymers and the influences of substrate-monomer interactions and the polarity effects using new methods for XRR analysis. Two main approaches to overcoming the problems with the accuracy of the fitting of reflectivity data are available. One approach is to improve the inversion scheme used to convert the reflectivity data into an electron density profile, and the other approach is to improve the data correction that is carried out before the fitting process. Several inversion schemes have been used, such as the scheme based on Parratt’s recursive formula mentioned above, the DWBA (distortedwave Born approximation) and the kinematic approximation (Born approximation). The model-independent DWBA approach is generally thought to be the best method for fitting reflectivity results for ultrathin films. Both Parratt’s method and the DWBA approach were used in this study. Second, smearing effects and numerical errors during data handling need to be minimized. We introduce a novel method for the correction of the smearing effect due to finite sample size.
Materials and Methods Materials. Poly(methyl methacrylate) (PMMA, Pressure Chemical), poly(4-vinylpyridine) (P4VP, Pressure Chemical), polystyrene (PS, Pressure Chemical), and poly(R-methyl styrene) (PAMS, Pressure Chemical) thin films and poly(styrene-ran-methylmethacrylate)s (Polymer Source) with three different compositions (12%, 46%, 84% styrene mole fraction) were spin-coated (2000 rpm, 60 s) onto Si wafers, which were cut into 25 25 mm2 pieces and cleaned with piranha solution, followed by rinsing with DI water and drying in a nitrogen stream. The molecular weights of the polymers were 93 300 g/mol for PMMA, 200 000 g/mol for P4VP, 90 000 g/mol for PS, and 450 000 g/mol for PAMS. In the cases of PMMA and PS, two different film thicknesses were prepared; the thicknesses of the other films were approximately 20-35 nm. The spin-coated samples were thermally treated at Tg + 50 C for 24 h and cooled at room temperature before the X-ray reflectivity measurements. X-ray Reflectivity Analysis. Specular X-ray reflectivity measurements were carried out using synchrotron radiation sources at the X-ray diffraction beamline 10C1 of the Pohang Light Source in Pohang, South Korea. An X-ray beam with a wavelength of 1.54 A˚ was focused onto each sample with a collimating mirror, and a Huber six-circle goniometer was used. Since the angle of the incident beam was fixed horizontally, the detector was rotated by 2θ while the sample was rotated by θ during the measurements. The reflectivity was measured in the range 0.1-5.2 of the angle of the detector (2θ). The measurement range was subdivided into 500 steps, and the detector counted X-rays for 1 s at each point. Different numbers of aluminum attenuators were applied in subdivided ranges of the detecting angle to cover the narrow effective dynamic range (approximately 10-3) of the scintillation counter21. The analyses of the reflectivity curves were carried out with the widely used Parratt32 software and A. van der Lee’s program that implements a DWBA (distorted-wave Born approximation) based fitting algorithm. Parratt32 describes films with layer-based models, so several different models consisting of two to four layers were tested and compared. In contrast to Parratt’s recursive equation, the DWBA fitting program can determine small density fluctuations inside ultrathin films from X-ray reflectivity curves. The (21) van der Lee, A.; Hamon, L.; Holl, Y.; Grohens, Y. Langmuir 2001, 17, 7664–7669.
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Figure 1. Vertical profile of incident beam: the asymmetry of the beam shape originates in beam collimation and the use of other optical devices for the enhancement of beam intensity. model-independent fitting scheme based on DWBA is appropriate for fitting ultrathin homopolymer films with thicknesses less than 400 A˚,22 as is the case for the films investigated in this study. A fitting technique based on the DWBA approach was used to obtain the electron density profiles, and their goodnessof-fits23 (fitness) were compared with those obtained with the Parratt32 software. The fitness is a measure of how well the computed result fits the experimental reflectivity and, here, is defined in eq 1. 2
χmean
2
N X Rex;i -Rcalc;i ¼4 Rex;i i ¼1
!2 3 5=N
ð1Þ
Rex,i is the measured reflectivity, Rcalc,i is the reflectivity calculated from the electron density profile, and N is the number of data points. Generally, the χ2 value is calculated using the standard deviation value (σ) which normalizes errors at each data point.24 However, here we used measured reflectivity for normalizing,25 since incident beam intensities were strong enough to make the standard deviation meaninglessly small (less than 0.0001% of specular reflectivity). Moreover, measurements of XRR were carried out in several divided angle regions, and that makes standard deviations roughly proportional to the measured reflectivity in the whole angle region. Both the Parratt32 software and the DWBA fitting program fit Rcalc,i to Rex,i by minimizing the χ2mean value defined by eq 1, although their algorithms for the calculation of Rcalc,i are different. Therefore, the results obtained with each program and model were also evaluated and compared by examining the χ2mean values.
All the reflectivity data were treated with the new geometrical correction technique before fitting. The experimental XRR data are inevitably different from the calculated results because of the finite sample size, especially for low angles of the incidence beam.26 Therefore, the smearing effect needs to be corrected before fitting is carried out. Gibaud et al.22 have suggested two correction methods. In the first method (eq 2), (22) Banerjee, S.; Ferrari, S.; Chateigner, D.; Gibaud, A. Thin Solid Films 2004, 450, 23–28. (23) Massey , F. J.Jr. J. Am. Stat. Assoc. 1951, 46, 68. (24) Press, W. H.; Teukolsky, S. A.; Vetterling, W. H.; Flannery, B. P. Numerical Recipes in C++; Cambridge University Press: 2002; p 659. (25) Dane, A. D.; Veldhuis, A.; de Boer, D. K. G.; Leenaers, A. J. G.; Buydens, L. C. M. Phys. B 1998, 253, 254. (26) Gibaud, A.; Vignaud, G.; Sinha, S. K. Acta Crystallogr. 1993, A49, 642.
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the vertical intensity profile of the X-ray beam is assumed to be uniform so that the ratio of ideal incident intensity to the actual one can be simply represented by the ratio of a vertical beam thickness (L) to a vertical height for the inclined film sample (L0 ). Icorrected ¼ IExp
L L ¼ IExp L0 x sin θ
R¥ GðxÞ dx Ra I ¼ I0 -¥ , 2 0 GðxÞ dx
a ¼
l sin θ 2
asymmetrical with respect to the vertical center of the beam because of the collimating geometry or the slit system. Therefore, the vertical intensity profile of the actual beam was used for geometrical correction in this study (Figure 1).
Results and Discussion
ð2Þ
Electron Density Profiles of PS and PAMS. Figure 2a and b shows the electron density profiles of PS and PAMS calculated with the Parratt32 and DWBA fitting programs. The results obtained with the two layer Parratt32 model feature depletion layers of electron density near the interfaces between the films and the substrates as previously reported.16 There is also depletion near the interfaces in the results obtained with the DWBA approach, but there are density fluctuations even inside the films in the resulting electron density profiles, which is not the case for the two layer model. The density profiles obtained with the three and four layer Parratt models are similar to those obtained with the DWBA approach because of the supplementary layers. As the reflectivity curves in Figure 2 show, fitness of each model is almost impossible to be figured out with naked eyes. Therefore, Table 1 shows the fitness, χ2mean, values for each film and model. In all cases, the fitness improves as the number of layers inside the model of the films increases and, by extension, as the DWBA approach is introduced into the fitting process.
ð3Þ
This assumption for a beam of rectangular shape is widely used in the correction of reflectivity data, but it is inaccurate because of its oversimplification of the beam shape. The use of a Gaussian profile (G(x) in eq 3) for the vertical beam intensity is an alternative method for reducing the error between the ideal reflectivity and the corrected value (eq 3). However, this is not always appropriate, especially in the case of the precise fitting of small density fluctuations. The vertical intensity profiles of actual beams cannot be exactly modeled with Gaussian profiles or any mathematical equation because most beam sources for X-ray reflectivity are collimated with several optical mirror systems. In some cases, the vertical intensity profiles of actual beams are
Figure 2. Reflectivity curves and electron density profiles of PS (a) and PAMS (b). Open tilted square symbols represent results obtained with DWBA fitting, and open square and triangle symbols represent results obtained with two layer and four (or three) layer Parratt32 models, respectively. Insets of reflectivity graphs show the magnifications for the part of the curves. Table 1. χ2mean Values for Each Fit Method and the Film fit method
χ2mean of PS
χ2mean of PAMS
χ2mean of PMMA
χ2mean of P4VP
two layer three to four layers DWBA
0.010 0.006 0.001
0.021 0.013 0.004
0.011 0.005 0.003
0.013 0.007 0.003
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have been overcome. In addition, the density profiles at the surface are quite similar. All the electron density models for both PMMA and P4VP indicate that there is a sharp enrichment of density near the surface, which is different from the results obtained for PS and P4VP.
Figure 3. Electron density profiles of PS films with 44 nm thicknesses. The inset shows that of a PS film with 28 nm thickness for comparison.
Figure 4. Electron density profiles of PMMA film with 33 nm thicknesses. The inset shows that of a PMMA film with 16 nm thickness for comparison. These two polymer films barely interact with the Si wafer, so the density profiles near their interfaces are expected to be similar. Near the interface, relatively large depletions of the electron density are observed in both films. For PS films of greater thickness, such depletion layers are still found near the interface. Figures 3 and 4 show the density profiles of PS and PMMA films that are almost twice as thick. The shapes of the density profiles near the surface and the interface are not significantly different despite this increase in thickness. There is instead a plateau region present in the middle of the film density profile for both PS and PMMA. Depletion layers are present near the interface, density waves are present near the surface, and their shapes are similar. These results provide evidence that these density profiles are related to actual phenomena near the interface and the surface. Electron Density Profiles of PMMA and P4VP. The density profiles of PMMA and P4VP are expected to be different from those of PS and PAMS, which interact only weakly with the Si substrates, and are shown in Figure 5. Relatively substantial densities are present near the interface for both the PMMA and P4VP films. These characteristics are in agreement with the results of another group,20 and also show that the sensitivity limitations of XRR analysis 5670
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Discussion There have been several previous studies of how the interaction between the polymer film and the solid substrate affect density profiles and the macromolecular conformations of films near interfaces.27-29 The four different films investigated in this study can be divided into two groups: films with a strong interaction with the Si substrate (PMMA and P4VP) and films with a weak interaction (PS and PAMS). And these polymer-substrate interactions are due to acid-base interaction between pendant groups of polymers and substrate.30 Accordingly, differences in density perturbation of these polymer films can be rationalized by the polarity effect of these matters.20 Since the densities inside the films are not uniform according to the results obtained with the DWBA approach, the density profiles near the substrate need to be compared with those of the other group, rather than with their own mean densities (Figure 6). The densities of PS and PAMS films near the substrate drop to 60-70% of their maximum density, whereas those of the PMMA and P4VP films drop to only 80-90%. The shapes of the depletion layers also differ between the two groups: the depletions of the PS and PAMS films are more sharp and rapid. Indeed, it is well-known theoretically that a strong interaction between a substrate surface and a monomer unit increases the density near the substrate.27 In contrast, there is more free volume for the PS and PAMS chains near the substrate, which results in conformational entropy gains because their interactions with the substrate are weak. The density profiles of PMMA and P4VP are quite similar, but a slight increase in the density is only observed for the P4VP film, which arises because the substrate-monomer interaction of P4VP is much stronger than that of PMMA. Further, the density profiles at the surfaces and near the interfaces can also be classified into two types. In the case of the film surfaces, there is no interaction between air or vacuum and the polymer chains, so the configurational entropies of the polymer chains and chain packing are the driving factors determining the surface density profiles.31,32 Here, we suggest that the polar pendant groups of PMMA and P4VP which undergo strong interactions with polar native oxide on the Si substrate near the interface33 also affect the chain packing at the surface. To minimize the surface energy, the polar pendant groups are directed toward the bulk, not the surface side.34 Therefore, abrupt electron density enrichments in PMMA and P4VP films can arise at their surfaces, whereas there are only mild density waves in the PS and PAMS films. To ensure these correlations between the (27) Theodorou, D. N. Macromolecules 1989, 22, 4589. (28) Mansfield, K. F.; Theodorou, D. N. Macromolecules 1991, 24, 4295. (29) Bitsanis, I. A.; ten Brinke, G. J. Chem. Phys. 1993, 99, 3100. (30) Fowkes, F.; Kaczinski, M. B.; Dwight, D. W. Langmuir 1991, 7, 2464. (31) Yethiraj, A.; Kumar, S.; Hariharan, A.; Schweizer, K. S. J. Chem. Phys. 1994, 100(6), 4691. (32) Yethiraj, A.; Hall, C. K. Macromolecules 1990, 23, 1865. (33) Grohens, Y.; Brogly, M.; Labbe, C.; David, M. O.; Schultz, J. Langmuir 1998, 14, 2929. (34) Eynde, X. V.; Weng, L. T.; Bertrand, P. Surf. Interface Anal. 1997, 25, 41.
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Figure 5. Reflectivity curves and electron density profiles of PMMA (a) and P4VP (b) obtained with the various fitting techniques. Open tilted square symbols represent results obtained with DWBA fitting, and open square and triangle symbols represent results obtained with two layer and three layer Parratt32 models, respectively. Insets of reflectivity graphs show the magnifications for the part of the curves.
Figure 6. Density profiles for the four different polymer samples obtained with the DWBA approach. polarity of the polymers and electron density profiles at the surface and the interface, PS-PMMA random copolymer thin films were also tested. Langmuir 2009, 25(10), 5667–5673
Electron Density Profiles of PS-PMMA Random Copolymers. The suggestions in the discussions above can be justified by verifying that density enrichments near the DOI: 10.1021/la804260t
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Figure 7. Reflectivity curves and density profiles (inset) for the three random copolymer samples obtained with the DWBA approach: (a) MRAN (12 mol % stryrene), (b) MAS (46 mol % styrene), and (c) SRAN (84 mol % styrene) surface and interface have the composition dependency in random copolymers. X-ray analysis only can show the result of the electron density profile, not the material itself. The electron density of PMMA, however, is higher than that of PS, especially in the case of the polar pendent group as results in Figure 2 show. Therefore, it can be considered that the excess density of random copolymer over that of PS results from PMMA. To prove this, three different PS-PMMA random copolymers (MRAN, 12 mol % styrene; MAS, 46 mol % styrene; SRAN, 84 mol % styrene) were prepared, and Figure 7 shows the results of them. Intuitively, density profiles of random copolymers are expected to be of an intermediate form of the density profiles in each homopolymer. And, in fact, the density profiles of MRAN, MAS, and SRAN are 5672
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presented between the profiles of PMMA and PS. In addition, the density profile of MRAN (MMA rich copolymer) near both the surface and the interface is similar to that of PMMA rather than PS, and also SRAN resembles PS. In Figure 8, density profiles of two homopolymers (PS and PMMA) and three copolymers above were aligned to the interface and the surface to focus on the composition dependency of density profiles at the surface and the interface, respectively. Sharp density depletion at the interface (Figure 8a) disappears as the fraction of PMMA increases, and the increase in electron density near the interface is more drastic than that in other regions. All these facts represent that the tendency differences in density profiles result from the pendant polar group of PMMA, not a backbone chain or other parts. At the film surface (Figure 8b), the surface enrichment decreases by degree as the fraction of PMMA decreases. Nevertheless, extra parts upon the smooth density profiles obviously exist and have composition dependency in MAS and SRAN. Considering the rms roughness values (σ) at the surface and interface of all these polymer films are within the sub-nanometer range, these extra densities can be regarded as PMMA (in detail, methacrylate group). In the case of MAS which has a nearly equal mole fraction of styrene and methylmethacrylate, the overall shape of the density profile is closer to that of PS or SRAN (Figure 7b). Information is absolutely not enough to explain this tendency, but common similitude can be found in our previous research.35 In that study, we found that the decreasing behavior of the glass transition temperature in the PS(46 mol %)-PMMA(54 mol %) random copolymer thin film (same one with MAS) follows the parallel additive rule rather the Fox equation or serial additive rule. This fact implies that PS which has weaker interaction with Si oxide substrate than PMMA is dominant in Tg behavior of the random copolymer, as the density profile of MAS takes after that of PS. Since the density of the polymer matter has a deep connection with the glass transition behavior,36 the electron density profile of MAS can also be assumed to correlate with the Tg behavior of it, and further investigations on this are needed. Reproducibility of the Fitting Techniques. Several films spin-coated under the same conditions were analyzed repeatedly in order to confirm the reproducibility of the fitting techniques. Figure 9 shows the electron density profiles obtained with the repeated analyses. A slight fluctuation in the film thickness is present, but the shapes of the density profiles are consistent, with observational errors that are less than 2% in most regions.
Conclusion The electron density profiles of four different homopolymer films (PS, PAMS, PMMA, and P4VP) and three PS-PMMA random copolymer films with different compositions were obtained with XRR analysis. A realistic method for the geometrical correction of reflectivity data was developed and applied with either Parratt32 fitting software or van der Lee’s fitting program based on the DWBA approach. The new correction method using the actual beam profile (35) Park, C. H.; Kim, J. H.; Ree, M.; Sohn, B.-H.; Jung, J. C.; Zin, W. C. Polymer 2004, 45, 4507. (36) Kim, J. H.; Jang, J.; Zin, W. C. Langmuir 2001, 17, 2703.
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Figure 8. Density profiles of two homopolymers and three copolymers with different compositions: (a) aligned with the interface between polymers and substrate and (b) aligned with surfaces of films. and fitting based on the DWBA approach were found to overcome the limits of resolution of X-ray reflectivity analysis and to minimize smearing effects due to finite sample size. We have shown that the electron density near the interface is strongly dependent on the substrate-monomer interaction, and a correlation between the polarity of the polymer pendant groups and the surface density profiles was suggested. In addition to that, this suggestion for correlation was approved by the composition dependency of surface density enrichment at the PS-PMMA random copolymer film surface.
Figure 9. Results from the fitting procedures for PMMA films spin-coated under the same conditions. Inset shows mean density and its standard deviations (less than 2%).
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Acknowledgment. The authors thank to Dr. A. van der Lee for providing the fitting program and for many valuable discussions. The authors also thank Samsung Electronics Co., Ltd. for funding this research. This work was also supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD)(KRF-2006005-J01301).
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