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Crystallization of Soft Crystals Max Wolff,*,† Andreas Magerl,‡ and Hartmut Zabel† Institute for Experimental Physics/Solid-State Physics/EP IV, Ruhr-UniVersity Bochum, D-44780 Bochum, Germany, and Crystallography and Structural Physics, UniVersity of Erlangen-Nu¨rnberg, Staudstrasse 3, D-91058 Erlangen, Germany ReceiVed September 14, 2008. ReVised Manuscript ReceiVed NoVember 6, 2008 The crystallization of micelles formed by surfactant F127 solvated by 20% in water was investigated in the vicinity of a hydrophilic interface. Upon entering the crystalline phase from low temperature, a large correlation length develops without preferential texture. Upon heating, the correlation length decreases and Oswald ripening is observed with crystallites orienting with respect to each other while retaining long-range and textured correlation.
The crystallization of metals or ionic crystals either propagates throughout the melt starting from a single seed or small grains grow and develop simultaneously at different locations. In the first case, a single crystal is formed, and the second case results in a polycrystal, which may show pronounced texture. The driving force is the ionic or metallic interaction with binding energies on the order of 100kBT at room temperature. Inert gas crystals form as a result of much weaker van der Waals forces, and regarding the spherical shape of atoms, in most cases an fcc structure. Soft matter is also characterized by relatively weak binding energies of hydrogen bonds, entropic forces, or hydrophobic interaction. Regarding this fact, crystallization is expected to proceed similarly to that for inert gases.1 Additionally, micelles often have an elliptical shape, and crystal growth should show similarities to alkali cyanide with a highly anisotropic form of the molecule.2 The striking difference is the tendency of selfordering of polymeric systems on the mesoscopic scale used to template nanomaterials.3-7 To achieve the best performance in this context, detailed knowledge of crystallization in soft matter is indispensable. Mixtures of amphiphilic block copolymers with a selective solvent are known to form micelles.8 These may crystallize in various structures at moderate and high concentrations. In contact with a solid wall, the intermicelle interaction competes with the micelle-wall interaction, which may result in the preferential orientation of crystallites.9 Upon shear, the finite correlation length of a crystalline structure results in secondary Bragg peaks.10 Well-suited methods for monitoring * Corresponding author. Present address: Institute Laue-Langevin, BP 156, F-38042 Grenoble, Cedex 9, France. Tel: +33-476207981. Fax: +33476207120. E-mail:
[email protected]. † Ruhr-University Bochum. ‡ University of Erlangen-Nu¨rnberg. (1) Kittel, C. Introduction to Solid State Physics, 8th ed.; Wiley: Hoboken, NJ,November 11, 2004. (2) Rowe, J. M.; Hinks, G. D.; Price, D. L.; Susman, S.; Rush, J. J. J. Chem. Phys. 1973, 58, 2039. (3) Ludwigs, S.; Boker, S.; Voronov, A.; Rehse, N.; Magerle, R.; Krausch, G. Nat. Mater. 2003, 2, 744. (4) Register, R. A. Nature (London) 2003, 424, 378. (5) Kim, S. O.; Solak, H. H.; Stoykovich, M. P.; Ferrier, N. J.; Pablo, J. J.; Nearley, P. F. Nature (London) 2003, 424, 411. (6) De Rosa, C.; Park, C.; Thomas, E. L.; Lotz, B. Nature (London) 2000, 405, 433. (7) Cheng, J. Y.; Ross, C. A.; Thomas, E. L.; Smith, H. I.; Vancso, G. J. Appl. Phys. Lett. 2002, 81, 3657. (8) Amphiphilic Block Copolymers, edited by Alexandritis, P., Lindman, B., Eds.; Elsevier Science: Amsterdam, 2000; p 1. (9) Wolff, M.; Magerl, A.; Zabel, H. Thin Solid Films 2007, 515, 5724. (10) Fo¨rster, S.; Timmann, A.; Schellbach, C.; Fo¨rmsdorf, A.; Kornowski, A.; Weller, H.; Roth, S. V.; Lindner, P. Nat. Mater. 2007, 6, 888.
structure in the near surface region are grazing incidence smallangle neutron scattering (GISANS) and neutron reflectometry (NR).11,12 In this letter, we extract the crystalline structure and correlation length in a soft crystal with weak binding energy between micelles and close to a solid substrate. After entering the crystalline phase at low temperature with correlations in the micrometer range but with random orientation, first a reduction of the correlation length is observed upon heating before the crystallites align with respect to each other. The latter effect is known in the literature as Oswald ripening.13 The sample is a 18.5% (in weight) solution of Pluronic F127 ((ethylene oxide)99-(propylene oxide)65-(ethylene oxide)99) in deuterated water. The bulk properties of this material have been reported in literature in great detail.14,15 The polymer was purchased from Sigma-Aldrich and used without further purification. The molecules were solvated in deuterated water (for better contrast) at a low temperature of 6 °C under constant stirring until a homogeneous solution was formed. The sample cell was then filled with the sample in its liquid state (T ) 5 °C). The solid wall was an SiO2-terminated silicon wafer cleaned with Caro’s acid and showed a contact angle of water of around 50°. The GISANS experiments were performed with the D22 smallangle scattering machine at the Insitute Laue-Langevin (Grenoble, France) using a neutron wavelength of 0.6 nm ( 10%. The collimation distance was 11.2 m, and the incident beam angle of 0.27° was slightly above the critical angle of total external reflection of 0.25°. For the given setup, neutrons penetrate 20 µm into the liquid. The heating rate was 25 °C/h. The ADAM reflectometer at the Insitute Laue-Langevin (Grenoble, France)16 with a neutron wavelength of 0.441 nm ( 0.6% was employed for the NR measurement. Rocking scans on the first-order specular reflection were recorded with an incident beam divergence of 0.055°. The heating rate was 7 °C/h. On both instruments, data were continuously collected during a heating and cooling cycle in the range of 5-60 °C. The temperature was controlled by water circulating from a water bath. The scattering geometry is described in detail in ref 12, and (11) Wolff, M.; Scholz, U.; Hock, R.; Magerl, A.; Leiner, V.; Zabel, H. Phys. ReV. Lett. 2004, 92, 255501. (12) Wolff, M.; Magerl, A.; Zabel, H. Euro. Phys. J. E 2005, 16, 141. (13) Ostwald, W. Lehrbruch der Allgemeinen Chemie; Engelmann: Leipzig, Germany, 1896; Vol. 2, part 1. (14) Mortensen, K. Polym. AdV. Technol. 2001, 12, 2. (15) Mortensen, K.; Batsberg, W.; Hvidt, S. Macromolecules 2008, 41, 1720. (16) Wolff, M.; Zhernenkov, K.; Zabel, H. Thin Solid Films 2007, 515, 5712.
10.1021/la803015t CCC: $40.75 2009 American Chemical Society Published on Web 11/25/2008
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a similar type of sample cell was used in ref 17. Neutrons collimated to a rectangular cross section of 5 × 2 mm2 enter a single-crystalline silicon block of size 50 × 50 × 10 mm3 on the narrow side (50 × 10 mm2) and are partially reflected at the bottom of the liquid sample. The scattering (reflected) intensity is then registered via a position-sensitive detector. Figure 1 shows a typical result for a reflectivity (main panel) and GISANS (bottom right) measurement with the sample in the crystalline phase. In both cases, the intensity is plotted over Qin-plane, defined in the plane of the interface, and Qout-of-plane, defined along the normal to the interface. Q denotes the momentum transfer of the neutrons. The white and black colors symbolize high and low intensity, respectively. The specular reflectivity is found along the vertical dashed gray line. The area of total external reflection, indicated by high intensity, is visible close to Qin-plane ) 0 and Qout-of-plane < 0.15 nm-1. The pronounced reflection visible at Qout-of-plane ≈ 0.4 nm-1 is the first-order Bragg reflection on the specular line corresponding to the (111) reflection assuming an fcc structure (cubic close packing).11 Note that Qinplane probes different length scales for the reflectivity and GISANS data. The neutron coherence length parallel to the projection of the incident beam on the interface can be up to 100 µm whereas it is only on the order of 10-100 nm along the perpendicular direction. The use of Qin-plane in both cases is justified if a 2D random orientation of the crystallites in the plane of the interface is assumed.11 For a single-crystalline arrangement, in general none but at maximum one, either the primed or the unprimed reflection could be visible. The reflection without the prime marks a possible Bragg reflection for a single-crystalline arrangement whereas the primed one marks the intersection of the 2D powder ring with the Ewald sphere visible for only a 2D powder. Figure 2 shows rocking curves of the first-order specular (111) reflection taken in-plane and plotted for different temperatures. The intensity is normalized to the incident beam intensity. The micelles of this sample are already known to form a cubic dense packing area close to a solid interface with a lattice constant of 29.5 nm in the temperature range investigated.11 Clearly, two components have to be separated. This is expected for scattering treated in the Born approximation with a cutoff length.18 In this case, the in-plane pair correlation function may be separated into two parts:
C(R) ) 〈F(O) F(R) 〉 -〈F(O)〉2 where R symbolizes the in-plane distance, C is the height-height correlation function, and F is the scattering length density. Accordingly, the in-plane scattering function separates into two parts:
Figure 1. Reflectivity and GISANS scattering pattern taken for the F127 sample in the fcc phase.
layering (mean scattering potential) of the micelles along the normal of the interface. This fact is also supported by the resolution-limited width of the Bragg peak in the reflectivity measurement (out-of-plane direction). The circles in Figure 3 (left panel) depict the correlation length as extracted from the broad component in the rocking curve plotted versus temperature. Two regimes can be separated. Between 20 and 35 °C an exponential decay (black line) is found. At higher temperatures (35-55 °C), the correlation length is constant at 1.63 ( 0.02 µm or about 55 unit cells. The squares in Figure 3 (left panel) represent the intensity scattered diffusely into the (111) reflection. After an initial increase, the reflection becomes weaker. The maximum matches well the point when the correlation length reaches the minimum constant value. The squares in Figure 3 (right panel) represent the difference in intensity (I) extracted from the GISANS pattern of the primed and the unprimed reflections divided by the sum I(-111) + I(002) - I(-111)′ - I(002)′/I(-111) + I(-111)′ + I(002) + I(002)′. For a single-crystalline arrangement in the maximum, one of the two reflections could be visible, but never both at the same time. Moreover, the two reflections appear on a circle and are separated by 180° in reciprocal space with respect to the (111) direction. Accordingly, for a textured fcc crystal the intensity of the primed reflection is minimal when the unprimed one shows its maximum intensity. The relative difference between the two intensities offers a quantitative measure of the texture in the sample in the plane of the interface. Note that the information extracted in this way is complementary to the correlation length extracted from the width of the (111) reflection along the inplane direction. Initially, for temperatures around 20 °C all reflections have the same intensity. At around 35 °C, texture develops. This is exactly the point where the correlation length changes from exponentially decaying to a constant value. This point also coincides with the maximum of the diffuse scattering intensity.
From this expression, it is seen that the narrow component (specular reflection) is related to scattering from the mean potential, averaged along the in-plane direction and over the coherence volume of the neutron beam, along the interface normal. The broad one (diffuse scattering) reflects the structural correlations resulting from fluctuations parallel to the interface, which are on a length scale in the micrometer range.18 For the narrow component, a constant intensity and resolution-limited line width are extracted for all temperatures. This is related to an unchanged (17) van der Grinten, D.; Wolff, M.; Zabel, H.; Magerl, A. Meas. Sci. Technol. 2008, 19, 034016. (18) Sinha, S. K.; Sirota, E. B.; Garoff, S.; Stanley, H. B. Phys. ReV. B 1988, 38, 2297.
Figure 2. Rocking curve taken along the in-plane direction at the (111) reflection for different temperatures with the sample in the fcc phase.
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Figure 3. (Left) Circles and squares represent the correlation length and the intensity as obtained for a Gaussian fit to rocking curves not including the narrow line, respectively. (Right) Squares depict the change in texture.
Figure 4. Time dependence of the rocking curve of the (111) reflection for different temperatures.
Figure 5. Model for the crystallization of micelles at the solid-liquid interface. The circles symbolize crystallites. The dark regions show good correlation, and the brighter ones, bad correlation.
Figure 4 depicts rocking curves that exemplify two temperatures taken immediately after the temperature was reached and 4 h later. The intensity is normalized to the peak maximum and does not change with time. This proves that the results presented above do not depend on the heat rate. A rocking curve from an intermediate temperature is presented to show the development of the shape as a function of temperature. Figure 5 is a model illustration of how the crystallization in the investigated type of soft crystal proceeds. Dark and bright colors represent strong and weaker correlations, respectively. First, crystallites are formed at different positions in the sample, and then the crystallinity changes in a two-step process. First (at 20-35 °C), the orientation of the crystallites remains random while they grow to sizes larger than 5 µm. With further increasing temperature, more and more micelles agglomerate, the micelle
core becomes more compact, and the agglomeration number increases.19,20 Increasing potential fluctuations along the interface result in increased diffuse intensity. However, the changing micellar shape introduces strain, enforcing a rearrangement of micelles and reducing the correlation length parallel to the interface. Second (at 35-55 °C), the crystallites interpenetrate and start to rearrange their orientation. In addition, large crystallites take up the smaller ones. This process is known as Oswald ripening and results in the formation of a highly textured crystalline structure. The decreasing intensity in the diffuse component reveals that at the same time the fluctuations parallel to the interface are reduced. This happens at constant correlation length and could be related to anisotropic correlations resulting from Oswald ripening. No change in the mean potential (layering) is found over the whole temperature range, indicating a welllayered structure. Because we find a qualitatively similar behavior for decreasing temperatures, we assign the results as fundamental for the growth of soft crystals and not as an effect of increasing temperature resulting in larger fluctuations. In summary, we have extracted a complete picture of near surface crystallization in a soft crystal by use of GISANS and NR. Micelles initially crystallize with a long correlation length, but random orientation of the crystallites before a reduction of the correlation length and reorientation is found. We expect research following along the presented line to contribute to a deeper understanding of crystallization. Additionally, our work will have an impact on optimization in templating nanostructures. Acknowledgment. We thank Nicole Voss for fruitful discussion and gratefully acknowledge financial support from the BMBF (03ZA7BOC) and DFG grants MA801/12-1 and ZA161/18-1 within priority program (SPP) 1164. LA803015T (19) Goldmints, I.; Yu, G.; Booth, C.; Smith, K. A.; Hatton, T. A. Langmuir 1999, 15, 1651. (20) Pedersen, J. S.; Gerstenberg, M. C. Colloids Surf., A 2003, 213, 175.
