In Situ and Ex Situ SAXS Investigation of Colloidal Sedimentation onto

Corresponding author: E-mail: [email protected]; phone: +41 56 310 5988; ... sedimentation from a colloidal suspension onto a prepatterned support us...
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In Situ and Ex Situ SAXS Investigation of Colloidal Sedimentation onto Laterally Patterned Support Beate Reinhold,† Thomas Geue,*,‡ Patrick Huber,‡ Tushar Sant,§ Ullrich Pietsch,§ and Michael Sztucki| Institute of Physics, UniVersity of Potsdam, 14415 Potsdam, Germany, Laboratory for Neutron Scattering, ETHZ & PSI, 5232 Villigen PSI, Switzerland, Solid State Physics, UniVersity of Siegen, 57068 Siegen, Germany, and High Brilliance Beamline ID2, European Synchrotron Radiation Facility, BP 220, 38043 Grenoble Cedex, France ReceiVed September 19, 2008. ReVised Manuscript ReceiVed NoVember 13, 2008 We report on in situ investigations of colloidal ordering during gravity sedimentation from a colloidal suspension onto a prepatterned support using a polymeric surface relief grating (SRG) as the support. The ordering of colloids with a diameter of 420 nm was investigated by means of grazing-incidence small-angle X-ray scattering (GISAXS) and transmission SAXS using a preparation cell guaranteeing stable temperature and humidity. GISAXS was used for in situ monitoring of the time evolution of colloidal ordering within the whole illuminated sample area. The onset of ordering was indicated by the increase of integrated intensity within a small time frame shortly before complete evaporation of the dispersant. Single domains of coated samples were investigated ex situ by SAXS in transmission geometry where the irradiated sample area was 200 × 200 µm2 only. Domains with the typical size of a few millimeters were observed varying in orientation and crystallographic structure for various positions at the sample. They were mainly oriented along the grooves of the grating, confirming the influence of the underlying grating on colloidal ordering.

1. Introduction Ordered colloidal structures are interesting materials for many optical applications, such as photonic crystals or optical band gap materials.1,2 A lot of techniques have been developed for the preparation of these materials.1,3-5 The technical exploitation of the physical effects mainly depends on the structural perfection of fabricated colloidal structures. Unfortunately, the formation energy of face-centered cubic and primitive cubic packed structures is quite similar6 which makes it very difficult to produce large single crystals of colloids. In order to improve the degree of ordering and, in particular, to force the colloids to form domains with single orientation, one can use prepatterned substrates during preparation.3 Although highly ordered colloidal crystals have been prepared by several groups,7,8 there is still a need to improve existing techniques to get defect-free, largely expanded colloidal crystals with low instrumental effort and in short time. A better understanding of the deposition can be achieved by in situ investigations of the process. Common methods are optical9,10 and confocal11 microscopy. The first method may suffer from the limited lateral resolution; the second one is * Corresponding author: E-mail: [email protected]; phone: +41 56 310 5988; fax: +41 56 310 2939. † University of Potsdam. ‡ ETHZ & PSI. § University of Siegen. | European Synchrotron Radiation Facility.

(1) Lopez, C. AdV. Mater. 2003, 15, 1679. (2) Kobayashi, N.; Egami, C. Opt. Lett. 2005, 30, 299. (3) Dziomkina, N. V.; Vansco, G. J. Soft Matter 2005, 1, 265. (4) Xia, Y.; Gates, B.; Yin, Y.; Lu, Y. AdV. Mater. 2000, 12, 693. (5) Wang, D.; Mo¨hwald, H. J. Mater. Chem. 2004, 14, 459. (6) Koch, H.; Radin, C.; Sadun, L. Phys. ReV. E 2005, 72, 016708. (7) van Blaaderen, A.; Ruel, R.; Wiltzius, P. Nature 1997, 385, 321. (8) Park, S. H.; Dong, Q.; Xia, Y. AdV. Mater. 1998, 10, 1028. (9) Dushkin, C. D.; Lazarov, G. S.; Kotsev, S. N.; Yoshimura, H.; Nagayama, K. Colloid Polym. Sci. 1999, 277, 914. (10) Yin, Y.; Lu, Y.; Gates, B.; Xia, Y. J. Am. Chem. Soc. 2001, 123, 8718. (11) Hoogenboom, J. P.; Vergeer, P.; van Blaaderen, A. J. Chem. Phys. 2003, 119, 3371.

restricted to fluorescence-labeled particles. X-ray scattering is a method for three-dimensional structure analysis of materials in the size-range of a few nanometers up to several microns. It has already been used for ex situ investigations of colloidal crystals by small-angle X-ray scattering (SAXS) in transmission geometry.12-14 In this paper, we present the results of in situ investigations of the deposition process of colloidal layers on prepatterned substrates.

2. Materials and Methods We used a monodisperse polystyrene latex with a sphere diameter of 420 nm delivered from Microparticles, Berlin. In the experiment itself, the colloidal deposition during the evaporation of dispersant was examined continuously. For this purpose, a droplet of colloidal dispersion was put onto the patterned substrate by a pipet. For the sake of homogeneity, the concentration of the colloids was chosen to be very small (about 0.01-0.04%). In order to follow the process in temperature and humidity, the sedimentation was performed in a spatially limited, closed volume of 104 cm3. Because of the small cell volume, the deposition process takes place close to the thermodynamic equilibrium between solid phase and colloidal droplet.15 Using the Stokes equation

2(Fp - Fl)gr2 V) 9η

(1)

where Fp ) 1.05 g/cm3 and Fl ) 1.0 g/cm3 are the densities of the particles and the dispersant water, respectively, r ) 210 nm is the particle radius, η ) 1005 × 10-6 Pa · s is the dynamical viscosity of water, g is the gravity constant, and the sedimentation velocity of spherical particles is estimated to be on the order of V ) 20 µm/h. (12) Megens, M.; van Kats, C. M.; Bo¨secke, P.; Vos, W. L. J. Appl. Crystallogr. 1997, 30, 637. (13) Zhang, J.; Alsayed, A.; Lin, K. H.; Sanyal, S.; Zhang, F.; Pao, W.-J.; Balagurusamy, V. S. K.; Heiney, P. A.; Yodh, A. G. Appl. Phys. Lett. 2002, 81, 3176. (14) Narayanan, S.; Wang, J.; Lin, X.-M. Phys. ReV. Lett. 2004, 93, 135503. (15) Micheletto, R.; Fukuda, H.; Ohtsu, M. Langmuir 1995, 11, 3333.

10.1021/la803078b CCC: $40.75  2009 American Chemical Society Published on Web 12/29/2008

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Therefore, several hours of stable experimental conditions are needed to follow the deposition process. The sample cell contains a metallic plate with a Peltier element of size 4 × 4 cm2. The temperature can be varied between -20 to + 60 °C with an accuracy of 0.1 K. The temperature is controlled by a temperature sensor close to the sample and another sensor displays the humidity of the closed cell with an accuracy of 5%. For incidence and exit of the probing X-ray beam, the left and right wall of the perspex made sample cell were replaced by two Kapton foils. Surface relief gratings (SRGs) were used as prestructured substrates. They were produced with a polymer containing side chains with an azobenzene group. Amorphous azobenzene side chain polymers have been found to be interesting materials upon which one can directly generate an SRG without any other pre- or postprocessing steps. The azo-group changes its conformation upon irradiation with visible light with a wavelength close to 500 nm. Under holographic exposure conditions, repeated trans-cis and cis-trans switching is induced, and cooperative processes result in an SRG with sinusoidal shape.16,17 The light induces material flow even at temperatures far below the glass transition temperature, TG, of the polymers, and a periodic surface relief with approximately sinusoidal shape appears. T - TG may approach 100 K and more. Depending on the incident light power and time of illumination, the period of the grating and its height can be varied between 600-1000 nm and 20-250 nm, respectively.18,19 A number of mechanisms have been proposed to explain the massive material displacement, but they do not cover all aspects of the dynamics in the polymer SRG. During the formation of SRG, a change in polymer elastic properties due to light exposure can explain the massive material transport in viscoelastic flow regime. The interference pattern produced by two counter-rotating circularly polarized waves on the sample is most effective as the light intensity is almost uniform. The SRG formation is sometimes accompanied by a periodic density pattern (density grating, DG) beneath the SRG in the volume of the polymer film. Both film thickness and total absorbed energy play an important role in the simultaneous formation of a DG. From calculations carried out in a framework of linear elasticity theory using the “finite element” method, we know that this initial DG is created close to the film surface and can extend down to the substrate.20 We performed X-ray measurements at the undulator beamline ID02 of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The setup was used with an energy of 12.4 keV corresponding to a wavelength of λ ≈ 0.1 nm. The beam size was 200 × 200 µm2. The sample cell was installed on a two-circle goniometer. The distance between the sample and the FReLoN charge-coupled device (CCD) camera was 10 m. In situ measurements of the sedimentation process of the colloids were done in noncoplanar reflection geometry (grazing-incidence SAXS, GISAXS) illustrated in Figure 1. The GISAXS technique uses the phenomenon of total external reflection. A variation of the angle of incidence Ri around the critical angle of total external reflection, Rc ) 1.6 mrad, results in different penetration depths into the material varying from about 10 nm (Ri < Rc) to several 100 nm (Ri > Rc). X-ray scattering data are evaluated in reciprocal space coordinates applying eq 2:

2π (cos Rf · sin φ) λ 2π qz ) ((sin2 Rf - sin2 Rc)1 ⁄ 2 + (sin2 Ri - sin2 Rc)1 ⁄ 2) λ qy )

(2)

with Ri being the incidence, Rf being the exit angle with respect to the sample surface (x-y plane), and φ being the exit angle with respect to the x-z plane (see Figure 1).

Figure 1. (a) Schematic diagram of the scattering geometry used for the in situ GISAXS measurements with incident X-ray beam ki, scattered beam kf, incidence angle Ri, and exit angle Rf with respect to the surface (x-y plane) and φ the exit angle with respect to the x-z plane. (b) AFM image of a coated SRG showing colloids aligned along the grating grooves.

Figure 2. Scattering image of an SRG without colloids. The period of SRG amounts to 660 nm. 420 nm polystyrene particles were sedimented; this gives a ratio diameter of colloid versus SRG period of 0.64.

The ex situ measurements were performed on dried samples covered with colloids in transmission geometry (SAXS). Here refraction effects can be neglected. Applying the Bragg equation (eq 3) both components of Q-space are

Qx )

Rf 4π 4π φ sin Qy ) sin λ 2 λ 2

(3)

we use Q for the SAXS momentum transfer to distinguish from the q generated from reflectivity/GISAXS measurements.

3. Results and Discussion (16) Rochon, P.; Batalla, E.; Natansohn, A. Appl. Phys. Lett. 1995, 66, 136. (17) Yi, D. K.; Kim, M. J.; Kim, D.-Y. Langmuir 2002, 18, 2019. (18) Allard, M.; Sargent, E. H.; Lewis, P. C.; Kumacheva, E. AdV. Mater. 2004, 16, 1360.

3.1. GISAXS Measurements. As a reference we measured a bare SRG without colloids first. It was positioned on the goniometer, with Ri smaller than Rc in order to be sensitive to

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Figure 3. Scattering images (a) at the start of an experiment, (b) after 334 min, (c) after 339 min, and (d) after 344 min. The SRG shown in Figure 2 was used. A 0.02% colloidal PS suspension in water was applied; the droplet volume was 0.3 mL, Ri 0.08°. The sample-to-detector distance was 10 m. CCD frames with a time resolution of 2 min were recorded.

the sample surface. The rotation angle ω (sample rotation about the surface) was chosen that the effective grating period D ) Do/cos ω provides grating peaks at qy ) 2π/D close to the specular peak (qy ) 0). Figure 2 shows a CCD camera frame of an SRG with a period Do ) 660 nm at an incident angle of Ri ) 0.08°. The vertical stripe in the middle of the image is caused by the metallic beam stop shielding the intense primary and specular reflected beam. The grating peaks appear along qy at left and right side parallel to the qz axis. From their distance ∆qy, the grating period Do can be calculated:

∆qy ) 2π cos ω ⁄ Do

(4)

The measured period of Do ) 656.1 nm is in good agreement with the period of 664 nm determined by atomic force microscopy (AFM) measurements. Next a droplet of colloidal dispersion was put onto the surface of the already aligned and cleaned SRG, and a CCD image was taken marking the starting point of each in situ experiment. The process of drying was then inspected by subsequent CCD images taken in regular intervals of a few minutes. The experiment was finished when the droplet was dried up completely, i.e., if no more change in the scattering image could be observed. The in situ experiments usually took around 350 min. Figure 3 shows four selected CCD images that are characteristic for the course of the experiment and the observed process of drying. In the first frames (see Figure 3a), the scattering intensity is very low, and the grating peaks are almost vanished. The X-ray beam is mainly scattered by the liquid dispersant, which produces nearly isotropic scattering into all directions of space. Moreover, the condition of total external reflection is not fulfilled as a result of droplet curvature. Even after 336 min, there is almost no change of the scattering intensity (see Figure 3b), although a large amount of water has evaporated. At this time, the droplet is very flat and hence the concentration of the colloids in water has become much enhanced. In the next CCD frame taken after 338 min (see Figure 3c), the intensity has clearly increased, and it continues to increase until the frame shown in Figure 3d after 344 min. CCD frames taken thereafter do not show changes anymore. The grating peaks are visible again as the droplet is completely dried up. No additional coherent scattering peaks appeared, indicating the colloidal ordering in a direct way. Nevertheless, the averaged scattering from differently oriented colloidal domains produces strong diffuse scattering, which is superimposed to the scattering from the SRG.

In order to detect the onset of colloidal ordering, we reduced the standby time between two CCD frames dramatically from 10 min, as used for Figure 3, to 3 s. The respective course of the integral intensity (sum over the intensities of one CCD frame) is shown in Figure 4. One can clearly see that the intensity increases within a small time interval ∆t from nearly zero to a plateau level. This increase in intensity is attributed to the ordering of the colloids and not to the change in concentration of the colloidal dispersion. Although there is a large increase in concentration as the last water evaporates, the number of colloids in the last remaining film of water contributing to the scattering does not change much. The Bragg intensity is low, because the particles are randomly distributed in the water film. It changes in the moment of drying where the random distribution changes into an ordered one driven by the underlying regular support. Since the X-ray intensity measures the number of regularly ordered colloids, the jump in intensity in Figure 4 shows the process of ordering but not a significant change in concentration. The experiment was repeated for different temperatures (21-35 °C) and droplet volumes (0.04-0.30 mL). In all cases, the achieved variation in ∆t is on the order of 2-6 min. Qualitatively, the time constant is larger for lower temperatures and for bigger volumes, as expected. In order to determine the crystallographic order of the colloids, we extracted line scans along the qy-direction in the CCD images. For this purpose, we integrated the intensity in a small box of 10 pixels along the qz-direction to enhance the signal-to-noise ratio. Figure 5 shows several such line scans for qy > 0.0015 Å-1 taken at different times during the experiment. At lower qy values, the intensity is attenuated by the beam stop. The scattering intensity is very low at the beginning (0 min, open squares) and 336 min later (solid stars) and starts to increase after 338 min (solid triangles) until it stays constant after 344 min (open stars). Apart from the increase in intensity, undulations emerge corresponding to a periodicity of 430 nm. These peaks are definitely different from those originating from the uncovered grating (see solid squares; D ) 640 nm). The peak height and the number of scattering orders increase with time, indicating the growth of colloidal domains. 3.2. Transmission SAXS Measurements. Because of the large illuminated sample area, single domains could not be resolved in GISAXS. Therefore, ex situ measurements of the samples were performed using SAXS to get information on the degree of colloidal ordering. In transmission geometry, the beam size was 200 × 200 µm2.

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Figure 4. Development of the integral intensity recorded with a frame rate of 0.33/s. The total integral intensity over the full CCD frame was used for evaluation.

good accordance with the results obtained from dynamic light scattering (R ) 210 ( 10 nm, not shown). Colloidal ordering on the SRG is indicated by peaks appearing in addition to the rings caused by the form factor. Figure 7a shows that situation for a SRG with a period of 680 nm coated with colloids of 420 nm diameter. The peaks are always located on top of the intensity maximum of the rings and can be connected by parallel lines in the horizontal direction (indicated by four white arrows). From the symmetry of the peak arrangement, one can derive the arrangement of the colloids. The scattered intensity is described by the colloidal form factor multiplied by a structure factor. From AFM measurements (Figure 1b) and from the ratio of grating period to the diameter of the colloids (smaller than 1), one can deduce that the colloids are mainly arranged along the valleys of the SRG. The structure factor is then described by a sinc-function.22 The resulting scattering intensity shows the proportionality

I∝

|

(

p 2

)

| | ( )| | sin NgQx

3(sin(QR) - QR cos(QR)) · p (QR)3 sin Qx 2 2

2

·

sin(NrQyR) sin(QyR)

Figure 5. Line scans parallel to the sample surface for different times of an experiment that shows the development of a colloidal ordering. The beam stop protecting the CCD camera prevented the evaluation of data below qy ) 0.0015.

The scattering intensity of randomly distributed particles with well-defined geometric shape can be expressed by the square of their form factor. For spherically shaped colloids, the radial symmetric term of the form factor21 results in the intensity distribution I(Q):

I(Q) ) F2V2

9(sin(QR) - QR cos(QR))2 (QR)6

(5)

SAXS patterns were taken for samples that were coated without control of the evaporation parameters, i.e., without using a sample cell, and therefore underwent a rapid evaporation. Similar scattering patterns also resulted from colloidal arrangements without a topologically structured support. Figure 6b shows a scattering image of colloids with a diameter of 420 nm on a SRG with a period of 950 nm taken in transmission geometry. The scattering image shows concentric rings measuring the form factor of the colloids. The azimuthally integrated scattering intensity presented in Figure 6a is adequately described by a sphere form factor (see eq 5) taking into account a particle polydispersity according to a Schulz size distribution. The determined particle radius R ) 205 ( 5 nm with a polydispersity of about 3% is in (19) Ye, Y.-H.; Badilescu, S.; Truong, V.-V.; Rochon, P.; Natansohn, A. Appl. Phys. Lett. 2001, 79, 872. (20) Geue, T. M.; Saphiannikova, M. G.; Henneberg, O.; Pietsch, U.; Rochon, P. L.; Natansohn, A. L. J. Appl. Phys. 2003, 93, 3161. (21) Roe, R.-J. Methods of X-ray and Neutron Scattering in Polymer Science; Oxford University Press: New York, 2000.

|

2

(6)

where the first factor is the form factor of a spherical object (see eq 5). The two other factors form the structure factor of the system described by two sinc-functions: one in direction Qx and one in direction Qy. p is the grating period, R is the particle radius, and Nr × Ng describes the domain size. In detail, Nr is the correlation length in the direction of the colloidal chain, and Ng is the correlation length perpendicular to the grating valleys: Q ) (Qx2 + Qy2)1/2. A scattering image comparable with the one measured (see Figure 7a,b) can be generated for Ng ) 1 and Nr ) 4. Because a chain of colloids in one groove of the grating does not touch the chains in the neighboring grooves and the arrangement of colloids in one groove fluctuates in the direction perpendicular to the groove, there is no correlation between neighbored chains, and Ng is 1. The chain length, i.e., the number of colloids in a single chain is small. As shown by AFM, numerous chains are short and consist of less than 10 colloids. The mean value obtained from the statistical analysis of an AFM image yields 3.4. Thus, the obtained X-ray correlation length of Nr ) 4 is realistic. The colloidal arrangement along the grooves of an SRG was determined for several samples by SAXS measurements and AFM measurements. Ordering occurs as long as the ratio between the grating period and the colloidal diameter is smaller than unity. The observed domain size correlates with the size of the grating area. At a few points of the sample, peaks were found corresponding to a hexagonal ordering. This again denotes that the colloidal ordering is not homogeneous. Figure 8a shows a scattering image of colloids on a grating with a period of 680 nm. The ring structure originates from the form factor of colloids. A series of peaks appears along vertical lines (indicated by three white arrows) corresponding to the situation shown in Figure 7a, but rotated by 90°. An additional pattern of peaks can be seen indicating a hexagonal order (depicted by guide lines). The angle between the guide lines deviates from the ideal value of 60°. A bigger angle of 82° and two smaller angles of 49° were determined (22) Warren, B. E. X-ray Diffraction; Dover Publications: New York, 1990. (23) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Nature 1993, 361, 26.

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Figure 6. (a) Radially averaged scattering data and appropriate fit function to determine the particle radius of the colloids. (b) Scattering image of a coated SRG in transmission geometry. The ring structure can be attributed to the form factor of spherical particles.

Figure 7. (a) Scattering image of a coated SRG (period 680 nm, 420 nm PS colloids) in transmission geometry with intensity rings originating from the form factor and peaks indicating colloidal ordering. (b) Calculation of the expected intensity distribution according to eq 6 with the coherence length Ng ) 1 along Qx (corresponding to the direction perpendicular to the grooves) and Nr ) 4 along Qy (corresponding to the direction along the grooves). (c) Illustrates the case where the two correlation lengths along Qx and Qy are identical.

Figure 8. Scattering images of a coated SRG (period 680 nm, 420 nm PS colloids) in transmission geometry with both form factor rings and hexagonally arranged peaks (marked by dotted and dashed lines, respectively) indicating hexagonal colloidal ordering.

corresponding to a deformed hexagonal unit cell. Some more peaks in the scattering image that could not be clearly associated, propose the existence of different domains. A relatively high concentration of colloidal dispersion of 0.05% was chosen for this sample, suggesting the formation of colloidal bilayers. One can assume that the bottom layer shows a colloidal ordering along the grating grooves that changes to a hexagonal ordering in the layers above. The peaks that represent the hexagonal order are poorly developed. This may be caused by a small domain size. However, it can not be deduced clearly whether different domains are lying side by side in one layer or one upon the other

in different layers as exact measurement of thickness of colloidal layer has not been done during the described experiment. It would need exact azimutal alignment of the grating parallel to the incoming beam in a precision on the order of 0.05°. This was not done during the described experiment. Figure 8b shows another sample with hexagonal domains. Here, a grating with a period of 670 nm was coated with colloids. In this case, the form factor of the colloids and peaks of a hexagonal ordering are superposed. Peaks that indicate a colloidal ordering along the grooves are poorly developed. Two hexagonal

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domains could be clearly identified. They are rotated by 24° to each other.

4. Conclusions and Outlook The in situ measurements in GISAXS geometry show that the process of colloidal ordering takes place in a small time interval of a few minutes before the complete drying of the droplet. This is in agreement with Denkov et al.23 Using optical microscopy he found out that two-dimensional crystallization starts when the thickness of the water layer approaches the particle radius. The time interval ∆t in which the ordering appears depends on the temperature, humidity, and the volume of the droplet. In our studies, we found only small variations in ∆t due to the relatively small variation of parameters. However, our experiment demonstrates the capability of GISAXS measurements for time-resolved investigations of the evaporation process. In contrast to previous GISAXS studies at small metallic colloids,14 the colloids in our studies are large in size and of low scattering power. This results in an increased sensitivity on small fluctuations in size of colloids and position on the sinusoidal SRG and explains why no coherent peaks are visible in GISAXS geometry. The colloids are aligned along the grooves, but their position fluctuates in the direction perpendicular to it. Small fluctuations in the position of individual colloids change the scattering phase by large fractions of 2π and destroy the coherent scattering signal due to the large size of colloids and the large sample area illuminated. Therefore, our GISAXS experiment provides an integrated signal only, which is proportional to the total number of ordered particles. As long as the spheres are randomly distributed, the scattering signal remains low. When ordered domains start to grow, a significant increase in the scattering signal is observed. Although the scattering of individual particles is extremely low, the intensity for the whole assembly is remarkably high and allows measurement with a time resolution as small as technically possible with the used CCD camera. Transmission SAXS measurements have proven the influence of the grating on the colloidal ordering. Domains of sufficient crystallographic order of the colloids were detected at several points on the sample. The beam size in SAXS geometry was 200 × 200 µm2, which is enough to separate even very small individual colloidal domains, which is partially hard to achieve with optical microscopy only. A lateral scanning of the sample with the X-ray beam reveals an average size of the colloidal domains on the order of up to 1 mm2. Thus, SAXS measurements in transmission geometry are a suitable method to characterize coated samples relating to a crystallographic order, even for smaller domain sizes. Both, SAXS and GISAXS can be combined into one experiment. Because of the chosen X-ray energy, one can find

Figure 9. Scattering image of a coated SRG in GISAXS geometry (period 660 nm, 420 nm PS colloids, Ri ) 0.3°) showing grating peaks in reflection (upper part) and form factor rings in transmission (lower part).

experimental conditions where some part of the incident beam goes through the edge of the sample and can be measured in a forward direction creating a SAXS pattern. At same time, the other part of the beam is reflected at the sample surface providing a GISAXS pattern. This situation is shown in Figure 9. The transmitted part of the beam provides the form factor of the colloids whereas the GISAXS pattern shows the grating pattern and its change due to covering by colloids. In further experiments, one has to exclude a possible superposition of the ordering peaks of the colloids with the grating peaks of the SRG. This can be achieved by use of SRG with a much smaller grating period compared to the size of colloids. An alternative approach is the use of a flat substrate where selective deposition of the colloidal particles is achieved by microprinting, for instance, subdividing the substrate into areas of positive and negative charge density.24 Although the colloids used for this experiment are in a size range accessible for optical microscopy also, our method is more general and can be applied to a wider variety of diameters of colloidal spheres. Acknowledgment. The authors thank the ESRF for allocation of beam time and the crew from beamline ID2 for their support, K. Morawetz for inscribing the surface relief gratings, A. Pucher for technical support, B. Stiller for AFM measurements, and J. Grenzer for helpful discussions. LA803078B (24) Aizenberg, J.; Braun, P. V.; Wiltzius, P. Phys. ReV. Lett. 2000, 84, 2997.