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APPLIED
CRYSTALLOGRAPHY
ISSN: 1600-5767

Structural changes in gradient colloidal thin gold films deposited from aqueous solution

aHASYLAB at DESY, Notkestr. 85, D-22607 Hamburg, Germany, and bPhysik-Department LS E13, Technische Universität München, James-Franck-Str. 1, D-85748 Garching, Germany
*Correspondence e-mail: stephan.roth@desy.de

(Received 16 August 2006; accepted 15 February 2007; online 1 April 2007)

Pattern formation is investigated in a one-dimensional gradient prepared from an aqueous colloidal gold nanoparticle solution. The hydrodynamic process can be reconstructed by determining the prominent length scales and surface roughness in the dried gradient. The structural information is obtained using a combination of grazing-incidence small-angle X-ray scattering, which is a method of high-statistical relevance, and a moderate microfocused beam. This allows for scanning the gradient and to locally reveal the structure of the thin film. Our results, based on a simplified hydrodynamic model, indicate a system oscillating between depleted regions, nanoparticle domains and complete nanoparticle layers.

1. Introduction

Nano-structured noble metal thin films are of great scientific and technological importance (Bauer et al., 2003[Bauer, G., Hassmann, J., Walter, H., Haglmüller, J., Mayer, C. & Schalkhammer, T. (2003). Nanotechnology, 14, 1289-1311.]; de Heer et al.1987[Heer, W. A. de, Selby, K., Kresin, V., Masui, J., Vollmer, M., Chatelain, A. & Knight, W. D. (1987). Phys. Rev. Lett. 59, 1805-1808.]; Ditlbacher et al., 2000[Ditlbacher, H., Krenn, J. R., Lamprecht, B., Leitner, A. & Aussenegg, F. R. (2000). Opt. Lett. 25, 563-565.]; Schmid & Chi, 1998[Schmid, G. & Chi, L. F. (1998). Adv. Mater. 10, 515-526.]; Jin et al., 2001[Jin, R., Cao, Y., Mirkin, C. A., Kelly, K. L., Schatz, G. C. & Zheng, J. G. (2001). Science, 294, 1901-1903.]; Maier et al., 2001[Maier, S. A., Brongersma, M. L., Kik, P. G., Meltzer, S., Requicha, A. A. G. & Atwater, H. A. (2001). Adv. Mater. 13, 1501-1505.]). They play a major role in biotechnology, e.g. DNA scanning (Vo-Dinh et al., 1999[Vo-Dinh, T., Stokes, D. L., Griffin, G. D., Volkan, M., Kim, U. J. & Simon, M. I. (1999). J. Raman Spectrosc. 30, 785-793.]; Dubertret et al., 2001[Dubertret, B., Calame, M. & Libchaber, A. J. (2001). Nat. Biotechnol. 19, 365-370.]; Bauer et al., 1999[Bauer, G., Pittner, F. & Schalkhammer, T. (1999). Mikrochim. Acta, 131, 107-114.]; Taton et al., 2000[Taton, T. A., Mirkin, C. A. & Letsinger, R. L. (2000). Science, 289, 1757-1760.]), in solar cells (Westphalen et al., 2000[Westphalen, M., Kreibig, U., Rostalski, J., Lüth, H. & Meissner, D. (2000). Sol. Energy Mater. Sol. Cells, 61, 97-105.]; Stenzel et al., 1995[Stenzel, O., Stendal, A., Voigtsberger, K. & von Borczyskowski, C. (1995). Sol. Energy Mater. Sol. Cells, 37, 337-348.]), anti-counterfeiting (Bauer et al., 2003[Bauer, G., Hassmann, J., Walter, H., Haglmüller, J., Mayer, C. & Schalkhammer, T. (2003). Nanotechnology, 14, 1289-1311.]) and optical data storage (Ditlbacher et al., 2000[Ditlbacher, H., Krenn, J. R., Lamprecht, B., Leitner, A. & Aussenegg, F. R. (2000). Opt. Lett. 25, 563-565.]). These areas of research and applied science exploit the so-called `plasmon resonance' of the noble metal nanoparticles. It occurs due the excitation of free electron gas in the confinement of the nanoparticle (Zeman & Schatz, 1987[Zeman, E. J. & Schatz, G. C. (1987). J. Chem. Phys. 91, 634-643.]; Hulteen et al., 1997[Hulteen, J. C., Patrissi, C. J., Miner, D. L., Crosthwait, E. R., Oberhauser, E. B. & Martin, C. R. (1997). J. Phys. Chem. B, 101, 7727-7731.]). The plasmon resonance leads to distinct extinction bands in the optical spectrum. The field enhancement accompanying the resonance can be exploited e.g. in solar cells to increase efficiency (Westphalen et al., 2000[Westphalen, M., Kreibig, U., Rostalski, J., Lüth, H. & Meissner, D. (2000). Sol. Energy Mater. Sol. Cells, 61, 97-105.]), in optical filters (Park & Xia, 1999[Park, S. H. & Xia, Y. (1999). Langmuir, 15, 266-273.]) or to detect single molecules, using surface enhanced Raman spectroscopy (Garell, 1989[Garell, R. L. (1989). Anal. Chem. 61, 401A-410A.]). All of these methods rely upon a nanostructured noble metal layer on top of a highly reflecting substrate.

The spectral width and energy of the plasmon resonance strongly depends upon the nanoparticle morphology and the noble metal layer's structure (Hulteen et al., 1997[Hulteen, J. C., Patrissi, C. J., Miner, D. L., Crosthwait, E. R., Oberhauser, E. B. & Martin, C. R. (1997). J. Phys. Chem. B, 101, 7727-7731.]). Deposition methods of choice include vapour deposition techniques (Roth et al., 2003[Roth, S. V., Burghammer, M., Riekel, C., Müller-Buschbaum, P., Diethert, A., Panagiotou, P. & Walter, H. (2003). Appl. Phys. Lett. 82, 1935-1937.]; Bhat et al., 2003[Bhat, R. R., Genzer, J., Chaney, B. N., Sugg, H. W. & Liebmann-Vinson, A. (2003). Nanotechnology, 14, 1145-1152.]), sputtering (Roth, Walter et al., 2006[Roth, S. V., Walter, H., Burghammer, M., Riekel, C., Lengeler, B., Schroer, C., Kuhlmann, M., Walther, T., Sehrbrock, A., Domnick, R. & Müller-Buschbaum, P. (2006). Appl. Phys. Lett. 88, 021910.]; Bauer et al., 2003[Bauer, G., Hassmann, J., Walter, H., Haglmüller, J., Mayer, C. & Schalkhammer, T. (2003). Nanotechnology, 14, 1289-1311.]), pulsed laser deposition (Krebs et al., 2003[Krebs, H.-U., Weisheit, M., Faupel, J., Süske, E., Scharf, T., Fuhse, C., Störmer, M., Sturm, K., Seibt, M., Kijewski, H., Nelke, D., Panchenko, E. & Buback, M. (2003). Adv. Solid State Phys. 43, 505-517.]) and solution casting (Park & Xia, 1999[Park, S. H. & Xia, Y. (1999). Langmuir, 15, 266-273.]; Su, 2004[Govor, L. V., Bauer, G. H., Reiter, G. & Parisi, J. (2004). Phys. Rev. E, 69, 061609-1-061609-8.]; Narayanan et al., 2004[Narayanan, S., Wang, J. & Lin, X.-M. (2004). Phys. Rev. Lett. 93, 135503.]). All these methods aim to produce a large and homogeneous surface area. However, for combinatorial investigations (Roth et al., 2003[Roth, S. V., Burghammer, M., Riekel, C., Müller-Buschbaum, P., Diethert, A., Panagiotou, P. & Walter, H. (2003). Appl. Phys. Lett. 82, 1935-1937.]; Roth, Walter et al., 2006[Roth, S. V., Walter, H., Burghammer, M., Riekel, C., Lengeler, B., Schroer, C., Kuhlmann, M., Walther, T., Sehrbrock, A., Domnick, R. & Müller-Buschbaum, P. (2006). Appl. Phys. Lett. 88, 021910.]), it is often useful to install several morphologies on one single sample. This is frequently achieved by creating a gradient for one specific parameter, such as concentration or thickness. These one-dimensional gradients can then be investigated via high-throughput methods. This allows several morphologies, prepared under identical conditions, to be screened. Gradients are typically installed by deposition from a vapour phase. However, within this work we concentrate on solution deposition, based on a colloidal nanoparticle solution. Microbeam grazing-incidence small-angle X-ray scattering (µGISAXS) (Roth et al., 2003[Roth, S. V., Burghammer, M., Riekel, C., Müller-Buschbaum, P., Diethert, A., Panagiotou, P. & Walter, H. (2003). Appl. Phys. Lett. 82, 1935-1937.]; Roth, Walter et al., 2006[Roth, S. V., Walter, H., Burghammer, M., Riekel, C., Lengeler, B., Schroer, C., Kuhlmann, M., Walther, T., Sehrbrock, A., Domnick, R. & Müller-Buschbaum, P. (2006). Appl. Phys. Lett. 88, 021910.]; Müller-Buschbaum et al., 2003[Müller-Buschbaum, P., Roth, S. V., Burghammer, M., Diethert, A., Panagiotou, P. & Riekel, C. (2003). Europhys. Lett. 61, 639-645.]) is used for the ex-situ investigation of a one-dimensional gradient of nearly monodisperse gold nanoparticles. The gradient was created by a solution casting technique, followed by drying. The results presented here indicate a crossover and oscillation from a homogeneous layer to depleted regions due to capillary forces (Denkov et al., 1993[Denkov, N. D., Velev, O. D., Kralchevsky, P. A., Ivanov, I. B., Yoshimura, H. & Nagayama, K. (1993). Nature, 361, 26.]).

This paper is structured as follows. In the first experimental part we describe sample preparation. In the second experimental part we introduce the measuring technique, namely µGISAXS. In the third section we present a semi-quantitative analysis of the experiment by extracting the most prominent length scales present along the gradient. A fully quantitative analysis, as e.g. carried out by Revenant et al. (2004[Revenant, C., Leroy, F., Lazzari, R., Renaud, G. & Henry, C. R. (2004). Phys. Rev. B, 69, 305411.]), is beyond the scope of this paper. We finalize our paper with a conclusion of this combinatorial study.

2. Experimental part I: sample preparation

Solution casting was performed using a colloidal gold solution (Kisker Biotechnologie). The gold nanoparticles with a nominal diameter of 5.4 nm were in an aqueous solution with a concentration of 5 x 1013 particles ml−1. Silicon wafers with (111) orientation (Si-Mat, Landsberg, Germany) were used as substrate for the nanoparticle layer. The wafers were cleaned in an acid bath to ensure a well defined oxide layer. The acid bath consisted of a solution containing 110 ml deionized water, 160 ml sulfuric acid and 70 ml hydrogen peroxide at 353 K. The wafers were cleaned in the bath for 15 min, and afterwards rinsed several times with deionized water before being dried carefully in a nitrogen atmosphere.

A one-dimensional gradient was created using a new geometry as shown in Fig. 1[link]. Part of the surface of the cleaned wafer was covered with a second wafer piece to install a barrier against liquid flow. A drop (diameter 3 mm) of colloidal solution was deposited on the uncovered part of the base wafer surface using a syringe. The drop immediately wets the surface until it encounters the barrier and thereby installs a thin solution film. This thin film dries by evaporation of the solvent water (Denkov et al., 1992[Denkov, N. D., Velev, O. D., Kralchevsky, P. A., Ivanov, I. B., Yoshimura, H. & Nagayama, K. (1992). Langmuir, 8, 3183-3190.]; Denkov et al., 1993[Denkov, N. D., Velev, O. D., Kralchevsky, P. A., Ivanov, I. B., Yoshimura, H. & Nagayama, K. (1993). Nature, 361, 26.]; Deegan et al., 1997[Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. (1997). Nature, 389, 827-829.]; Deegan, 2000[Deegan, R. D. (2000). Phys Rev. E, 61, 475-485.]). Due to the increased amount of colloidal solution near the barrier and the pinning of the three-phase contact line at the barrier, a one-dimensional concentration gradient in close vicinity to the barrier is installed. This is in contrast to drying drops, where typical ring-shaped patterns were observed (Deegan et al., 1997[Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. (1997). Nature, 389, 827-829.]; Deegan, 2000[Deegan, R. D. (2000). Phys Rev. E, 61, 475-485.], Su et al., 2004[Su, P. Y., Hu, J. C., Cheng, S. L. & Chen, L. J. (2004). Appl. Phys. Lett. 84, 3480-3482.]). Similar to drying drops, the patterned regions are small compared with the wetted area. After a drying for 22 h under controlled conditions (room temperature and a humidity of 78%), all the water was completely evaporated, having creating a one-dimensional gradient. Finally the barrier is lifted off.

[Figure 1]
Figure 1
Sketch of the applied sample preparation to install a one-dimensional (1D) gradient (length ~20 mm, width ~2.5 mm). The initial droplet and the wetted area including the one-dimensional gradient are indicated. The extension of the one-dimensional gradient is approximately 2.5 mm.

3. Experimental part II: microbeam grazing-incidence small-angle X-ray scattering

Structural changes across the one-dimensional gradient were investigated using an advanced X-ray scanning technique, namely microbeam grazing-incidence small-angle X-ray scattering (Roth et al., 2003[Roth, S. V., Burghammer, M., Riekel, C., Müller-Buschbaum, P., Diethert, A., Panagiotou, P. & Walter, H. (2003). Appl. Phys. Lett. 82, 1935-1937.]; Roth, Walter et al., 2006[Roth, S. V., Walter, H., Burghammer, M., Riekel, C., Lengeler, B., Schroer, C., Kuhlmann, M., Walther, T., Sehrbrock, A., Domnick, R. & Müller-Buschbaum, P. (2006). Appl. Phys. Lett. 88, 021910.]; Müller-Buschbaum et al., 2003[Müller-Buschbaum, P., Roth, S. V., Burghammer, M., Diethert, A., Panagiotou, P. & Riekel, C. (2003). Europhys. Lett. 61, 639-645.]). The experiments were carried out at beamline BW4 of HASYLAB/DESY (Gehrke, 1992[Gehrke, R. (1992). Rev. Sci. Instrum. 63, 455-458.]; Roth, Döhrmann et al., 2006[Roth, S. V., Döhrmann, R., Dommach, M., Kuhlmann, M., Kröger, I., Gehrke, R., Walter, H., Schroer, C. G., Lengeler, B. & Müller-Buschbaum, P. (2006). Rev. Sci. Instrum. 77, 085106.]). BW4 is a dedicated materials science beamline with focus on grazing-incidence techniques. Being initially designed as an ultra-small-angle X-ray scattering (USAXS) beamline, an ongoing upgrade led to the installation of dedicated SAXS stations with sample-to-detector distances SDD <4 m to increase the accessible q-range. q is the modulus of the scattering vector and defined as q = (4π/λ)sinθ, where λ is the wavelength and θ is half the scattering angle. Owing to its high flux given by the wiggler source and high resolution and stability, BW4 has been shown to be capable of performing microbeam experiments using beryllium compound refractive lenses (BeCRLs) (Schroer et al., 2006[Schroer, C. G., Kuhlmann, M., Roth, S. V., Gehrke, R., Stribeck, N., Almendarez-Camarillo, A. & Lengeler, B. (2006). Appl. Phys. Lett. 88, 164102.]; Roth, Döhrmann et al., 2006[Roth, S. V., Döhrmann, R., Dommach, M., Kuhlmann, M., Kröger, I., Gehrke, R., Walter, H., Schroer, C. G., Lengeler, B. & Müller-Buschbaum, P. (2006). Rev. Sci. Instrum. 77, 085106.]).

For the ex-situ experiments described here, the incident X-ray beam was collimated using a slit system 20 m from the wiggler source (slit opening: 0.8 × 0.4 mm2, horizontal × vertical, h x v). The beam was then focused using a set of 15 parabolic BeCRLs (Lengeler et al., 2005[Lengeler, B., Schroer, C. G., Kuhlmann, M., Benner, B., Günzler, T. F., Kurapova, O., Zontone, F., Snigirev, A. & Snigireva, I. (2005). J. Phys. D Appl. Phys. 38, A218-A222.]) yielding a focal spot size of 71 × 60 µm2 (h × v). The parameters of the parabolic BeCRLs were an aperture of 0.8 mm and a radius of 0.208 mm (Lengeler et al., 2005[Lengeler, B., Schroer, C. G., Kuhlmann, M., Benner, B., Günzler, T. F., Kurapova, O., Zontone, F., Snigirev, A. & Snigireva, I. (2005). J. Phys. D Appl. Phys. 38, A218-A222.]). The achieved beam size in the focus allows lateral scanning of heterogeneous samples. This moderate microbeam was combined with a reflection setup used for GISAXS experiments. This method has been described previously (Roth et al., 2003[Roth, S. V., Burghammer, M., Riekel, C., Müller-Buschbaum, P., Diethert, A., Panagiotou, P. & Walter, H. (2003). Appl. Phys. Lett. 82, 1935-1937.]; Roth, Walter et al., 2006[Roth, S. V., Walter, H., Burghammer, M., Riekel, C., Lengeler, B., Schroer, C., Kuhlmann, M., Walther, T., Sehrbrock, A., Domnick, R. & Müller-Buschbaum, P. (2006). Appl. Phys. Lett. 88, 021910.]; Müller-Buschbaum et al., 2003[Müller-Buschbaum, P., Roth, S. V., Burghammer, M., Diethert, A., Panagiotou, P. & Riekel, C. (2003). Europhys. Lett. 61, 639-645.]; Roth et al., 2004[Roth, S. V., Müller-Buschbaum, P., Burghammer, M., Walter, H., Panagiotou, P., Diethert, A. & Riekel, C. (2004). Spectrochim. Acta Part B, 59, 1765-1773.]; Müller-Buschbaum et al., 2006[Müller-Buschbaum, P., Bauer, E., Pfister, S., Roth, S. V., Burghammer, M., Riekel, C., David, C. & Thiele, U. (2006). Europhys. Lett. 73, 35-41.]). Thus we introduced µGISAXS – GISAXS with microbeams – at BW4. The wavelength used was λ = 1.38 Å and the sample-to-detector distance, SDD = 2063 mm. The detector was a two-dimensional charge-coupled device detector (Mar Research) with 2048 × 2048 pixels and a pixel size of 79.1 µm. Upstream of the sample, a guard slit was installed to suppress parasitic scattering. The incident beam was monitored using ionization chambers.

Fig. 2[link] shows the schematic setup of the µGISAXS experiment including a typical µGISAXS pattern in the two-dimensional detector plane. The X-ray beam impinges onto the sample at an incident angle of αi = 0.7°. Specular and diffuse scattering contributions are observed. The exit angle with respect to plane defined by the sample surface normal (parallel to the z-direction) and the incident beam is denoted by αf, the out-of-plane angle is denoted as 2θ. Both direct and specular reflected beams are blocked by two separate point-like beam stops to avoid overexposure of the detector. Owing to the small beam size, the footprint on the sample is only 0.071 × 4.9 mm2 (h × v). Thus it is well suited for lateral scanning of one-dimensional gradients. Thus the gradient was placed parallel to the y-direction perpendicular to the beam. The step size was Δy = 150 µm, in order to scan a large area of several mm.

[Figure 2]
Figure 2
Scattering geometry of the µGISAXS experiment. αi is incident angle, αf is exit angle, 2θ is out-of-plane angle. x, y and z denote a Cartesian coordinate system and qy and qz a reciprocal space coordinate system. qy and qz are the components of the wavevector transfer parallel and vertical to the sample surface and are defined as qz = 2π/λ(sinαi + sinαf) and qy ≃ 2π/λsin2θ with λ being the wavelength. The µGISAXS data are recorded on a two-dimensional detector. SBS denotes the specular beam stop and Yon the Yoneda peak.

A typical µGISAXS pattern is shown in Fig. 2[link]. Included is a reciprocal space coordinate system (qy, qz). qy and qz denote the components of the wavevector parallel and perpendicular to the surface, respectively, with qz = 2π/λ(sinαi + sinαf) and qy ≃ 2π/λsin2θ. Hence the off-specular intensity contains the structural (distance between isolated objects D) and morphological information (shape of the individual objects) (Salditt et al., 1995[Salditt, T., Metzger, T. H., Brandt, C., Klemradt, U. & Peisl, J. (1995). Phys. Rev. B, 51, 5617-5627.]; Naudon & Thiaudière, 1996[Naudon, A. & Thiaudière, D. (1996). Surf. Coat. Technol. 79, 103-107.]). The two-dimensional data can then be analyzed in terms of so-called out-of-plane cuts and detector cuts (Müller-Buschbaum, 2003[Müller-Buschbaum, P. (2003). Anal. Bioanal. Chem. 376, 3-11.]). It is worthwhile to note, that the term `out-of-plane' refers to the scattering plane defined by the incoming beam and the surface normal. Thus, this cut is parallel to the sample surface, whereas the detector cut is perpendicular to it. A detector cut along qz at qy = 0 reveals correlations vertical to the sample surface. This includes resonant diffuse scattering (Müller-Buschbaum, 2003[Müller-Buschbaum, P. (2003). Anal. Bioanal. Chem. 376, 3-11.]) and the so-called Yoneda peak (Yoneda, 1963[Yoneda, Y. (1963). Phys. Rev. 131, 2010-2013.]). The Yoneda peak arises due to an interference effect of the incident and scattered wave. If αi,f = αc, the field is enhanced to twice the incident field because the standing wavefield of the incident and reflected waves reach their maximum. αc denotes the critical angle of the materials involved and can be calculated from the real part of the refractive index δ as αc = (2δ)0.5. In the case of silicon this angle is αc(Si) = 0.2°. In a so-called out-of-plane cut along qy at fixed qz correlations parallel to the sample surface are detected. In the case of nanoparticles the occurrence of side maxima in qy allows determination of their most prominent distances approximately in a very simple approach via

[d \approx 2\pi/q_{\rm y}. \eqno (1)]

A more elaborate approach would include a detailed modelling of shape and shape distribution of the particles (Roth et al., 2003[Roth, S. V., Burghammer, M., Riekel, C., Müller-Buschbaum, P., Diethert, A., Panagiotou, P. & Walter, H. (2003). Appl. Phys. Lett. 82, 1935-1937.]; Roth, Walter et al., 2006[Roth, S. V., Walter, H., Burghammer, M., Riekel, C., Lengeler, B., Schroer, C., Kuhlmann, M., Walther, T., Sehrbrock, A., Domnick, R. & Müller-Buschbaum, P. (2006). Appl. Phys. Lett. 88, 021910.]; Revenant et al., 2004[Revenant, C., Leroy, F., Lazzari, R., Renaud, G. & Henry, C. R. (2004). Phys. Rev. B, 69, 305411.]).

4. Results and discussion

Fig. 3[link](a) shows a map of the out-of-plane cuts at each scan position along y. Two exemplary two-dimensional µGISAXS patterns are shown as insets in Fig. 4[link]. All intensities are normalized to the incoming flux. In the presentation chosen in Fig. 3[link](a), all cuts at qz corresponding to αc(Si) as a function of 2θ are mapped in one single plot. From these cuts, the most-prominent in-plane length scales are determined and displayed as a function of the scan position y in Fig. 4[link](a). The y axis is defined with the barrier being at y = 0 mm. A clear change in the diffusively scattered signal is visible. The intensity oscillates between large 2θ values indicating a change from small correlation distances (dS ≃ 10 nm at e.g. y = 0.65 mm) to large correlation distances (dL is of the order of 100 nm) e.g. at y = 1.05 mm). The corresponding mapping of the detector cuts in Fig. 3[link](b) correlate well with the out-of-plane map. In the region where short correlation distances prevail, the diffusively scattered radiation between the Yoneda and specular peak is increased. This indicates an increased surface roughness, induced by packing the nanoparticles with distance dS. The decrease of this diffuse intensity in regions where no small correlation distances are observed indicates a depleted nanoparticle region. This qualitative analysis already shows the existence of a one-dimensional concentration gradient.

[Figure 3]
Figure 3
(a) Mapping of the out-of-plane cuts. The scan direction is y (step size Δy = 150 µm). The scanning range of 2.5 mm is indicated. S denotes the position of the correlation maxima (distance dS) of the gold nanoparticles. DC notes the position of the detector cut in (b) (2θ = 0°, qy = 0, respectively). (b) Mapping of the detector cuts. SBS denotes the specular beamstop, Yon the Yoneda maxima of silicon (αf = 0.2°). In both cases the intensity is shown on a logarithmic scale and is adapted to put emphasis on the visibility of the reported features. The out-of-plane cuts in (a) were done at the position Yon, i.e. the critical angle of silicon.
[Figure 4]
Figure 4
Crossover regimes in the one-dimensional gradient. (a) Plot of the most prominent in-plane length scales as a function of the scan position y. Two typical two-dimensional µGISAXS patterns at y = 0.65 mm and y = 2.55 mm are shown as insets. (b) Schematic representation of transition from largely separated nanoparticles (distance dS) to packed nanoparticles with distance dS approximately twice the nanoparticle diameter. The grey shaded region indicates a cross-over regime where domains (distance dL) of nanoparticles, being separated by dS, have formed.

Fig. 4[link](a) presents the semi-quantitative analysis of the flow processes involved in establishing the one-dimensional gradient. From the out-of-plane cuts the position of side maxima can be determined. Using equation (1)[link] the most-prominent in plane length can be calculated. The vertical error bar indicates the fitting error, while the horizontal error bar takes into account the beam size (defining the area over which is averaged the scattering experiment). Two length scales prevail: dL is of the order of 100 nm indicating largely separated nanoparticles and dS ≃ 10 nm indicating nearest neighbour distances between individual gold nanoparticles of 5.4 nm diameter. In order to make the maxima evident, Fig. 5[link] shows the out-of-plane cut for the two-dimensional µGISAXS pattern shown in Fig. 4[link](a). The maxima corresponding to dL and dS are clearly visible.

[Figure 5]
Figure 5
Out-of-plane cuts for the corresponding two-dimensional µGISAXS pattern in Fig. 4[link](a; insets). At y = 1.2 mm the largest, at y = 2.55 mm the smallest most prominent in-plane length scales are marked by arrows. The dashed vertical lines represent the resolution.

Based on earlier work (Govor et al., 2004[Govor, L. V., Bauer, G. H., Reiter, G. & Parisi, J. (2004). Phys. Rev. E, 69, 061609-1-061609-8.]; Deegan et al., 1997[Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. (1997). Nature, 389, 827-829.]; Deegan, 2000[Deegan, R. D. (2000). Phys Rev. E, 61, 475-485.]; Denkov et al., 1992[Denkov, N. D., Velev, O. D., Kralchevsky, P. A., Ivanov, I. B., Yoshimura, H. & Nagayama, K. (1992). Langmuir, 8, 3183-3190.]; Denkov et al., 1993[Denkov, N. D., Velev, O. D., Kralchevsky, P. A., Ivanov, I. B., Yoshimura, H. & Nagayama, K. (1993). Nature, 361, 26.]), we establish a simple qualitative model for the structure formation. With the barrier placed at y = 0 mm, first a drop of colloidal solution is deposited on the substrate at a position y = 5 mm. The drop wets the cleaned Si surface until it hits the barrier. This leads to an increased amount of solution in the vicinity of the barrier. Immediately after deposition, solvent evaporation sets in. This leads to a backflow of colloidal nanoparticles from the barrier in the direction of the drop position. The drop itself can be regarded as a reservoir delivering colloidal solution. Due to evaporation, the evolving colloidal solution film has its smallest thickness due to evaporation between the barrier and the drop position. Hence, the capillary forces are strongest when the thickness tW of the water film is in the order of the nanoparticle size (tW ~ 5–10 nm). It drives the gold nanoparticles away from the barrier and from the drop. According to this model, a maximum concentration will be established at a certain distance from the barrier at y = 0 mm. In Fig. 4[link](a) its onset can be estimated at y = 0.3 mm and its extension to 0.45 mm. Between y = 0.3 mm and y = 0.45 mm in the grey shaded area in Fig. 4(a), we determine a coexistence region of the two length scales dL and dS. This can be explained in according to Fig. 4[link](b). Firstly, for y < 0.3 mm the individual nanoparticles are largely separated [Fig. 4[link](b), left]. Between 0.15 mm < y < 0.6 mm [grey shaded region in Fig. 4[link](a)] domains of nanoparticles have formed. Still, they are centred around nuclei having a distance dL. Inside these domains the nanoparticles are packed at a distance of approximately 10 nm [Fig. 4[link](b), middle]. This explains the appearance of the second length scale dS. Finally, these domains coalesce. Only the length scale dS is prevailing [Fig. 4[link](b), right]. Scanning further towards the initial drop position, we see that a second transition at y = 0.9 mm to large separations occurs. At y = 1.8 mm, the structure oscillates back to a layer with nanoparticle distance dS. Thus due to hydrodynamic flow a third length scale in the order of several 100 µm becomes evident in addition to the nanoscopic length scales dS and dL.

5. Conclusion

Scanning µGISAXS measurements on the one-dimensional gradient of a dried colloidal gold solution are presented. From the µGISAXS pattern we are able to derive two most-prominent length scales, namely dS (approximately twice the colloid diameter) and dL (approximately 10 × dS). The latter indicates depleted regions with largely separated nanoparticles. According to a simple hydrodynamic model based on the drying behaviour of colloidal solutions (Govor et al., 2004[Govor, L. V., Bauer, G. H., Reiter, G. & Parisi, J. (2004). Phys. Rev. E, 69, 061609-1-061609-8.]; Deegan et al., 1997[Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. (1997). Nature, 389, 827-829.]; Deegan, 2000[Deegan, R. D. (2000). Phys Rev. E, 61, 475-485.]; Denkov et al., 1992[Denkov, N. D., Velev, O. D., Kralchevsky, P. A., Ivanov, I. B., Yoshimura, H. & Nagayama, K. (1992). Langmuir, 8, 3183-3190.]; Denkov et al., 1993[Denkov, N. D., Velev, O. D., Kralchevsky, P. A., Ivanov, I. B., Yoshimura, H. & Nagayama, K. (1993). Nature, 361, 26.]) the crossover regimes between depleted regions, domain formation and nanoparticle layers can be described qualitatively. Moreover, a new, third length scale in the 100 µm range exists, indicating an oscillation of the structure formation between the three regions (depleted, domains, packed). With respect to future technological applications, the ability to install the reported oscillatory pattern might be useful to tune optical properties of the noble metal layer. Further µGISAXS investigations should include in-situ investigations of drying colloidal solution not only at the surface (Narayanan et al., 2004[Narayanan, S., Wang, J. & Lin, X.-M. (2004). Phys. Rev. Lett. 93, 135503.]), but at the three-phase-boundary solution–air–substrate. In-situ monitoring of the process of nanostructuring induced by the interaction of the noble metal with the substrate is of special interest. Such investigations exploit the in-situ possibilities of µGISAXS and might even be combined with nanoscopic beams.

Acknowledgements

We would like to thank F.-U. Dill, R. Döhrmann and M. Dommach (HASYLAB) for their help in setting up the experiment. We thank the DFG SPP 1181 `NANOMAT' (Mu1487/5) for financial support.

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