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Langmuir 2009, 25, 952-958
Gold Nanoparticles at the Liquid-Liquid Interface: X-ray Study and Monte Carlo Simulation Stephan Kubowicz,*,†,⊥ Markus A. Hartmann,†,⊥ Jean Daillant,† Milan K. Sanyal,‡ Ved V. Agrawal,§ Christian Blot,† Oleg Konovalov,| and Helmuth Mo¨hwald⊥ CEA, IRAMIS, LIONS, CEA-Saclay, 91191 Gif-sur-YVette Cedex, France, Surface Physics DiVision, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata-7000064, India, Chemistry and Physics of Materials Unit, Jawaharlal Nehru Center for AdVanced Scientific Research, Jakkur P.O., Bangalore-560064, India, European Synchrotron Radiation Facility, Beamline ID10b, 38043 Grenoble Cedex, France, and Max Planck Institute of Colloids and Interfaces, Research Campus Golm, 14424 Potsdam, Germany ReceiVed August 29, 2008. ReVised Manuscript ReceiVed October 29, 2008 The behavior of mixed-ligand-coated gold nanoparticles at a liquid-liquid interface during compression has been investigated. The system was characterized by measuring pressure-area isotherms and by simultaneously performing in situ X-ray studies. Additionally, Monte Carlo (MC) simulations were carried out in order to interpret the experimental findings. With this dual approach it was possible to characterize and identify the different stages of compression and understand what happens microscopically: first, a compression purely in-plane, and, second, the formation of a second layer when the in-plane pressure pushes the particles out of the plane. The first stage is accompanied by the emergence of an in-plane correlation peak in the scattering signal and a strong increase of the pressure in the isotherm. The second stage is characterized by the weakening of the correlation peak and a slower increase in pressure.
Introduction Nanoparticles with a metal core stabilized by a ligand shell have aroused a lot of interest in recent years because of their unique electrical, magnetic, and optical properties, which give rise to many potential applications in nanotechnology.1 One of the major challenges to exploit these novel properties is the controlled integration of such particles into two- or threedimensional (2D or 3D) structures. 2D assemblies of nanoparticles are usually prepared making use of the controlled evaporation of a droplet of a colloidal solution or by means of the Langmuir-Blodgett (LB) technique.2,3 While the self-assembly by drop evaporation is experimentally simple to realize, it is often accompanied by complex phenomena (e.g., capillary forces), typically leading to a reduced long-range order and the formation of a mixture of 2D and 3D structures.4,5 In contrast, nanoparticle monolayer prepared at a liquid interface and transferred to a solid substrate by the LB deposition technique show uniform structures and yield high surface coverage.6-8 Recent X-ray scattering studies on gold nanoparticles at the air/water interface showed the high reproducibility of the LB technique and that the surface pressure has little effect on the morphology of the * To whom correspondence should be addressed. Present address: SINTEF Materials and Chemistry, Department of Synthesis and Properties, N-7465 Trondheim, Norway. E-mail:
[email protected]. † CEA Saclay. ‡ Saha Institute of Nuclear Physics. § Jawaharlal Nehru Center for Advanced Scientific Research. | European Synchrotron Radiation Facility. ⊥ Max Planck Institute of Colloids and Interfaces. (1) Sun, S.; Murray, C. B.; Weller, D.; Folks, L.; Moser, A. Science 2000, 287, 1989–1992. (2) Collier, C. P.; Vossmeyer, T.; Heath, J. R. Annu. ReV. Phys. Chem. 1998, 49, 371–404. (3) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Annu. ReV. Mater. Sci. 2000, 30, 545–610. (4) Motte, L.; Billoudet, F.; Lacaze, E.; Douin, J.; Pileni, M. P. J. Phys. Chem. B 1997, 101, 138–144. (5) Stowell, C.; Korgel, B. A. Nano Lett. 2001, 1, 595–600.
transferred film.9,10 However, at high surface pressures, the monolayer film shows reversible buckling, that can partly be annealed thermally to improve the surface coverage.10 This experimentally observed buckling was also found earlier for a monolayer of micron-sized particles,11 and molecular dynamics simulations suggest that it is the usual way of a particle monolayer to collapse.12 Besides understanding the behavior of particles at the air/ water interface, their behavior at the interface between two immiscible liquids is also of great interest. The latter has the ability to alter the stability of emulsions and foams.13 Most of the existing studies on these systems were focused on micronsized particles, which are irreversibly adsorbed at the interface11 and can be studied by optical microscopy. By reducing the particle size to the nanometer scale, the energy of attachment decreases and eventually becomes comparable to the thermal energy. In this case, thermal fluctuations can be large enough to enable an exchange of nanoparticles between interface and bulk,14 which opens the possibility of “self-healing”, i.e., removal of defects. In the present study we investigated the structure and properties of gold nanoparticles at the oil/water interface in an LB-trough using X-ray reflectivity (XRR) and diffraction. In order to verify (6) Heath, J. R.; Knobler, C. M.; Leff, D. V. J. Phys. Chem. B 1997, 101, 189–197. (7) Paul, S.; Pearson, C.; Molloy, A.; Cousins, M. A.; Green, M.; Kolliopoulou, S.; Dimitrakis, P.; Normand, P.; Tsoukalas, D.; Petty, M. C. Nano Lett. 2003, 3, 533–536. (8) Ohno, K.; Koh, K.; Tsujii, Y.; Fukuda, T. Angew. Chem., Int. Ed. 2003, 42, 2751–2754. (9) Schultz, D. G.; Lin, X. M.; Li, D.; Gebhardt, J.; Meron, M.; Viccaro, J.; Lin, B. J. Phys. Chem. B 2006, 110, 24522–24529. (10) Bera, M. K.; Sanyal, M. K.; Pal, S.; Daillant, J.; Datta, A.; Kulkarni, G. U.; Luzet, D.; Konovalov, O. Europhys. Lett. 2007, 78, 56003. (11) Aveyard, R.; Clint, J. H.; Nees, D.; Quirke, N. Langmuir 2000, 16, 8820– 8828. (12) Fenwick, N. I. D.; Bresme, F.; Quirke, N. J. Chem. Phys. 2001, 114, 7274–7282. (13) Binks, B. P. Curr. Opin. Colloid Interface Sci. 2002, 7, 21–41. (14) Lin, Y.; Skaff, H.; Emrick, T.; Dinsmore, A. D.; Russell, T. P. Science 2003, 299, 226–229.
10.1021/la802837k CCC: $40.75 2009 American Chemical Society Published on Web 12/29/2008
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Figure 1. (a) SAXS curve of the gold nanoparticles dissolved in isopropanol. The solid line represents a calculated scattering curve of gold nanoparticles with r ) 1.1 nm and σ ) 0.1. (b) TEM micrograph of the gold nanoparticles (Bar ) 20 nm).
and interpret the experimental results, additional Monte Carlo (MC) simulations were performed.
Experimental Section For the X-ray studies at the liquid-liquid interface, a specially designed LB-trough was mounted on an active antivibration system. A detailed description of the LB-trough has been published elsewhere.15 The n-tetradecane, which forms the upper liquid layer in the trough, was purchased from Sigma Aldrich. It was passed three times through an alumina column in order to remove impurities. The n-tetradecane-water interfacial tension at 22 °C is 54.5 mN/ m.16 Gold nanoparticles stabilized by a mixed ligand shell of 1-hexanethiol and 11-mercapto-1-undecanol were synthesized according to a procedure published elsewhere.17 The size of the gold core was determined by small-angle X-ray scattering (SAXS), which yields a radius of 1.1 ( 0.1 nm (Figure 1a). The experimental SAXS data were fitted with a simple sphere model. The deviation of the fit from the scattering curve for low q-values is due to the presence of some larger particles or agglomerates in the sample. This small fraction of larger species, which emerge during the particle preparation, is expected to have no significant influence on the overall behavior of the interfacial layer but will most likely reduce the degree of in-plane order. The SAXS result was confirmed by transmission electron microscopy (TEM) as shown in Figure 1b. From the size of the nanoparticles the molecular weight was estimated to be around 78 000 g/mol.18 The mixed-monolayer-protected gold nanoparticles were dissolved in isopropanol at a concentration of 2.0 g/L. Forty microliters of this solution was spread at the n-tetradecane-water interface using a microsyringe. The compression of the formed particle layer was monitored by recording the pressure-area isotherm, and the surface of the trough was simultaneously observed using Brewster angle microscopy. To achieve the Brewster angle at the n-tetradecane-water interface (R ) 41.97°) and to avoid disturbing reflections at the oil/air interface, the laser beam was guided through a small capillary dipped into the n-tetradecane. On the objective, a specially designed cone was mounted to directly observe the n-tetradecane-water interface. Experiments were carried out at room temperature (22 °C). The X-ray scattering measurements were performed at beamline ID10B at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The energy of the monochromatic beam was set (15) Fradin, C.; Luzet, D.; Braslau, A.; Alba, M.; Muller, F.; Daillant, J.; Petit, J. M.; Rieutord, F. Langmuir 1998, 14, 7327–7330. (16) Goebel, A.; Lunkenheimer, K. Langmuir 1997, 13, 369–372. (17) Kubowicz, S.; Dubois, M.; Daillant, J.; Delsanti, M.; Verbavatz, J.-M.; Mo¨hwald, H. To be submitted for publication. (18) Hostetler, M. J.; Wingate, J. E.; Zhong, C. J.; Harris, J. E.; Vachet, R. W.; Clark, M. R.; Londono, J. D.; Green, S. J.; Stokes, J. J.; Wignall, G. D.; Glish, G. L.; Porter, M. D.; Evans, N. D.; Murray, R. W. Langmuir 1998, 14, 17–30.
Figure 2. The geometry of a typical, surface sensitive scattering experiment.
to 21.9 keV (wavelength λ ) 0.057 nm) to allow the X-ray beam to pass through the upper liquid (n-tetradecane here), and reflectivity and diffuse scattering data were collected from the n-tetradecane-water interface. Two thin silicon wafers of equal heights were used near the entry and exit X-ray windows of the Langmuir trough to anchor the n-tetradecane-water interface. In this setup, the X-ray intensity reduces by a factor of 0.142 as the 21.9 keV beam passes through 7 cm of n-tetradecane. All of the measurements were performed at room temperature (22 °C) with the incident beam size of 0.015 × 0.5 mm2 (V × H) defined using conventional slits. The position of the liquid-liquid interface was adjusted in order to minimize the meniscus by controlling the amount of water in the trough and monitoring the peak shape of the reflected beam at small grazing angle of incidence θi. The wavevector transfer b q can be calculated from the grazing angle of incidence θi, the grazing scattering angle θout, and the azimuth of the scattering angle Ψ (Figure 2). Two types of experiments were performed in this study. A reflectivity experiment consists of a qz scan at qx and qy ) 0 and gives access to the vertical electron density profile across the interface. qy scans (in-plane diffraction or diffuse scattering) were also performed in order to determine the in-plane ordering of the nanoparticles. Reflectivity data were collected using a point detector. For each θi value, θi and the detector angle θout were scanned around the reflection as θi - δθ, θi + δθ (rocking scans) in order to scan the reflected intensity (at approximately constant qz) and subtract the background. For scattering measurements a vertically mounted position sensitive detector (PSD) was used. The data were recorded as a function of the in-plane angle (Ψ), keeping the grazing angleof-incidence (θi) fixed at 0.32 mrad below the critical angle for total external reflection, following the method of ref 10. Two vertical slits
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Kubowicz et al. direction, i.e., normal to the interface, hard wall boundary conditions were used, i.e., the particles were not allowed to leave the interface. According to a standard Metropolis algorithm,21 a simulation step consisted of a jump trial in the (x,y) direction followed by a jump trial in the z direction. By slowly changing the box length a and subsequent equilibration, configurations of different area fractions were produced. For each desired area fraction up to 1000 independent configurations were produced, which were then averaged to obtain the final results. The pressure p was calculated via22
pA ) NkBT -
〈 ∑∑ 1 3
i
j>i
rij∇rijU(rij)
〉
(3)
where rij is a vector joining two particles in the (x,y) plane, and A is the through area. Figure 3. The interaction potential used for the MC simulations. Shown is the interaction of two particles with an identical gold core radius of 1.1 nm (resulting in a hard core repulsion of range 2.2 nm), each of them coated with an additional ligand layer of thickness 1.1 nm. Note the logarithmic energy scale.
of width wd ) wc ) 0.3 mm were at a distance Lc ) 270 mm and Ld ) 830 mm from the goniometer center in order to define the scattering geometry. As the data were collected under total external reflection condition, the background was simply measured by lowering the trough by 0.2 mm and repeating the same measurement. Thus, the beam path in n-tetradecane remains the same. Furthermore, for better understanding and interpretation of the experimental findings, MC simulations of a simplified model system were performed. The gold cores of the nanoparticles were modeled as hard spheres (i.e., the cores were not allowed to overlap), whose radii were drawn from a normal distribution with mean r0 ) 1.1 nm and standard deviation σ ) 0.1 nm to account for the polydispersity of the particles, as determined by SAXS (see Figure 1). The interaction of the ligand layers around the particles was modeled by a soft, short ranged, repulsive potential, proposed by de Gennes:19
U(d) ) -2π
kBT
[
R1R2 -16 (2L)2.25 + s3 (R1 + R2) 5 (d - R1 - R2)0.25
]
2.75 16 (d - R1 - R2) 48 48 - (2L(d - R1 - R2)) + (2L)2 (1) 77 35 11 (2L)0.75
where R1 and R2 are the radii of the two spheres, d is their centerto-center distance, L is the thickness of the ligand layer, s is the average distance between the attachment points of two ligands, kB is Boltzmann’s constant, and T is the temperature. In the simulations, L ) 1.1 nm and s ) 0.41 nm, which is the mean distance calculated by assuming 116 ligand molecules are attached to one nanoparticle. Note that U(d) is zero for distances d larger than R1 + R2 + 2L (see also Figure 3). In addition to the particle-particle interactions, the nanoparticles are attached to the interface. For colloids with a contact angle of 90° this attachment energy is given by20
[
UAttach(z) ) π(R + L)2γ
]
z2 -1 (R + L)2
(2)
where γ ) 12.5 kBT/nm2 (∼50 mN/m) is the interfacial tension at the oil/water interface, and z is the distance of the center of the colloid from the interface. In the course of a simulation, N ) 1000 particles were placed in a square box of length a. In the x and y directions, i.e. parallel to the interface, periodic boundary conditions were used. In the z (19) de Gennes, P. G. AdV. Colloid Interface Sci. 1987, 27, 189–209. (20) Pieranski, P. Phys. ReV. Lett. 1980, 45, 569.
Results and Discussion The mixed-monolayer-protected gold nanoparticles were spread directly at the n-tetradecane-water interface in the LBtrough. Then a waiting time of 30 min was allowed to let the system equilibrate. By compressing the interfacial layer with two movable barriers, pressure-area isotherms were recorded. The speed of the barriers was set as low as possible (V ) 0.02 cm2/s) to ensure equilibration of the particle layer. The pressure-area isotherm, as shown in Figure 4a has a characteristic shape and can be split into three regions. In region I, at large areas, the surface pressure increases slowly during compression. This is followed by a significant increase of the surface pressure in region II, which originates from the repulsion between the particles. In this region, the ligand shells start to overlap, but the particles still stay in the plane z ) 0. When the trough area is further decreased, the repulsion of the particles increases. The transition from region II to region III, characterized by a reduction of the slope of the isotherm, marks the beginning of the collapse of the monolayer. This leads to a displacement of the particles from their position at z ) 0 and the interfacial layer starts to buckle. A further compression in region III leads only to a small increase in surface pressure. The shape of the recorded isotherm can be reproduced by several compression and expansion cycles, indicating that even at high surface pressures there is no loss of particles to either of the bulk phases. The small hysteresis of the isotherm shows that, although the compression rate was very small, the particle layer is not completely equilibrated. True equilibrium would require an infinitely small compression rate. Comparing the experimental isotherm to the simulated one (Figure 4b), it can be seen that, in the simulation, the surface pressure increase of region II starts at lower surface areas and is steeper and higher than in the experiment. This feature is most likely due to the simplifications in the model where, for example, no long-range interaction between the particles is taken into account. Furthermore, the simulated isotherm is recorded when the system is equilibrated, a state that was not completely achieved in the experiment. Nevertheless, the surface pressure coincides remarkably well with the experimental curve. The three regions found in the experimental curve can also be recognized in the simulated one. In addition, the latter shows an extra fourth region, which corresponds to the formation of a second layer when the particles have no possibility to elude a further compression. Thus, the pressure rises dramatically and diverges at full packing (region IV). The formation of a second layer in the simulation is due to the high surface pressure and to the chosen hard wall boundary (21) Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. J. Chem. Phys. 1953, 21, 1087–1092. (22) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: Oxford, U.K., 1987.
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Figure 4. (a) Surface pressure-area isotherm of the gold nanoparticle monolayer spread at the n-tetradecane-water interface. The insets show Brewster angle micrographs at different points of the isotherm. (b) Simulated surface pressure-area isotherm for the described model. The same regions as in the experimental curve can be recognized.
Figure 5. (a) The points represent the reflectivity as measured in the experiment (black squares: 21.5 nm2; red circles: 13.8 nm2; green triangles: 9.1 nm2). The solid lines are fitted using eq 4, and the dashed lines are the result from the MC simulations. (b) The electron density profiles obtained from the fit (solid) and the MC simulations (dashed).
condition, which impose this special ordering on the particles at low trough areas. However, in the experimental isotherm, the low surface areas necessary to observe region IV could not be achieved. The surface pressure measurement was simultaneously accompanied by Brewster angle microscopy to monitor the morphological changes in the interfacial layer. It was found that the particles are homogeneously distributed at the interface without any visible formation of domains. Compression and expansion of the particle layer led to a continuous increase or decrease, respectively, of the reflected laser light intensity and no morphological structures could be observed (see insets in Figure 4a). This indicates that the interfacial layer is macroscopically homogeneous and the particles are not aggregating to larger assemblies at higher surface pressure. To get information on the vertical structure of the interfacial particle layer, XRR measurements were performed. The in-plane structure of the layer was investigated using grazing incidence X-ray diffraction (GIXD). Normalized XRR data of the gold nanoparticle layer at three different areas per particle (26.9 nm2, 17.2 nm2, and 11.4 nm2) are shown in Figure 5a. The absence of a minimum in the measured q-range of the reflectivity curves indicate that the interfacial particle layer has a thickness below 3 nm, and thus, as expected, the particles form a monolayer at the interface. Furthermore, it can be seen that, below the collapse of the layer, the reflectivity curves are almost identical as the thickness of the layer stays constant. Figure 5a shows the measured reflectivity
data together with a standard fit (solid lines) and the reflectivity obtained by the MC simulations (dashed lines) calculated via23
R(qz) )
RF (Fw - Fo)
2
|∫
|
∂F(z) iqzz 2 -σ2qz2 e dz e ∂z
(4)
where RF is the Fresnel reflectivity, Fw and Fo are the electron densities of water and oil (n-tetradecane), respectively, F(z) is the electron density profile in the z direction, and σ2 is the effective mean square interface roughness.24 Fitting of the experimental reflectivity curves using eq 4 was done by the standard slicing technique where the electron density profile was modeled as a sum of error functions. Thus, the derivative of the electron density profile in eq 4 can be written as a sum of Gauss functions:
∂F(z) ) ∂z
∑
-(z - zi)2
∆Fie
σ2
(5)
i
where ∆Fi is the density difference between two adjacent slices. The electron density profiles calculated from the fit of the three reflectivity curves are shown in Figure 5b. The effective mean square interface roughness, σ2 obtained by fitting are 0.09 nm2 at an area per particle of 21.5 nm2, 0.1 nm2 at 13.8 nm2, and 0.18 nm2 at 9.1 nm2. In the MC simulations, the electron density at height z is the sum of the contributions of gold and solvent present in this layer. (23) Gibaud, A.; Hazra, S. Curr. Sci. 2000, 78, 1467–1477. (24) Sanyal, M. K.; Sinha, S. K.; Huang, K. G.; Ocko, B. M. Phys. ReV. Lett. 1991, 66, 628.
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Figure 6. Snapshots for the three investigated areas per particle. Particles shown in red have z-coordinates greater than 0, particles in blue have z-coordinates less than 0. The additional graph shows the corresponding distributions of z-coordinates.
It was assumed that the amount of volume not occupied by gold is occupied by solvent (water for z > 0 and oil for z < 0). Because of the small contrast with either solvent, the ligand shell was not explicitly taken into account. While F is a direct output from the simulations, σ has to be adjusted to fit the experimental data. In our case, σ2 ) 0.1 nm2 (black line), 0.27 nm2 (red line), and 0.8 nm2 (green line), respectively (see Figure 5a). A simple capillary-wave model analysis gives
σ2 )
kBT qmax log 2πγ qmin
(6)
where qmax and qmin are high and low wave-vector cut-offs equal to 2π/r and √∆F · g⁄γ where r is the particle radius 4F is the difference in mass density, and g is the gravitational constant. With these values, one finds approximately σ2 ) 0.09 nm2 for the low compression states, which is in good agreement with the experimental values. Note that, besides the need to determine σ, no other free parameter is remaining. Thus, the calculated reflectivity curves are no fits to the data, but direct outputs from the MC simulations. The electron density profiles obtained by simulation are shown in Figure 5b as dashed lines. Remarkable is that the calculated XRR curves from the fit and the simulations exhibit only minor differences and the electron density profiles for the large areas are almost identical. For the smallest area (9.1 nm2), the simulated system already showed the formation of two distinct layers, which, as mentioned before, was not achieved in the experiment. This also explains the observed differences. This indicates that the chosen model represents the experiment well in the region of low and intermediate pressures (above areas of ∼10 nm2). Both the fit and the MC simulations show that in region I and II of the pressure-area isotherm, the electron density practically does
not change its width, only its height since less space is left to accommodate all the electrons. At a surface pressure well above the collapse, the particle layer is buckled, which leads to an apparent higher layer thickness and therefore to a slight change in the reflectivity curve. This observation is also supported by the fit and by the MC results. Figure 6 shows typical snapshots of the structure for the three investigated areas per particle and corresponding distributions of the particles’ z-coordinates. The fitted curves describe the measured data of course better than the MC simulations, as all parameters are adjusted. For large to intermediate areas per particle, the form of the electron density obtained by the simulations and the fit coincide almost perfectly. Slight deviations can be observed at the flanks of the curve, where the results of the MC simulations decay faster than the fitted curves. The asymmetric profile obtained for small areas per particle from the fit of the reflectivity data cannot be reproduced with the MC simulations. Most likely this asymmetric profile shows that the contact angle of the colloids is not exactly 90° as assumed in the simulations, but less, meaning that the particles are slightly more hydrophilic. The measured scattering intensity as a function of horizontal and vertical components of the wave-vector transfer qxy and qz provides information regarding the in-plane and out-of-plane ordering of the nanoparticles at the oil-water interface. The wave-vector transfer qxy and qz are related to the out-of-plane and in-plane angles θout and Ψ as follows:
qx ) k0(cos(θi) - cos(θout) cos(ψ))
(7)
qy ) k0(cos(θout) sin(ψ))
(8)
qz ) k0(sin(θi) + sin(θout))
(9)
Au Nanoparticles at a Liquid-Liquid Interface
qxy ) √qx2 + qy2
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(10)
with k0 ) 2π/λ. The differential scattering cross-section dσ/dΩ can be written as
dσ b)| × |F(q b)| ) Are2|S(q dΩ
(11)
where A ) (wi × wc × Ld)/(Lc × tan(ψ)) is the illuminated area seen by the detector, S(q b) is the so-called structure factor, and F(q b) is the “form” factor of the nanoparticles. In the simulations, the scattered intensity can be calculated according to
N
∑
A I(q b) ∝ | VjFj(q b)eibr ibq |2 N j)1
(12)
where b rj is the position vector of the jth particle, and Fj(q b) and Vj are its corresponding form factor and volume, respectively. Note that, because of the polydispersity of the particle sizes, structure and form factor can not be factorized as usual for monodisperse systems. The relation A∝1/qxy accounts for the change in illuminated area according to the experimental settings. N is the number of particles. Contour plots of the measured and calculated scattering intensity in the qxy-qz plane for different areas per particle (Figure
Figure 7. The scattered intensity measured in the experiment (left) and given by the MC simulations (right). Note the linear and the logarithmic scale in the experimental and the simulated curves, respectively.
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distance decreases with decreasing area per particle from 4.1 to 3.5 nm. For comparison, the core diameter plus twice the length of the stabilizing ligand (75% of the fully stretched length) yields 4.4 nm. Also, as described on the contour plots, one can see that, because of the compression the intensity of the maximum is first increasing and then decreases with further decrease in area per particle as the interfacial layer becomes rougher due to the buckling.
Conclusion and Outlook
Figure 8. Scattered intensity as a function of qxy along qz ) 0.3 nm-1 extracted from the contour plots.
7) show a Bragg rod, which is characteristic for a 2D assembly of particles with no long-range order at the interface. The intensity of the Bragg rod increases with decreasing area per particle as the in-plane order and the number density of the nanoparticles increases. With further compression the nanoparticle monolayer starts to buckle, which dramatically decreases the in-plane order and thus the Bragg rod intensity. The formation of an “arc” in the contour plots, as observed in an earlier experiment with gold nanoparticles at the air-water interface,10 could also be observed but is less pronounced. The MC data show similar results. In the right part of Figure 7 contour plots of the scattering intensity are shown, which were calculated for the same systems as the reflectivity in Figure 5. The correlation peak is already visible for the lowest investigated concentration. This shows that the correlation of the particles in z-direction is stronger than in the experiment. Most probably this is due to the constant value of the contact angle for all the particles leading to the same equilibrium position of the particles with respect to the interface. Like in the experiment, the peak shifts to larger values of qxy for higher compressions and becomes considerably sharper. When the pressure exceeds a critical value, the formation of a second layer starts, which weakens the inplane correlation peak and increases the off-plane intensity (region III in the isotherm; see Figure 4). In the simulation further compression leads due to the hard wall boundary conditions to a well-defined second layer, weakening the in-plane peak more and more and transferring intensity to the out-of plane peak. The appearance of this new Bragg rod could not be observed experimentally indicating that there is no real 3D distance correlation in the buckled nanoparticle layer. In Figure 8, the scattered intensity as a function of qxy along qz ) 0.3 nm-1 extracted from the contour plots is presented. The maximum of the curves, which can be assigned to the interparticle distance shifts from qxy ) 1.55 nm-1 at 17.5 nm2 to qxy ) 1.8 nm-1 at 8.3 nm2. This indicates that, as expected, the interparticle
In the present study we have investigated the behavior of mixed-ligand-coated gold nanoparticles at a liquid-liquid interface. The high brilliance synchrotron radiation source ESRF gave us the possibility to investigate the system over a wide angular space. Supplementary MC modeling helped to interpret the results. The performed experiments and simulation revealed a homogeneous compression of the particles at high to intermediate areas per particle and a reversible buckling of this layer at low areas per particle. A very good agreement between experiment and simulation above areas of 10 nm2 has been found. The minor discrepancies can be most likely ascribed to model simplifications. In the simulation, unlike in real systems, the particles were strictly confined to the interface, thus leading to unrealistically high pressures for small trough areas. As well, the particles were modeled with a contact angle of 90° leading to exactly symmetrical electron densities. In real systems, the contact angle can be different than 90° and also vary for different particles, leading to less pronounced Bragg rods in the qz direction. Furthermore, in our model, the interface stays perfectly flat during compression, and the particles have to arrange themselves in the vicinity of this interface leaving their preferred position determined by their contact angle. This might also lead to the higher values of the mean interface roughness found in the simulation compared to the experimental data. The other extreme case would be the assumption that the interface deforms in such a way that locally for all the particles the equilibrium contact angle is maintained.12 Most probably the real system shows a behavior between these two extremes. Thus, to further improve the agreement between model and experiment, it seems desirable to account also for the deformation of the interface in the simulations. This can be done by a triangulation of the interface, which allows it to evolve. Acknowledgment. We thank Corinne Chevallard for her help with the Brewster angle microscopy as well as Dayang Wang, Erik W. Edwards, and Luc Belloni for their help and fruitful discussions. Furthermore, we acknowledge the support from the Deutsche Forschungsgemeinschaft (DFG) through the FrenchGerman Network, Complex Fluids: From 3 to 2 Dimensions. LA802837K
