Letter pubs.acs.org/NanoLett
Angular Trapping of Anisometric Nano-Objects in a Fluid Michele Celebrano,† Christina Rosman,‡ Carsten Sönnichsen,‡ and Madhavi Krishnan*,§ †
CNISM - Department of Physics, Politecnico di Milano, Piazza Leonardo Da Vinci 32, 20133 Milan, Italy Institute for Physical Chemistry, Duesbergweg 10-14, University of Mainz, D-55128 Mainz, Germany § Institute of Physical Chemistry & Institute of Physics, Winterthurerstrasse 190, University of Zurich, CH 8057 Zurich, Switzerland ‡
S Supporting Information *
ABSTRACT: We demonstrate the ability to trap, levitate, and orient single anisometric nanoscale objects with high angular precision in a fluid. An electrostatic fluidic trap confines a spherical object at a spatial location defined by the minimum of the electrostatic system free energy. For an anisometric object and a potential well lacking angular symmetry, the system free energy can further strongly depend on the object’s orientation in the trap. Engineering the morphology of the trap thus enables precise spatial and angular confinement of a single levitating nano-object, and the process can be massively parallelized. Since the physics of the trap depends strongly on the surface charge of the object, the method is insensitive to the object’s dielectric function. Furthermore, levitation of the assembled objects renders them amenable to individual manipulation using externally applied optical, electrical, or hydrodynamic fields, raising prospects for reconfigurable chip-based nano-object assemblies. KEYWORDS: Angular trapping, electrostatic fluidic trap, silver nanorods, single particle scattering
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prospects for reconfiguring an assembly of particles. A nanoobject manipulation technique that combines the precise control and potential reconfigurability of external field-based techniques with the massively parallel and versatile nature of template-driven assembly would be highly desirable in emerging areas of research and technology.2 We recently demonstrated an important step in the direction of reconfigurable nano-object assemblies, namely, highly parallel spatial trapping and levitation of dielectric and metallic spheres and dielectric shells, 20−100 nm diameter, using an array of electrostatic traps on a fluidic chip.15 The experimental system consists of a slit structure created by two parallel surfacesone glass and the other SiO2; the SiO2 surface in turn carries indentations that define the location and morphology of each trap. Negatively charged objects in an aqueous suspension introduced into the slit sample the landscape by Brownian motion, fall into the electrostatic potential wells created by the surface indentations, and remain trapped for a time period that scales as eΔF/(kBT). In a radially symmetric potential well, the electrostatic system Helmholtz free energy, F, is solely a function of the object’s location, confining it spatially15 but permitting it to rotate freely in both polar (θ) and azimuthal (ϕ) dimensions. Here we report on the use of an electrostatic fluidic trap to effectively control the angular orientation of single spatially trapped, levitating anisometric objects such as
he shape and spatial arrangement of nano-objects in an assembly has profound effects on its interaction with light and is a central theme in hybrid photonic devices, metamaterials, and plasmonics.1−8 However, few techniques are capable of orienting and assembling individual nanoscale elements of arbitrary shape and composition. One of two broad approaches to controlling nanoscale matter involves the application of external fields to the object of interest, and another relies on template-assisted deposition of material out of the fluid phase at predefined locations on a substrate surface. In general external field-based techniques offer the advantages of reconfigurability9 and direct control over both the spatial location and angular orientation of an object10 but can suffer from limited potential for parallelization as well as constraints on the object’s size and/or polarizability. For example, the optical gradient force offers angular control of metal nanorods, but the high incident power required not only causes extraneous thermal effects but also make the technique hard to parallelize. Optoelectronic tweezing and dielectrophoretic trapping have been used to orient nanowires several micrometers in length,9,11 but like optical tweezing these methods depend strongly on the object’s volume and ultimately fail when its size approaches the nanometer scale in all dimensions. Template-driven assembly techniques on the other hand offer massively parallel and highly precise spatial control of nanoobjects on a substrate, independent of their size and dielectric properties,12,13 but angular control of an individual anisotropic object has not been demonstrated to date.14 Further, the fact that matter is deposited directly onto a substrate surface limits © 2012 American Chemical Society
Received: August 20, 2012 Revised: September 24, 2012 Published: September 27, 2012 5791
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Figure 1. (a) Schematic of the laser scanning microscope setup and fluidic device used to probe the orientation of single trapped silver nanorods. Also presented are electron micrographs of the rectangular pocket in the substrate (scanning electron micrograph, SEM) and silver nanorods (transmission electron micrograph, TEM) used in the study. (b) Calculated spatial electrostatic potential distribution in the xy plane arising due to a pocket of length l = 600 nm, width w = 100 nm, and depth 100 nm, in a slit of depth, 200 nm (left). The section displayed represents the plane of the electrostatic minimum in the axial dimension which occurs at z = 110 nm above the floor of the slit in this geometry. Slit and pocket depths are held constant in this study. Cross-sectional views of the potential distribution in the xz and yz planes are also displayed (right).
nanorods in a highly parallel fashion in a fluid. We further demonstrate theoretically that this principle may be extended to nanometer-scale objects of arbitrary shape. It is important to note that, although micrometer-scale objects displaying shape and/or optical anisotropy can be oriented using optical fields16,17 and a wealth of techniques exploiting nanostructured substrates and applied optical18−21 or electrical fields22,23 achieve spatial confinement of globular nano-objects, the ability to trap and orient an arbitrarily shaped object at the nanometer scale remains beyond the reach of the state-of-the-art. We chose nanorods as simple nonspherical test objects for a theoretical and experimental study and analyzed their behavior in electrostatic potential wells created by rectangular surface indentations in the fluidic slit (Figure 1b). The spatial distribution of electrostatic potential in the trapping nanostructure obtained by numerically solving the nonlinear Poisson− Boltzmann equation15 in 3D using COMSOL Multiphysics reveals that the trap due to such a structure has the shape of a cigar (Figure 1b) whose long and short axes can be tuned simply by changing the dimensions of the pocket. Engineering the morphology of the trap to closely mimic the shape and desired orientation of the object should cause the system free energy, F, to be not only a function of the spatial location of the object but also of its orientation in the potential well. In our theoretical investigation, we consider an ellipsoid of dimensions 160 nm × 60 nm and fixed surface charge density embedded in
an electrolyte, which is in turn bounded by charged surfaces representing the walls of the trapping nanostructure. The background electrolyte ionic strength (0.04 mM in the experiments reported here) and an estimate of the particle and wall charge densities (0.01 e/nm2) can be obtained from conductivity, light scattering, and electroosmotic flow measurements, respectively. The free energy of the system is found by summing the electrostatic field energies and entropies over all charges in the system.24,25 The center of mass of the ellipsoid was positioned at the spatial minimum of the electrostatic free energy and the calculation performed as a function of object orientation (θ, ϕ). The resulting angular free energy landscape of a spatially trapped ellipsoid indeed reveals minima in both θ and ϕ when the rod is aligned with the major axis of a cigarshaped well (Figure 2a); the depth of the well depends on the charge of the ellipsoid and walls of the nanostructure, the ionic strength of the solution, and the geometric parameters of the trap (Figure 2c). Calculations additionally bring to light the following interesting features: first, similar to nanorod alignment in an optical focus, the confining potential can be wellapproximated by a harmonic potential; that is, F(θ) = (1/2) kθθ2 for θ < (π/4) (Figure 2c). Second, while the rod is essentially free to rotate in ϕ around θ = 0°, for θ > 30°, its motion in ϕ is strongly restricted. This means that the further the object rotates in the x−y plane, the less likely rotation in the out-of-plane z-dimension becomes. Thus, in contrast to an 5792
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Figure 2. (a) 3D surface plot of the angular free energy of an ellipsoid of dimensions 160 nm × 60 nm, carrying a total charge of −255 e and trapped by a rectangular pocket of dimensions, l = 200 nm, w = 100 nm. (b) Schematic view of a nanorod in three different orientations: (0) θ = 0° (reference position), (1) θ = 30°, ϕ = 0°, and (2) θ = 60°, ϕ = −90°. These orientations are denoted on a 2D surface plot of the angular free energy. (c) Line plots of the calculated free energy in θ along the dotted contour line in (b) denoting ϕ = 0°, for four different geometries of the trapping pocket: circular pocket of diameter 500 nm (squares), rectangular pockets of dimensions l = 200 nm, w = 100 nm (circles), l = 600 nm, w = 100 nm (diamonds), l = 600 nm, w = 200 nm (triangles). The red curve represents a fit to a harmonic potential for the l = 600, w = 100 nm case of the form ΔF = (1/2)kθθ2, where kθ = 9.1kBT and θ is in radians. The solution ionic strength and particle and wall surface charge densities were 0.04 mM and 0.01 e/nm2, respectively.
Supporting Information). The nanorods under consideration have a broad longitudinal plasmon resonance centered at 776 nm, around which they strongly scatter light. Scattering at λ = 671 nm arises solely from the resonance associated with the long axis of the rod and thus serves as a sensitive probe of the rod’s orientation, θ relative to the incident polarization (see the Supporting Information). The nanorod scatters light strongest when aligned parallel to the polarization of the incident field and weakest when aligned orthogonal to it. Between these two limiting cases the light scattered by the object varies as cos2 θ, which thus yields a direct measure of its average orientation during the exposure time, σ. Note that given the cylindrical symmetry of the trap and the fact that the exposure time, σ = 1 ms, is much larger than the angular (polar) relaxation time of the rod, τθ ∼ 50 μs, the interferometric part of the signal15,28
optical focus, where the trap exerts no control on the nanorod in the azimuthal dimension,10 rotational Brownian fluctuations of an electrostatically trapped rod are confined predominantly to the polar dimension. To experimentally demonstrate angular trapping of an anisometric nano-object, we employed silver nanorods synthesized with a net negative surface charge in aqueous solution and of the same nominal dimensions as in the calculation, as test objects.26,27 A suspension of rods was introduced into the electrostatic landscape by the capillary effect; the flow was arrested, and the dynamics of single trapped rods were imaged using laser scanning microscopy at a rate of 1 kHz, with an excitation wavelength of 671 nm (Figure 1a) and a half-wave plate in the beam path to set the direction of polarization of the linearly polarized incident beam (see the 5793
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Figure 3. Upper panels: normalized intensity (contrast) data, I, acquired at 1 kHz using parallel (blue, I∥) and perpendicular (red, I⊥) polarizations, for single nanorods, trapped by (a) a circular pocket of diameter 500 nm and rectangular pockets of dimensions (b) l = 200 nm, w = 100 nm and (c) l = 600 nm, w = 100 nm. (d) Control measurement on a nanorod immobilized on the substrate surface. Also shown in each case are SEMs of the trapping nanostructure (scale bars, 400 nm) and representative optical images in each polarization. The lower panels present angular density distributions, P(θ) (blue) and P(90° − θ) (red), derived from the temporal contrast data (see the Supporting Information). Shaded vertical regions in each case denote the offset θSNR ≈ 12° due to noise in the measurement (see the Supporting Information).
exposure time; furthermore, the value of c can be quantitatively related to the stiffness of trapping in a harmonic angular confining potential, as described below.10 Figure 3 demonstrates that experimental values of c increase progressively, beginning with 1 for the limiting case of a disk-shaped trap of aspect ratio 1 (rod has no preferred orientation) and attaining a maximum value of c = 66 for nanorod attached to the surface (see inset, Figure 3d). Since under thermal equilibrium the time averages of the two signals may be equated to their respective ensemble (thermal) averages, we have
averages out, leaving just the scattered intensity in the measured signal (Supporting Information). We further point out that the optical field here is used solely for imaging purposes, at an incident power of ∼1 W/cm2, where the lightinduced torque on the nanorod and any resulting influence on its dynamics is utterly negligible. Temporal intensities of trapped nanorods, recorded at the rate of 1 kHz over a period of ∼1 s, with incident polarizations parallel and perpendicular to the trap axis, were converted to angular probability density distributions to obtain a qualitative picture of the angular dynamics of a trapped nanorod (Supporting Information). Figure 3 displays measured probability densities, P(θ) (parallel excitation, blue histogram) and P(90° − θ) (perpendicular excitation, red histogram), for representative rods in traps of various geometries. While the angular probability density distributions for trapping in a disk potential are essentially flat (Figure 3a), those for cigar potentials show distinct peaks close to θ = 0° (Figures 3b,c), similar to the case of a nanorod immobilized on the substrate surface (Figure 3d). This provides compelling evidence of the ability of a shape-matched electrostatic fluidic trap to levitate and orient an anisometric nano-object. The histograms display distinct offsetsof the order of 15°from the expected most probable orientation of the rod at θ = 0° (Figure 3b−d); this arises from the measurement conditions and consists of two contributions: (1) the signal-to-noise ratio, SNR ∼ 60, and (2) time-averaging of the angular motion (i.e., σ ≫ τθ), the effects of which we have confirmed in Brownian dynamics simulations (see Supporting Information). The angular probability density measurement on a stationary nanorod immobilized on the slit surface further confirms that the dominant contribution to the offset is indeed owing to the SNR in the measurement: θSNR ≈ 12° in the present investigation (Figure 3d). To estimate the angular stiffness of trapping we focus on the ratio of the time-averaged intensities recorded for parallel and perpendicular polarizations, which we call the contrast-ratio, c = (⟨I∥⟩t/⟨I⊥⟩t). The use of time-averaged quantities here effectively eliminates inaccuracies arising from SNR and
c=
⟨I ⟩t ⟨I⊥⟩t
=
⟨cos2 θ ⟩T ⟨sin 2 θ cos2 ϕ⟩T
(1)
where we note that the signal in the perpendicular polarization carries the contribution of any azimuthal motion of the rod. The right-hand side of eq 1 can be evaluated analytically for a harmonic potential, and under the assumption of limited rotation in ϕ, is exclusively a function of the trap stiffness, kθ in the polar dimension. We find that the simple relation c ≅ (kθ/ (kBT)) relates the measured contrast ratio to the angular trapping stiffness (Supporting Information). In addition, since kθ⟨θ2⟩ = kBT from the equipartition theorem, the measured stiffness of confinement, kθ, of a rod yields an estimate of its root-mean-square angular displacement, θRMS, in the trap. Trap stiffnesses kθ ≈ 32 pNnm and 64 pNnm deduced for the nanorods shown in Figure 3b,c correspond to rms angular displacements, θRMS = 21° and 16°, respectively. These values are comparable with those achieved for optical alignment of smaller gold nanorods10 and may be improved by fine-tuning the geometry of the well or changing the surface chemistry of the rod. For example, working with a well of dimensions 200 × 600 nm and using nanorods with twice the surface charge density would place the mean angular displacement in the range of θRMS < 7°. We point out that the experimentally measured trap stiffnesses are higher than those predicted by the free energy calculations; for example, for the l = 600 nm and w = 100 nm case, the value deduced from the experiment is kθ ≈ 5794
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14kBT (Figure 3c), while the calculation predicts kθ ≈ 9kBT (Figure 2c); since the angular stiffness is linear in the charge of the object, tuning the charge densities and accounting for the true shape of both the nanorod and potential landscape in the calculation (Figure 2a) would enhance the agreement with the experiment. Nonetheless, the theory correctly captures the qualitative trends in the experiment and unequivocally establishes trap morphology as a tool to manipulate the orientation of single levitating nanorods. Additional factors that permit us to tune the trap performance, for example, the depth of the well (ΔF), the stiffness of the potential (kθ), and the relaxation time of the rod (τθ), include the solution ionic strength (
