Directed Placement of Gold Nanorods Using a Removable Template

Aug 19, 2011 - (c) Cross-sectional profile perpendicular to the structures along the red and blue lines shown in panels a and b, respectively. The str...
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LETTER pubs.acs.org/NanoLett

Directed Placement of Gold Nanorods Using a Removable Template for Guided Assembly Felix Holzner,†,‡ Cyrill Kuemin,†,‡ Philip Paul,† James L. Hedrick,§ Heiko Wolf,† Nicholas D. Spencer,‡ Urs Duerig,† and Armin W. Knoll*,† †

IBM Research—Zurich, S€aumerstrasse 4, 8803 R€uschlikon, Switzerland ETH Zurich, Laboratory for Surface Science and Technology, Department of Materials, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland § IBM Research—Almaden, 650 Harry Road, San Jose, California 95120, United States ‡

bS Supporting Information ABSTRACT: We have used a temperature sensitive polymer film as a removable template to position, and align, gold nanorods onto an underlying target substrate. Shape-matching guiding structures for the assembly of nanorods of size 80 nm  25 nm have been written by thermal scanning probe lithography. The nanorods were assembled into the guiding structures, which determine both the position and the orientation of single nanorods, by means of capillary interactions. Following particle assembly, the polymer was removed cleanly by thermal decomposition and the nanorods are transferred to the underlying substrate. We have thus demonstrated both the placement and orientation of nanorods with an overall positioning accuracy of ≈10 nm onto an unstructured target substrate. KEYWORDS: Scanning probe lithography, nanopatterning, gold nanorods, directed assembly, capillary assembly

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he controlled synthesis of nanoparticles in the form of spheres, rods, or wires has led to a variety of applications in a host of scientific research areas.1 3 Bottom up synthesis leads to monocrystalline nanoparticles and enables the fabrication of core shell structures.4 These structural properties often provide unique or superior performance of the particles in comparison to their top-down-fabricated counterparts. However, for integrated devices and other applications the precise placement and alignment of asymmetric nanoparticles relative to other functional structures on the substrate is crucial. A potential solution to this challenge is to use top-down methods to guide the assembly of nanoparticles. A high degree of accuracy has been achieved using scanning probes to manipulate surfaces in order to generate guiding forces5 10 or topographic constraints11 for the directed placement of molecules, proteins, and particles. More generally, directed assembly has been implemented using electrostatic,12 16 (bio-)chemical,17 magnetic,18,19 light-induced,20 or topography-induced21 25 guiding forces. Directional positioning of asymmetric particles like nanorods,26 nanowires,27 and carbon nanotubes28 has been demonstrated.29 In particular, dielectrophoretic forces were used to simultaneously achieve alignment and positioning of micrometer-long nanowires30 32 or single-walled carbon nanotubes.28 Scaling to smaller objects is challenging because entropic energies become comparable to the trapping energies.33 Capillary assembly using topographical guiding structures to impose additional geometrical constraints provide a possible solution of the problem. The method has been shown to work for r 2011 American Chemical Society

particle sizes down to 2 nm22 and on a single-particle level.21 25 Patterns in a thin resist layer exposing the substrate can be used to guide the assembly into functional sites on the target substrate.22 However, exposing the target substrate requires its surface properties to be compatible with the assembly process. This limitation can be overcome by separating the assembly substrate and the target substrate. The particles are assembled onto a soft template, which is optimized for the assembly process, and subsequently transferred in a printing step to a target substrate of choice.23 The assembly process can be optimized for the template surface, and high yields can be obtained.25 However, the printing step limits the positioning precision of the particles on the target substrate. Here we propose an alternative pathway to position and orient nanoscale particles on a target substrate by means of a removable assembly template. Gold nanorods are assembled into guiding structures within a polymer layer, which are written by thermal scanning-probe lithography (SPL). In a second step, the polymer film is thermally decomposed and the assembled nanorods transferred onto the target substrate, preserving both position and orientation. The guiding structures are written into a thermally sensitive poly(phthalaldehyde) (PPA) polymer film. The chemical composition of PPA is depicted in Figure 1a. The polymer breaks up Received: July 5, 2011 Revised: August 12, 2011 Published: August 19, 2011 3957

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Figure 1. Polymer structure and process flow. (a) Chemical structure of the polyphthalaldehyde polymer used. (b e) Process flow. (b) First, shape-matching guiding structures are patterned into a PPA thin film by thermal SPL. (c) Gold nanorods are positioned and aligned by capillary assembly. (d) The PPA template is removed by heating to ≈215 °C for 10 s. (e) As a result the nanorods are assembled with specific position and orientation on the bare target substrate.

into volatile monomer constituents via self-amplified decomposition34 and is fully decomposed at a temperature of 200 °C. This property plays a major role in the process flow shown schematically in Figure 1b e. In a first step, guiding structures for the assembly process are written using heated probes34,35 as schematically shown in Figure 1b. The patterns are defined to match the shape of the gold nanorods. The nanorods are assembled from a suspension using capillary assembly (see Figure 1c) at room temperature. After assembly, the dry substrate is heated to globally trigger the decomposition reaction (see Figure 1d). The polymer template is removed and the nanorods are transferred onto the substrate surface, their lateral position and orientation —as defined by the written guiding structures—being preserved. In this way, the polymer film acts as a removable template, which ensures that the (surface) conditions for the assembly process are independent from the surface properties of the underlying substrate. As a result, we achieve the precise and oriented positioning of gold nanorods onto arbitrary target substrates. For thermal SPL patterning a resistive heater in contact with the tip is heated to 700 °C. Due to the finite thermal resistance of the tip and the polymer, the polymer surface in contact with the tip reaches a temperature of ≈350 °C (see Supporting Information). At these conditions the decomposition process of the PPA is thermally triggered at microsecond time scales and complex 3D patterns can be written.34,35 Electrostatic actuation is used to pull the tip into contact from a rest position of ≈50 nm above the surface. The depth of the written pixels varies between 80 and 20 nm for loading forces of 60 20 nN, respectively. The force was applied for a duration of 15 μs, and the pixel writing rate was 5 kHz at a pixel pitch of 15 nm. The writing of an individual pixel creates a V-shaped void in the polymer film. If two or more neighboring pixels are written at a pixel pitch of 15 nm, the voids merge into a continuous groove. Figure 2a shows an example of a patterned field of 8  9 guiding structures in the PPA film. The total patterning time per

Figure 2. Patterning of guiding structures. (a) SFM topographical image of a field of guiding structures for the assembly process written by thermal SPL into a 90 nm thick PPA film. (b) Zoom into an individual structure marked in panel a. (c) Cross-sectional profile perpendicular to the structures along the red and blue lines shown in panels a and b, respectively. The structures have a different width, providing varying confinement to the positioning of the nanorods as indicated by the yellow circle. (d) Cross-sectional profile along the structure shown in panel b (green line). The arms are designed to have a length of nominally 270 nm, separated by a nominally 30 nm wide ridge. Each arm can accommodate three nanorods of nominal size 80 nm  25 nm as indicated by the yellow bars.

field was 65 s. A linear array of 20 similar fields was written at a field pitch of 30 μm. The depth of the guiding structures lies between 15 and 80 nm in the different fields. The individual structures consist of two straight arms, one arm has a fixed horizontal orientation and the other arm is rotated by 30°, 45°, 60°, 90°, 120°, 135°, and 150° from one column to the next. The top four rows are written with four pixel wide arms, the bottom four rows with one pixel wide arms. Figure 2b shows a zoom into the area marked by the white box in Figure 2a. The cross section of the wide (red line in Figure 2a) and narrow (blue line in Figure 2b) guiding structures is depicted in Figure 2c. The structures are ≈80 nm deep. They have a side-wall angle of 60°, which corresponds to the opening angle of our tips. To exclude imaging artifacts, the shape was verified in ex situ AFM experiments using ultrasharp probes. The wider structure has a flat profile at the bottom with the programmed width of 45 nm. 3958

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Figure 3. Assembly of gold nanorods by guided assembly using capillary interaction. (a) SFM tapping-mode phase image of a field of guiding structures filled with assembled gold nanorods. (b, c) Zoom in on the phase image shown in panel a. The control of orientation and position of the particles depends strongly on the width of the guiding structures. (d) SFM topography image of the assembly site marked in panel c, showing six assembled and aligned rods as targeted by the design. The red outline indicates the position of the nanorods determined by SEM after PPA evaporation.

Figure 2d shows a cross-sectional profile along the long axis of the guiding structure shown in Figure 2b. The programmed arm length of 270 nm is designed to fit three nanorods of size 80 nm  25 nm along the axis of each arm. High-yield assembly of nanoparticles into the guiding structures from a suspension requires exquisite control of the contact angle and the particle and surfactant concentrations.24 The measured contact angle of the template material to water of ≈63° for PPA is sufficient to allow dragging the solution across the template without unspecific deposition of particles. However, for highyield assembly the particle and surfactant concentrations are crucial. For the proof-of-principle experiment described here, we used a drying droplet of nanorod suspension to systematically increase the concentrations during the course of the experiment. The nanorod suspension was obtained from Nanopartz Inc. (Loveland, CO) and was adjusted to a concentration of 2  1011 particles/mL stabilized by the ionic surfactant CTAB (cetyltrimethylammonium bromide) at a concentration of 0.1 mM (see Supporting Information). The droplet contact line moved over the 20 written assembly fields. The initial assembly yield in the first fields was low, only a few rods being assembled per field. A high yield was obtained for the last three assembly fields, when the nanorod concentration was very high, close to drying of the droplet. Those fields had a depth of the guiding structures of ≈15 30 nm. This suggests that the assembly yield depends more critically on the particle and surfactant concentrations than on the depth of the guiding structures. Figure 3a shows a scanning force microscopy (SFM) tapping mode phase image of such a field after assembly of nanorods. A total of 483 nanorods were assembled within the guiding

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structures, 11 rods being deposited unspecifically on the flat surface next to the grooves. This particular field had a depth of only 20 ( 5 nm, and the assembled particles protruded by up to 10 nm above the surface. In the first four rows of wide guiding structures, nine nanorods were deposited on average in each structure, three more than targeted by the design. A zoom into the phase image showing nine wide structures is depicted in Figure 3b. The width of the structures measured at a depth of 10 nm in the SFM topography was ≈80 ( 20 nm, which led to a tilted and overcrowded assembly. A second zoom into an area containing narrow guiding structures is shown in Figure 3c. Here the grooves had a width of ≈35 ( 15 nm. The narrow grooves provide much better guiding for the assembly, resulting in wellaligned and -positioned nanorods. On average, four rods were assembled per structure. Figure 3d shows an SFM topography image of one of the guiding structures having a tilt angle of 150° and filled, as intended, with three nanorods per arm (the red line in Figure 3d indicates the particles’ position after polymer removal, which is discussed below). The example demonstrates that the nanorods can be aligned by the geometrical constraints of the guiding grooves. After assembly the sample was heated to ≈215 °C on a hot plate for 10 s. The low processing temperature and duration minimize the chance for thermally induced nanoparticle deformation.36 The polymer decomposition process can be optically inspected via a color change of the substrate. The thinning of the polymer film proceeds very uniformly over the entire substrate and is completed after less than 10 s. During the process the film does not break up into droplets, which indicates that there is effectively no liquid transition phase as the polymer decomposes into monomers from the glassy state. In other words, the decomposition process is triggered before or at the glass transition temperature of the polymer. This direct “sublimation” of the polymer film provides the basis of the high placement accuracy of the nanoparticles onto the underlying substrate. For a potential fabrication of future devices, it is crucial to remove the polymer template without residues, for example to establish electrical contact from a nanoobject to underlying electrodes. We used time-of-flight secondary ion mass spectrometry (ToF-SIMS) to study the effectiveness of the evaporation process. An untreated 70 nm thick PPA film on a silicon wafer was compared to the same sample heated to 215 °C. Figure 4a shows the average yield of positive ions for the untreated film and the heated film. The signal of the heated sample is shown 5 times amplified. For the untreated film, the most prominent fragments relate to the monomers and corresponding fragments as indicated in Figure 4a. The corresponding signals after evaporation of the PPA are for most atomic numbers below the noise level of ≈100 ion counts. The average count numbers of the two most prominent polymer peaks for the untreated film at 118 and 135 amu are 1.3  105 and 1.1  105, respectively. The corresponding signals for the heated sample are below the detection threshold. For a coarse estimation of the monolayer coverage, we therefore use the noise level as reference. Assuming a sampling depth of one monolayer, we obtain a residual coverage of less than 1  10 3 of a monolayer. More direct evidence for a clean removal of the polymer underneath the gold nanorods was obtained by measuring the electrical contact resistance using conductive SFM. A 40 nm thick TiN film and a 25 nm thick amorphous carbon layer were sputtered onto a silicon wafer and served as a conductive substrate. The carbon layer covering the TiN layer provides a 3959

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Figure 4. Efficiency of polymer removal and transfer of the assembled nanorods onto a target substrate. (a) ToF-SIMS result of positive ion yield measured on a PPA film on a silicon substrate and on the same substrate after thermal decomposition of the polymer, marked by black and red bars, respectively. The signal of the heated sample is amplified by a factor of 5. The monomer fragments corresponding to the major peaks are shown schematically. (b d) Conductive SFM measurements of a nanorod island after transfer from a 90 nm thick PPA film onto a carboncoated conductive substrate. Topographical (b) and current (c) image of the island. (d) Current as a function of approach distance and respective force for seven representative spots marked by crosses in panels b and c. The red and black curves were obtained on top of the island and on the substrate, respectively.

current-limiting serial resistance of 100 200 kΩ to the tip contact. A 90 nm thick PPA film was spin-cast onto the substrate, and gold nanorods were deposited by droplet drying. The sample was heated to 215 °C on a hot plate for 10 s and subsequently rinsed in deionized water to remove residual surfactant. Conductive SFM was performed using platinum silicide tips37,38 biased at 1 V to record force and current versus distance curves at each pixel position of the image, termed “force volume” mode (see Supporting Information). We note that single nanorods are very loosely bound to the surface and were pushed to the side or picked up by the tip in contact mode or in the force volume mode. However, islands of agglomerated nanorods were stable in the force volume imaging mode. The island shown in Figure 4c is two to three layers thick as inferred from the measured stepheights of ≈45 and ≈62 nm. The corresponding conduction image shown in Figure 4d was recorded at the maximal applied force of ≈150 nN. The current as a function of approach distance and applied force is shown for seven representative pixels in Figure 4e. On top of the island (red curves and crosses) the current reaches more then 15 μA, more than three times the maximum current of 5 μA on the carbon background (black curves and white crosses). Therefore, the series resistance of the tip to the island and the island to the substrate is smaller than the contact resistance of the tip to the carbon surface directly. The observation confirms that the polymer is removed cleanly, even between the gold particles and the substrate. Perhaps even more important than the clean removal of the polymer is the question on how much the removal process

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Figure 5. Evaluation of positioning accuracy. (a) SEM image after assembly and evaporation of the template film. (b) Zoom into the SEM image shown in panel a. The red lines mark the positions of the guiding structures written by thermal SPL as determined by the programmed pattern. The lines were registered relative to the SEM image using the entire assembly field. Histograms of (c) the orientation misalignment angle α and (d) of the off-axis displacement d, of the particles from the written grooves were measured. The standard deviations of α and d are 25.2° and 10.3 nm, respectively.

influences the position and orientation of the nanorods. For this purpose we examined the fields after transfer by scanning electron microscopy (SEM). An outline of the SEM image was generated and superimposed onto the SFM topography image, which was taken before polymer decomposition. Figure 3d shows the result of this procedure for this particular guiding structure, whereby the SEM outline is shown in red. Both the position and the orientation of the rods are conserved after polymer removal. This is all the more remarkable considering the fact that the guiding structure was only 20 nm deep. Therefore a total of ≈70 nm of polymer material was removed between particles and substrate. To quantify the positioning accuracy of the overall process, we analyzed the field featuring the highest assembly yield in more detail. Figure 5a displays a SEM micrograph of this field after template removal. Interestingly, the yield does not depend on the orientation of the grooves. We overlaid the target center line of the written grooves (red lines) with the SEM image; see Figure 5b. Some overfilling occurred due to the nonuniformity of the nanoparticles, for example, a rod of half the nominal size is seen in Figure 5b in the bottom right corner. As a measure of positioning accuracy, we determine the distance d of the nanorods’ geometric center to the groove’s center line. The positioning along the axis of the structures is not well-defined. This is due 3960

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Nano Letters to the facts that along the groove direction there is no confinement structure for the single particle (see Figure 2d) and, more importantly, that the nanorods are polydisperse. As a measure of orientational accuracy, we determined the angle α between the long axis of the nanorods and the center line. The histogram of α is shown in Figure 5c. It is maximum at zero degree misalignment and has a standard deviation of σα = 25.2°. The orientational guiding depends on the width of the grooves and the aspect ratio of 3:1 of the assembled particles. Taking into account the polydispersity and the low aspect ratio of the nanorods, the observed distribution is in accordance with the geometry of the written grooves. The histogram for d is shown in Figure 5d. The standard deviation of the normal distance is σd = 10.3 nm, which is less than the pixel pitch of 15 nm used for patterning the guiding structures. We attribute the high accuracy to the V-shape of the guiding grooves. In summary we demonstrate precise placement with defined orientation of gold nanorods on a target substrate using a polymer layer as a removable template to guide the assembly of the nanoobjects. The template renders the assembly process independent of the underlying substrate, which makes the overall process insensitive to the nature of the target substrate. The decomposition process of the template is very clean, as evidenced by the low resistivity connection of the metal nanorods to a conductive substrate. The PPA material requires only moderate decomposition temperatures, and therefore the integrity of the particles is not compromised during the transfer process. Finally, the transfer accomplished by the decomposition and evaporation of the template does not alter the position and orientation of the nanorods within the limits of the imaging resolution of ≈2 nm. The position accuracy of the nanoparticle placement including assembly and the transfer to the target substrate was determined to be on the order of 10 nm, less than half the particle diameter and less than the pixel resolution for writing the guiding structures. In addition, the orientational alignment of the nanorods did not depend on the orientation of the guiding structures, enabling an oriented placement over the entire angular range. For future applications, our SFM-based method enables high-resolution imaging and accurate detection of features on the target substrate prior to the patterning process using the same tip. Applying the removable template strategy opens up novel perspectives to register the guiding structures to precise locations of functional elements on the target substrate. Meeting a requirement for advanced photonic applications, the direct integration of asymmetric nanoparticles into devices with a high degree of control over particle position and orientation thus becomes feasible.39

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional details on materials and methods used. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the Swiss National Science Foundation (SNSF). The authors thank P. Rossbach from the

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Swiss Federal Laboratories for Materials Science and Technology (EMPA) for the ToF-SIMS measurements and fruitful discussions. The authors gratefully acknowledge NanoWorld AG for the supply of the beta platinum-silicide cantilevers. We thank Abu Sebastian for supplying the conductive substrates and for fruitful discussions and Michel Despont and Walter Riess for their support.

’ REFERENCES (1) Shipway, A.; Katz, E.; Willner, I. ChemPhysChem 2000, 1, 18–52. (2) Kamat, P. J. Phys. Chem. B 2007, 111, 2834–2860. (3) Stewart, M.; Anderton, C.; Thompson, L.; Maria, J.; Gray, S.; Rogers, J.; Nuzzo, R. Chem. Rev 2008, 108, 494–521. (4) Liu, K.; Zhao, N.; Kumacheva, E. Chem. Soc. Rev. 2011, 40, 656–671. (5) Liu, S.; Maoz, R.; Schmid, G.; Sagiv, J. Nano Lett. 2002, 2, 1055–1060. (6) Rolandi, M.; Suez, I.; Scholl, A.; Frechet, J. M. Angew. Chem., Int. Ed. 2007, 46, 7477. (7) Zachary, M.; Frechet, J. J. Am. Chem. Soc. 2005, 127, 8302–8303. (8) Martnez, R.; Martnez, J.; Chiesa, M.; Garcia, R.; Coronado, E.; Pinilla-Cienfuegos, E.; Tatay, S. Adv. Mater. 2010, 22, 588–591. (9) Wang, D.; Kodali, V. K.; Underwood, W. D., II; Jarvholm, J. E.; Okada, T.; Jones, S. C.; Rumi, M.; Dai, Z.; King, W. P.; Marder, S. R.; Curtis, J. E.; Riedo, E. Adv. Funct. Mater. 2009, 19, 3696–3702. (10) Paxton, W.; Spruell, J.; Stoddart, J. J. Am. Chem. Soc. 2009, 131, 6692–6694. (11) Shin, C.; Jeon, I.; Jeon, S.; Khim, Z. Appl. Phys. Lett. 2009, 94, 163107. (12) Prost, W.; Kruis, F.; Otten, F.; Nielsch, K.; Rellinghaus, B.; Auer, U.; Peled, A.; Wassermann, E.; Fissan, H.; Tegude, F. Microelectron. Eng. 1998, 41, 535–538. (13) Krinke, T.; Fissan, H.; Deppert, K.; Magnusson, M.; Samuelson, L. Appl. Phys. Lett. 2001, 78, 3708. (14) Jacobs, H.; Whitesides, G. Science 2001, 291, 1763. (15) Fudouzi, H.; Kobayashi, M.; Shinya, N. Adv. Mater. 2002, 14, 1649–1652. (16) Viallet, B.; Ressier, L.; Czornomaz, L.; Decorde, N. Langmuir 2010, 26, 4631–4634. (17) Gu, H.; Chao, J.; Xiao, S.; Seeman, N. Nature 2010, 465, 202–205. (18) Rungsawang, R.; da Silva, J.; Wu, C.; Sivaniah, E.; Ionescu, A.; Barnes, C.; Darton, N. Phys. Rev. Lett. 2010, 104, 255703. (19) Wolf, H.; Birringer, R. J. Appl. Phys. 2005, 98, 074303. (20) Urban, A.; Lutich, A.; Stefani, F.; Feldmann, J. Nano Lett. 2010, 10, 4794–4798. (21) Yin, Y.; Lu, Y.; Gates, B.; Xia, Y. J. Am. Chem. Soc. 2001, 123, 8718–8729. (22) Cui, Y.; Bj€ork, M.; Liddle, J.; S€onnichsen, C.; Boussert, B.; Alivisatos, A. Nano Lett. 2004, 4, 1093–1098. (23) Kraus, T.; Malaquin, L.; Schmid, H.; Riess, W.; Spencer, N.; Wolf, H. Nat. Nanotechnol. 2007, 2, 570–576. (24) Kuemin, C.; Cathrein Huckstadt, K.; L€ortscher, E.; Rey, A.; Decker, A.; Spencer, N.; Wolf, H. Adv. Mater. 2010, 22, 2804–2808. (25) Kuemin, C.; Stutz, R.; Spencer, N.; Wolf, H. Langmuir 2011, 27, 6305–6310. (26) Ahmed, W.; Kooij, E.; van Silfhout, A.; Poelsema, B. Nano Lett. 2009, 9, 3786–3794. (27) Huang, Y.; Duan, X.; Wei, Q.; Lieber, C. Science 2001, 291, 630. (28) Li, P.; Xue, W. Nanoscale Res. Lett. 2010, 5, 1072–1078. (29) Wang, M.; Gates, B. Mater. Today 2009, 12, 34–43. (30) Smith, P.; Nordquist, C.; Jackson, T.; Mayer, T.; Martin, B.; Mbindyo, J.; Mallouk, T. Appl. Phys. Lett. 2000, 77, 1399. (31) Li, M.; Bhiladvala, R.; Morrow, T.; Sioss, J.; Lew, K.; Redwing, J.; Keating, C.; Mayer, T. Nat. Nanotechnol. 2008, 3, 88–92. (32) Papadakis, S.; Hoffmann, J.; Deglau, D.; Chen, A.; Tyagi, P.; Gracias, D. Nanoscale 2011, 3, 10591065 3961

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(33) In thermodynamic equilibrium the free energy F of a particle in interaction with a trapping field can be written F = Uint TS, where Uint is the trapping potential and S is in essence the entropy of mixing of the untrapped particle in solution. For dielectrophoretic forces Uint scales with the volume of the particle. To capture a particle, Uint has to be significantly larger than the entropy term, which is on the order of kbT. (34) Coulembier, O.; Knoll, A.; Pires, D.; Gotsmann, B.; Duerig, U.; Frommer, J.; Miller, R.; Dubois, P.; Hedrick, J. Macromolecules 2010, 43, 572. (35) Knoll, A. W.; Pires, D.; Coulembier, O.; Dubois, P.; Hedrick, J. L.; Frommer, J.; Duerig, U. Adv. Mater. 2010, 22, 3361–3365. (36) Petrova, H.; Juste, J.; Pastoriza-Santos, I.; Hartland, G.; LizMarzan, L.; Mulvaney, P. Phys. Chem. Chem. Phys. 2006, 8, 814–821. (37) Bhaskaran, H.; Sebastian, A.; Despont, M. IEEE Trans. Nanotechnol. 2009, 8, 128–131. (38) Platinums silicide tips were supplied by NanoWorld AG, Switzerland. (39) Hennessy, K.; Badolato, A.; Winger, M.; Gerace, D.; Atat€ure, M.; Gulde, S.; F€alt, S.; Hu, E.; Imamoglu, A. Nature 2007, 445, 896–899.

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