Letter pubs.acs.org/NanoLett
Light-Assisted, Templated Self-Assembly of Gold Nanoparticle Chains Eric Jaquay,† Luis Javier Martínez,†,§ Ningfeng Huang,† Camilo A. Mejia,§ Debarghya Sarkar,† and Michelle L. Povinelli*,† †
Ming Hsieh Department of Electrical Engineering and §Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, United States S Supporting Information *
ABSTRACT: We experimentally demonstrate the technique of light-assisted, templated self-assembly (LATS) to trap and assemble 200 nm diameter gold nanoparticles. We excite a guided-resonance mode of a photonic-crystal slab with 1.55 μm laser light to create an array of optical traps. Unlike our previous demonstration of LATS with polystyrene particles, we find that the interparticle interactions play a significant role in the resulting particle patterns. Despite a two-dimensionally periodic intensity profile in the slab, the particles form onedimensional chains whose orientations can be controlled by the incident polarization of the light. The formation of chains can be understood in terms of a competition between the gradient force due to the excitation of the mode in the slab and optical binding between particles. KEYWORDS: Optical trapping, self-assembly, optical binding, photonic crystal, optical manipulation, plasmonics
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slab is two-dimensionally periodic, the assembled gold particles form one-dimensionally periodic chains. The orientation of the chains, which may contain as many as 15 particles, can be rotated with the incident laser polarization. We observe that interparticle interactions result in a self-stabilization effect; particles in chains remain trapped for much longer than isolated particles. Our results suggest that the emergence of 1D periodic patterns within a 2D periodic optical potential can be understood in terms of a competition between particletemplate and particle-particle interactions. The system is shown schematically in Figure 1. Light is incident from below on a photonic crystal slab, which consists of a silicon device layer patterned with a periodic array of holes. For certain laser wavelengths, the incident light will excite a spatially extended mode in the slab called a guided resonance mode.25 Such modes have strong electromagnetic field intensities that decay exponentially away from the upper surface of the slab. The gradient in the electric field intensity attracts particles in solution toward the slab, which serves as a template for assembly.8 We designed, fabricated, and characterized a photonic crystal template for use in the current experiment. Figure 2a shows a scanning electron micrograph of the device, which contains a square lattice of holes in a 250 nm thick silicon device layer. The lattice constant a is 780 nm, and the hole radii are r = 0.106a = 82.5 nm and 0.086a = 67 nm. The lateral extent of the
ear-field optical trapping uses the strong electromagnetic gradients near dielectric microphotonic structures for low-power, integrated manipulation of nanoscale objects.1−7 While much previous work has studied single-particle trapping, the trapping of multiple particles in extended, periodic arrays suggests the exciting possibility of creating synthetic nanomaterials “from the bottom up.” In recent work, we have demonstrated a near-field, microphotonic trapping technique capable of assembling a square array of over 100 dielectric particles on demand.8 Our method, called light-assisted, templated self-assembly (LATS), uses a photonic-crystal slab to resonantly enhance an incident laser beam, forming a 2D array of strong, closely spaced optical traps. We have demonstrated the controlled assembly and release of regular, defect-free arrays of particles. Moreover, calculations predict that the lattice structure and basis of the array can be reconfigured by changing the incident laser wavelength.9 It is natural to ask whether the LATS technique can be extended to form more complex structures, such as metallic or mixed metallo-dielectric10 systems. Such structures are of great interest for applications such as plasmonics and metamaterials11−15 and can potentially be extended to enable multiplexed, on-chip biological trapping and analysis.3,16−18 For metallic particles, however, it is unknown whether and how the types of interparticle interactions observed in template-free systems19−24 change the nature of the LATS process. In this paper, we observe dramatic effects of interparticle interactions in LATS experiments on gold nanoparticles, resulting in the assembly of completely different nanoparticle patterns. While the template provided by the photonic crystal © 2014 American Chemical Society
Received: June 4, 2014 Revised: August 19, 2014 Published: August 25, 2014 5184
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respect to the x-direction. The electric field intensity is largely concentrated in the holes in both cases. Assembly experiments were carried out in a microfluidic chamber filled with 200 nm diameter gold nanoparticles, using a laser power of 64 mW. The chamber was less than 1 μm high to minimize hydrodynamic effects.26 (See Methods for details of the chamber fabrication.) Figure 3 shows results from a typical experiment. Unlike our previous results for polystyrene particles, the trapped gold particles do not form close-packed arrays. Instead, we observe the formation of chains. In each panel of Figure 3, the incident light polarization is indicated by red arrows. In Figure 3a, the polarization is aligned with a diagonal of the square lattice. Two chains are clearly visible, which are oriented at 90° with respect to the incident polarization. When the polarization is aligned with the nearest-neighbor direction of the square lattice (Figure 3b), chains form along both diagonals. For a polarization aligned with the other diagonal of the square lattice (Figure 3c), chains are again observed perpendicular to the polarization. Upon blocking the beam, the particles immediately diffuse back into solution. Detuning of the trapping wavelength by ±1 nm (comparable to the fwhm of the resonance) also results in release of trapped particles. The measured stiffness for trapped particles had an average value of 66 pN nm−1 W−1, which is more than an order of magnitude greater than previous experiments with polystyrene particles.8 (See Methods for details.) The formation of 1D chains within the 2D-periodic near field of the photonic crystal slab indicates that interparticle interactions are playing a strong role in the observed behavior. To quantify the process of chain formation and reconfiguration, we recorded video of an assembly experiment. We counted the number of trapped particles in each video frame that were in a chain of at least three particles. Untrapped particles, trapped particles that were isolated, and trapped particles that had just one nearest neighbor were not counted. These results are shown in Figure 4, and the full video is available as Video 1 in the Supporting Information. At the beginning of the experiment, the polarization is at −45° with respect to the x-direction, as shown in the first pane of the figure. The number of particles trapped in chains oriented at 90° with respect to the polarization increases quickly (gray line), whereas particles in chains that are aligned with the polarization are observed only occasionally (black line). The initial rate of chain formation is limited by delivery of particles to the trapping volume and can be decreased by using a solution with a higher particle concentration. The fluctuations in particle number are due to trapping and untrapping of particles with time. The polarization is then rotated by 45° to align with the xdirection of the lattice. While the original chains largely persist, we observe chains forming along the opposite diagonal. Finally, the polarization is rotated another 45°, and immediately we notice that the original chains disappear, whereas the newer chains persist. We can thus control the orientation of chains by changing the polarization of the incident light. The relationship between incident light polarization and chain direction was repeatable across multiple experiments recorded on different days. These results are summarized in Table 1, which represents data taken from more than 14,000 frames. Since the videos were recorded in time-lapse fashion at one frame per second, the table represents almost 4 h of data. At no time did we observe the formation of 2D clusters, despite the extended, 2D periodic nature of the resonant mode of the
Figure 1. Schematic view of LATS. Normally incident light excites a mode in the slab whose evanescent decay attracts particles toward the slab.
Figure 2. Silicon photonic crystal device. (a) Scanning electron micrograph of the device used in the experiments. The scale bar represents 1 μm. (b) Measured transmission spectrum of the device. (c) Mode profile (E2) on resonance for x-polarized incident light calculated using 3D-FDTD. The circles represent the positions of the holes. (d) E2 for light polarized at +45° with respect to the x-axis.
patterned photonic crystal region was 50 μm × 50 μm. The device was designed to support a doubly degenerate, TE-like mode near 1.55 μm. The measured transmission spectrum of the device with x-polarized light is shown in Figure 2b. The dip in the transmission spectrum represents the excitation of the guided resonance mode. A quality factor Q of approximately 880 was obtained by fitting the spectrum to a Fano-resonance line shape. Figure 2c shows the electric field intensity profile (E2) for x-polarized incident light, which was calculated using a 3D finite-difference time domain (FDTD) simulation. The field profile for y-polarized incident light is rotated by 90°. Figure 2d shows the same simulation with light polarized at +45° with 5185
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Figure 3. Assembly of nanoparticle chains. (a) The incident light is initially polarized at −45° with respect to the x-axis, as indicated by the red arrow. (b) The polarization is rotated to align with the x-axis. (c) The polarization is rotated to +45°.
written in a circular pattern with a 50 μm diameter, each having the same lattice parameters. In all cases we observed similar behavior. For the specific device reported above in Figure 3, trapping of particles in chains was observed for power levels between 30 and 200 mW. To probe the effects of interparticle interactions on trapping stability, we analyzed the length of time that particles remained trapped. Figure 5a shows the results for particles that were part of chains. Blue circles indicate trapping sites that were occupied by a particle in a chain at any point during the video, and the colorbar indicates the maximum length of time, in seconds, that the site remained occupied. The video (available as video 2 in the Supporting Information) was 2000 frames in total. Sites near the center of chains had the longest occupation times, reflecting the fact that chains tend to grow outward from the center. Figure 5b shows results for particles that were not part of chains. The maximum time that a site was continuously occupied by a particle not in a chain was 255 s, much shorter than the 1915 s value observed for particles in chains in Figure 5a. The average value over all trapping sites was also much shorter for particles not in chains than for particles in chains (12 vs 180 s, respectively). This trend held across several videos whenever the polarization was aligned with a diagonal of the lattice. We conclude that the chains of gold particles are selfstabilizing; particles that join chains remain stably trapped for longer than isolated particles trapped elsewhere on the template. Our experimental results suggest that pattern formation (e.g., the emergence of particle chains) arises from the competition between particle-template and particle-particle interactions. A calculation of the optical forces acting on a single particle (see Supporting Information Figure S1) predicts that each hole in the template is a stable trapping site, and that the optical field pulls the metallic particle down into the hole. Absent any interparticle interactions, we would expect a regular, closepacked square lattice of particles to form. Interparticle interactions change this behavior. Given an initially trapped particle, a nearby particle in solution will experience optical forces not only due to the template but also due to the scattered field of the first particle. This interparticle interaction (similar to “optical binding”19,21,27−30) will influence the trapping site in which the second particle is most likely to settle. Full numerical calculations of multiparticle trapping dynamics are computationally prohibitive and beyond the scope of this paper. However, we can gain some insight from a simplified model, which calculates the interparticle interactions
Figure 4. Chain formation as a function of polarization angle. The red arrows indicate the incident polarization, and the black and gray lines represent the number of particles in chains with orientations indicated in the legend. Vertical, dashed lines represent the time at which the polarization was changed.
Table 1. Average Number of Particles Trapped in Chains along Different Orientations as a Function of Incident Polarizationa
a
The average is taken over approximately four hours of video.
photonic crystal slab. In each experiment, the initial arrangement of trapped particles was seemingly random, but eventually the pattern collapsed into a 1D chain or chains. We note that chain formation was observed in a variety of devices and experimental conditions. In addition to the square lattice with perturbed holes along alternating diagonals reported here, we also observed chain formation in a square lattice with the same lattice constant and uniform hole sizes. The behavior was also robust to total device size. We fabricated devices that were 100 μm × 100 μm, and devices that were 5186
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systems.10,23 An understanding of the physics of such strongly coupled, multiparticle systems may even yield insight into other cases of pattern formation within a 2D periodic potential, such as the formation of defects within layer-by-layer atomic growth methods. Methods. Fabrication. The photonic-crystal device consists of a square lattice of holes etched into a SOI wafer with a 3 μm thick buried oxide layer. Standard e-beam lithography and etching techniques were used; full details are provided elsewhere.8 The photonic crystal sample is mounted on a circular glass slide and inserted in a rotary stage. The sample is covered with a solution of 200 nm diameter gold particles in a citrate buffer (Sigma-Aldrich) to which 1% Triton-X was added to minimize particle stiction to the sample surface. On a second glass slide, an open-topped microfluidic chamber (5 mm × 5 mm) was fabricated in a 500 nm layer of PDMS using photolithography and lift-off. The PDMS chamber was pressed on to the sample and sealed inside the rotary stage. Optical Setup. A Santec tunable laser with a tuning range from 1500 to 1620 nm was connected to an erbium-doped fiber amplifier. An adjustable, neutral-density filter and polarizationcontrol optics were used to control the power and polarization of the beam. A fiber-to-free-space collimator directed the beam to a f = 30 mm achromatic doublet lens, which focused the beam onto the top surface of the sample from the back side. A 20× objective was used in conjunction with a beam splitter to collect the light from the top surface and to image the particle motion on a CMOS camera. Prior to each self-assembly experiment, the transmission was measured in cross-polarization mode, and the wavelength of the transmission peak was identified. The laser was then tuned to the peak wavelength to carry out light-assisted self-assembly. Stiffness Analysis. After the assembly of a cluster, we recorded videos with a fixed exposure time of 33 ms at 25 fps. Videos were 600 or more frames in length. The coarse positions of the particles were obtained using the scale-space blob detection algorithm31 and refined by calculating the brightness weighted centroid proposed by Crocker and Grier,32 enabling subpixel positional accuracy. The measured variances were corrected for motion blur due to the finite integration time of the camera and for the measured value of the diffusion coefficient.33 We used the equipartition theorem to estimate the stiffness of our traps.8 The power per trap was taken to be 11.9 μW, which represents the average value within the 1/e2 radius of the Gaussian beam intensity. Stability of Trapped Particles. We processed a time-lapse video that was 1990 frames in length, taken at a rate of 1 frame per second, and thus representing more than 30 min of trapping time. During the entire video, the polarization was aligned with a diagonal of the square lattice. For each frame and for each trapped particle, it was determined whether or not that particle was part of a chain.
Figure 5. Stability of trapped particles. (a) Maximum length of time (in seconds) per trap site that particles in chains remain trapped. (b) Maximum length of time per trap site that particles not in chains remained trapped. Blue circles indicate trap sites that were occupied at any point during the video.
due to an incident plane wave in water (see Supporting Information). The model predicts that given an initially trapped particle, interparticle interactions favor the nearest-neighbor sites perpendicular to the polarization direction, which is in agreement with experiment. In summary, we have presented the first demonstration of the LATS method for self-assembly of gold nanoparticles. We observe that strong interparticle interactions lead to the emergence of self-stabilizing, 1D particle chains within the 2D periodic potential of the optical field. The emergence of nanoparticle patterns due to cooperative behavior is an intriguing area for future research. Because both particletemplate and particle-particle interactions scale with incident intensity, these competing effects are fundamentally inseparable. Exploration of how the template might be redesigned to give rise to other nanoparticle patterns (such as regular, 2D arrays) is ongoing in our laboratory and is particularly intriguing in the context of mixed metal/dielectric particle
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Additional figures and video clips showing the assembly processes. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author
*E-mail: [email protected]. 5187
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Present Address
(28) Mohanty, S.; Andrews, J.; Gupta, P. Opt. Express 2004, 12, 2746−2753. (29) Mellor, C. D.; Fennerty, T. A.; Bain, C. D. Opt. Express 2006, 14, 10079−10088. (30) Dholakia, K.; Zemánek, P. Rev. Mod. Phys. 2010, 82, 1767− 1791. (31) Lindeberg, T. Scale-space theory in computer vision; Springer: New York, 1993. (32) Crocker, J. C.; Grier, D. G. J. Colloid Interface Sci. 1996, 179, 298−310. (33) Wong, W. P.; Halvorsen, K. Opt. Express 2006, 14, 12517− 12531.
Laboratoire Aimé Cotton, École Normale Supérieure de Cachan, CNRS UPR 3321, Université Paris Sud, 91405 Orsay, France. §
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank Mia Ferrera Wiesenthal for rendering the schematic in Figure 1. This project was funded by an Army Research Office PECASE Award under Grant 56801-MS-PCS. Computation for work described in this paper was supported by the University of Southern California Center for HighPerformance Computing and Communications.
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REFERENCES
(1) Kawata, S.; Tani, T. Opt. Lett. 1996, 21, 1768−1770. (2) Barth, M.; Benson, O. Appl. Phys. Lett. 2006, 89, 253114. (3) Yang, A. H. J.; Moore, S. D.; Schmidt, B. S.; Klug, M.; Lipson, M.; Erickson, D. Nature 2009, 457, 71−75. (4) Lin, S.; Schonbrun, E.; Crozier, K. Nano Lett. 2010, 10, 2408− 2411. (5) Mandal, S.; Serey, X.; Erickson, D. Nano Lett. 2010, 10, 99−104. (6) Descharmes, N.; Dharanipathy, U. P.; Diao, Z.; Tonin, M.; Houdre, R. Lab Chip 2013, 13, 3268−3274. (7) Renaut, C.; Cluzel, B.; Dellinger, J.; Lalouat, L.; Picard, E.; Peyrade, D.; Hadji, E.; de Fornel, F. Sci. Rep. 2013, 3, 2290. (8) Jaquay, E.; Martínez, L. J.; Mejia, C. A.; Povinelli, M. L. Nano Lett. 2013, 13, 2290−2294. (9) Mejia, C. A.; Dutt, A.; Povinelli, M. L. Opt. Express 2011, 19, 11422−11428. (10) Mejia, C. A.; Huang, N.; Povinelli, M. L. Opt. Lett. 2012, 37, 3690−3692. (11) Auguié, B.; Barnes, W. L. Phys. Rev. Lett. 2008, 101, 143902. (12) Auguié, B.; Bendaña, X. M.; Barnes, W. L.; García de Abajo, F. J. Phys. Rev. B 2010, 82, 155447. (13) Wong, H. M. K.; Righini, M.; Gates, J. C.; Smith, P. G. R.; Pruneri, V.; Quidant, R. Appl. Phys. Lett. 2011, 99, 061107−3. (14) Slaughter, L. S.; Willingham, B. A.; Chang, W.-S.; Chester, M. H.; Ogden, N.; Link, S. Nano Lett. 2012, 12, 3967−3972. (15) Edel, J. B.; Kornyshev, A. A.; Urbakh, M. ACS Nano 2013, 7, 9526−9532. (16) Roxworthy, B. J.; Johnston, M. T.; Lee-Montiel, F. T.; Ewoldt, R. H.; Imoukhuede, P. I.; Toussaint, K. C., Jr. PLoS One 2014, 9, e93929. (17) Soltani, M.; Lin, J.; Forties, R. A.; Inman, J. T.; Saraf, S. N.; Fulbright, R. M.; Lipson, M.; Wang, M. D. Nat. Nanotechnol. 2014, 9, 448−452. (18) Al Balushi, A. A.; Gordon, R. ACS Photonics 2014, 1, 389−393. (19) Taylor, J. M.; Wong, L. Y.; Bain, C. D.; Love, G. D. Opt. Express 2008, 16, 6921−6929. (20) Wong, L.; Bain, C. In Optical trapping and binding in evanescent optical landscapes; SPIE NanoScience+Engineering; International Society for Optics and Photonics, San Diego, California, 2009; pp 74001F−74001F-10. (21) Demergis, V.; Florin, E.-L. Nano Lett. 2012, 12, 5756−5760. (22) Yan, Z.; Shah, R. A.; Chado, G.; Gray, S. K.; Pelton, M.; Scherer, N. F. ACS Nano 2013, 7, 1790−1802. (23) Yan, Z.; Manna, U.; Qin, W.; Camire, A.; Guyot-Sionnest, P.; Scherer, N. F. J. Phys. Chem. Lett. 2013, 4, 2630−2636. (24) Yan, Z.; Gray, S. K.; Scherer, N. F. Nat. Commun. 2014, 5, 4751. (25) Fan, S.; Joannopoulos, J. D. Phys. Rev. B 2002, 65, 235112. (26) Donner, J. S.; Baffou, G.; McCloskey, D.; Quidant, R. ACS Nano 2011, 5, 5457−5462. (27) Burns, M. M.; Fournier, J.-M.; Golovchenko, J. A. Phys. Rev. Lett. 1989, 63, 1233−1236. 5188
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Light-Assisted, Templated Self-Assembly of Gold Nanoparticle Chains Eric Jaquay,† Luis Javier Martínez,†,§ Ningfeng Huang,† Camilo A. Mejia,§ Debarghya Sarkar,† and Michelle L. Povinelli*,† †
Ming Hsieh Department of Electrical Engineering and §Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, United States S Supporting Information *
ABSTRACT: We experimentally demonstrate the technique of light-assisted, templated self-assembly (LATS) to trap and assemble 200 nm diameter gold nanoparticles. We excite a guided-resonance mode of a photonic-crystal slab with 1.55 μm laser light to create an array of optical traps. Unlike our previous demonstration of LATS with polystyrene particles, we find that the interparticle interactions play a significant role in the resulting particle patterns. Despite a two-dimensionally periodic intensity profile in the slab, the particles form onedimensional chains whose orientations can be controlled by the incident polarization of the light. The formation of chains can be understood in terms of a competition between the gradient force due to the excitation of the mode in the slab and optical binding between particles. KEYWORDS: Optical trapping, self-assembly, optical binding, photonic crystal, optical manipulation, plasmonics
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slab is two-dimensionally periodic, the assembled gold particles form one-dimensionally periodic chains. The orientation of the chains, which may contain as many as 15 particles, can be rotated with the incident laser polarization. We observe that interparticle interactions result in a self-stabilization effect; particles in chains remain trapped for much longer than isolated particles. Our results suggest that the emergence of 1D periodic patterns within a 2D periodic optical potential can be understood in terms of a competition between particletemplate and particle-particle interactions. The system is shown schematically in Figure 1. Light is incident from below on a photonic crystal slab, which consists of a silicon device layer patterned with a periodic array of holes. For certain laser wavelengths, the incident light will excite a spatially extended mode in the slab called a guided resonance mode.25 Such modes have strong electromagnetic field intensities that decay exponentially away from the upper surface of the slab. The gradient in the electric field intensity attracts particles in solution toward the slab, which serves as a template for assembly.8 We designed, fabricated, and characterized a photonic crystal template for use in the current experiment. Figure 2a shows a scanning electron micrograph of the device, which contains a square lattice of holes in a 250 nm thick silicon device layer. The lattice constant a is 780 nm, and the hole radii are r = 0.106a = 82.5 nm and 0.086a = 67 nm. The lateral extent of the
ear-field optical trapping uses the strong electromagnetic gradients near dielectric microphotonic structures for low-power, integrated manipulation of nanoscale objects.1−7 While much previous work has studied single-particle trapping, the trapping of multiple particles in extended, periodic arrays suggests the exciting possibility of creating synthetic nanomaterials “from the bottom up.” In recent work, we have demonstrated a near-field, microphotonic trapping technique capable of assembling a square array of over 100 dielectric particles on demand.8 Our method, called light-assisted, templated self-assembly (LATS), uses a photonic-crystal slab to resonantly enhance an incident laser beam, forming a 2D array of strong, closely spaced optical traps. We have demonstrated the controlled assembly and release of regular, defect-free arrays of particles. Moreover, calculations predict that the lattice structure and basis of the array can be reconfigured by changing the incident laser wavelength.9 It is natural to ask whether the LATS technique can be extended to form more complex structures, such as metallic or mixed metallo-dielectric10 systems. Such structures are of great interest for applications such as plasmonics and metamaterials11−15 and can potentially be extended to enable multiplexed, on-chip biological trapping and analysis.3,16−18 For metallic particles, however, it is unknown whether and how the types of interparticle interactions observed in template-free systems19−24 change the nature of the LATS process. In this paper, we observe dramatic effects of interparticle interactions in LATS experiments on gold nanoparticles, resulting in the assembly of completely different nanoparticle patterns. While the template provided by the photonic crystal © 2014 American Chemical Society
Received: June 4, 2014 Revised: August 19, 2014 Published: August 25, 2014 5184
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respect to the x-direction. The electric field intensity is largely concentrated in the holes in both cases. Assembly experiments were carried out in a microfluidic chamber filled with 200 nm diameter gold nanoparticles, using a laser power of 64 mW. The chamber was less than 1 μm high to minimize hydrodynamic effects.26 (See Methods for details of the chamber fabrication.) Figure 3 shows results from a typical experiment. Unlike our previous results for polystyrene particles, the trapped gold particles do not form close-packed arrays. Instead, we observe the formation of chains. In each panel of Figure 3, the incident light polarization is indicated by red arrows. In Figure 3a, the polarization is aligned with a diagonal of the square lattice. Two chains are clearly visible, which are oriented at 90° with respect to the incident polarization. When the polarization is aligned with the nearest-neighbor direction of the square lattice (Figure 3b), chains form along both diagonals. For a polarization aligned with the other diagonal of the square lattice (Figure 3c), chains are again observed perpendicular to the polarization. Upon blocking the beam, the particles immediately diffuse back into solution. Detuning of the trapping wavelength by ±1 nm (comparable to the fwhm of the resonance) also results in release of trapped particles. The measured stiffness for trapped particles had an average value of 66 pN nm−1 W−1, which is more than an order of magnitude greater than previous experiments with polystyrene particles.8 (See Methods for details.) The formation of 1D chains within the 2D-periodic near field of the photonic crystal slab indicates that interparticle interactions are playing a strong role in the observed behavior. To quantify the process of chain formation and reconfiguration, we recorded video of an assembly experiment. We counted the number of trapped particles in each video frame that were in a chain of at least three particles. Untrapped particles, trapped particles that were isolated, and trapped particles that had just one nearest neighbor were not counted. These results are shown in Figure 4, and the full video is available as Video 1 in the Supporting Information. At the beginning of the experiment, the polarization is at −45° with respect to the x-direction, as shown in the first pane of the figure. The number of particles trapped in chains oriented at 90° with respect to the polarization increases quickly (gray line), whereas particles in chains that are aligned with the polarization are observed only occasionally (black line). The initial rate of chain formation is limited by delivery of particles to the trapping volume and can be decreased by using a solution with a higher particle concentration. The fluctuations in particle number are due to trapping and untrapping of particles with time. The polarization is then rotated by 45° to align with the xdirection of the lattice. While the original chains largely persist, we observe chains forming along the opposite diagonal. Finally, the polarization is rotated another 45°, and immediately we notice that the original chains disappear, whereas the newer chains persist. We can thus control the orientation of chains by changing the polarization of the incident light. The relationship between incident light polarization and chain direction was repeatable across multiple experiments recorded on different days. These results are summarized in Table 1, which represents data taken from more than 14,000 frames. Since the videos were recorded in time-lapse fashion at one frame per second, the table represents almost 4 h of data. At no time did we observe the formation of 2D clusters, despite the extended, 2D periodic nature of the resonant mode of the
Figure 1. Schematic view of LATS. Normally incident light excites a mode in the slab whose evanescent decay attracts particles toward the slab.
Figure 2. Silicon photonic crystal device. (a) Scanning electron micrograph of the device used in the experiments. The scale bar represents 1 μm. (b) Measured transmission spectrum of the device. (c) Mode profile (E2) on resonance for x-polarized incident light calculated using 3D-FDTD. The circles represent the positions of the holes. (d) E2 for light polarized at +45° with respect to the x-axis.
patterned photonic crystal region was 50 μm × 50 μm. The device was designed to support a doubly degenerate, TE-like mode near 1.55 μm. The measured transmission spectrum of the device with x-polarized light is shown in Figure 2b. The dip in the transmission spectrum represents the excitation of the guided resonance mode. A quality factor Q of approximately 880 was obtained by fitting the spectrum to a Fano-resonance line shape. Figure 2c shows the electric field intensity profile (E2) for x-polarized incident light, which was calculated using a 3D finite-difference time domain (FDTD) simulation. The field profile for y-polarized incident light is rotated by 90°. Figure 2d shows the same simulation with light polarized at +45° with 5185
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Figure 3. Assembly of nanoparticle chains. (a) The incident light is initially polarized at −45° with respect to the x-axis, as indicated by the red arrow. (b) The polarization is rotated to align with the x-axis. (c) The polarization is rotated to +45°.
written in a circular pattern with a 50 μm diameter, each having the same lattice parameters. In all cases we observed similar behavior. For the specific device reported above in Figure 3, trapping of particles in chains was observed for power levels between 30 and 200 mW. To probe the effects of interparticle interactions on trapping stability, we analyzed the length of time that particles remained trapped. Figure 5a shows the results for particles that were part of chains. Blue circles indicate trapping sites that were occupied by a particle in a chain at any point during the video, and the colorbar indicates the maximum length of time, in seconds, that the site remained occupied. The video (available as video 2 in the Supporting Information) was 2000 frames in total. Sites near the center of chains had the longest occupation times, reflecting the fact that chains tend to grow outward from the center. Figure 5b shows results for particles that were not part of chains. The maximum time that a site was continuously occupied by a particle not in a chain was 255 s, much shorter than the 1915 s value observed for particles in chains in Figure 5a. The average value over all trapping sites was also much shorter for particles not in chains than for particles in chains (12 vs 180 s, respectively). This trend held across several videos whenever the polarization was aligned with a diagonal of the lattice. We conclude that the chains of gold particles are selfstabilizing; particles that join chains remain stably trapped for longer than isolated particles trapped elsewhere on the template. Our experimental results suggest that pattern formation (e.g., the emergence of particle chains) arises from the competition between particle-template and particle-particle interactions. A calculation of the optical forces acting on a single particle (see Supporting Information Figure S1) predicts that each hole in the template is a stable trapping site, and that the optical field pulls the metallic particle down into the hole. Absent any interparticle interactions, we would expect a regular, closepacked square lattice of particles to form. Interparticle interactions change this behavior. Given an initially trapped particle, a nearby particle in solution will experience optical forces not only due to the template but also due to the scattered field of the first particle. This interparticle interaction (similar to “optical binding”19,21,27−30) will influence the trapping site in which the second particle is most likely to settle. Full numerical calculations of multiparticle trapping dynamics are computationally prohibitive and beyond the scope of this paper. However, we can gain some insight from a simplified model, which calculates the interparticle interactions
Figure 4. Chain formation as a function of polarization angle. The red arrows indicate the incident polarization, and the black and gray lines represent the number of particles in chains with orientations indicated in the legend. Vertical, dashed lines represent the time at which the polarization was changed.
Table 1. Average Number of Particles Trapped in Chains along Different Orientations as a Function of Incident Polarizationa
a
The average is taken over approximately four hours of video.
photonic crystal slab. In each experiment, the initial arrangement of trapped particles was seemingly random, but eventually the pattern collapsed into a 1D chain or chains. We note that chain formation was observed in a variety of devices and experimental conditions. In addition to the square lattice with perturbed holes along alternating diagonals reported here, we also observed chain formation in a square lattice with the same lattice constant and uniform hole sizes. The behavior was also robust to total device size. We fabricated devices that were 100 μm × 100 μm, and devices that were 5186
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systems.10,23 An understanding of the physics of such strongly coupled, multiparticle systems may even yield insight into other cases of pattern formation within a 2D periodic potential, such as the formation of defects within layer-by-layer atomic growth methods. Methods. Fabrication. The photonic-crystal device consists of a square lattice of holes etched into a SOI wafer with a 3 μm thick buried oxide layer. Standard e-beam lithography and etching techniques were used; full details are provided elsewhere.8 The photonic crystal sample is mounted on a circular glass slide and inserted in a rotary stage. The sample is covered with a solution of 200 nm diameter gold particles in a citrate buffer (Sigma-Aldrich) to which 1% Triton-X was added to minimize particle stiction to the sample surface. On a second glass slide, an open-topped microfluidic chamber (5 mm × 5 mm) was fabricated in a 500 nm layer of PDMS using photolithography and lift-off. The PDMS chamber was pressed on to the sample and sealed inside the rotary stage. Optical Setup. A Santec tunable laser with a tuning range from 1500 to 1620 nm was connected to an erbium-doped fiber amplifier. An adjustable, neutral-density filter and polarizationcontrol optics were used to control the power and polarization of the beam. A fiber-to-free-space collimator directed the beam to a f = 30 mm achromatic doublet lens, which focused the beam onto the top surface of the sample from the back side. A 20× objective was used in conjunction with a beam splitter to collect the light from the top surface and to image the particle motion on a CMOS camera. Prior to each self-assembly experiment, the transmission was measured in cross-polarization mode, and the wavelength of the transmission peak was identified. The laser was then tuned to the peak wavelength to carry out light-assisted self-assembly. Stiffness Analysis. After the assembly of a cluster, we recorded videos with a fixed exposure time of 33 ms at 25 fps. Videos were 600 or more frames in length. The coarse positions of the particles were obtained using the scale-space blob detection algorithm31 and refined by calculating the brightness weighted centroid proposed by Crocker and Grier,32 enabling subpixel positional accuracy. The measured variances were corrected for motion blur due to the finite integration time of the camera and for the measured value of the diffusion coefficient.33 We used the equipartition theorem to estimate the stiffness of our traps.8 The power per trap was taken to be 11.9 μW, which represents the average value within the 1/e2 radius of the Gaussian beam intensity. Stability of Trapped Particles. We processed a time-lapse video that was 1990 frames in length, taken at a rate of 1 frame per second, and thus representing more than 30 min of trapping time. During the entire video, the polarization was aligned with a diagonal of the square lattice. For each frame and for each trapped particle, it was determined whether or not that particle was part of a chain.
Figure 5. Stability of trapped particles. (a) Maximum length of time (in seconds) per trap site that particles in chains remain trapped. (b) Maximum length of time per trap site that particles not in chains remained trapped. Blue circles indicate trap sites that were occupied at any point during the video.
due to an incident plane wave in water (see Supporting Information). The model predicts that given an initially trapped particle, interparticle interactions favor the nearest-neighbor sites perpendicular to the polarization direction, which is in agreement with experiment. In summary, we have presented the first demonstration of the LATS method for self-assembly of gold nanoparticles. We observe that strong interparticle interactions lead to the emergence of self-stabilizing, 1D particle chains within the 2D periodic potential of the optical field. The emergence of nanoparticle patterns due to cooperative behavior is an intriguing area for future research. Because both particletemplate and particle-particle interactions scale with incident intensity, these competing effects are fundamentally inseparable. Exploration of how the template might be redesigned to give rise to other nanoparticle patterns (such as regular, 2D arrays) is ongoing in our laboratory and is particularly intriguing in the context of mixed metal/dielectric particle
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Additional figures and video clips showing the assembly processes. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author
*E-mail: [email protected]. 5187
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Present Address
(28) Mohanty, S.; Andrews, J.; Gupta, P. Opt. Express 2004, 12, 2746−2753. (29) Mellor, C. D.; Fennerty, T. A.; Bain, C. D. Opt. Express 2006, 14, 10079−10088. (30) Dholakia, K.; Zemánek, P. Rev. Mod. Phys. 2010, 82, 1767− 1791. (31) Lindeberg, T. Scale-space theory in computer vision; Springer: New York, 1993. (32) Crocker, J. C.; Grier, D. G. J. Colloid Interface Sci. 1996, 179, 298−310. (33) Wong, W. P.; Halvorsen, K. Opt. Express 2006, 14, 12517− 12531.
Laboratoire Aimé Cotton, École Normale Supérieure de Cachan, CNRS UPR 3321, Université Paris Sud, 91405 Orsay, France. §
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank Mia Ferrera Wiesenthal for rendering the schematic in Figure 1. This project was funded by an Army Research Office PECASE Award under Grant 56801-MS-PCS. Computation for work described in this paper was supported by the University of Southern California Center for HighPerformance Computing and Communications.
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REFERENCES
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