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Self-Organization of Metal Nanoparticles in Light: ElectrodynamicsMolecular Dynamics Simulations and Optical Binding Experiments Patrick McCormack, Fei Han, and Zijie Yan J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b03188 • Publication Date (Web): 16 Jan 2018 Downloaded from http://pubs.acs.org on January 18, 2018

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The Journal of Physical Chemistry Letters

Self-Organization of Metal Nanoparticles in Light: Electrodynamics-Molecular Dynamics Simulations and Optical Binding Experiments Patrick McCormack,† Fei Han,† and Zijie Yan*

Department of Chemical and Biomolecular Engineering, Clarkson University, Potsdam, NY 13699, USA †

These authors contributed equally to this work

ACS Paragon Plus Environment

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ABSTRACT: Light-driven self-organization of metal nanoparticles (NPs) can lead to unique optical matter systems, yet simulation of such self-organization (i.e., optical binding) is a complex computational problem that increases non-linearly with system size. Here we show that a combined electrodynamics-molecular dynamics simulation technique can simulate the trajectories and predict stable configurations of silver NPs in optical fields. The simulated dynamic equilibrium of a two-NP system matches the probability density of oscillations for two optically bound NPs obtained experimentally. The predicted stable configurations for up to eight NPs are further compared to experimental observations of silver NP clusters formed by optical binding in a Bessel beam. All configurations are confirmed to form in real systems, including pentagonal clusters with five-fold symmetry. Our combined simulations and experiments have revealed a diverse optical matter system formed by anisotropic optical binding interactions, providing a new strategy to discover artificial materials.

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Novel electronic and photonic materials not only rely on the intrinsic properties of underlying constituents but also depend on the integration approach.1-2 Light can induce self-organization of microscopic particles into mesoscale clusters by harnessing their interparticle electrodynamic interactions.3-4 The particles scatter light and modify the incident field, causing interactions between the particles. If the interactions are strong, e.g., in an intense laser field, the particles can self-organize into specific configurations with well-defined interparticle separations. This optical phenomenon was first observed by Burns, Fournier, and Golovchenko in 1989.5 By trapping polystyrene microparticles on a glass surface using a line-shaped laser trap, they noticed that two trapped particles tended to maintain their separation at the integral multiples of the laser wavelength in the host medium – a behavior they termed “optical binding”5 while the optically bound particles were termed “optical matter”.6 Yet since then nearly all the experimental reports on optical binding have been focused on dielectric microparticles,3, 4 because the optical binding force depends on the scattering cross-section,3 which is usually too small for dielectric nanoparticles (NPs). Plasmonic metal NPs have stronger scattering and thus can show more significant optical binding interactions.7 Similar to molecular isomers with the same chemical formula but different atomic arrangements, metal NPs have shown the ability to self-organize into a great variety of photonic clusters (i.e., optical matter isomers) by optical binding.7-10 However, accurately predicting the optical matter isomers is not a trivial task. Due to the nature of multi-body and directional interactions, the complexity of optical binding increases nonlinearly with the number of particles involved.3, 11 In pioneering work, Ng et al. applied a multiple scattering technique to predict various geometric configurations of photonic clusters formed by dielectric microspheres.12 Later we developed a coupled-dipole model for optical binding of multiple NPs.8 The strong electrodynamic interactions between metal NPs suggest an analogy to molecular assembly and the formation of atomic clusters.13-15 Therefore, inspired by the role of potential energy surface (PES) in molecular science, we recently found that particular equilibrium configurations of optically bound NPs are governed by the electrodynamic PES, and more importantly, by the initial positions and pathways of the NPs accessing particular stationary points of the PES.9 This electrodynamic PES method was effective in explaining the formation of certain optical matter clusters, but the scattering field from additional NPs will affect the optical binding interactions between the existing NPs, so their interparticle separation will


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change. In principle, the PES of optical matter is not static but dynamic, so the PES for the dynamics of self-organization needs to be continually modified. Very recently, a combined electrodynamics-Langevin dynamics approach has been developed to understand optical binding of Ag NPs.16 The reported results, however, were limited up to 3 NPs since it would take prohibitive amounts of time and computational requirements to simulate larger clusters on a single processor.16 In this letter, we report an integrated electrodynamics-molecular dynamics simulation (EDMD) technique to improve the search of optical matter isomers and experimentally verify the predictions. We calculate the optical binding interactions among Ag NPs with finite-difference time-domain (FDTD) simulations, and integrate the equations of motion using an modified algorithm17-18 from molecular dynamics simulations to find the optical matter configurations accurately and efficiently. We have simulated the trajectories and stable configurations of optical matter system with up to eight Ag NPs, and predicted how the configurations evolve as new NPs enter the system. The predicted configurations are further confirmed through experimental observations of the optical binding behaviors of Ag NPs. In particular, we found the existence of pentagonal photonic clusters from both simulations and experiments, which may lead to optical matter quasicrystals with five-fold symmetry.19 We first tested the ED-MD simulation approach (see Methods and Figure S1 in Supporting Information) using a 2-particle system where the optical binding behaviors have been wellstudied.5,

8-9, 15, 20

It is known that the dimer has a preferred stable configuration with an

interparticle separation around the wavelength of light in the medium, and an orientation perpendicular to the linear polarization. Only when two NPs are assembled along the polarization direction, can a dimer form along this direction, but it is unstable.9 Figure 1a shows the simulated trajectories of two Ag NPs assembled from different initial positions and orientations in a plane wave polarized along x-direction. A single stable configuration was found for a two-particle system, with both NPs aligned perpendicular to the polarization direction, and a metastable configuration was found in the horizontal direction, which matches known behavior. It is worth noting the trajectories around the stable configurations are elliptical instead of round, because the equilibrium optical binding separation along the polarization is longer than that along the perpendicular polarization.


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We further simulated the self-organization of 3 and 4 Ag NPs in a plane wave. For these cases, all but one of the NPs were placed in a stable configuration and then the last NP was placed at various angles near the cluster. This was done to mimic a new NP adding itself to a cluster that had already formed9 so we can observe how one configuration leads to another (see Figure S2, Supporting Information). When a third NP is added there are two distinct conformations the cluster can take. If the third NP enters so that it has a y-position between the existing two NPs, it will tend to form an isosceles triangle, oriented as shown in Figure 1b-I. The two NPs aligned in the y direction are closer to each other than the third NP by a small amount. If the NP comes from above or below, the system forms a vertical line of three NPs as shown in Figure 1b-II. In both cases the equilibrium of the two existing NPs is disrupted, and their separation distance changes slightly.

Figure 1. ED-MD simulation of light-driven self-organization of Ag NPs (150 nm dia.) in water illuminated by a plane wave (λvacuum = 800 nm). The light is linearly polarized along x-direction. (a) Trajectories of 2 NPs from different initial positions and orientations. The open circles indicate the equilibrium positions. The NPs can also reach equilibrium positions when they assemble along x-direction, but the positions are metastable since fluctuation will cause the NPs to rotate to open circle positions. Positions of the two NPs are always central-symmetric in the


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trajectories. (b) Trajectories of 3 NPs. The red spheres indicate the initial positions and the open cyan circles show the equilibrium positions. (c) Trajectories of 4 NPs. I, III and IV are stable configurations while two NPs in II have collapsed. The dashed red circles in V and VI are metastable configurations; when the NPs have thermal fluctuations, e.g., to the positions indicated by the red solid spheres, they will transit to other configurations marked by the open cyan circles. VII is a new stable cluster assembled from 4 Ag NPs with surface charges. All scale bars are 200 nm.

When a fourth NP is added there are 3 distinct configurations that form as plotted in Figure 1c. If the starting configuration is the triangle and the new NP comes from above, the triangle will rotate so two of the NPs are aligned in the x-direction and the new NP sits above the tip of triangle (c-I). This same configuration will form starting from the vertically aligned three NPs if the new NP comes from the side (c-III). In case II of the four-NP system, two of the NPs collapse and contact each other. This indicates that although there is a potential energy barrier along x-direction for a dimer, adding two NPs in the vertical direction decreases the energy barrier and makes the horizontal dimer unstable. The final configuration of the four-NP system is extending the chain configuration along the y-direction. However, as the chain gets longer it becomes less likely to occur. In the three-NP system, as long as the third NP came from a yposition above or below the existing two it would go into the chain conformation. In the four-NP case, the NP must come much more closely to vertical for this configuration to form. This indicates that although forming a vertical chain may always be possible, a configuration with a lower average distance between the NPs is more likely. The simulation method has also revealed several metastable configurations as shown by the dashed red circles in Figure 1c-V and VI. These clusters are stable due to their symmetry, but a small perturbation causes the cluster to change into one of the stable configurations seen previously. In Figure 1c-V, the cluster is the same shape as one of the stable configurations, just rotated by 90 degrees. When perturbed, this system simply rotates to its normal vertical position. In Figure 1c-VI, the starting conformation is not one of the stable ones, but its symmetry allows it to be metastable. When this system is perturbed, it cannot simply rotate to form a stable configuration. Instead the two pairs rotate separately and one of them eventually collapses, leading to case II of Figure 1c.


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Since the silver NPs are coated with surfactants with negative charges, the electrostatic forces may also contribute to the light-driven self-organization. We found adding charges to 4 NPs in the simulation can lead to a new configuration, shown in Figure 1c-VI with surface charges of 6.67×10-17 C for each particle assuming a laser intensity of 100 mW/µm2. This configuration comes from the same starting positions as in Figure 1c-II, yet with electrostatic repulsions the NPs have enough force keeping them apart that they do not collapse. This indicates that electrostatic forces are not insignificant in determining conformation and separation distance.

Figure 2. Experimental results of light-driven self-organization of 2 Ag NPs. (a) I. Trajectories of 2 NPs in 10.3 s with a time interval of 1/300 s. II. Replotted trajectories where centroid of the 2 NPs at each time is chosen as the origin of the coordinate system, i.e., the Brownian motion of the dimer system is removed. III. Initial trajectories of the assembly where rotation of the dimer from nearly horizontal to vertical can be seen. (b) The corresponding dark-field optical images of the NPs recorded by a camera with a frame rate of 300 fps. (c) Probability density of the NP positions.

We have conducted experiments to validate the predicted light-driven self-organization of 150 nm Ag NPs in the relatively flat central spot of a zero-order Bessel beam. Previously we studied optical binding in a defocused Gaussian beam, but the trapping force was so strong that it


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prevented observations of the intrinsic optical binding configurations.9 Figure 2a shows the trajectories of two NPs where the 2nd one entered the field from a top-right position. When the raw data is plotted there is too much noise due to strong Brownian motion in a relatively flat optical field (panel I), but when the NP positions are plotted so the centroid of the pair is always at the origin, the noise is almost entirely removed (panel II). The NPs quickly move toward the equilibrium points (panel III), in only around 0.04 s in this case. The corresponding optical images of this assembly process are displayed in Figure 2b. Brownian motion then causes the dimer to oscillate around the equilibrium points. However, these oscillations are not equal in all directions; instead they form crescent moon shapes, exactly the same as shown in the simulation (Figure 1a). These shapes follow the lowest gradient in potential energy, which shows that the two NPs are being held at a specific distance much more strongly than they are being held in their vertical orientation. These oscillations are confirmed though a probability density plot of the two NPs (Figure 2c), where the highest probabilities, i.e., the preferred optical binding positions, occur at the vertical orientation. These results suggest that our simulation method can correctly predict the optical binding behaviors of the NPs.

Figure 3. Experimental results of light-driven self-organization of 3 and 4 Ag NPs. (a) Optical images of typical photonic clusters at equilibrium positions. (b) Representative trajectories of


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NPs assembling into the photonic clusters. Red spheres indicate the initial positions and open circles are the final positions. All scale bars are 600 nm.

Optical binding experiments were also conducted for three and four-NP systems as shown in Figure 3a. All the configurations predicted in Figures 1 and 2 were observed in the experiments, and representative trajectories for forming these clusters are plotted in Figure 3b. These images and trajectories give evidence that the simulation method is correctly simulating the motion and interactions of the NPs. It also confirms that electrostatic forces are important, since the cluster that relies on those forces to form appears here (Figure 3b-III). The trajectories also show how each cluster can form from a random starting position. They also give insight into which configurations are preferred. For example, in case IV the starting position is close to one of the stable ones (Figure 1c-I), but with the NPs slightly offset. Under Brownian motion the NPs form a different configuration (Figure 1c-II). In our experiments, this configuration is the most stable one and it can hardly change to another configuration. Case VI also shows that the four-long chain is relatively difficult to form, requiring a starting position close to the final configuration. In contrast, the three-long chain is much easier to form (Figure 3b-II).


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Figure 4. Predicted and observed optical matter isomers consisting of up to 8 Ag NPs. The plotted schematics are the equilibrium configurations predicted by simulations, while the optical images show the corresponding clusters observed in the experiments. The two scale bars in the last panel are 600 nm.

We have further simulated the equilibrium configurations for optical matter isomers of 5 and 6 Ag NPs, and verified the predicted results with experiments. Figure 4 shows the predicted and observed optical matter isomers formed by stable optical binding interactions. Clusters with collapsed dimers, similar to the case of cluster 4-II, are thus not shown here. For optical matter isomers with 5 NPs, we found 5 configurations from the simulations and all have been observed in the experiments as shown in the first row of Figure 4. For optical matter isomers with 6 NPs, the simulations predicted thirteen configurations and again all were observed in our experiments. The simulation typically finds a new cluster by adding a new NP to an existing one, but in a


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special case of 6-XI, we have to move the central NP in 6-IX to get the ring. In experiments, the momentum of a new NP entering the system is sometimes enough to disrupt the existing NPs and cause a new configuration to reform. In particular, a stable pentagonal photonic cluster (6-XIII) appeared in both simulations and experiments, and clusters with 7 and 8 NPs (7-I & 8-I) expanded from the pentagonal photonic cluster were also observed. These clusters show fivefold symmetry, which are apparently different from the ordinary hexagonal clusters formed in traditional colloidal self-assembly.21 These results demonstrate that new structures can arise from the anisotropic optical binding interactions, which may lead to optical matter quasicrystals.19 It is worth mentioning that in the current study, all photonic clusters are planar structures due to the strong radiation pressure in the laser propagation direction, which confines the NPs near a glass surface. To compensate for the radiation pressure and create 3D optical matter, one needs a dual-beam optical assembly system using two counter-propagating laser beams. Accordingly, our simulation method can be extended to model the 3D self-organization by releasing and tracking particle motion in the third dimension. This will largely increase the possible configurations for optical binding and create new 3D optical matter lattices. An optical lattice can also be created by interference of three or more laser beams,6, 22 or by holographic optical tweezers.23 However, the former method only allows certain interference patterns and lacks structural tunability, and the latter generally only works for microparticles with minimal particle (lattice) separations of several micrometers. While the 3-D project is beyond the scope of our current work, our work compares favorably against previous simulations.8, 12, 16 The multiple scattering and Maxwell stress tensor method is efficient, yet many of the structures predicted by those simulations were not observed in our experiments while some observed structures were missing.12 Similar issues exist for the coupleddipole model that we have developed previously.8 The electrodynamics-Langevin dynamics approach is accurate but the results were limited up to 3 NPs due to the heavy computational burden,16 and in order to simulate the NP motion using Langevin dynamics, the simulation sets the displacement of a NP less than 1/10th of its diameter in each step. Our method shows that it is not necessary to take steps as small as previously thought to get accurate simulations of optical binding interactions. A large improvement of our method is in the maximum size of the steps taken between force calculations, and our method allows the simulation of larger systems in reasonable time (see Figure S3 and note on computational cost in Supporting Information). In


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addition, our simulation method can provide new physical insight into the properties of optical matter, e.g., spatial inhomogeneity of stability in an 8-NP cluster (Figure S4) that has been verified by experiments (Figure S5, Supporting Information). In conclusion, we have developed a combined ED-MD method to simulate optical binding of silver NPs. We show that this method can predict the stable configurations of optical matter, as well as the trajectories that the NPs take to get to those conformations. Experimental images of silver NP clusters show that all predictions are correct. These simulations also show that metastable conformations can exist in theory, but under a small perturbation they change to one of the stable conformations, causing them not to appear in practice. One conformation which was observed in experiments was only predicted by the simulation when electrostatic forces were included, demonstrating that these forces play a significant role in cluster formation. These experiments and simulations have found many new types of photonic clusters, including a pentagonal cluster which remains stable as more NPs are added. This could lead to larger structures which retain the five-fold symmetry found here. The insights gained through these combined experiments and simulations can lead to a new way of discovering artificial materials.

ASSOCIATED CONTENT *Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Experimental and simulation methods, note on the computational cost, flow chart of the simulation, family tree of the optical matter system, and new physical insight on inhomogeneous optical binding strength (PDF)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] ORCID Zijie Yan: 0000-0003-0726-7042 Notes The authors declare no competing financial interest.


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ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. 1610271.

ACKNOWLEDGMENTS (1)

Whitesides, G. M.; Grzybowski, B. Self-Assembly at All Scales. Science 2002, 295,

2418–2421. (2)

Benson, O. Assembly of Hybrid Photonic Architectures from Nanophotonic Constituents.

Nature 2011, 480, 193–199. (3)

Dholakia, K.; Zemánek, P. Colloquium: Gripped by Light: Optical Binding. Rev. Mod.

Phys. 2010, 82, 1767–1791. (4)

Čižmár, T.; Romero, L. C. D.; Dholakia, K.; Andrews, D. L. Multiple Optical Trapping

and Binding: New Routes To Self-Assembly. J. Phys. B: At. Mol. Opt. Phys. 2010, 43, 102001. (5)

Burns, M. M.; Fournier, J. M.; Golovchenko, J. A. Optical Binding. Phys. Rev. Lett.

1989, 63, 1233–1236. (6)

Burns, M. M.; Fournier, J. M.; Golovchenko, J. A. Optical Matter: Crystallization and

Binding in Intense Optical Fields. Science 1990, 249, 749–754. (7)

Demergis, V.; Florin, E.-L. Ultrastrong Optical Binding of Metallic Nanoparticles. Nano

Lett. 2012, 12, 5756–5760. (8)

Yan, Z.; Shah, R. A.; Chado, G.; Gray, S. K.; Pelton, M.; Scherer, N. F. Guiding Spatial

Arrangements of Silver Nanoparticles by Optical Binding Interactions in Shaped Light Fields. ACS Nano 2013, 7, 1790–1802. (9)

Yan, Z.; Gray, S. K.; Scherer, N. F. Potential Energy Surfaces and Reaction Pathways for

Light-Mediated Self-Organization of Metal Nanoparticle Clusters. Nat. Commun. 2014, 5, 3751. (10) Yan, Z. J.; Manna, U.; Qin, W.; Camire, A.; Guyot-Sionnest, P.; Scherer, N. F. Hierarchical Photonic Synthesis of Hybrid Nanoparticle Assemblies. J. Phys. Chem. Lett. 2013, 4, 2630–2636. (11) Andrews, D. L.; Bradshaw, D. S.; Romero, L. C. D. Multiple Light Scattering and Optomechanical Forces. J. Nanophotonics 2010, 4, 041565-041565-15.


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(12) Ng, J.; Lin, Z. F.; Chan, C. T.; Sheng, P. Photonic Clusters Formed by Dielectric Microspheres: Numerical Simulations. Phys. Rev. B 2005, 72, 085130. (13) Gordon, R. J.; Rice, S. A. Active Control of the Dynamics of Atoms and Molecules. Annu. Rev. Phys. Chem. 1997, 48, 601–641. (14) Maitland, G. C.; Rigby, M.; Smith, E. B. Intermolecular Forces: Their Origin and Determination. Clarendon: Oxford, 1981. (15) Rodriguez, J.; Davila Romero, L. C.; Andrews, D. L. Optical Binding in Nanoparticle Assembly: Potential Energy Landscapes. Phys. Rev. A 2008, 78, 043805. (16) Sule, N.; Rice, S. A.; Gray, S. K.; Scherer, N. F. An Electrodynamics-Langevin Dynamics (ED-LD) Approach to Simulate Metal Nanoparticle Interactions and Motion. Opt. Express 2015, 23, 29978–29992. (17) Beeman, D. Some Multistep Methods for Use in Molecular Dynamics Calculations. J. Comput. Phys. 1976, 20, 130–139. (18) Levitt, M.; Meirovitch, H.; Huber, R. Integrating the Equations of Motion. J. Mol. Biol. 1983, 168, 617–620. (19) Caspar, D. L. D.; Fontano, E. Five-Fold Symmetry in Crystalline Quasicrystal Lattices. Proc. Natl. Acad. Sci. U.S.A 1996, 93, 1427114278. (20) Dapasse, F.; Vigoureux, J. M. Optical Binding Force between Two Rayleigh Particles. J. Phys. D: Appl. Phys. 1994, 27, 914. (21) Zhang, J.; Li, Y.; Zhang, X.; Yang, B. Colloidal Self-Assembly Meets Nanofabrication: From Two-Dimensional Colloidal Crystals to Nanostructure Arrays. Adv. Mater. 2010, 22, 4249–4269. (22) Slama-Eliau, B.; Raithel, G. Three-Dimensional Arrays of Submicron Particles Generated by a Four-Beam Optical Lattice. Phys. Rev. E 2011, 83, 051406. (23) Grier, D. G. A Revolution in Optical Manipulation. Nature 2003, 424, 810–816.


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