# Publications

2012
Fan, J. A. ; Bao, K. ; Sun, L. ; Bao, J. ; Manoharan, V. N. ; Nordlander, P. ; Capasso, F. Plasmonic Mode Engineering with Templated Self-Assembled Nanoclusters . Nano Letters 2012, 12, 5318-5324. Publisher's VersionAbstract

Plasmonic nanoparticle assemblies are a materials platform in which optical modes, resonant frequencies, and near-field intensities can be specified by the number and position of nanoparticles in a cluster. A current challenge is to achieve clusters with higher yields and new types of shapes. In this Letter, we show that a broad range of plasmonic nanoshell nanoclusters can be assembled onto a lithographically defined elastomeric substrate with relatively high yields using templated assembly. We assemble and measure the optical properties of three cluster types: Fano-resonant heptamers, linear chains, and rings of nanoparticles. The yield of heptamer clusters is measured to be over 30%. The assembly of plasmonic nanoclusters on an elastomer paves the way for new classes of plasmonic nanocircuits and colloidal metamaterials that can be transfer-printed onto various substrate media.

Perry, R. W. ; Meng, G. ; Dimiduk, T. G. ; Fung, J. ; Manoharan, V. N. Real-space studies of the structure and dynamics of self-assembled colloidal clusters . Faraday Discussions 2012, 159, 211-234. Publisher's VersionAbstract

The energetics and assembly pathways of small clusters may yield insights into processes occurring at the earliest stages of nucleation. We use a model system consisting of micrometer-sized, spherical colloidal particles to study the structure and dynamics of small clusters, where the number of particles is small (N <= 10). The particles interact through a short-range depletion attraction with a depth of a few k_B T. We describe two methods to form colloidal clusters, one based on isolating the particles in microwells and another based on directly assembling clusters in the gas phase using optical tweezers. We use the first technique to obtain ensemble-averaged probabilities of cluster structures as a function of N. These experiments show that clusters with symmetries compatible with crystalline order are rarely formed under equilibrium conditions. We use the second technique to study the dynamics of the clusters, and in particular how they transition between free-energy minima. To monitor the clusters we use a fast three-dimensional imaging technique, digital holographic microscopy, that can resolve the positions of each particle in the cluster with 30-45 nm precision on millisecond timescales. The real-space measurements allow us to obtain estimates for the lifetimes of the energy minima and the transition states. It is not yet clear whether the observed dynamics are relevant for small nuclei, which may not have sufficient time to transition between states before other particles or clusters attach to them. However, the measurements do provide some glimpses into how systems containing a small number of particles traverse their free-energy landscape.

2011
Kaz, D. M. Colloidal Particles and Liquid Interfaces: A Spectrum of Interactions , 2011.Abstract

Young's law predicts that a colloidal sphere in equilibrium with a liquid interface will straddle the two fluids, its height above the interface defined by an equilibrium contact angle. This equilibrium analysis has been used to explain why colloids often bind to liquid interfaces, an effect first observed a century ago by Ramsden and Pickering and later exploited in a wide range of material processes, including emulsi⬚cation, water puri⬚cation, mineral recovery, encapsulation, and the making of nanostructured materials. But little is known about the dynamics of binding, or any aspect of the interaction between a particle and an interface outside of equilibrium. This thesis explores the spectrum of particle-interface interactions, from non-binding to non-adsorptive binding and ⬚finally adsorptive binding and the relaxation toward equilibrium that ensues. Chapter 2 reviews the importance of interfacial particles in materials science, and serves as a partial motivation for the work presented here. Chapter 3 describes the apparatus and experimental procedures employed in the acquisition of our data, with a short review of experiments that led to the current set. Special attention is paid to the optical apparatus and the custom sample cells we designed. Chapter 4 deals with non-adsorptive interactions between colloidal particles and liquid interfaces. A theoretical discussion founded on (but not wedded to) classical DLVO theory is presented before the results of our experiments are analyzed. It is shown that particle interface interactions may be purely repulsive or contain an attractive component that results in binding to the interface that is not associated with breach. In chapter 5 the adsorption of polystyrene microspheres to a water-oil interface is shown to be characterized by a sudden breach and an unexpectedly slow relaxation. Particles do not reach equilibrium even after 100 seconds, and the relaxation appears logarithmic in time, suggesting that complete equilibration may take months. Surprisingly, viscous dissipation appears to play little role. Instead, the observed dynamics, which bear strong resemblance to aging in glassy systems, agree well with a model describing activated hopping of the contact line over nanoscale surface heterogeneities. Finally, in chapter 6, I propose a number of intriguing experiments that build on the knowledge presented in this thesis, and probe areas that were inaccessible because of the ⬚finiteness of my tenure in graduate school.

McGorty, R. Colloidal Particles at Fluid Interfaces and the Interface of Colloidal Fluids , 2011.Abstract

Holographic microscopy is a unifying theme in the different projects discussed in this thesis. The technique allows one to observe microscopic objects, like colloids and droplets, in a three-dimensional (3D) volume. Unlike scanning 3D optical techniques, holography captures a sample’s 3D information in a single image: the hologram. Therefore, one can capture 3D information at video frame rates. The price for such speed is paid in computation time. The 3D information must be extracted from the image by methods such as reconstruction or fitting the hologram to scattering calculations. Using holography, we observe a single colloidal particle approach, penetrate and then slowly equilibrate at an oil–water interface. Because the particle moves along the optical axis (z-axis) and perpendicular to the interface holography is used to determine its position. We are able to locate the particle’s z-position to within a few nanometers with a time resolution below a millisecond. We find that the capillary force pulling the particle into the interface is not balanced by a hydrodynamic force. Rather, a larger-than-viscous dissipation associated with the three-phase contact-line slipping over the particle’s surface results in equilibration on time scales orders of magnitude longer than the minute time scales over which our setup allows us to examine. A separate project discussed here also examines colloidal particles and fluid-fluid interfaces. But the fluids involved are composed of colloids. With a colloid and polymer water-based mixture we study the phase separation of the colloid-rich (or liquid) and colloid-poor (or gas) region. In comparison to the oil–water interface in the previously mentioned project, the interface between the colloidal liquid and gas phases has a surface tension nearly six orders of magnitude smaller. So interfacial fluctuations are observable under microscopy. We also use holographic microscopy to study this system but not to track particles with great time and spatial resolution. Rather, holography allows us to observe nucleation of the liquid phase occurring throughout our sample volume.

Arkus, N. ; Manoharan, V. N. ; Brenner, M. P. Deriving Finite Sphere Packings . SIAM Journal on Discrete Mathematics 2011, 25, 1860. Publisher's VersionAbstract

Sphere packing problems have a rich history in both mathematics and physics; yet, relatively few analytical analyses of sphere packings exist, and answers to seemingly simple questions are unknown. Here, we present an analytical method for deriving all packings of $n$ spheres in $\mathbb{R}^3$ satisfying minimal rigidity constraints ($\geq 3$ contacts per sphere and $\geq 3n-6$ total contacts). We derive such packings for $n \leq 10$ and provide a preliminary set of maximum contact packings for $10 < n \leq 20$. The resultant set of packings has some striking features; among them are the following: (i) all minimally rigid packings for $n \leq 9$ have exactly $3n-6$ contacts; (ii) nonrigid packings satisfying minimal rigidity constraints arise for $n \geq 9$; (iii) the number of ground states (i.e., packings with the maximum number of contacts) oscillates with respect to $n$; (iv) for $10 \leq n \leq 20$ there are only a small number of packings with the maximum number of contacts, and for $10 \leq n < 13$ these are all commensurate with the hexagonal close-packed lattice. The general method presented here may have applications to other related problems in mathematics, such as the Erdös repeated distance problem and Euclidean distance matrix completion problems.

Fan, J. A. ; He, Y. ; Bao, K. ; Wu, C. ; Bao, J. ; Schade, N. B. ; Manoharan, V. N. ; Shvets, G. ; Nordlander, P. ; Liu, D. R. ; et al. DNA-Enabled Self-Assembly of Plasmonic Nanoclusters. Nano Letters 2011, 11, 4859-4864. Publisher's VersionAbstract

DNA nanotechnology provides a versatile foundation for the chemical assembly of nanostructures. Plasmonic nanoparticle assemblies are of particular interest because they can be tailored to exhibit a broad range of electromagnetic phenomena. In this Letter, we report the assembly of DNA-functionalized nanoparticles into heteropentamer clusters, which consist of a smaller gold sphere surrounded by a ring of four larger spheres. Magnetic and Fano-like resonances are observed in individual clusters. The DNA plays a dual role: it selectively assembles the clusters in solution and functions as an insulating spacer between the conductive nanoparticles. These particle assemblies can be generalized to a new class of DNA-enabled plasmonic heterostructures that comprise various active and passive materials and other forms of DNA scaffolding.

Fung, J. ; Martin, E. K. ; Perry, R. W. ; Kaz, D. M. ; McGorty, R. ; Manoharan, V. N. Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy . Optics Express 2011, 19, 8051-8065. Publisher's VersionAbstract

We discuss a new method for simultaneously probing translational, rotational, and vibrational dynamics in dilute colloidal suspensions using digital holographic microscopy (DHM). We record digital holograms of clusters of 1-μm-diameter colloidal spheres interacting through short-range attractions, and we fit the holograms to an exact model of the scattering from multiple spheres. The model, based on the T-matrix formulation, accounts for multiple scattering and near-field coupling. We also explicitly account for the non-asymptotic radial decay of the scattered fields, allowing us to accurately fit holograms recorded with the focal plane located as little as 15 μm from the particle. Applying the fitting technique to a time-series of holograms of Brownian dimers allows simultaneous measurement of six dynamical modes — three translational, two rotational, and one vibrational — on timescales ranging from 10−3 to 1 s. We measure the translational and rotational diffusion constants to a precision of 0.6%, and we use the vibrational data to measure the interaction potential between the spheres to a precision of ∼50 nm in separation distance. Finally, we show that the fitting technique can be used to measure dynamics of clusters containing three or more spheres.

Manoharan, V. N. Molecular Forces and Self Assembly: In Colloid, Nano Sciences and Biology (Book Review) . Physics Today 2011, 64, 48. Publisher's Version
2010
Perro, A. ; Manoharan, V. N. Bulk Synthesis of Polymer-Inorganic Colloidal Clusters . Langmuir 2010, 26, 18669-18675. Publisher's VersionAbstract

We describe a procedure to synthesize colloidal clusters with polyhedral morphologies in high yield (liter quantities at up to 70% purity) using a combination of emulsion polymerization and inorganic surface chemistry. We show that the synthesis initially used for silica-polystyrene hybrid clusters can be generalized to create clusters from other inorganic and polymer particles. We also show that high yields of particular morphologies can be obtained by precise control of the inorganic seed particle size, a finding that can be explained using a hard-sphere packing model. These clusters can be further chemically modified for a variety of applications. Introducing a cross-linker leads to colloidal clusters that can be index matched in an appropriate solvent, allowing them to be used for particle tracking or optical studies of colloidal self-assembly. Also, depositing a thin silica layer on these colloids allows the surface properties to be controlled using silane chemistry.

McGorty, R. ; Fung, J. ; Kaz, D. ; Manoharan, V. N. Colloidal self-assembly at an interface. Materials Today 2010, 13, 34-42. Publisher's VersionAbstract

Mix a drop of water into a vial of oil. With some surfactant and a vigorous shake, that one droplet has become thousands, and the total interfacial area has increased by an order of magnitude or more. Like the folded membranes in our mitochondria, the alveoli in our lungs, and the catalytic converters in our cars, oil-water emulsions contain a vast reservoir of interfacial area that can be used to control and transform the things that encounter it. The oil-water interface is especially well-suited to directing the assembly of colloidal particles, which bind to it rapidly and often irreversibly.

Fan, J. A. ; Bao, K. ; Wu, C. ; Bao, J. ; Bardhan, R. ; Halas, N. J. ; Manoharan, V. N. ; Shvets, G. ; Nordlander, P. ; Capasso, F. Fano-like Interference in Self-Assembled Plasmonic Quadrumer Clusters . Nano Letters 2010, 10, 4680-4685. Publisher's VersionAbstract

Assemblies of strongly interacting metallic nanoparticles are the basis for plasmonic nanostructure engineering. We demonstrate that clusters of four identical spherical particles self-assembled into a close-packed asymmetric quadrumer support strong Fano-like interference. This feature is highly sensitive to the polarization of the incident electric field due to orientation-dependent coupling between particles in the cluster. This structure demonstrates how careful design of self-assembled colloidal systems can lead to the creation of new plasmonic modes and the enabling of interference effects in plasmonic systems.

Fan, J. A. ; Wu, C. ; Bao, K. ; Bao, J. ; Bardhan, R. ; Halas, N. J. ; Manoharan, V. N. ; Nordlander, P. ; Shvets, G. ; Capasso, F. Self-Assembled Plasmonic Nanoparticle Clusters. Science 2010, 328, 1135-1138. Publisher's VersionAbstract

The self-assembly of colloids is an alternative to top-down processing that enables the fabrication of nanostructures. We show that self-assembled clusters of metal-dielectric spheres are the basis for nanophotonic structures. By tailoring the number and position of spheres in close-packed clusters, plasmon modes exhibiting strong magnetic and Fano-like resonances emerge. The use of identical spheres simplifies cluster assembly and facilitates the fabrication of highly symmetric structures. Dielectric spacers are used to tailor the interparticle spacing in these clusters to be approximately 2 nanometers. These types of chemically synthesized nanoparticle clusters can be generalized to other two- and three-dimensional structures and can serve as building blocks for new metamaterials.

Dimiduk, T. G. ; Kosheleva, E. A. ; Kaz, D. ; McGorty, R. ; Gardel, E. J. ; Manoharan, V. N. A Simple, Inexpensive Holographic Microscope. In Digital Holography and Three-Dimensional Imaging 2010 (OSA Topical Meeting); Optical Society of America: Miami, FL, 2010; pp. Paper JMA38. Publisher's VersionAbstract

We have built a simple holographic microscope completely out of consumer components. We obtain at least 2.8 μm resolution and depth of field greater than 200 μm from an instrument costing less than \$1000.

Manoharan, V. N. Digital Holographic Microscopy for 3D Imaging of Complex Fluids and Biological Systems. Frontiers of Engineering: Reports on Leading-edge Engineering from the 2009 Symposium, 2010, 5-12. Full Text
Meng, G. ; Arkus, N. ; Brenner, M. P. ; Manoharan, V. N. The Free-Energy Landscape of Clusters of Attractive Hard Spheres. Science 2010, 327, 560-563. Publisher's VersionAbstract

The study of clusters has provided a tangible link between local geometry and bulk condensed matter, but experiments have not yet systematically explored the thermodynamics of the smallest clusters. Here we present experimental measurements of the structures and free energies of colloidal clusters in which the particles act as hard spheres with short-range attractions. We found that highly symmetric clusters are strongly suppressed by rotational entropy, whereas the most stable clusters have anharmonic vibrational modes or extra bonds. Many of these clusters are subsets of close-packed lattices. As the number of particles increases from 6 to 10, we observe the emergence of a complex free-energy landscape with a small number of ground states and many local minima.

2009
Perro, A. ; Meng, G. ; Fung, J. ; Manoharan, V. N. Design and Synthesis of Model Transparent Aqueous Colloids with Optimal Scattering Properties. Langmuir 2009, 25, 11295-11298. Publisher's VersionAbstract

We demonstrate the synthesis and self-assembly of colloidal particles with independently controlled diameter and scattering cross section. We show that it is possible to prepare bulk colloidal suspensions that are nearly transparent in water, while the particles themselves can be individually resolved using optical microscopy. These particles may be ideal model colloids for real-space studies of self-assembly in aqueous media. Moreover, they illustrate the degree to which the optical properties of colloids can be engineered through straightforward chemistry.

Arkus, N. ; Manoharan, V. N. ; Brenner, M. P. Minimal Energy Clusters of Hard Spheres with Short Range Attractions. Physical Review Letters 2009, 103, 118303-4. Publisher's VersionAbstract

We calculate the ground states of hard-sphere clusters, in which n identical hard spherical particles bind by isotropic short-ranged attraction. Combining graph theoretic enumeration with basic geometry, we analytically solve for clusters of n<=10 particles satisfying minimal rigidity constraints. For n<=9 the ground state degeneracy increases exponentially with n, but for n>9 the degeneracy decreases due to the formation of structures with >3n-6 contacts. Interestingly, for n=10 and possibly at n=11 and n=12, the ground states of this system are subsets of hexagonal close-packed crystals. The ground states are not icosahedra at n=12 and n=13. We relate our results to the structure and thermodynamics of suspensions of colloidal particles with short-ranged attractions.

Ali, N. ; Manoharan, V. N. RNA folding and hydrolysis terms explain ATP-independence of RNA interference in human systems. Oligonucleotides 2009, 19, 341-346. Publisher's VersionAbstract

Although RNA interference (RNAi) has emerged as an important tool for studying the effects of gene knockdown, it is still difficult to predict the success of RNAi effectors in human systems. By examining the basic thermodynamic equations for RNA interactions in RNAi, we demonstrate how the free energies of RNA folding and phosphoester bond hydrolysis can drive RNAi without ATP. Our calculations of RNAi efficiency are close to actual values obtained from in vitro experimental data from 2 previous studies, for both silencing complex formation (2.50 vs. 2.40 for relative efficiency of RISC formation) and mRNA cleavage (0.50 vs. 0.56 for proportion cleaved). Our calculations are also in agreement with previous observations that duplex unwinding and target site folding are major energy barriers to RNAi.

Perro, A. ; Duguet, E. ; Ravaine, S. ; Manoharan, V. N. Self-Assembly of Polyhedral Hybrid Colloidal Particles. MRS Proceedings, 2009, 1135, 1135-CC06-08. Publisher's VersionAbstract

We have developed a new method to produce hybrid particles with polyhedral shapes in very high yield (liter quantities at up to 70% purity) using a combination of emulsion polymerization and inorganic surface chemistry. The procedure has been generalized to create complex geometries, including hybrid line segments, triangles, tetrahedra, octahedra, and more. The optical properties of these particles are tailored for studying their dynamics and self-assembly. For example, we produce systems that consist of index-matched spheres allowing us to define the position of each elementary particle in three-dimensional space. We present some preliminary studies on the self-assembly of these complex shaped systems based on electron and optical microscopy.

2008
McGorty, R. ; Fung, J. ; Kaz, D. ; Ahn, S. ; Manoharan, V. N. Measuring Dynamics and Interactions of Colloidal Particles with Digital Holographic Microscopy. In Digital Holography and Three-Dimensional Imaging Proceedings; Optical Society of America Technical Digest (CD): St. Petersburg, Florida, 2008; Vol. paper DTuB1. Publisher's VersionAbstract

Micrometer-sized colloidal particles are a model system for understanding self-assembly in condensed matter. Here I present the results of digital holographic microscopy experiments that probe the 3D structure and dynamics of these systems.