# Publications

2013
Small, A. ; Fung, J. ; Manoharan, V. N. Generalization of the optical theorem for light scattering from a particle at a planar interface . Journal of the Optical Society of America A 2013, 30, 2519-2525. Publisher's VersionAbstract

The optical theorem provides a powerful tool for calculating the extinction cross section of a particle from a solution to Maxwell’s equations, relating the cross section to the scattering amplitude in the forward direction. The theorem has been generalized by a number of other workers to consider a particle near an interface between media with different refractive indices. Here we present a derivation of the generalized optical theorem that is valid for a particle embedded in the interface, as well as an incident beam undergoing total internal reflection. We also obtain an additional useful physical result: we show that the far-field scattered field must be zero in the direction parallel to the interface. Our results enable the verification of computations of scattering by particles embedded in interfaces and may be relevant to experiments on colloidal particles at fluid interfaces.

Bala Subramaniam, A. ; Guidotti, G. ; Manoharan, V. N. ; Stone, H. A. Glycans pattern the phase behaviour of lipid membranes. Nature Materials 2013, 12, 128-133. Publisher's VersionAbstract

Hydrated networks of glycans (polysaccharides)—in the form of cell walls, periplasms or gel-like matrices—are ubiquitously present adjacent to cellular plasma membranes. Yet, despite their abundance, the function of glycans in the extracellular milieu is largely unknown. Here we show that the spatial configuration of glycans controls the phase behaviour of multiphase model lipid membranes: inhomogeneous glycan networks stabilize large lipid domains at the characteristic length scale of the network, whereas homogeneous networks suppress macroscopic lipid phase separation. We also find that glycan-patterned phase separation is thermally reversible—thus indicating that the effect is thermodynamic rather than kinetic—and that phase patterning probably results from a preferential interaction of glycans with ordered lipid phases. These findings have implications for membrane-mediated transport processes, potentially rationalize long-standing observations that differentiate the behaviour of native and model membranes and may indicate an intimate coupling between cellular lipidomes and glycomes.

Fung, J. ; Manoharan, V. N. Holographic Measurements of Anisotropic Three-Dimensional Diffusion of Colloidal Clusters . Physical Review E 2013, 88, 020302. Publisher's VersionAbstract

We measure all nonzero elements of the three-dimensional diffusion tensor D for clusters of colloidal spheres to a precision of 1% or better using digital holographic microscopy. We study both dimers and triangular trimers of spheres, for which no analytical calculations of the diffusion tensor exist. We observe anisotropic rotational and translational diffusion arising from the asymmetries of the clusters. In the case of the three-particle triangular cluster, we also detect a small but statistically significant difference in the rotational diffusion about the two in-plane axes. We attribute this difference to weak breaking of threefold rotational symmetry due to a small amount of particle polydispersity. Our experimental measurements agree well with numerical calculations and show how diffusion constants can be measured under conditions relevant to colloidal self-assembly, where theoretical and even numerical prediction is difficult.

Fung, J. Measuring the 3D Dynamics of Multiple Colloidal Particles with Digital Holographic Microscopy, 2013. Download PDFAbstract

We discuss digital holographic microscopy (DHM), a 3D imaging technique capable of measuring the positions of micron-sized colloidal particles with nanometer precision and sub-millisecond temporal resolution. We use exact electromagnetic scattering solutions to model holograms of multiple colloidal spheres. While the Lorenz-Mie solution for scattering by isolated spheres has previously been used to model digital holograms, we apply for the first time an exact multisphere superposition scattering model that is capable of modeling holograms from spheres that are sufficiently close together to exhibit optical coupling.

Wang, A. ; Kaz, D. M. ; McGorty, R. ; Manoharan, V. N. Relaxation dynamics of colloidal particles at liquid interfaces. AIP Conference Proceedings, 2013, 1518, 336-343. Publisher's VersionAbstract

We study the dynamics of colloidal particles as they approach and breach a water-oil interface. We use a fast 3D imaging technique, digital holographic microscopy, to track particles with 2 nm precision and sub-millisecond time resolution. We find that polystyrene particles dispersed in water or water-glycerol mixtures relax logarithmically with time after breaching the interface and do not reach equilibrium on experimental timescales. By contrast, decane-dispersed PMMA particles show fast dynamics and reach a steady-state height within milliseconds. We attribute the difference to the surface properties of the particles. We also probe the dependence of the relaxation rate on surface charge by studying carboxyl-functionalized particles under varying acid concentrations. We conclude that the slow relaxation may be due to contact-line pinning on topographical defects rather than surface charges.

Schade, N. B. ; Holmes-Cerfon, M. C. ; Chen, E. R. ; Aronzon, D. ; Collins, J. W. ; Fan, J. A. ; Capasso, F. ; Manoharan, V. N. Tetrahedral colloidal clusters from random parking of bidisperse spheres . Physical Review Letters 2013, 110, 148303. Publisher's VersionAbstract

Using experiments and simulations, we investigate the clusters that form when colloidal spheres stick irreversibly to—or “park” on—smaller spheres. We use either oppositely charged particles or particles labeled with complementary DNA sequences, and we vary the ratio α of large to small sphere radii. Once bound, the large spheres cannot rearrange, and thus the clusters do not form dense or symmetric packings. Nevertheless, this stochastic aggregation process yields a remarkably narrow distribution of clusters with nearly 90% tetrahedra at α=2.45. The high yield of tetrahedra, which reaches 100% in simulations at α=2.41, arises not simply because of packing constraints, but also because of the existence of a long-time lower bound that we call the “minimum parking” number. We derive this lower bound from solutions to the classic mathematical problem of spherical covering, and we show that there is a critical size ratio αc=(1+√2)≈2.41, close to the observed point of maximum yield, where the lower bound equals the upper bound set by packing constraints. The emergence of a critical value in a random aggregation process offers a robust method to assemble uniform clusters for a variety of applications, including metamaterials.

Lee, Y. - J. ; Schade, N. B. ; Sun, L. ; Fan, J. A. ; Bae, D. R. ; Mariscal, M. M. ; Lee, G. ; Capasso, F. ; Sacanna, S. ; Manoharan, V. N. ; et al. Ultrasmooth, Highly Spherical Monocrystalline Gold Particles for Precision Plasmonics . ACS Nano 2013, 7 11064-11070. Publisher's VersionAbstract

Ultrasmooth, highly spherical monocrystalline gold particles were prepared by a cyclic process of slow growth followed by slow chemical etching, which selectively removes edges and vertices. The etching process effectively makes the surface tension isotropic, so that spheres are favored under quasi-static conditions. It is scalable up to particle sizes of 200 nm or more. The resulting spherical crystals display uniform scattering spectra and consistent optical coupling at small separations, even showing Fano-like resonances in small clusters. The high monodispersity of the particles we demonstrate should facilitate the self-assembly of nanoparticle clusters with uniform optical resonances, which could in turn be used to fabricate optical metafluids. Narrow size distributions are required to control not only the spectral features but also the morphology and yield of clusters in certain assembly schemes.

Wang, A. ; Dimiduk, T. G. ; Fung, J. ; Razavi, S. ; Kretzschmar, I. ; Chaudhary, K. ; Manoharan, V. N. Using the discrete dipole approximation and holographic microscopy to measure rotational dynamics of non-spherical colloidal particles . Journal of Quantitative Spectroscopy and Radiative Transfer 2013, 146, 499–509. Publisher's VersionAbstract

We present a new, high-speed technique to track the three-dimensional translation and rotation of non-spherical colloidal particles. We capture digital holograms of micrometer-scale silica rods and sub-micrometer-scale Janus particles freely diffusing in water, and then fit numerical scattering models based on the discrete dipole approximation to the measured holograms. This inverse-scattering approach allows us to extract the position and orientation of the particles as a function of time, along with static parameters including the size, shape, and refractive index. The best-fit sizes and refractive indices of both particles agree well with expected values. The technique is able to track the center of mass of the rod to a precision of 35 nm and its orientation to a precision of 1.5°, comparable to or better than the precision of other 3D diffusion measurements on non-spherical particles. Furthermore, the measured translational and rotational diffusion coefficients for the silica rods agree with hydrodynamic predictions for a spherocylinder to within 0.3%. We also show that although the Janus particles have only weak optical asymmetry, the technique can track their 2D translation and azimuthal rotation over a depth of field of several micrometers, yielding independent measurements of the effective hydrodynamic radius that agree to within 0.2%. The internal and external consistency of these measurements validate the technique. Because the discrete dipole approximation can model scattering from arbitrarily shaped particles, our technique could be used in a range of applications, including particle tracking, microrheology, and fundamental studies of colloidal self-assembly or microbial motion.

2012
Wang, Y. ; Wang, Y. ; Breed, D. R. ; Manoharan, V. N. ; Feng, L. ; Hollingsworth, A. D. ; Weck, M. ; Pine, D. J. Colloids with valence and specific directional bonding . Nature 2012, 491, 51-55. Publisher's VersionAbstract

The ability to design and assemble three-dimensional structures from colloidal particles is limited by the absence of specific directional bonds. As a result, complex or low-coordination structures, common in atomic and molecular systems, are rare in the colloidal domain. Here we demonstrate a general method for creating the colloidal analogues of atoms with valence: colloidal particles with chemically distinct surface patches that imitate hybridized atomic orbitals, including sp, sp2, sp3, sp3d, sp3d2 and sp3d3. Functionalized with DNA with single-stranded sticky ends, patches on different particles can form highly directional bonds through programmable, specific and reversible DNA hybridization. These features allow the particles to self-assemble into |[lsquo]|colloidal molecules|[rsquo]| with triangular, tetrahedral and other bonding symmetries, and should also give access to a rich variety of new microstructured colloidal materials.

Magkiriadou, S. ; Park, J. - G. ; Kim, Y. - S. ; Manoharan, V. N. Disordered packings of core-shell particles with angle-independent structural colors . Optical Materials Express 2012, 2 1343-1352. Publisher's VersionAbstract

Making materials that display angle-independent structural color requires control over both scattering and short-range correlations in the refractive index. We demonstrate a simple way to make such materials by packing core-shell colloidal particles consisting of high-refractive-index cores and soft, transparent shells. The core-shell structure allows us to control the scattering cross-section of the particles independently of the interparticle distance, which sets the resonance condition. At the same time, the softness of the shells makes it easy to assemble disordered structures through centrifugation. We show that packings of these particles display angle-independent structural colors that can be tuned by changing the shell diameter, either by using different particles or simply by varying the concentration of the suspension. The transparency of the suspensions can be tuned independently of the color by changing the core diameter. These materials might be useful for electronic displays, cosmetics, or long-lasting dyes.

Fung, J. ; Perry, R. W. ; Dimiduk, T. G. ; Manoharan, V. N. Imaging Multiple Colloidal Particles by Fitting Electromagnetic Scattering Solutions to Digital Holograms . Journal of Quantitative Spectroscopy and Radiative Transfer 2012, 113, 2482-2489. Publisher's VersionAbstract

Digital holographic microscopy is a fast three-dimensional (3D) imaging tool with many applications in soft matter physics. Recent studies have shown that electromagnetic scattering solutions can be fit to digital holograms to obtain the 3D positions of isolated colloidal spheres with nanometer precision and millisecond temporal resolution. Here we describe the results of new techniques that extend the range of systems that can be studied with fitting. We show that an exact multisphere superposition scattering solution can fit holograms of colloidal clusters containing up to six spheres. We also introduce an approximate and computationally simpler solution, Mie superposition, that is valid for multiple spheres spaced several wavelengths or more from one another. We show that this method can be used to analyze holograms of several spheres on an emulsion droplet, and we give a quantitative criterion for assessing its validity.

Kaz, D. M. ; McGorty, R. ; Mani, M. ; Brenner, M. P. ; Manoharan, V. N. Physical ageing of the contact line on colloidal particles at liquid interfaces . Nature Materials 2012, 11, 138-142. Publisher's VersionAbstract

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 has been used to explain why colloids often bind to liquid interfaces, and has been exploited in emulsification, water purification, mineral recovery, encapsulation and the making of nanostructured materials. However, little is known about the dynamics of binding. Here we show that the adsorption of polystyrene microspheres to a water/oil interface is characterized by a sudden breach and an unexpectedly slow relaxation. The relaxation appears logarithmic in time, indicating that complete equilibration may take months. Surprisingly, viscous dissipation appears to play little role. Instead, the observed dynamics, which bear strong resemblance to ageing in glassy systems, agree well with a model describing activated hopping of the contact line over nanoscale surface heterogeneities. These results may provide clues to longstanding questions on colloidal interactions at an interface.

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