Cates, M. E. ; Manoharan, V. N. Celebrating Soft Matter's 10th anniversary: Testing the foundations of classical entropy: colloid experiments. Soft Matter 2015, 11, 6538-6546. Publisher's VersionAbstract

Defining the entropy of classical particles raises a number of paradoxes and ambiguities, some of which have been known for over a century. Several, such as Gibbs' paradox, involve the fact that classical particles are distinguishable, and in textbooks these are often ‘resolved’ by appeal to the quantum-mechanical indistinguishability of atoms or molecules of the same type. However, questions then remain of how to correctly define the entropy of large poly-atomic particles such as colloids in suspension, of which no two are exactly alike. By performing experiments on such colloids, one can establish that certain definitions of the classical entropy fit the data, while others in the literature do not. Specifically, the experimental facts point firmly to an ‘informatic’ interpretation that dates back to Gibbs: entropy is determined by the number of microstates that we as observers choose to treat as equivalent when we identify a macrostate. This approach, unlike some others, can account for the existence of colloidal crystals, and for the observed abundances of colloidal clusters of different shapes. We also address some lesser-known paradoxes whereby the physics of colloidal assemblies, which ought to be purely classical, seems to involve quantum mechanics directly. The experimental symptoms of such involvement are predicted to be ‘isotope effects’ in which colloids with different inertial masses, but otherwise identical sizes and properties, show different aggregation statistics. These paradoxes are caused by focussing one's attention on some classical degrees while neglecting others; when all are treated equally, all isotope effects are found to vanish.

Cates and Manoharan - 2015 - Testing the foundations of classical entropy.pdf
Faez, S. ; Latin, Y. ; Weidlich, S. ; Garmann, R. F. ; Wondraczek, K. ; Zeisberger, M. ; Schmidt, M. A. ; Orrit, M. ; Manoharan, V. N. Fast, label-free tracking of single viruses and weakly scattering nanoparticles in a nanofluidic optical fiber. ACS Nano 2015, 9 12349-12357. Publisher's VersionAbstract

High-speed tracking of single particles is a gateway to understanding physical, chemical, and biological processes at the nanoscale. It is also a major experimental challenge, particularly for small, nanometer-scale particles. Although methods such as confocal or fluorescence microscopy offer both high spatial resolution and high signal-to-background ratios, the fluorescence emission lifetime limits the measurement speed, while photobleaching and thermal diffusion limit the duration of measurements. Here we present a tracking method based on elastic light scattering that enables long-duration measurements of nanoparticle dynamics at rates of thousands of frames per second. We contain the particles within a single-mode silica fiber having a subwavelength, nanofluidic channel and illuminate them using the fiber’s strongly confined optical mode. The diffusing particles in this cylindrical geometry are continuously illuminated inside the collection focal plane. We show that the method can track unlabeled dielectric particles as small as 20 nm as well as individual cowpea chlorotic mottle virus (CCMV) virions—26 nm in size and 4.6 megadaltons in mass—at rates of over 3 kHz for durations of tens of seconds. Our setup is easily incorporated into common optical microscopes and extends their detection range to nanometer-scale particles and macromolecules. The ease-of-use and performance of this technique support its potential for widespread applications in medical diagnostics and micro total analysis systems.

Faez et al. - 2015 - Fast Label-Free Tracking of Single Viruses.pdf
Perry, R. W. Internal Dynamics of Equilibrium Colloidal Clusters, 2015. Publisher's VersionAbstract

Colloidal clusters, aggregates of a few micrometer-sized spherical particles, are a model experimental system for understanding the physics of self-assembly and processes such as nucleation. Colloidal clusters are well suited for studies on these topics because they are the simplest colloidal system with internal degrees of freedom. Clusters made from particles that weakly attract one another continually rearrange between different structures. By characterizing these internal dynamics and the structures connected by the rearrangement pathways, we seek to understand the statistical physics underlying self-assembly and equilibration.

In this thesis, we examine the rearrangement dynamics of colloidal clusters and analyze the equilibrium distributions of ground and excited states. We prepare clusters of up to ten microspheres bound by short-range depletion interactions that are tuned to allow equilibration between multiple isostatic arrangements. To study these clusters, we use bright-field and digital holographic microscopy paired with computational post-processing to amass ensemble-averaged and time-averaged probabilities.

We study both two-dimensional (2D) and three-dimensional (3D) clusters composed of either one or two species of particles. To learn about geometrical nucleation barriers, we track rearrangements of particles within freely rotating and translating 3D clusters. We show that rearrangements occur on a timescale of seconds, consistent with diffusion-dominated internal dynamics. To better understand excited states and transition pathways, we track hundreds of rearrangements between degenerate ground states in 2D clusters. We show that the rearrangement rates can be understood using a model with two parameters, which account for the diffusion coefficient along the excited-state rearrangement pathways and the interaction potential. To explore new methods to control self-assembly, we analyze clusters of two species with different masses and different interactions. We find that the interactions allow for control over the intracluster placement of each species, while the masses have no influence. To provide a theoretical framework for understanding these observations, we derive the classical partition function of colloidal clusters in terms of translational, rotational, and vibrational degrees of freedom. We show that the masses of the particles enter the partition function through the kinetic energy but have no effect on the probabilities of states that differ only in where the masses are placed. This result is consistent with our experiments.

Overall, this work shows that the equilibrium distribution of self-assembled colloidal clusters is well-modeled by classical statistical physics, and that the rearrangement dynamics of colloidal clusters can be understood by incorporating diffusion and the effect of the interaction potential. Because both the structures and dynamics can be accurately predicted, these clusters are a promising system for self-assembling novel materials and for studying the emergence of phase transitions.

Schade, N. B. Self-Assembly of Plasmonic Nanoclusters for Optical Metafluids, 2015. Publisher's VersionAbstract

I discuss experimental progress towards developing a material with an isotropic, negative index of refraction at optical frequencies. The simplest way to make such a material is to create a metafluid, or a disordered collection of subwavelength, isotropic electromagnetic resonators. Small clusters of metal particles, such as tetrahedra, serve as these constituents. What is needed are methods for manufacturing these structures with high precision and in sufficient yield that their resonances are identical.

Jonathan Fan et al. [Science, 328 (5982), 1135-1138, 2010] demonstrated that colloidal self-assembly is a means of preparing electromagnetic resonators from metal nanoparticles. However, the resonances are sensitive to the separation gaps between particles. Standard synthesis routes for metal nanoparticles yield crystals or nanoshells that are inadequate for metafluids due to polydispersity, faceting, and thermal instabilities. To ensure that the separation gaps and resonances are uniform, more monodisperse spherical particles are needed. An additional challenge is the self-assembly of tetrahedral clusters in high yield from these particles. In self-assembly approaches that others have examined previously, the yield of any particular type of cluster is low.

In this dissertation I present solutions to several of these problems, developed in collaboration with my research group and others. We demonstrate that slow chemical etching can transform octahedral gold crystals into ultrasmooth, monodisperse nanospheres. The particles can serve as seeds for the growth of larger octahedra which can in turn be etched. The size of the gold nanospheres can therefore be adjusted as desired. We further show that in colloidal mixtures of two sphere species that strongly bind to one another, the sphere size ratio determines the size distribution of self-assembled clusters. At a critical size ratio, tetrahedral clusters assemble in high yield. We explain the experimentally observed 90% yield with a nonequilibrium “random parking” model based on irreversible binding. Simulations based on this model reveal that 100% yield of tetrahedra is possible in principle. Finally, we combine these results and present methods for the self-assembly and purification of tetrahedral plasmonic nanoclusters, the simplest building blocks for isotropic metafluids.

Garmann, R. F. ; Sportsman, R. ; Beren, C. ; Manoharan, V. N. ; Knobler, C. M. ; Gelbart, W. M. A Simple RNA-DNA Scaffold Templates the Assembly of Monofunctional Virus-Like Particles. JACS 2015, 137, 7584–7587. Publisher's VersionAbstract

Using the components of a particularly well-studied plant virus, cowpea chlorotic mottle virus (CCMV), we demonstrate the synthesis of virus-like particles (VLPs) with one end of the packaged RNA extending out of the capsid and into the surrounding solution. This construct breaks the otherwise perfect symmetry of the capsid and provides a straightforward route for monofunctionalizing VLPs using the principles of DNA nanotechnology. It also allows physical manipulation of the packaged RNA, a previously inaccessible part of the viral architecture. Our synthesis does not involve covalent chemistry of any kind; rather, we trigger capsid assembly on a scaffold of viral RNA that is hybridized at one end to a complementary DNA strand. Interaction of CCMV capsid protein with this RNA-DNA template leads to selective packaging of the RNA portion into a well-formed capsid but leaves the hybridized portion poking out of the capsid through a small hole. We show that the nucleic acid protruding from the capsid is capable of binding free DNA strands and DNA-functionalized colloidal particles. Separately, we show that the RNA-DNA scaffold can be used to nucleate virus formation on a DNA-functionalized surface. We believe this self-assembly strategy can be adapted to viruses other than CCMV.

Magkiriadou, S. Structural Color From Colloidal Glasses, 2015. Publisher's VersionAbstract

When a material has inhomogeneities at a lengthscale comparable to the wavelength of light, interference can give rise to structural colors: colors that originate from the interaction of the material's microstructure with light and do not require absorbing dyes. In this thesis we study a class of these materials, called photonic glasses, where the inhomogeneities form a dense and random arrangement. Photonic glasses have angle-independent structural colors that look like those of conventional dyes. However, when this work started, there was only a handful of colors accessible with photonic glasses, mostly hues of blue.

We use various types of colloidal particles to make photonic glasses, and we study, both theoretically and experimentally, how the optical properties of these glasses relate to their structure and constituent particles. Based on our observations from glasses of conventional particles, we construct a theoretical model that explains the scarcity of yellow, orange, and red photonic glasses. Guided by this model, we develop novel colloidal systems that allow a higher degree of control over structural color. We assemble glasses of soft, core-shell particles with scattering cores and transparent shells, where the resonant wavelength can be tuned independently of the reflectivity. We then encapsulate glasses of these core-shell particles into emulsion droplets of tunable size; in this system, we observe, for the first time, angle-independent structural colors that cover the entire visible spectrum. To enhance color saturation, we begin experimenting with inverse glasses, where the refractive index of the particles is lower than the refractive index of the medium, with promising results. Finally, based on our theoretical model for scattering from colloidal glasses, we begin an exploration of the color gamut that could be achieved with this technique, and we find that photonic glasses are a promising approach to a new type of long-lasting, non-toxic, and tunable pigment.

Perry, R. W. ; Holmes-Cerfon, M. C. ; Brenner, M. P. ; Manoharan, V. N. Two-Dimensional Clusters of Colloidal Spheres: Ground States, Excited States, and Structural Rearrangements. Phys. Rev. Lett. 2015, 114, 228301. Publisher's VersionAbstract

We study experimentally what is arguably the simplest yet nontrivial colloidal system: two-dimensional clusters of six spherical particles bound by depletion interactions. These clusters have multiple, degenerate ground states whose equilibrium distribution is determined by entropic factors, principally the symmetry. We observe the equilibrium rearrangements between ground states as well as all of the low-lying excited states. In contrast to the ground states, the excited states have soft modes and low symmetry, and their occupation probabilities depend on the size of the configuration space reached through internal degrees of freedom, as well as a single “sticky parameter” encapsulating the depth and curvature of the potential. Using a geometrical model that accounts for the entropy of the soft modes and the diffusion rates along them, we accurately reproduce the measured rearrangement rates. The success of this model, which requires no fitting parameters or measurements of the potential, shows that the free-energy landscape of colloidal systems and the dynamics it governs can be understood geometrically.

Perry_PRL_2015.pdf Perry_PRL_2015-SupplementaryInformation.pdf
Choi, T. M. ; Park, J. - G. ; Kim, Y. - S. ; Manoharan, V. N. ; Kim, S. - H. Osmotic-Pressure-Mediated Control of Structural Colors of Photonic Capsules. Chemistry of Materials 2015, 27, 1014–1020. Publisher's VersionAbstract

Crystalline or glassy materials made of colloidal nanoparticles show distinctive photonic effects; the crystals exhibit sparkling colors with strong iridescence, while the glasses show noniridescent colors. Both colors are the results of constructive interference of the reflected light by the nonadsorbing nanostructures. Such colored materials have potential applications as nonfading colorants in reflective color displays, optical sensors, coatings, and cosmetics. All of these applications require granular format of the nanostructures; however, precise control of the nanostructures from amorphous to crystalline over the submillimeter length scale remains challenging. Here, we present micrometer-level control of photonic nanostructures confined in microcapsules through osmotic-pressure-mediated concentration. We encapsulate aqueous suspensions of colloidal particles using double-emulsion drops with ultrathin layers of photocurable resin. The microcapsules are then isotropically compressed by imposing a positive osmotic pressure difference that forces the water out through the thin resin membrane. We find that the internal nanostructure of our photonic microcapsules can be kinetically controlled from crystalline to amorphous; slow concentration in small pressure gradients yields colloidal crystals with sparkling color patterns, whereas fast concentration in large pressure gradients yields glassy packing with only short-range order, which show uniform color with little iridescence. By polymerizing the thin monomeric shell, we permanently fix these nanostructures. Our findings provide new insights into the design and synthesis of optical materials with controlled structural colors.

Choi_ChemMater_2015.pdf Choi_ChemMater_2015-SupplementaryInformation.pdf
Rogers, W. B. ; Manoharan, V. N. Programming colloidal phase transitions with DNA strand displacement. Science 2015, 347, 639-642. Publisher's VersionAbstract

DNA-grafted nanoparticles have been called “programmable atom-equivalents”: Like atoms, they form three-dimensional crystals, but unlike atoms, the particles themselves carry information (the sequences of the grafted strands) that can be used to “program” the equilibrium crystal structures. We show that the programmability of these colloids can be generalized to the full temperature-dependent phase diagram, not just the crystal structures themselves. We add information to the buffer in the form of soluble DNA strands designed to compete with the grafted strands through strand displacement. Using only two displacement reactions, we program phase behavior not found in atomic systems or other DNA-grafted colloids, including arbitrarily wide gas-solid coexistence, reentrant melting, and even reversible transitions between distinct crystal phases.

Collins, J. W. Self-Assembly of Colloidal Spheres with Specific Interactions, 2014. Publisher's VersionAbstract

In this thesis, I discuss engineering colloidal particles to have specific, isotropic interactions and studying their cluster geometries in equilibrium. I discuss light scattering experiments showing that a highly specific protein, Dscam, is unstable against thermal aggregation. This result lead me to use DNA instead to control interparticle specificity. I coated 1-micron diameter polystyrene particles uniformly with DNA. I used fluorescence microscopy with oxygen-scavenging enzymes to observe these particles self-assembling in clusters. These experiments show that a packing of 6 spheres that is rarely seen in a single-component system is observed very often in an optimized 3-species system. Then I show experiments using the same 3 species but 9 total particles, finding that the equilibrium yields of the most likely cluster relative to other stable clusters are lower than at 6 particles. I conclude from these experiments that optimizing the assembly of an otherwise unlikely configuration may require nearly as many species as particles. Finally, I investigate the scalability of self-assembly of particles with isotropic and specific interactions theoretically. I use both exact and approximate partition functions to show that spheres with specific interactions can have energy landscapes with thermodynamically large numbers of strictly local minima relative to the number of their ground states. Compared to single-component systems, these systems of many different species may spend much more time in kinetic traps and never reach their ground states. Finally, I discuss briefly some directions for further study, including questions of how the results in this thesis may be related to protein folding and complex formation.

Magkiriadou, S. ; Park, J. - G. ; Kim, Y. - S. ; Manoharan, V. N. Absence of red structural color in photonic glasses, bird feathers, and certain beetles. Physical Review E 2014, 90, 062302. Publisher's VersionAbstract

Colloidal glasses, bird feathers, and beetle scales can all show structural colors arising from short-ranged spatial correlations between scattering centers. Unlike the structural colors arising from Bragg diffraction in ordered materials like opals, the colors of these photonic glasses are independent of orientation, owing to their disordered, isotropic microstructures. However, there are few examples of photonic glasses with angle-independent red colors in nature, and colloidal glasses with particle sizes chosen to yield structural colors in the red show weak color saturation. Using scattering theory, we show that the absence of angle-independent red color can be explained by the tendency of individual particles to backscatter light more strongly in the blue. We discuss how the backscattering resonances of individual particles arise from cavity-like modes and how they interact with the structural resonances to prevent red. Finally, we use the model to develop design rules for colloidal glasses with red, angle-independent structural colors.

Manoharan, V. ; Magkiriadou, S. ; Park, J. - G. Photonic balls containing a microstructure of core-shell particles exhibiting angularly-independent structural color, 2014.Abstract

A photonic assembly for observing a preselected color includes an assembly of colloidal particles in a continuous liquid phase, the colloidal particles comprising a core scattering center and a shell layer surrounding the core, wherein the core scattering center is selected to scatter light having a predetermined wavelength, and wherein the shell has a thickness selected to provide an overall colloidal particle size that is about the same dimension as the wavelength of preselected color to be observed.

Dimiduk, T. G. ; Perry, R. W. ; Fung, J. ; Manoharan, V. N. Random-subset fitting of digital holograms for fast three-dimensional particle tracking [Invited]. Applied Optics 2014, 53, G177-G183. Publisher's VersionAbstract

Fitting scattering solutions to time series of digital holograms is a precise way to measure three-dimensional dynamics of microscale objects such as colloidal particles. However, this inverse-problem approach is computationally expensive. We show that the computational time can be reduced by an order of magnitude or more by fitting to a random subset of the pixels in a hologram. We demonstrate our algorithm on experimentally measured holograms of micrometer-scale colloidal particles, and we show that 20-fold increases in speed, relative to fitting full frames, can be attained while introducing errors in the particle positions of 10 nm or less. The method is straightforward to implement and works for any scattering model. It also enables a parallelization strategy wherein random-subset fitting is used to quickly determine initial guesses that are subsequently used to fit full frames in parallel. This approach may prove particularly useful for studying rare events, such as nucleation, that can only be captured with high frame rates over long times.

Zeravcic, Z. ; Manoharan, V. N. ; Brenner, M. P. Size limits of self-assembled colloidal structures made using specific interactions. PNAS 2014, 111, 15918 – 15923. Publisher's VersionAbstract

We establish size limitations for assembling structures of controlled size and shape out of colloidal particles with short-ranged interactions. Through simulations we show that structures with highly variable shapes made out of dozens of particles can form with high yield, as long as each particle in the structure binds only to the particles in their local environment. To understand this, we identify the excited states that compete with the ground-state structure and demonstrate that these excited states have a completely topological characterization, valid when the interparticle interactions are short-ranged. This allows complete enumeration of the energy landscape and gives bounds on how large a colloidal structure can assemble with high yield. For large structures the yield can be significant, even with hundreds of particles.

Zeravcic_PNAS_2014.pdf Zeravcic_PNAS_2014-SupportingInformation.pdf
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 2014, 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.

Meng, G. ; Paulose, J. ; Nelson, D. R. ; Manoharan, V. N. Elastic Instability of a Crystal Growing on a Curved Surface . Science 2014, 343, 634-637. Publisher's VersionAbstract

Although the effects of kinetics on crystal growth are well understood, the role of substrate curvature is not yet established. We studied rigid, two-dimensional colloidal crystals growing on spherical droplets to understand how the elastic stress induced by Gaussian curvature affects the growth pathway. In contrast to crystals grown on flat surfaces or compliant crystals on droplets, these crystals formed branched, ribbon-like domains with large voids and no topological defects. We show that this morphology minimizes the curvature-induced elastic energy. Our results illustrate the effects of curvature on the ubiquitous process of crystallization, with practical implications for nanoscale disorder-order transitions on curved manifolds, including the assembly of viral capsids, phase separation on vesicles, and crystallization of tetrahedra in three dimensions.

Kim, S. - H. ; Park, J. - G. ; Choi, T. M. ; Manoharan, V. N. ; Weitz, D. A. Osmotic-pressure-controlled concentration of colloidal particles in thin-shelled capsules . Nature Communications 2014, 5 3068. Publisher's VersionAbstract

Colloidal crystals are promising structures for photonic applications requiring dynamic control over optical properties. However, for ease of processing and reconfigurability, the crystals should be encapsulated to form ‘ink’ capsules rather than confined in a thin film. Here we demonstrate a class of encapsulated colloidal photonic structures whose optical properties can be controlled through osmotic pressure. The ordering and separation of the particles within the microfluidically created capsules can be tuned by changing the colloidal concentration through osmotic pressure-induced control of the size of the individual capsules, modulating photonic stop band. The rubber capsules exhibit a reversible change in the diffracted colour, depending on osmotic pressure, a property we call osmochromaticity. The high encapsulation efficiency and capsule uniformity of this microfluidic approach, combined with the highly reconfigurable shapes and the broad control over photonic properties, make this class of structures particularly suitable for photonic applications such as electronic inks and reflective displays.

Rogers, W. B. ; Corbett, M. ; Magkiriadou, S. ; Guarillof, P. ; Manoharan, V. N. Breaking trade-offs between translucency and diffusion in particle-doped films. Optical Materials Express 2014, 4 2621-2631. Publisher's VersionAbstract

Particle-doped thin films that are translucent and diffusive have applications in cosmetics, coatings, and display technologies, but finding material combinations that produce these effects simultaneously is challenging: formulations tend to be either transparent or opaque. Using a combination of Mie scattering calculations and spectral transmission measurements on monodisperse colloidal suspensions, we demonstrate that the two characteristic optical properties of the films, total transmittance and haze, scale with the effective backscattering and forward scattering cross sections, both of which are properties of single particles. These scalings enable an efficient computational search for combinations of particle sizes, concentrations, and refractive indices that break the trade-off between translucency and diffusion. The optimum particle sizes and concentrations obey power-law dependences on the refractive index difference, a result of the interference condition for resonances in the scattering cross sections. The power laws serve as design equations for formulating particle-doped thin films.

Park, J. - G. ; Kim, S. - H. ; Magkiriadou, S. ; Choi, T. M. ; Kim, Y. - S. ; Manoharan, V. N. Full-Spectrum Photonic Pigments with Non-iridescent Structural Colors through Colloidal Assembly. Angewandte Chemie International Edition 2014, 53, 2899-2903. Publisher's VersionAbstract

Structurally colored materials could potentially replace dyes and pigments in many applications, but it is challenging to fabricate structural colors that mimic the appearance of absorbing pigments. We demonstrate the microfluidic fabrication of “photonic pigments” consisting of microcapsules containing dense amorphous packings of core–shell colloidal particles. These microcapsules show non-iridescent structural colors that are independent of viewing angle, a critical requirement for applications such as displays or coatings. We show that the design of the microcapsules facilitates the suppression of incoherent and multiple scattering, enabling the fabrication of photonic pigments with colors spanning the visible spectrum. Our findings should provide new insights into the design and synthesis of materials with structural colors.

Lee, M. ; Collins, J. W. ; Aubrecht, D. M. ; Sperling, R. ; Solomon, L. ; Ha, J. - W. ; Yi, G. - R. ; Weitz, D. A. ; Manoharan, V. N. Synchronized reinjection and coalescence of droplets in microfluidics. Lab on a Chip 2014, 14, 509-513. Publisher's VersionAbstract

Coalescence of two kinds of pre-processed droplets is necessary to perform chemical and biological assays in droplet-based microfluidics. However, a robust technique to accomplish this does not exist. Here we present a microfluidic device to synchronize the reinjection of two different kinds of droplets and coalesce them, using hydrostatic pressure in conjunction with a conventional syringe pump. We use a device consisting of two opposing T-junctions for reinjecting two kinds of droplets and control the flows of the droplets by applying gravity-driven hydrostatic pressure. The hydrostatic-pressure operation facilitates balancing the droplet reinjection rates and allows us to synchronize the reinjection. Furthermore, we present a simple but robust module to coalesce two droplets that sequentially come into the module, regardless of their arrival times. These re-injection and coalescence techniques might be used in lab-on-chip applications requiring droplets with controlled numbers of solid materials, which can be made by coalescing two pre-processed droplets that are formed and sorted in devices.