# Colloids and interfaces

Using digital holographic microscopy, we study how colloidal particles bind to oil-water interfaces. Small particles have a natural affinity for interfaces, and this affinity can be used to control their self-assembly and make some interesting materials. However, the dynamics of the particles before and after they breach the interface are not well-understood. We do experiments to observe these dynamics and find some surprising results.

If you shake up a mixture of oil and vinegar, you will disperse droplets of one into the other only very briefly before the vinegar and oil separate into distinct layers. Colloidal particles can bind to the interface to reduce the total oil-water surface area (and energy). Once these particles bind to the interface it's virtually impossible for them to detach. This means the interface can be used as a scaffold for assembling the particles, or the particles can be used to coat the interface and stabilize it, forming what is called a "Pickering emulsion".

The affinity of colloidal particles for liquid interfaces has been studied for more than a century. In 1903, W. Ramsden published a paper about solids accumulating at the interface between oil and water. Since then, there have been thousands of studies on micron-scale particles at immiscible fluid-fluid interfaces, but the dynamics of such systems are still quite poorly understood.

We study the non-equilibrium behavior of these systems using  digital holographic microscopy, which can track the particles in three dimensions at high speed and with high spatial precision. Dave Kaz and Ryan McGorty, the first students to work on this project, built a holographic microscope outfitted with an optical tweezer that could be used to exert a force on the particles. They pushed particles toward a planar water-oil interface and found something surprising happened when the particles started poking through the interface.

Once the particles breach the interface, they relax logarithmically in time towards equilibrium. The velocity of the particles gets smaller and smaller the closer they get to equilibrium, despite the huge driving force. In fact, if we extrapolate our results, we find that a 1-micrometer particle could take months or even years to reach equilibrium. The explanation most consistent with this observation, proposed by Madhav Mani (working with Michael Brenner), is that nanoscale surface features on the particles pin the three-phase contact line and hinder the progress of the particle toward equilibrium. We have since seen this behavior in a wide variety of different colloidal particles.

We are also studying the rotational dynamics of particles at interfaces by tracking ellipsoids near and at an interface. Here is an example of the type of information we can get from holograms - 3D position, and angular motion all from a single snapshot. The video was taken at 100 fps, analysed with HoloPy, then rendered and played back at 25 fps. Just like its spherical counterparts, the movement of the ellipsoid towards its equilibrium configuration is orders of magnitude slower than expected. It also rotates in the plane of the interface as it slowly relaxes, suggesting that there is enough asymmetry in the system to produce a torque.

Wang, A. ; Rogers, W. B. ; Manoharan, V. N. Effects of Contact-Line Pinning on the Adsorption of Nonspherical Colloids at Liquid Interfaces. Physical Review Letters 2017, 119, 108004. Publisher's VersionAbstract
The effects of contact-line pinning are well known in macroscopic systems but are only just beginning to be explored at the microscale in colloidal suspensions. We use digital holography to capture the fast three-dimensional dynamics of micrometer-sized ellipsoids breaching an oil-water interface. We find that the particle angle varies approximately linearly with the height, in contrast to results from simulations based on the minimization of the interfacial energy. Using a simple model of the motion of the contact line, we show that the observed coupling between translational and rotational degrees of freedom is likely due to contact-line pinning. We conclude that the dynamics of colloidal particles adsorbing to a liquid interface are not determined by the minimization of interfacial energy and viscous dissipation alone; contact-line pinning dictates both the time scale and pathway to equilibrium.
Wang, A. ; McGorty, R. ; Kaz, D. M. ; Manoharan, V. N. Contact-line pinning controls how quickly colloidal particles equilibrate with liquid interfaces. Soft Matter 2016, 12, 8958-8967. Publisher's VersionAbstract
Previous experiments have shown that spherical colloidal particles relax to equilibrium slowly after they adsorb to a liquid-liquid interface, despite the large interfacial energy gradient driving the adsorption. The slow relaxation has been explained in terms of transient pinning and depinning of the contact line on the surface of the particles. However, the nature of the pinning sites has not been investigated in detail. We use digital holographic microscopy to track a variety of colloidal spheres---inorganic and organic, charge-stabilized and sterically stabilized, aqueous and non-aqueous---as they breach liquid interfaces. We find that nearly all of these particles relax logarithmically in time over timescales much larger than those expected from viscous dissipation alone. By comparing our results to theoretical models of the pinning dynamics, we infer the area per defect to be on the order of a few square nanometers for each of the colloids we examine, whereas the energy per defect can vary from a few $kT$ for non-aqueous and inorganic spheres to tens of $kT$ for aqueous polymer particles. The results suggest that the likely pinning sites are topographical features inherent to colloidal particles---surface roughness in the case of silica particles and grafted polymer hairs'' in the case of polymer particles. We conclude that the slow relaxation must be taken into account in experiments and applications, such as Pickering emulsions, that involve colloids attaching to interfaces. The effect is particularly important for aqueous polymer particles, which pin the contact line strongly.
Rahmani, A. M. ; Wang, A. ; Manoharan, V. N. ; Colosqui, C. E. Colloidal particle adsorption at liquid interfaces: capillary driven dynamics and thermally activated kinetics. Soft Matter 2016, 12, 6365-6372. Publisher's VersionAbstract
The adsorption of single colloidal microparticles (0.5–1 μm radius) at a water–oil interface has been recently studied experimentally using digital holographic microscopy [Kaz et al., Nat. Mater., 2012, 11, 138–142]. An initially fast adsorption dynamics driven by capillary forces is followed by an unexpectedly slow relaxation to equilibrium that is logarithmic in time and can span hours or days. The slow relaxation kinetics has been attributed to the presence of surface “defects” with nanoscale dimensions (1–5 nm) that induce multiple metastable configurations of the contact line perimeter. A kinetic model considering thermally activated transitions between such metastable configurations has been proposed [Colosqui et al., Phys. Rev. Lett., 2013, 111, 028302] to predict both the relaxation rate and the crossover point to the slow logarithmic regime. However, the adsorption dynamics observed experimentally before the crossover point has remained unstudied. In this work, we propose a Langevin model that is able to describe the entire adsorption process of single colloidal particles by considering metastable states produced by surface defects and thermal motion of the particle and liquid interface. Invoking the fluctuation dissipation theorem, we introduce a drag term that considers significant dissipative forces induced by thermal fluctuations of the liquid interface. Langevin dynamics simulations based on the proposed adsorption model yield close agreement with experimental observations for different microparticles, capturing the crossover from (fast) capillary driven dynamics to (slow) thermally activated kinetics.
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.

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.

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.

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.

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.

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.