Reports: ND1055260-ND10: Analogies between Dense Microparticle Monolayers at Fluid Interfaces and 2D Granular Matter
Kathleen J. Stebe, PhD, University of Pennsylvania
We study structure and rearrangement in monolayers of particles at fluid interfaces. Particles become trapped at fluid interfaces; the reduction by locating at the interface is typically orders of magnitude larger than thermal energies. In these trapped layers, particles assemble in structures that range from densely packed, jammed layers to open structures, cemented by capillary interactions.
Capillary interactions occur between pairs of particles to minimize the distortion the particles make in the interface. Interface distortion can be caused by particle weight or by particles with undulated contact lines. Capillary interactions also occur as particles interact with the interface shape; these interactions are of two types. The first is due to particle weight for particles on a sloped interface; the component of weight tangent to the interface moves the particle to minimize its potential energy. The second is due to curvature capillary interaction; particles move along gradients in interface deviatoric curvature. These packings dictate stresses at the interface that we aim to elucidate, with factors including the collective weight of all particles above any reference plane, capillary interactions, Van der Waals and electrostatic interactions, steric interactions and friction. The response to compression will differ for particles strongly trapped at the interface, which cannot relieve the compression by simply desorbing, but can rearrange eg by buckling out of plane, and for particles weakly trapped at the interface, which can relieve the stress by desorbing.
2. Research Progress and Results
In prior work, we have fabricated and studied structures stabilized by jammed layers and developed libraries of particles with strong trapping energies including disks with weak interactions, anisotropically shaped particles with strong, directional interactions, and particles with weak trapping energies. Our current work has two focal points: to develop (1) magnetic tweezers to move individual particles, (via leveraged funding, not reported here) and (2) methods to compact layers of particles study them as they are perturbed. We are working first with monodisperse disks with significant trapping energies. These disks form a percolating network rather than a crystallized layer, already underscoring the important distinctions attractive interactions bring to this field. We find that many particles on a tilted interface form a gradient in packing as the weight of particles above a reference plane compresses particles beneath that plane.
We begin with monodisperse disks made by standard photolithographic methods of radius a=12.5 microns and thickness d=5 micron with typical RMS surface roughness of 18-25 nm as determined by AFM. These particles have Bond number , where is the difference in densities between the particles and the surrounding fluids, and is the interfacial tension. These disks interact with neighboring particles in the very near field owing to contact line undulations, and slide down a weakly curved meniscus to minimize potential energy. The disks can be fabricated with fluorescent patterns by incorporating a fluorophore in the epoxy resin and photobleaching, allowing their rotation and translation to be discerned and tracked.
The particles are placed on the hexadecane- aqueous interface in a vessel 1.7 cm in diameter with an aluminum cylindrical base and a Teflon cylindrical top. The vessel is filled with water to the line where the aluminum and Teflon meet; 10uL suspension of particles in 10 vol% IPA in water is spread on the interface. After 5 minutes, a layer of hexadecane is gently introduced on this layer. We focus on the pinned meniscus at the outer edge of the cell, which has a weak downward slope and very weak interfacial curvatures. The shape of this interface decays to the reference plane of the fluid in the cell with an exponential decay over distances comparable to the capillary length of order millimeters. Hence, slopes are steepest for particles near the wall. Particles move in creeping flow down the interface slope and accumulate at the edge. As particles accumulate, each particle above the reference plane of the interface height at the outer wall exerts a force that compresses the layer. As a result, particles have a gradient in packingdensely packed near the wall, and an increasingly open and lacy structure away from it. The apparatus and the packings are shown in Figure 1.
Plans for the coming year:
We will exploit this method for studying stress response of monolayers of different densities. By molding interfaces with controlled slopes and weak curvature gradients, capillary migration will be used to form and to compact particle layers. Force balances above reference planes, involving simple counting of particles and contacts, will be used to calculate the compressive mechanical, non-thermodynamic surface pressure on the aggregates below the reference plane by the particles above the reference plane. Furthermore, for few, point contacts, the magnitude of local point forces on particular points of contact can be calculated. We will perturb or disrupt this layer by allowing large, heavy particles to move down the interface into these packings, effectively acting as 2D wrecking balls impacting the layers.
Re-organization of these layers will be studied in two frameworks: as a continuum sheet and as an ensemble of particles. In the continuum limit, the principal normal stress and shear stress can be determined using elementary relationships (Mohrs circle) to probe e.g. for ductile, brittle or plastic responses. Should the packings display dissipative properties, we will study them as viscoelastic media. As individual elements, we will track particle positions and rotations to generate information including the density profile g(r) (a measure of translational order), the bond oriental order parameter (a measure of short-range order), contact numbers, as well as the extent of non-affine deformation using D2min. Contact numbers and bond oriental order parameter φ6 will be found using a Delaunay triangulation.