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School of Biological Sciences

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School of Chemistry and Biochemistry

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School of Earth and Atmospheric Sciences

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School of Mathematics

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School of Physics

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Active defects in flat and curved spaces

(Georgia Institute of Technology, 2022-12-13) Nambisan, Jyothishraj

The interaction and dynamics of topological defects have inspired numerous studies across physics over centuries. They manifest as salient features in liquid crystalline materials, as regions where the underlying director field is undefined. Liquid crystals can be intrinsically driven out of equilibrium via an energy input at the level of the constituent particles, thus forming a unique class of non-equilibrium systems, known as active liquid crystals. In this thesis, we explore the rich phenomenology of topological defects observed in the microtubule-kinesin active nematic system, confined to surfaces of different topology and varying curvature. In 2D flat space, we observe short-range ferromagnetic alignment of +1/2 defects, mediated by -1/2 defects in between. This is primarily driven by passive elastic mechanisms, as confirmed via hydrodynamic simulations of active and passive liquid crystals. However, the system does not develop any long-range or quasi-long-range order over time. The qualitative features of defect-defect correlations are found to be independent of defect density. In curved space experiments, we observe a clear preference for the orientation of defects and persistent long-range order detected on highly curved regions of toroidal drops. This is a remarkable confirmation that curvature, and gradients of it, have a major role in intrinsically biasing the alignment of defects. This is in stark contrast to random, isotropic defect orientations found in locally flat regions. We then propose an idealized mechanism of defect alignment subject to curvature gradients, which is currently being inspected via agent-based simulations of an active multi-defect system. The observation of surface curvature as an aligning field is much more fundamental than recent works in similar systems, where patterned substrates and external fields have been used to align defects and create order. We also present the first experimental confirmation of hyperuniformity in an active system of topological defects. Originally conceived from the mathematical study of point patterns, hyperuniform systems are characterized by the suppression of large-scale fluctuations in the number (or density) of particles like a perfect crystal, while being isotropic like a liquid that has no long-range spatial or orientational order. Our discovery is unique, as it is the entire system that is hyperuniform, and not any specific snapshot or microstate of it. We quantify the degree of hyperuniformity using existing tests in literature and contrast the results with randomly distributed and manually dragged point patterns. The origins of hyperuniformity is found to be connected to the intrinsic creation-annihilation mechanisms of the defects and the constant average number of defects, even in the active turbulent state. The confirmation of hyperuniformity in our system also contrasts with giant number fluctuations, that are generally seen as a hallmark of active matter. Overall, our work explores the rich interplay of activity, topology and curvature in a liquid crystalline system and how topological defects interact to develop correlations and orientational order subject to the governing factors. More generally, our work provides an exciting test bed with associated techniques to study active matter in a controlled experimental setting.
Clusters, Waves, and Force Chains in Fire-Ant Collectives: Emergent Behavior in Out-of-Equilibrium Particulate Systems

(Georgia Institute of Technology, 2021-07-29) Anderson, Caleb J.

Unlike other out-of-equilibrium systems, active matter is held far from equilibrium by energy input at the single particle level. The field includes a wide range of systems, but the most familiar examples, including flocks of birds and schools of fish, are biological. Despite the prevalence of biological systems, most of the important experimental work over the last two decades has examined synthetic systems with relatively simple particle interactions that closely approximate theoretical models. In this thesis, we examine fire ants, a biological system with complicated social interactions, and compare their behavior to expectations from active matter theory. We find surprising evidence of two hallmark aspects in active matter, collective-motion and motility-induced phase separation. Then, we demonstrate that the ants propagate a new type of nonlinear solitary wave in 2D columns, in which the ants activate and deactivate as the wave passes them, indicating the importance of time-dependent activity in future models of active matter. We also compare 3D columns of ants to columns of fluids and passive grains. Our results show that activity is not enough to fully wash out the granular nature of the ants. Finally, we turn to a synthetic system, vibrated polar disks, to examine the nature of the collective-motion phase transition in finite systems and find that the phase transition is qualitatively different than in the infinite-size limit. We argue that, in contrast to equilibrium systems, finite size effects are likely important in predicting the behavior of most practical active matter systems. Altogether, our work shows that the universal predictions of active matter theory are robust to the nature of particle interactions and proposes simple new directions for future theory to encompass more complicated active matter systems.
Mechanics of fire ant aggregations: An experimental study of active matter

(Georgia Institute of Technology, 2019-07-17) Tennenbaum, Michael Jacob

Fire ant aggregations are inherently active materials. Each ant converts its own stored energy into motion, and it is these motions that contribute to the bulk material properties of the aggregation. However, the level of activity is not constant in time. This allows us measure the material properties of this active material at different activity levels. As the aggregation changes in time we monitor the changes in activity through the mechanics of the aggregation, the normal force, and by looking at a 2D system. We find that the frequency response of active aggregations at low volume fraction is similar to that of critical gels whereas inactive aggregations are frequency independent. At high volume fraction active ants lose their frequency dependence. We construct a model of the level of activity that is dependent on the number of currently active ants in the system. The activity also affects how homogeneous the system is which we see from the 2D system. Active aggregations are more homogeneous than inactive aggregations. We apply large amplitude oscillations to the aggregation and find that at large strain amplitude the effect of the activity is washed out. In that case there is no difference in the level of viscous or elastic nonlinearity with activity. At intermediate strain amplitudes we do see an effect but only in the viscous nonlinearity. We attribute this to linking/unlinking events taking place in the aggregation. The elastic nonlinearity is dependent on the rate at which linking and unlinking events occur but the level of viscous nonlinearity is related not to the rate but to the number of linking/ unlinking events. This number increases when changing from an inactive to an active aggregation and when increasing the effective volume fraction. Activity also affects how the aggregation responds to applied stresses, at low applied stresses active ants flow in the direction of the applied stress but at intermediate applied stresses, active ants resist the applied stress. At high applied stress the aggregation is not able to resist the applied stress and flows like a simple liquid. If instead of a stress, a strain rate is applied we see no difference between a live and a dead aggregation. We find that the viscosity of the aggregation shear thins massively. Overall, we learn that the level of activity affects the mechanics of the system. The activity level changes naturally in ant aggregations in time which allows us to measure the mechanics at different activity levels. We show that it is possible to overwhelm an active system through external perturbations such that the activity does not play a role in the mechanics. However, within the realm where the activity plays a role, it can be used to tune the material properties of the system without changing the structure of the system itself.
Generation and Stability of Charged Toroidal Droplets

(Georgia Institute of Technology, 2018-05) Aizenman, Aaron

In this project, we have determined the quantitative parameters governing the transition phases of charged toroidal droplets. An instability reminiscent of the Saffman-Taylor Instability (viscous fingers) has been observed when toroidal droplets are exposed to a significantly high voltage source, but this is the only recorded development of this instability in a three-dimensional situation (Alberto Fernandez-Nieves 2016). We created a silicon oil environment of extremely high viscosity with aminopropyl terminated silicon oil (ATSO) added to lower surface tension. We utilized surfactants to minimize the surface tension between the inner and outer fluids to slow down the dynamics of the system enough to give the surface a chance to reach equipotential, thus allowing us to test the theories that currently exist in the field. In an attempt to disprove the possibility that this was the Saffman-Taylor Instability, we also attempted viscosity inversion experiments. These failed, thus giving us almost conclusive proof that this was indeed the Saffman-Taylor Instability. By proving that this is indeed the Saffman-Taylor Instability, we have also proven that this three-dimensional problem can be analyzed as a series of two-dimensional problems. This approach vastly simplifies further calculations and analysis of similar systems. A secondary focus of this project was to perfect a method of automated generation of inherently unstable shapes in viscoelastic materials. By using a novel method of 3D printing, the project attempted to increase the efficiency with which we can generate samples for testing and observation while also adding uniformity and consistency to the trials and experiments.
Nematic materials in curved spaces

(Georgia Institute of Technology, 2018-03-19) Ellis, Perry W.

When confined to curved surfaces or to bounded volumes, ordered materials often experience geometric frustration, where the order cannot be satisfied everywhere on the surface or in the volume. This frustration induces unavoidable distortions in the material, possibly resulting in the generation of one or more defects in the order. In this thesis, we focus on materials with nematic order and investigate the role of geometry in the interplay between order and confinement. We first consider a nematic confined to the surface of a toroidal droplet. The nematic is active such that the individual particles do work on their surroundings. This activity results in a nematic that spontaneously undergoes creation and annihilation of opposite-signed pairs of topological defects; these defects continually move and explore the surface of the torus. Despite the activity, we find that the defects couple to the underlying curvature of the surface: on average, the positive defects migrate towards the outside of the torus, where the Gaussian curvature is positive, and the negative defects migrate towards the inside of the torus, where Gaussian curvature is negative. When we compare our results to equilibrium predictions as well as to computer simulations of our active nematic, we find that adding activity to order resembles bringing an equilibrium system to high temperature; that is, activity plays the role of thermal fluctuations in driving the defects to explore configuration space. There are, however, significant differences with equilibrium nematics that bring richness to the problem. We next consider a nematic liquid crystal (NLC) confined to toroidal droplets with homeotropic anchoring. We find a twisted equilibrium configuration, where the nematic spontaneously develops chirality and the amount of twist depends on the ratio of the torus ring and tube radii. Experiments with a NLC confined to straight and bent cylindrical capillaries under similar conditions reveal that the twist is a response to the additional curvature that arises when bending a cylinder into a torus. Lastly, we consider a NLC confined to a capillary bridge under homeotropic anchoring such that the topology requires the presence of a defect in the bulk. We perform experiments with waist-shaped and barrel-shaped bridges and find that waist-shaped bridges contain hyperbolic defects while barrel-shaped bridges contain radial defects. In addition, we find that the ratio of the bridge height to its width determines whether the defect is a ring defect or a point defect. Overall, our results illustrate the variety of ways curvature affects nematic order: it can control defect type, defect location, and can even tune specific distortions in the order.
Toroidal instabilities in the presence of charge and non-Newtonian fluids

(Georgia Institute of Technology, 2017-05-16) Fragkopoulos, Alexandros A.

Cylindrical jets break into spherical droplets due to surface-tension driven, Rayleigh-Plateau instabilities. Interestingly, toroidal droplets can also transform into a spherical droplet via a shrinking instability whereby the handle of the torus progressively disappears. We study this instability using particle image velocimetry and determining the velocity field inside the droplet. Using the experiments as a guide, we theoretically analyze the problem and account for the discrepancy between previous theoretical and simulation work. This allows elucidating which of the many possible modes controlling the toroidal droplet evolution are needed to capture the evolution and deformation of the droplet as seen experimentally. We then apply a voltage difference across the droplet and a controlled ground to charge the toroidal droplet. In this case, surface tension stresses compete with electrostatic stresses due to the presence of surface charge; qualitatively changing the behavior of the droplet, which, for sufficiently high voltages, is able to transition from a shrinking torus to an expanding torus. Remarkably, an additional transition happens at even higher voltages; in this case, the torus produces finger-like structures reminiscent of the Saffman-Taylor instability. Despite the three-dimensional character of our experiments, charge and geometry both combine to allow observing an instability that is most often seen in quasi-two dimensional situations. We study and model all these transitions, and identify the essential physics needed to describe them. Finally, we exploit that thin toroidal droplets approach the cylindrical limit to also study the effect of charge over jet break-up. We do this by comparing the experimentally determined wavelength associated to the fastest unstable mode to theoretical expectation for charged cylindrical jets. Furthermore, we study the break-up dynamics in the presence of rheologically non-linear materials. In this case, the droplets resist break-up for long times compare to when we use simple liquids. We show that we can explain our data by incorporating the non-linearities into a linear treatment of the problem through the strain-rate-dependent viscosity.
Structural relaxation of supercooled liquids based on soft particles: Avoiding the glass transition at high concentrations

(Georgia Institute of Technology, 2016-07-29) Hyatt, John S.

Using 3D dynamic and static light scattering (DLS and SLS) and small-angle neutron scattering (SANS), we investigate the intra-particle structure of neutral and partially ionized (N-isopropylacrylamide)-co-(acrylic acid) (NIPAM-co-AAc) microgels. In the case of neutral microgels, we find that the collapse of polyNIPAM above the LCST is partially frustrated, due to breakup of the NIPAM sequences by large amounts of copolymerized AAc. In the case of the partially ionized microgels, we find that at high temperatures, the combination of poor solvent conditions and weakly-charged polymer results in phase separation between the charged and uncharged regions of the network. We also investigate the structural relaxation of dense suspensions of the microgels in conditions of good solvent and high charge using DLS, SLS, and oscillatory and steady-state rheology. We find that even at very high particle concentrations, the suspensions remain in the supercooled-liquid regime, and never enter the glassy state. This is caused primarily by a combination of deswelling due to increasing ionic osmotic pressure and the inherent softness of the microgel particles. This represents a key difference between dense suspensions of soft and hard colloidal particles, and between atomic and colloidal glassformers in general.
Toroidal droplets: instabilities, stabilizing and nematic order

(Georgia Institute of Technology, 2014-04-08) Pairam, Ekapop

The goal of this thesis is to study the ground or metastable state structure of nematic liquid crystal systems confined inside handled shapes such as a torus or double torus. We begin our work by introducing a new method to generate a toroidal droplet from a Newtonian liquid inside another, immiscible, Newtonian liquid. In this situation, a toroidal droplet is unstable and follows one of two routes in transforming into a spherical droplet: (i) its tube breaks in a way reminiscent to the breakup of a cylindrical jet, or (ii) its tube grows until it finally coalesces onto itself. However, to be able to probe the nematic structure, we need to address the issue of instabilities. This is done by replacing the outer liquid with a yield stress material, which ultimately leads to the stabilization of the toroidal droplet. Through the experimental investigation, we are able to establish the stabilization conditions. Finally, we generate and stabilize toroidal droplets with a nematic liquid crystal as the inner liquid and a yield stress material as the outer medium. Here we observe that in the ground state, the nematic liquid crystal exhibits an intriguing twisted structure irrespective of the aspect ratio of the torus. While there are no defects observed in a toroidal droplet case, two defects with -1 topological charge each emerge each time we increase the number of handles.
From soft to hard sphere behavior: the role of single particle elasticity over the phase behavior of microgel suspensions

(Georgia Institute of Technology, 2010-11-11) Lietor-Santos, Juan-Jose

The goal of this thesis is to study the role of single particle elasticity in the overall behavior of particulate systems. For this purpose, we use microgel particles, which are crosslinked polymer networks immersed in a solvent. In these systems, the amount of cross-linker determines their elasticity and ultimately the stiffness of the particle. For a system of hard spheres, the phase behavior is solely determined by the volume fraction occupied by the particles. Based on the volume fraction, liquid, crystal and glassy phases are observed. Interestingly, microgel particles display a richer and fascinating set of different behaviors depending on the particle stiffness. Previous results obtained in our group show that for highly cross-linked microgels, the glass phase disappears and there are only liquid and crystalline phases. By contrast, preliminary measurements indicate that for ultrasoft microgel particles the system does not show any signature of crystalline or glassy phases. The system seems to remain liquid irrespective of volume fractions. In this Thesis, we will address this striking result using light scattering as well as rheology, in order to access both static and dynamic properties in a wide range of length and time scales. In addition, we will also perform additional studies using very stiff microgels and use their swelling capabilities to change the volume fraction. We will use hydrostatic pressure to change the miscibility of the polymer network and thus change the microgel size; the use of this external variable allows fast equilibration times and homogeneous changes throughout the sample. By using neutron scattering techniques, we study the structural and dynamical properties of the system in its different phases involved.