Emergent dynamics and self-assembly of out-of-equilibrium colloids
- Jure Dobnikar (Institute of Physics, Chinese Academy of Sciences and University of Cambridge, Department of Chemistry, United Kingdom)
- Alexey Snezhko (Argonne National Laboratory, Lemont, USA)
- Anand Yethiraj (Memorial University, St John's, Canada)
Modern self-assembly techniques aiming to produce complex structural order or functional diversity often rely on non-equilibrium conditions in the system. Light, electric, or magnetic fields are often used to induce complex out-of-equilibrium colloidal ordering. Such dissipative colloidal materials use energy to generate and maintain structural complexity. The energy injection rates, properties of the environment are important control parameters that influence the outcome of these active (dynamic) self-assembling systems. Nontrivial collective dynamics and emerging large-scale structures are often observed [1-24].
Dynamics and self-assembly in out-of-equilibrium (active) colloidal systems is now a rapidly growing area of research that is aimed towards prediction and discovery of novel multifunctional dynamic architectures that are not generally available at equilibrium [7,31, 32]. Active self-assembled materials in living systems are made of building blocks that consume food as energy input, and spontaneously organize into hierarchical structures . In physical systems, the buildings blocks can be simpler, and the kind of driving forces that is available is also broader. In model colloidal systems, alternating magnetic, electric and hydrodynamic fields have successfully been used to force colloidal systems out of equilibrium and thus to promote new self-organized structures and emergent collective dynamics [31, 34, 35]. Active self-assembled structures, which are generally not available through equilibrium thermodynamics, have been reported [8-17, 34]. Static electrical fields in combination with electro-hydrodynamic convective flows create emergent structures like toroidal vortices and pulsating rings when applied to metallic microparticles immersed in a weakly conducting liquid . AC electric fields and patterned electrodes have been exploited to achieve dynamic templating of 3D colloidal patterns . Biaxial rotating electric/magnetic fields are a versatile tool to promote active colloidal assembly and non-trivial emergent dynamics [20, 36]. A variety of low dimensional structures such as chains, foams, membranes and clusters exhibiting viscoelastic properties [5, 11, 13, 14] have been observed. Unusual dynamic advection lattices have been reported in a suspension of magnetic platelets subjected to a time dependent biaxial magnetic field with a prescribed frequency or phase relation . Life-like collective dynamics (self-propulsion, swarming) has been reported in far-from-equilibrium magnetic fluid suspended in immiscible liquid and driven by complex multi-axial magnetic fields . Magnetic colloidal particles suspended at a liquid–air interface and energized by alternating magnetic fields dynamically self-assemble into complex structures and swimmers exhibiting remarkable behavior due to the additional coupling of particles to liquid through the interface excitations [6, 12, 22, 23, 32]. Synchronization has been exploited as a tool towards dynamic self-assembly  where magnetic Janus particles suspended in a liquid assembled in dynamic microtubes by the precessing magnetic field [10, 37]. Nontrivial collective behavior and emergence of macroscopic directed motion has been observed in an ensemble of self-propelled colloids actuated by electro-hydrodynamics (Quincke rotations) [38, 39]. Reconfigurable swarming and directed transport has been successfully demonstrated in actively driven colloid (AC electrophoresis) coupled to a nematic host liquid . The motion of self-assembled microscopic worm-like structures resulting from the cooperative flow generated by the spinning particles which act as a hydrodynamic “conveyor belt” has been observed in ensembles of colloidal rotors dynamically assembled and driven in a viscous fluid upon application of an elliptically polarized rotating magnetic field . Flocking behavior and spontaneous symmetry breaking has been demonstrated recently in the ensemble of ferromagnetic colloidal rollers . Nontrivial topological defects dynamics has been reported in active swimmers-Liquid Crystal composites .
Achieving a general understanding of the dynamic interactions in complex nonequilibrium dissipative systems is a significant theoretical and computational challenge for a multiplicity of reasons: the inherent complexity of the systems, the overlapping length- and timescales, and the coupling of particle interactions to the fluid flow. Some of these features can be understood in the framework of the amplitude equation (Ginzburg-Landau type equation) [12, 15, 24] coupled to the conservation law equation describing the evolution of the particle density and the Navier-Stokes equation for hydrodynamic flows. Nevertheless, the fundamental microscopic mechanisms leading to the dynamic self-assembly and their relations to the emergent behavior often remain elusive. Computer simulations are often the only method to theoretically investigate such questions; however, modeling the nonequilibrium self-assembly presents a huge computational challenge due to the complex many-body interactions and collective dynamics on very different time scales. One of the major challenges is to properly account for the particle-fluid coupling. On a coarse grained level, the fluid flow around colloids is modeled by molecular dynamics methods like Lattice-Boltzmann  and Multi Particle Collision Dynamics [27, 28]. Flow around a single colloid is characterized by low Reynolds number, which simplifies the treatment of hydrodynamic interaction in these models, however, it becomes difficult to describe collective dynamics of self-assembled structures, which have a larger effective Reynolds number implying that inertia hydrodynamic terms become important. An alternative approach is to describe the colloidal dynamics by molecular dynamics simulations coupled to the Navier-Stokes equations describing large-scale time-averaged hydrodynamic flows generated by the colloids .
The current workshop will have emphasis on field driven colloidal systems, active matter and dynamics in anisotropic (liquid crystalline) media. In addition, the workshop plans to examine the non-equilibrium physics in a new emerging class of active systems, active spinner materials, with activity coming not through self-propulsion but rather through rotational degrees of freedom (rollers, spinners) These new active chiral colloids often create strong hydrodynamic vortical flows around them governing collective dynamics in the colloidal ensembles in highly nontrivial way [32, 38, 44, 45].
A workshop on emergent dynamics in far-from-equilibrium colloidal systems - as seen through experiment, computational models and theory - that is aimed at understanding underlying physical mechanisms behind emergent dynamics and dynamic self-assembly in non-equilibrium colloids will present a valuable discussion platform for the rapidly developing research fields of out of equilibrium and active soft matter. Treatment of out-of-equilibrium systems is always a challenge. A proper accounting (or ignoring) of the liquid particle coupling in simulation models describing driven colloidal systems should depend on the rate of energy injection into the colloid. Coarse-grained models that properly balance the direct many-body and fluid-mediated interactions provide vital information on the mechanisms governing out-of-equilibrium dynamics and assembly. However, an exact accounting of the particles-fluid coupling in response to external periodical excitations is computationally challenging and simplifying assumptions usually have to be made. Within the framework of this workshop, we aim to focus discussions on the role of fluid-particle coupling in the dynamics of self-assembly in externally driven and self-propelled colloids and on the appropriate simulation methods to address this coupling. We will include new emerging themes such as dynamics of active colloids and topological defects in anisotropic liquids (liquid crystals) [43, 46] and emergent dynamics in active spinner materials [44-47].
The planned workshop will be an ideal opportunity to create a constructive discussion between researches in the field of non-equilibrium self-assembly. The proposed workshop is a follow-up on the event organized by us in 2016. An attractive characteristic of the previous workshop was a good mixture of experiment, computational models and theory and we intend to keep this structure: We will bring together experimentalists and theoreticians and focus on bridging the gaps between the computational approaches on different levels of coarse graining . The previous workshop identified several areas of overlap as well as pointed out new promising areas of research and ignited a number of collaborations. We have put together a lively community of researchers from various backgrounds working on emergent dynamics. Due to the rapid progress in the field, the next workshop in 2018 would be essential in order to keep up the pace.
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