Dynamical structure formation in passive and active colloidal systems

Colloidal particles are model systems for a wide range of phenomena on mesoscopic length scales from 10s of nanometers to 10s of micrometers. "Colloidal physics" therefore applies to systems as diverse as proteins in dense solutions and magnetic particles in time-dependent external fields. In the dense and crowded environment of the cell cytoplasm, an individual protein feels the presence of and interacts with all surrounding proteins which leads to a strong coupling of their dynamics. We investigate the aggregation in protein solutions emerging from different interparticle interactions in an attempt to understand theoretical and experimental observations. Dispersions of particles with short-range attractive and long-range repulsive interactions, for example corresponding to low-salinity Lysozyme protein solutions, exhibit rich equilibrium microstructures and an intriguing phase behavior. We present simulation results in comparison with theoretical predictions for structural and, in particular, short-time diffusion properties of a colloidal model system with such interactions, both in the dispersed-fluid and equilibrium-cluster phase regions. Next, we extend our investigation to the study of colloids with anisotropic and patchy interactions. In quasi-elastic neutron scattering experiments, the short-time diffusion coefficient of the well-characterized and highly stable eye-lens protein gamma-crystallin at concentrations comparable to those present in the eye lens and on length scales comparable to the nearest-neighbor distance, has been observed to slow down significantly with increasing concentration. We find, via a comparison with simulations of patchy colloids, that the presence of attractive sites on the colloid surface play an essential role in determining the local short-time dynamics. Hence, our simulations clearly demonstrates the enormous effect of weak directed attractions can have on the short-time diffusion of proteins at concentrations comparable to those in the cellular cytosol. Further, we investigate a dispersion of magnetic spherical colloids energized by a uniaxial alternating magnetic field, which manifests dynamic self-assembly into spinners, short rod-like chains of a few particles, rotating in clockwise or counterclockwise direction. We report on active turbulence and transport in the gas of self-assembled spinners in comparison with experiments. We show that the spinners, emerging as a result of spontaneous symmetry breaking of clock/counterclockwise rotation of self-assembled particle chains, generate active vortical flows. These emergent self-induced currents promote active diffusion that can be tuned by the parameters of the external excitation field. We apply colloidal models also to active matter systems, where we study the active Brownian particle (ABP) model for active systems to achieve insight into the stationary-state distribution of confined ABPs and to derive an expression for the bulk pressure in a sub-volume of the system. The analytical solution of the Fokker-Planck equation for an active Ornstein-Uhlenbeck particle (AOUP) in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g., due to tumbling, even for large propulsion velocities (Peclet numbers). For the pressure in a local sub-volume, we derive corresponding expressions for ABPs confined by walls or with periodic boundaries using the virial theorem. In both cases, the local pressure comprises of an activity-induced contribution, which can be expressed in terms of a flux of particles, and a contribution by interparticle forces. We find that the local pressure of ABPs under confinement explicitly depends on the presence of the confining walls and the particle-wall interactions. Moreover, the local pressure in interacting ABP systems with periodic boundary conditions displays a nonmonotonic concentration dependence at higher activity