Nonlinear microrheology of dense colloidal suspensions: a mode-coupling theory

A mode-coupling theory for the motion of a strongly forced probe particle in a dense colloidal suspension is presented. Starting point is the Smoluchowski equation for $N$ bath and a single probe particle. The probe performs Brownian motion under the influence of a strong constant and uniform external force \Fex. It is immersed in a dense homogeneous bath of (different) particles also performing Brownian motion. Fluid and glass states are considered; solvent flow effects are neglected. Based on a formally exact generalized Green-Kubo relation, mode coupling approximations are performed and an integration through transients approach applied. A first-principles theory for the nonlinear velocity-force relations of the probe particle in a dense fluid and for the (de-) localized probe in a glass is obtained. It extends the mode coupling theory of the glass transition to strongly forced tracer motion and describes active microrheology experiments. A force threshold is identified which needs to be overcome to pull the probe particle free in a glass. For the model of hard sphere particles, the microscopic equations for the threshold force and the probability density of the localized probe are solved numerically. Neglecting the spatial structure of the theory, a schematic model is derived which contains two types of bifurcation, the glass transition and the force-induced delocalization, and which allows for analytical and numerical solutions. We discuss its phase diagram, forcing effects on the time-dependent correlation functions, and the friction increment. The model was successfully applied to simulations and experiments on colloidal hard sphere systems [I. Gazuz et. al., Phys. Rev. Lett. 102, 248302 (2009)], while we provide detailed information on its derivation and general properties.Comment: 24 pages, 14 figure

Schematic Models for Active Nonlinear Microrheology

We analyze the nonlinear active microrheology of dense colloidal suspensions using a schematic model of mode-coupling theory. The model describes the strongly nonlinear behavior of the microscopic friction coefficient as a function of applied external force in terms of a delocalization transition. To probe this regime, we have performed Brownian dynamics simulations of a system of quasi-hard spheres. We also analyze experimental data on hard-sphere-like colloidal suspensions [Habdas et al., Europhys. Lett., 2004, 67, 477]. The behavior at very large forces is addressed specifically

Active and Nonlinear Microrheology in Dense Colloidal Suspensions

We present a first-principles theory for the active nonlinear microrheology of colloidal model systems: for constant external force on a spherical probe particle embedded in a dense host dispersion, neglecting hydrodynamic interactions, we derive an exact expression for the friction. Within mode-coupling theory (MCT), we discuss the threshold external force needed to delocalize the probe from a host glass, and its relation to strong nonlinear velocity-force curves in a host fluid. Experimental microrheology data and simulations, which we performed, are explained with a simplified model

Dynamics of an Intruder in Dense Granular Fluids

We investigate the dynamics of an intruder pulled by a constant force in a dense two-dimensional granular fluid by means of event-driven molecular dynamics simulations. In a first step, we show how a propagating momentum front develops and compactifies the system when reflected by the boundaries. To be closer to recent experiments \cite{candelier2010journey,candelier2009creep}, we then add a frictional force acting on each particle, proportional to the particle's velocity. We show how to implement frictional motion in an event-driven simulation. This allows us to carry out extensive numerical simulations aiming at the dependence of the intruder's velocity on packing fraction and pulling force. We identify a linear relation for small and a nonlinear regime for high pulling forces and investigate the dependence of these regimes on granular temperature

Aktiver und passiver Teilchentransport in dichten kolloidalen Suspensionen

This thesis deals with nonlinear active transport of single colloidal particles in a colloidal suspension near the glass transition. We present a generalization of the mode-coupling theory of the glass transition to the case of a particle actively pulled by means of a time-and space constant external force. We predict such typical nonlinear effects like yielding (existence of a critical force needed to pull the particle free out of the cage of its nearest neighbors) and thinning (the decay of the friction coefficient with increasing external force). For the case of a hard sphere suspension, we succeeded to evaluate the value of the critical force, which is in semi-quantitative agreement with simulations and experiments. We present also simplified schematic versions of the microscopic equations of the theory, which retain some crucial properties of the whole equations, but are more easily treatable

Evidence of random copolymer adsorption at fluctuating selective interfaces from Monte-Carlo simulation studies

We perform Monte-Carlo simulations of a binary, strongly separated mixture of A- and B-type homopolymers with some amount of random AB copolymers added. The interface is analyzed and the interface tension is calculated using the model of capillary waves. We can clearly demonstrate that random copolymers are localized at real, fluctuating interfaces between incompatible polymer species and micellization is not favored over adsorption. Our study proves that random copolymers are potential candidates for compatibilization of polymer-polymer mixtures. By simulating random copolymers in a one-component bulk and comparing their free energy to the copolymers adsorbed at the two-phase interface we show that the adsorption is thermodynamically stable. We use scaling arguments developed for ideal and non-fluctuating interfaces to rationalize the simulation results and we calculate the reduction of interface tension with increasing amount of the adsorbed copolymers