We present a first-principles theory for the active nonlinear microrheology of colloidal model system; for a 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, 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.

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.

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 microscopic 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. PACS numbers:Recently, a generalization of the standard (quiescent) MCT for the case of nonlinearly pulled tracer was announced [22,23]. The new theory adopts and develops the ideas of the "integration through transients" approach to macrorheology [24][25][26] for the case of microrheology. The force-dependent probability density of a localized probe exhibits a bifurcation transition, thus accounting for the yielding effect. For the tracer friction coefficient (in the fluid state or above the yielding threshold in the jammed state), thinning behaviour is observed. In [23], the nonlinear probe velocity-force relations of the schematic model were compared to experiments and simulations. Including fluctuations perpendicular to the forcing directions, the schematic model was extended in [27], and discussed in detail in [28] The latter model also could be extended [29] to predict force-arXiv:1209.6475v2 [cond-mat.soft]

A versatile multiscale theoretical approach for the viscoelasticity of the homogeneous rubber matrix has been established taking into account relaxation processes at different time and length scales as well as nonpolymeric relaxation processes at extremely high frequencies. It allows to fit and describe the dynamic moduli of unfilled S-SBR rubbers over 16 frequency decades with a limited set of parameters (relaxation times, scaling exponents) which have a clear physical meaning and obey the relations motivated by the statistical− physical theory of polymer melts and polymer networks.