Non-Equilibrium relation between mobility and diffusivity of interacting Brownian particles under shear

We investigate the relation between mobility and diffusivity for Brownian particles under steady shear near the glass transition, using mode coupling approximations. For the two directions perpendicular to the shear direction, the particle motion is diffusive at long times and the mobility reaches a finite constant. Nevertheless, the Einstein relation holds only for the short-time in-cage motion and is violated for long times. In order to get the relation between diffusivity and mobility, we perform the limit of small wavevector for the relations derived previously [Phys. Rev. Lett. 102 (2009), 135701], without further approximation. We find good agreement to simulation results. Furthermore, we split the extra term in the mobility in an exact way into three terms. Two of them are expressed in terms of mean squared displacements. The third is given in terms of the (less handy) force-force correlation function.Comment: 14 pages, 4 figures, accepted for Prog. Theor. Phys. Suppl., issue for the workshop "Frontiers in Nonequilibrium Physics", Kyoto, 200

Nonlinear rheological properties of dense colloidal dispersions close to a glass transition under steady shear

The nonlinear rheological properties of dense colloidal suspensions under steady shear are discussed within a first principles approach. It starts from the Smoluchowski equation of interacting Brownian particles in a given shear flow, derives generalized Green-Kubo relations, which contain the transients dynamics formally exactly, and closes the equations using mode coupling approximations. Shear thinning of colloidal fluids and dynamical yielding of colloidal glasses arise from a competition between a slowing down of structural relaxation, because of particle interactions, and enhanced decorrelation of fluctuations, caused by the shear advection of density fluctuations. The integration through transients approach takes account of the dynamic competition, translational invariance enters the concept of wavevector advection, and the mode coupling approximation enables to quantitatively explore the shear-induced suppression of particle caging and the resulting speed-up of the structural relaxation. Extended comparisons with shear stress data in the linear response and in the nonlinear regime measured in model thermo-sensitive core-shell latices are discussed. Additionally, the single particle motion under shear observed by confocal microscopy and in computer simulations is reviewed and analysed theoretically.Comment: Review submited to special volume 'High Solid Dispersions' ed. M. Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009); some figures slightly cu

Elastic properties of colloidal solids with disorder

Recent progress in approaches to determine the elastic constants of solids starting from the microscopic particle interactions is reviewed. On the theoretical side, density functional theory approaches are discussed and compared to more classical ones using the actual pair potentials. On the experimental side, video microscopy has been introduced to measure the elastic constants in colloidal solids. For glasses and disordered systems, the theoretical basis is given for this novel technique, and some challenges and recent advances are reviewed.Comment: Lecture notes of a seminar at the International School on Physics 'Enrico Fermi': Physics of Complex Colloids, Varenna, Italy, July 3-13 2012; to be included in the Proceedings of Course CLXXXIV; version 2 with small addition

Structural Relaxations in a Simple Model Molten Salt

The structural relaxations of a dense, binary mixture of charged hard spheres are studied using the Mode Coupling Theory (MCT). Qualitative differences to non--ionic systems are shown to result from the long--range Coulomb interaction and charge ordering in dense molten salts. The presented non--equilibrium results are determined by the equilibrium structure, which is input using the well studied Mean Spherical Approximation.Comment: 6 pages, 4 Postscript figures, uses epsfig.sty, rotate.sty, here.st

Shear-thinning in dense colloidal suspensions and its effect on elastic instabilities: from the microscopic equations of motion to an approximation of the macroscopic rheology

In the vicinity of their glass transition, dense colloidal suspensions acquire elastic properties over experimental timescales. We investigate the possibility of a visco-elastic flow instability in curved geometry for such materials. To this end, we first present a general strategy extending a first-principles approach based on projections onto slow variables (so far restricted to strictly homogeneous flow) in order to handle inhomogeneities. In particular, we separate the advection of the microstructure by the flow, at the origin of a fluctuation advection term, from the intrinsic dynamics. On account of the complexity of the involved equations, we then opt for a drastic simplification of the theory, in order to establish its potential to describe instabilities. These very strong approximations lead to a constitutive equation of the White-Metzner class, whose parameters are fitted with experimental measurements of the macroscopic rheology of a glass-forming colloidal dispersion. The model properly accounts for the shear-thinning properties of the dispersions, but, owing to the approximations, the description is not fully quantitative. Finally, we perform a linear stability analysis of the flow in the experimentally relevant cylindrical (Taylor-Couette) geometry and provide evidence that shear-thinning strongly stabilises the flow, which can explain why visco-elastic instabilities are not observed in dense colloidal suspensions

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

Viscoelasticity and shear flow of concentrated, non-crystallizing colloidal suspensions: Comparison with Mode-Coupling Theory

We present a comprehensive rheological study of a suspension of thermosensitive particles dispersed in water. The volume fraction of these particles can be adjusted by the temperature of the system in a continuous fashion. Due to the finite polydispersity of the particles (standard deviation: 17%), crystallization is suppressed and no fluid-crystal transition intervenes. Hence, the moduli $G'$ and $G"$ in the linear viscoelastic regime as well as the flow curves (shear stress $\sigma(\dot{\gamma})$ as the function of the shear rate $\dot{\gamma}$) could be measured in the fluid region up to the vicinity of the glass transition. Moreover, flow curves could be obtained over a range of shear rates of 8 orders of magnitude while $G'$ and $G"$ could be measured spanning over 9 orders of magnitude. Special emphasis has been laid on precise measurements down to the smallest shear rates/frequencies. It is demonstrated that mode-coupling theory generalized in the integration through transients framework provides a full description of the flow curves as well as the viscoelastic behavior of concentrated suspensions with a single set of well-defined parameters

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts and Gels. I. General Formulation and Predictions

The transport coefficients of dense polymeric fluids are approximately calculated from the microscopic intermolecular forces. The following finite molecular weight effects are discussed within the Polymer-Mode-Coupling theory (PMC) and compared to the corresponding reptation/ tube ideas: constraint release mechanism, spatial inhomogeneity of the entanglement constraints, and tracer polymer shape fluctuations. The entanglement corrections to the single polymer Rouse dynamics are shown to depend on molecular weight via the ratio N/N_e, where the entanglement degree of polymerization, N_e, can be measured from the plateau shear modulus. Two microscopically defined non-universal parameters, an entanglement strength 1/alpha and a length scale ratio, delta= xi_rho/b, where xi_rho and b are the density screening and entanglement length respectively, are shown to determine the reduction of the entanglement effects relative to the reptation- -like asymptotes of PMC theory. Large finite size effects are predicted for reduced degrees of polymerization up to N/N_e\le10^3. Effective power law variations for intermediate N/N_e of the viscosity, eta\sim N^x, and the diffusion constant, D\sim N^{-y}, can be explained with exponents significantly exceeding the asymptotic, reptation-like values, x\ge 3 and y\ge2, respectively. Extensions of the theory to treat tracer dielectric relaxation, and polymer transport in gels and other amorphous systems, are also presented.Comment: Latex, figures and styles files included; Macromolecules, in press (1997