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Matthias Fuchs

Publications and source records attributed to Matthias Fuchs.

At least 73 records · Page 4Linked to original sources

Fluctuation dissipation relations in stationary states of interacting Brownian particles under shear

The fluctuation dissipation theorem (FDT) is studied close to the glass transition in colloidal suspensions under steady shear. Shear breaks detailed balance in the many-particle Smoluchowski equation, and gives response functions in the stationary state which are smaller at long times than estimated from the equilibrium FDT. During the final shear-driven decay, an asymptotically constant relation connects response and fluctuations, restoring the form of the FDT with, however, a ratio different from the equilibrium one.

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Comparison of structure and transport properties of concentrated hard and soft sphere fluids

Using Newtonian and Brownian dynamics simulations, the structural and transport properties of hard and soft spheres have been studied. The soft spheres were modeled using inverse power potentials ($V\sim r^{-n}$, with $1/n$ the potential softness). Although the pressure, diffusion coefficient and viscosity depend at constant density on the particle softness up to extremely high values of $n$, we show that scaling the density with the freezing point for every system effectively collapses these parameters for $n\geq 18$ (including hard spheres), for large densities. At the freezing points, the long range structure of all systems is identical, when the distance is measured in units of the interparticle distance, but differences appear at short distances (due to the different shape of the interaction potential). This translates into differences at short times in the velocity and stress autocorrelation functions, although they concur to give the same value of the corresponding transport coefficient (for the same density to freezing ratio); the microscopic dynamics also affects the short time behaviour of the correlation functions and absolute values of the transport coefficients, but the same scaling with the freezing density works for Newtonian or Brownian dynamics. For hard spheres, the short time behaviour of the stress autocorrelation function has been studied in detail, confirming quantitatively the theoretical forms derived for it.

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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 $σ(\dotγ)$ as the function of the shear rate $\dotγ$) 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.

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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.

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Glasses in Colloidal Systems. Attractive Interactions and Gelation

In this chapter, a study of the glass transitions in colloidal systems is presented, in connection with gelation, mainly from theoretical and simulation results. Mode Coupling Theory, which anticipated the existence of attraction driven glasses, is reviewed, and its predictions concerning attractive glasses discussed. Results from computer simulations will be presented for different models and the predictions of the theory will be tested. Starting from high density, where reasonable agreement is found, the study will be extended to low density, where new modes for the decay of density correlation functions appear. In all cases, the results will be also be brought into connection with experiments, and we will conclude with a discussion of the present understanding of the mechanisms leading to gelation.

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Structural and conformational dynamics of supercooled polymer melts: Insights from first-principles theory and simulations

We report on quantitative comparisons between simulation results of a bead-spring model and mode-coupling theory calculations for the structural and conformational dynamics of a supercooled, unentangled polymer melt. We find semiquantitative agreement between simulation and theory, except for processes that occur on intermediate length scales between the compressibility plateau and the amorphous halo of the static structure factor. Our results suggest that the onset of slow relaxation in a glass-forming melt can be described in terms of monomer-caging supplemented by chain connectivity. Furthermore, a unified atomistic description of glassy arrest and of conformational fluctuations that (asymptotically) follow the Rouse model, emerges from our theory.

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Aging in attraction-driven colloidal glasses

Aging in an attraction-driven colloidal glass is studied by computer simulations. The system is equilibrated without attraction and instantaneously ``quenched'', at constant colloid volume fraction, to one of two states beyond the glass transition; one is close to the transition, and the other one deep in the glass. The evolution of structural properties shows that bonds form in the system, increasing the local density, creating density deficits (holes) elsewhere. This process slows down with the time elapsed since the quench. As a consequence of bond formation, there is a slowing down of the dynamics, as measured by the mean squared displacement and the density, bond, and environment correlation functions. The density correlations can be time-rescaled to collapse their long time (structural) decay. The time scale for structural relaxation shows for both quenches a super-linear dependence on waiting time; it grows faster than the bond lifetime, showing the collective origin of the transition. At long waiting times and high attraction strength, we observe {\rem completely} arrested dynamics for more than three decades in time, although individual bonds are not permanent on this time scale. The localization length decreases as the state moves deeper in the glass; the non-ergodicity parameter oscillates in phase with the structure factor. Our main results are obtained for systems with a barrier in the pair potential that inhibits phase separation. However, when this barrier is removed for the case of a deep quench, we find changes in the static structure but almost none in the dynamics. Hence our results for the aging behavior remain relevant to experiments in which the glass transition competes with phase separation.

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Dynamical heterogeneities in an attraction driven colloidal glass

The dynamical heterogeneities (DH) in non-ergodic states of an attractive colloidal glass are studied, as a function of the waiting time. Whereas the fluid states close to vitrify showed strong DH, the distribution of squared displacements of the glassy states studied here only present a tail of particles with increased mobility for the lower attraction strength at short waiting times. These particles are in the surface of the percolating cluster that comprises all of the particles, reminiscent of the fastest particles in the fluid. The quench deeper into the attractive glass is dynamically more homogeneous, in agreement with repulsive glasses (i.e. Lennard-Jones glass).

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Integration through transients for Brownian particles under steady shear

Starting from the microscopic Smoluchowski equation for interacting Brownian particles under stationary shearing, exact expressions for shear-dependent steady-state averages, correlation and structure functions, and susceptibilities are obtained, which take the form of generalized Green-Kubo relations. They require integration of transient dynamics. Equations of motion with memory effects for transient density fluctuation functions are derived from the same microscopic starting point. We argue that the derived formal expressions provide useful starting points for approximations in order to describe the stationary non-equilibrium state of steadily sheared dense colloidal dispersions.

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Nonlinear rheology of dense colloidal dispersions: a phenomenological model and its connection to mode coupling theory

Rheological properties, especially 'shear-thinning', of dense colloidal dispersions are discussed on three different levels. A generalized phenomonological Maxwell model gives a broad framework connecting glassy dynamics to the linear and non-linear rheology of dense amorphous particle solutions. First principles mode coupling theory calculations for the time or frequency dependent shear modulus give quantitative results for dispersions of hard colloidal spheres in the linear regime. Schematic models extending mode coupling theory to the non-linear regime recover the phenomenology of the generalized Maxwell model, and predict universal features of flow curves, stress versus shear-rate.

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Flow curves of dense colloidal dispersions: schematic model analysis of the shear-dependent viscosity near the colloidal glass transition

A recently proposed schematic model for the non--linear rheology of dense colloidal dispersions is compared to flow curves measured in suspensions that consist of thermosensitive particles. The volume fraction of this purely repulsive model system can be adjusted by changing temperature. Hence, high volume fractions ($ϕ\leq 0.63$) can be achieved in a reproducible manner. The quantitative analysis of the flow curves suggests that the theoretical approach captures the increase of the low shear viscosity with increasing density, the shear thinning for increasing shear rate, and the yielding of a soft glassy solid. Variations of the high shear viscosity can be traced back to hydrodynamic interactions which are not contained in the present approach but can be incorporated into the data analysis by an appropriate rescaling.

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Dynamical heterogeneities close to a colloidal gel

Dynamical heterogeneities in a colloidal fluid close to gelation are studied by means of computer simulations. A clear distinction between some fast particles and the rest, slow ones, is observed, yielding a picture of the gel composed by two populations with different mobilities. Analyzing the statics and dynamics of both sets of particles, it is shown that the slow particles form a network of stuck particles, whereas the fast ones are able to move over long distances. Correlation functions show that the environment of the fast particles relaxes much faster than that of the slow ones, but at short times the bonds between fast particles are longer lived due to the flexibility of their structure. No string-like motion is observed for the fast particles, but they occupy preferential sites in the surface of the structure formed by the slow ones.

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Mode Coupling and Dynamical Heterogeneity in Colloidal Gelation: A Simulation Study

We present simulation results addressing the dynamics of a colloidal system with attractive interactions close to gelation. Our interaction also has a soft, long range repulsive barrier which suppresses liquid-gas type phase separation at long wavelengths. The new results presented here lend further weight to an intriguing picture emerging from our previous simulation work on the same system. Whereas mode coupling theory (MCT) offers quantitatively good results for the decay of correlators, closer inspection of the dynamics reveals a bimodal population of fast and slow particles with a very long exchange timescale. This population split represents a particular form of dynamic heterogeneity (DH). Although DH is usually associated with activated hopping and/or facilitated dynamics in glasses, the form of DH observed here may be more collective in character and associated with static (i.e., structural) heterogeneity.

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Static Properties of a Simulated Supercooled Polymer Melt: Structure Factors, Monomer Distributions Relative to the Center of Mass, and Triple Correlation Functions

We analyze structural and conformational properties in a simulated bead-spring model of a non-entangled, supercooled polymer melt. We explore the statics of the model via various structure factors, involving not only the monomers, but also the center of mass (CM). We find that the conformation of the chains and the CM-CM structure factor, which is well described by a recently proposed approximation [Krakoviack et al., Europhys. Lett. 58, 53 (2002)], remain essentially unchanged on cooling toward the critical glass transition temperature of mode-coupling theory. Spatial correlations between monomers on different chains, however, depend on temperature, albeit smoothly. This implies that the glassy behavior of our model cannot result from static intra-chain or CM-CM correlations. It must be related to inter-chain correlations at the monomer level. Additionally, we study the dependence of inter-chain correlation functions on the position of the monomer along the chain backbone. We find that this site-dependence can be well accounted for by a theory based on the polymer reference interaction site model (PRISM). We also analyze triple correlations by means of the three-monomer structure factors for the melt and for the chains. These structure factors are compared with the convolution approximation that factorizes them into a product of two-monomer structure factors. For the chains this factorization works very well, indicating that chain connectivity does not introduce special triple correlations in our model. For the melt deviations are more pronounced, particularly at wave vectors close to the maximum of the static structure factor.

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Simulation study of Non-ergodicity Transitions: Gelation in Colloidal Systems with Short Range Attractions

Computer simulations were used to study the gel transition occurring in colloidal systems with short range attractions. A colloid-polymer mixture was modelled and the results were compared with mode coupling theory expectations and with the results for other systems (hard spheres and Lennard Jones). The self-intermediate scattering function and the mean squared displacement were used as the main dynamical quantities. Two different colloid packing fractions have been studied. For the lower packing fraction, $α$-scaling holds and the wave-vector analysis of the correlation function shows that gelation is a regular non-ergodicity transition within MCT. The leading mechanism for this novel non-ergodicity transition is identified as bond formation caused by the short range attraction. The time scale and diffusion coefficient also show qualitatively the expected behaviour, although different exponents are found for the power-law divergences of these two quantities. The non-Gaussian parameter was also studied and very large correction to Gaussian behaviour found. The system with higher colloid packing fraction shows indications of a nearby high-order singularity, causing $α$-scaling to fail, but the general expectations for non-ergodicity transitions still hold.

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Theory of nonlinear rheology and yielding of dense colloidal suspensions

A first principles approach to the nonlinear flow of dense suspensions is presented which captures shear thinning of colloidal fluids and dynamical yielding of colloidal glasses. The advection of density fluctuations plays a central role, suppressing the caging of particles and speeding up structural relaxation. A mode coupling approach is developed to explore these effects.

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Non--Newtonian viscosity of interacting Brownian particles: comparison of theory and data

A recent first-principles approach to the non-linear rheology of dense colloidal suspensions is evaluated and compared to simulation results of sheared systems close to their glass transitions. The predicted scenario of a universal transition of the structural dynamics between yielding of glasses and non-Newtonian (shear-thinning) fluid flow appears well obeyed, and calculations within simplified models rationalize the data over variations in shear rate and viscosity of up to 3 decades.

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Schematic models for dynamic yielding of sheared colloidal glasses

The nonlinear rheological properties of dense suspensions are discussed within simplified models, suggested by a recent first principles approach to the model of Brownian particles in a constant-velocity-gradient solvent flow. 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. A mode coupling approach is developed to explore the shear-induced suppression of particle caging and the resulting speed-up of the structural relaxation.

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