Patrick Ilg

Stimuli-responsive hydrogels cross-linked by magnetic nanoparticles

Embedding magnetic nanoparticles into soft host media offers the opportunity to externally control material properties via a magnetic field. Choosing a hydrogel as the host medium allows modification of not only the elastic properties, but also the degree of swelling of the gel and the shape changes of the sample. Hydrogels where magnetic nanoparticles serve as the only crosslinking reagent of the network are a promising new class of such stimuli-responsive gels. The well-defined magneto-mechanical coupling present in these materials should allow for a better understanding and optimization of field-induced changes.

Corrections and Enhancements of Quasi-Equilibrium States

We give a compact non-technical presentation of two basic principles for reducing the description of nonequilibrium systems based on the quasi-equilibrium approximation. These two principles are: construction of invariant manifolds for the dissipative microscopic dynamics, and coarse-graining for the entropy-conserving microscopic dynamics. Two new results are presented: first, an application of the invariance principle to hybridization of micro‐macro integration schemes is introduced, and is illustrated with non-linear dumbbell models; second, Ehrenfest’s coarse-graining is extended to general quasi-equilibrium approximations, which gives the simplest way to derive dissipative equations from the Liouville equation in the short memory approximation.

Probing a critical length scale at the glass transition

We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size, which is typical of critical phenomena. Our approach is to introduce an external, static perturbation to extract the structural information from the systems response. In particular, we consider the transformation behavior of the local minima of the underlying potential energy landscape (inherent structures), under a static deformation. The finite-size scaling analysis of our numerical results indicate that the correlation length diverges at a temperature Tc, below the temperatures where the system can be equilibrated. Our numerical results are consistent with random first order theory, which predicts such a divergence with a critical exponent ν=2/3 at the Kauzmann temperature, where the extrapolated configurational entropy vanishes.

Canonical distribution functions in polymer dynamics. (I). Dilute solutions of flexible polymers

The quasi-equilibrium or maximum entropy approximation is applied in order to derive constitutive equations from kinetic models of polymer dynamics. It is shown in general and illustrated for an example how canonical distribution functions are obtained from the maximum entropy principle, how macroscopic and constitutive equations are derived therefrom and how these constitutive equations can be implemented numerically. In addition, a measure for the accuracy of the quasi-equilibrium approximation is proposed that can be evaluated while integrating the constitutive equations. In the example considered, it is confirmed that the accuracy of the approximation is increased by including more macroscopic variables. In steady elongational flow, it is found that more macroscopic variables need to be included above the coil-stretch transition to achieve the same accuracy as below.

Canonical distribution functions in polymer dynamics. (II). Liquid-crystalline polymers

The quasi-equilibrium approximation is employed as a systematic tool for solving the problem of deriving constitutive equations from kinetic models of liquid-crystalline polymers. It is demonstrated how kinetic models of liquid-crystalline polymers can be approximated in a systematic way, how canonical distribution functions can be derived from the maximum entropy principle and how constitutive equations are derived therefrom. The numerical implementation of the constitutive equations based on the intrinsic dual structure of the quasi-equilibrium manifold thus derived is developed and illustrated for a particular example. Finally, a measure of the accuracy of the quasi-equilibrium approximation is proposed that can be implemented into the numerical integration of the constitutive equation.

Magnetoviscous model fluids

We review, apply and compare diverse approaches to the theoretical understanding of the dynamical and rheological behaviour of ferrofluids and magnetorheological (MR) fluids subject to external magnetic and flow fields. Simple models are introduced which are directly solvable by nonequilibrium Brownian or molecular dynamics computer simulation. In particular, the numerical results for ferrofluids quantify the domain of validity of uniaxial alignment of magnetic moments (in and) out of equilibrium. A Fokker–Planck equation for the dynamics of the magnetic moments—corresponding to the Brownian dynamics approach—and its implications are analysed under this approximation. The basic approach considers the effect of external fields on the dynamics of ellipsoid shaped permanent ferromagnetic domains (aggregates), whose size should depend on the strength of flow and magnetic field, the magnetic interaction parameter and concentration (or packing fraction). Results from analytic calculations and from simulation are summarized for the anisotropy of the viscosity. In order to study the effect of flow on the anisotropic viscosities and shear-induced structures of MR fluids and ferrofluids subject to a strong external magnetic field, a simple model of perfectly oriented particles is considered.

Systematic time-scale-bridging molecular dynamics applied to flowing polymer melts

We present a thermodynamically guided, low-noise, time-scale-bridging, and pertinently efficient strategy for the dynamic simulation of microscopic models for complex fluids. The systematic coarse-graining method is exemplified for low-molecular polymeric systems subjected to homogeneous flow fields. We use established concepts of nonequilibrium thermodynamics and an alternating Monte Carlo-molecular-dynamics iteration scheme in order to obtain the model equations for the slow variables. For chosen flow situations of interest, the established model predicts structural as well as material functions beyond the regime of linear response. As a by-product, we present steady-state simulation results for polymers in general flow situations, including simple, planar, and yet unexplored equibiaxial elongation. The method is simple to implement and allows for the calculation of time-dependent behavior through quantities readily available from nonequilibrium steady states.

GENERATING MOMENT EQUATIONS IN THE DOI MODEL OF LIQUID-CRYSTALLINE POLYMERS

We present a self-consistent method for deriving moment equations for kinetic models of polymer dynamics. The Doi model [J. Polym. Sci., Polym. Phys. Ed. 19, 229 (1981)] of liquid-crystalline polymers with the Onsager excluded-volume potential is considered as an example. To lowest order, this method amounts to a simple effective potential different from the Maier-Saupe form. Analytical results are presented which indicate that this effective potential provides a better approximation to the Onsager potential than the Maier-Saupe potential. Corrections to the effective potential are obtained.

Soft Modes and Nonaffine Rearrangements in the Inherent Structures of Supercooled Liquids

We find that the hierarchical organization of the potential energy landscape in a model supercooled liquid can be related to a change in the spatial distribution of soft normal modes. For groups of nearby minima, between which fast relaxation processes typically occur, the localization of the soft modes is very similar. The spatial distribution of soft regions changes, instead, for minima between which transitions relevant to structural relaxation occur. This may be the reason why the soft modes are able to predict spatial heterogeneities in the dynamics. Nevertheless, the very softest modes are only weakly correlated with dynamical heterogeneities and instead show higher statistical overlap with regions in the local minima that would undergo nonaffine rearrangements if subjected to a shear deformation. This feature of the supercooled liquid is reminiscent of the behavior of nonaffine deformations in amorphous solids, where the very softest modes identify the loci of plastic instabilities.

Structure and rheology of ferrofluids: simulation results and kinetic models

Magnetoviscous and viscoelastic phenomena in ferrofluids are intimately related to their internal structures. The available kinetic models describing the rheological behaviour rely on strong assumptions and simplifications of these structures. Using equilibrium and nonequilibrium computer simulations, here we discuss the validity of the crucial assumption of rigid, chain-like aggregates underlying the chain model. The simulation results support the existence of chain-like aggregates in strongly interacting ferrofluids, at least for sufficiently strong magnetic fields. In addition, shear-induced degradation of the clusters is observed, which apparently is related to strong shear thinning behaviour. For weakly interacting ferrofluids, only slightly anisotropic spatial structures are observed. In this regime, the simulation results of the magnetoviscous effect are in good agreement with the predictions of a dynamical mean-field theory. Further, we explore some first steps towards a unified kinetic model that is applicable in both, the weakly and strongly interacting regimes.