Dynamics of active filaments in porous media

The motion of active polymers in a porous medium is shown to depend critically on flexibilty, activity and degree of polymerization. For given Peclet number, we observe a transition from localisation to diffusion as the stiffness of the chains is increased. Whereas stiff chains move almost unhindered through the porous medium, flexible ones spiral and get stuck. Their motion can be accounted for by the model of a continuous time random walk with a renewal process corresponding to unspiraling. The waiting time distribution is shown to develop heavy tails for decreasing stiffness, resulting in subdiffusive and ultimately caged behaviour

Elasticity of a semiflexible filament with a discontinuous tension due to a cross-link or a molecular motor

We analyze the stretching elasticity of a wormlike chain with a tension discontinuity resulting from a Hookean spring connecting its backbone to a fixed point. The elasticity of isolated semiflexible filaments has been the subject in a significant body of literature, primarily because of its relevance to the mechanics of biological matter. In real systems, however, these filaments are usually part of supramolecular structures involving cross-linkers or molecular motors which cause tension discontinuities. Our model is intended as a minimal structural element incorporating such a discontinuity. We obtain analytical results in the weakly bending limit of the filament, concerning its force-extension relation and the response of the two parts in which the filament is divided by the spring. For a small tension discontinuity, the linear response of the filament extension to this discontinuity strongly depends on the external tension. For large external tension $f$, the spring force contributes a subdominant correction $\sim 1/f^{3/2}$ to the well known $\sim 1/\sqrt{f}$ dependence of the end-to-end extension

Rheological Chaos of Frictional Grains

A two-dimensional dense fluid of frictional grains is shown to exhibit time-chaotic, spatially heterogeneous flow in a range of stress values, $\sigma$, chosen in the unstable region of s-shaped flow curves. Stress controlled simulations reveal a phase diagram with reentrant stationary flow for small and large stress $\sigma$. In between no steady flow state can be reached, instead the system either jams or displays time dependent heterogeneous strain rates $\dot\gamma({\bf r},t)$. The results of simulations are in agreement with the stability analysis of a simple hydrodynamic model, coupling stress and microstructure which we tentatively associate with the frictional contact network

Phase diagram of selectively cross-linked block copolymers shows chemically microstructured gel

We study analytically the intricate phase behavior of cross-linked $AB$ diblock copolymer melts, which can undergo two main phase transitions due to quenched random constraints: Gelation, i.e., spatially random localization of polymers forming a system-spanning cluster, is driven by increasing the number parameter $\mu$ of irreversible, type-selective cross-links between random pairs of $A$ blocks. Self-assembly into a periodic pattern of $A$/$B$-rich microdomains (microphase separation) is controlled by the $AB$ incompatibility $\chi$ inversely proportional to temperature. Our model aims to capture the system's essential microscopic features, including an ensemble of random networks that reflects spatial correlations at the instant of cross-linking. We identify suitable order parameters and derive a free-energy functional in the spirit of Landau theory that allows us to trace a phase diagram in the plane of $\mu$ and $\chi$. Selective cross-links promote microphase separation at higher critical temperatures than in uncross-linked diblock copolymer melts. Microphase separation in the liquid state facilitates gelation, giving rise to a novel gel state whose chemical composition density mirrors the periodic $AB$ pattern.Comment: 10 pages, 4 figure

Normal stresses at the gelation transition

A simple Rouse-type model, generalised to incorporate the effects of chemical crosslinks, is used to obtain a theoretical prediction for the critical behaviour of the normal-stress coefficients $\Psi_{1}$ and $\Psi_{2}$ at the gelation transition. While the exact calculation shows $\Psi_{2}\equiv 0$, a typical result for these types of models, an additional scaling ansatz is used to demonstrate that $\Psi_{1}$ diverges with a critical exponent $\ell = k+z$. Here, $k$ denotes the critical exponent of the shear viscosity and $z$ the exponent governing the divergence of the time scale in the Kohlrausch decay of the shear-stress relaxation function. For crosslinks distributed according to mean-field percolation, this scaling relation yields $\ell =3$, in a accordance with an exact expression for the first normal-stress coefficient based on a replica calculation. Alternatively, using three-dimensional percolation for the crosslink ensemble we find the value $\ell \approx 4.9$. Results on time-dependent normal-stress response are also presented.Comment: RevTeX4, 6 pages, 2 figures; changes: explanatory comments expande

Hydrodynamic Correlation Functions of a Driven Granular Fluid in Steady State

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function, F_incoh(q,t), is seen to follow time-density superposition with a relaxation time that increases significantly as volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,omega) we compare our results to the predictions of generalized fluctuating hydrodynamics which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,omega) and the longitudinal current correlation function C_l(q,omega). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.Comment: 10 pages, 16 figure

Heterogeneities in the Glassy State

We study heterogeneities in a binary Lennard-Jones system below the glass transition using molecular dynamics simulations. We identify mobile and immobile particles and measure their distribution of vibrational amplitudes. For temperatures near the glass transition the distribution of vibrational amplitudes obeys scaling and compares reasonably well with a mean field theory for the amorphous solid state. To investigate correlations among the immobile and mobile particles we identify clusters and analyze their size and shape. For a fixed number of immobile particles we observe that the immobile particles cluster more strongly together as the temperature is increased which allows the particles to block each other more effectively, and to therefore stay immobile. For the mobile particles, on the other hand, the clustering is most pronounced at small temperatures, indicating that mobility at low temperatures can only be sustained in cooperative motion.Comment: 9 pages, 15 figure