Session W53: Focus Session: Common Features of Soft Materials: Polymers, Colloids and Granular Media I

Athermal Jamming Vs Thermalized Glassiness in a Simple Model of Soft-Core Interacting Particles

Numerical simulations of soft-core frictionless disks in two dimensions are carried out to study shear viscosity $\eta$ and pressure $p$ of a simple model liquid, as a function of thermal temperature $T$, packing fraction $\phi$, and uniform applied shear strain rate $\dot\gamma$. We find that viscosity in the athermal hard-core limit, $\lim_{\dot\gamma\to 0}[\lim_{T\to 0} \eta]$, is singularly disconnected from viscosity in the hard-core thermal limit, $\lim_{T\to 0}[\lim_{\dot\gamma\to 0} \eta]$, demonstrating that thermal glassy behavior is not governed by the athermal jamming critical point, ``point J".   

Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter

In this presentation we propose a coherent scenario of the formation of permanent shear bands in the flow of yield stress materials. Within a minimalistic mesoscopic model we investigate the spatial organisation of plasticity. The most important parameter is the typical time needed to regain the original structure after a local rearrangement. In agreement with a recent mean field study [Coussot \textit{et al., Eur. Phys. J. E}, 2010, \textbf{33}, 183] we observe a spontaneous formation of permanent shear bands, when this restructuring time is large compared to the typical stress release time in a rearrangement. This heterogeneous flow behaviour is different in nature from the transient dynamical heterogeneities that one observes in the small shear rate limit in flow without shear-banding [Martens \textit{et al., Phys. Rev. Lett.}, 2011, \textbf{106}, 156001]. We analyse the dependence of the shear bands on system size, shear rate and restructuring time. Further we rationalise the scenario within a mean field version of the model, that explains the instability of the homogeneous flow below a critical shear rate. Our study therefore strongly supports the idea that the characteristic time scales involved in the local dynamics are at the physical origin of permanent shear bands.   

Creep and critical scaling in random spring networks

Random networks of springs are a minimal model for physical, biological, and engineered materials ranging from foams and emulsions to biopolymer and bar-joint networks. Near the central force isostatic point, the creep response of damped networks is intimately tied to the presence or absence of floppy motions in the long time limit. We show that nearly isostatic networks display dynamical critical scaling, and that this scaling connects viscous flow and elastic deformation via a critical creep regime. We give scaling arguments for the critical exponents and confirm our predictions with numerics.   

Rheology of particle assemblies close to a jamming transition

The jamming paradigm aims at providing a unified view for the elastic and rheological properties of materials as different as foams, emulsions, suspensions or granular media. Structurally, these systems can all be viewed as dense assemblies of particles, and the particle volume fraction $\phi$ plays the role of the coupling constant that tunes the distance to the jamming transition. Enhanced experimental techniques allow to visualize the dynamics of these systems on the level of the individual particles, generating huge amount of information. Several interesting, and partially conflicting, results have emerged. It therefore seems necessary to ask in how far the experimental results reveal genuine aspects of a universal jamming transition, or justsystem-specific properties that depend on microscopic details, the driving mechanism or the preparation protocol. By comparing different computational models we will discuss the question of universality on the macroscopic level of rheological observables as well as on the microscopic level of single particle trajectories and collective particle motion.   

Inhomogeneous structure and position-dependent dynamics in complex fluids

We present computer simulation results of model complex fluids, quantifying how inhomogeneous structuring and dynamics of particles can be tuned through interactions. We first illustrate how a tracer particle's interactions can be tuned to significantly modify its long-time diffusivity. We use a recently proposed propagator-based formalism to address how this enhancement can be understood in terms of the local dynamics of neighboring particles. We then discuss how these results compare to related behaviors of model confined colloidal and molecular fluids.   

Demonstration of Secondary Currents in the Pressure-Driven Flow of a Concentrated Suspension Through a Square Conduit

It has been known for several decades now that the pressure-driven flow of polymer melts in non-axisymmetric conduits is not unidirectional; the main flow through the channel is accompanied by secondary currents, whose origin can be attributed to second normal stress differences. However, only recently was it realized [Ramachandran and Leighton, \textit{J. Fluid Mech.} (2008)] that the same may be true for concentrated suspensions, which, upon shearing, exhibit strong second normal stress differences. This work confirms the existence of these secondary flows by carrying out pressure-driven suspension flow experiments through a square (non-axisymmetric) duct. By tracking the motion of a thin stream of a contrastingly-dyed suspension introduced into the bulk flow of another, it is demonstrated that the suspension flows out of the sidewalls of the geometry towards the corners of the square cross-section, and then flows towards the center. This is found to be qualitatively consistent with calculations based on the suspension balance model of Nott and Brady [\textit{J. Fluid Mech.} (1994)]. Secondary currents have been predicted to be the dominant mechanism determining particle distribution in suspension flows, and this work lends support to that idea.   

Understanding entangled polymers: What we can learn from athermal chain packings

The study of random and ordered packings (from atoms and colloidal particles to sand grains) has been the focus of extensive research. This is not surprising since an understanding of the mechanisms that control morphology and packing is the key to the design and synthesis of novel ``smart'' materials and functionalities. In particular, the study of packings of chain molecules presents challenges but also insights which are absent in monatomic systems and further allows for a direction comparison with them. In this contribution we give an overview of our work on very dense and nearly jammed packings of athermal polymers. We show that chain molecules can be as efficiently and as densely packed as monatomic analogs up to the same maximally random jammed state. We also show that an exact correspondence can be established between the statistical-mechanical ensembles of packings of monatomic, and chain systems, which yields insights on the universality of jamming. By studying the effect of concentration on polymer size and on the underlying network of topological hindrances we precisely identify the distinct universal scaling regimes and the corresponding exponents. An unsuspected connection, valid from dilute up to very dense assemblies, is established between knots (of intermolecular origin) and entanglements (intermolecular constraints). We finally show that, against expectations, entropy-driven crystallization can occur in dense systems of athermal polymers once a critical volume fraction is reached. Such phase transition is driven by the increase in translational entropy: ordered sites exhibit enhanced mobility as their local free volume becomes more spherical and symmetric. Incipient nuclei develop well defined, stack-faulted layered crystal morphologies with a single stacking direction. The ordering transition and the resulting complex morphologies are analyzed, highlighting similarities and differences with respect to monatomic crystallization.   

Sudden Chain Energy Transfer Events in Vibrated Granular Media

In a mixture of two species of grains of equal size but different mass, placed in a vertically vibrated shallow box, there is spontaneous segregation. Once the system is at least partly segregated and clusters of the heavy particles have formed, there are sudden peaks of the horizontal kinetic energy of the heavy particles, that is otherwise small. Together with the energy peaks the clusters rapidly expand and the segregation is partially lost. The process repeats once segregation has taken place again, either randomly or with some regularity in time depending on the experimental or numerical parameters. An explanation for these events is provided based on the existence of a fixed point for an isolated particle bouncing with only vertical motion. The horizontal energy peaks occur when the energy stored in the vertical motion is partly transferred into horizontal energy through a chain reaction of collisions between heavy particles.   

Equation of state and jamming density for equivalent bi-, tri- and polydisperse, smooth, elastic sphere systems

We study binary, ternary and polydisperse mixtures of hard particle fuids as models for granular matter, colloids and other soft matter. Size ratios between 1 and 100 are studied for different size distributions. Simulation results are compared with previously found analytical equations of state by looking at the compressibility factor, Z, and agreement is found with much better than 1{\%} deviation in the fluid regime. A slightly improved empirical correction to Z is proposed. When the density is further increased, the behavior of Z changes and there is a close relationship between many-component mixtures and their two- and three-component equivalents (where our contribution is to define the term ``equivalent''). We determine the size ratios for which the liquid-solid transition exhibits crystalline, amorphous or mixed system structure. Near the jamming density, Z is independent of the size distribution and follows a -1 power law as function of the difference from the jamming density. In this limit, Z depends only on one free parameter, the jamming density itself, as reported for several different size distributions with a wide range of widths.   

Recovery of polymer glasses from mechanical perturbation

There is a longstanding debate about the nature and extent of mechanical rejuvenation in aging glasses and most related studies have concentrated on the impact of aging during plastic deformation. Here we study the time period after nonlinear creep where the glass recovers, using molecular dynamics simulations of a bead-spring model for a wide range of stress amplitudes and glass ages. We compute $\alpha$-relaxation times as well as several quantities that characterize structural changes. From an analysis of the recovery paths we find a transition from memory effects to mechanical rejuvenation that is controlled by the total strain and not the stress amplitude. Although strong mechanical perturbation can make the dynamics appear very similar to that of a freshly quenched glass, various measures of short range order as well as inherent structure energies reveal systematic differences in the underlying thermodynamic state.   

Spatiotemporal stress/strain correlations in a quasi-2D jammed emulsion

We flow quasi-2D emulsions in a flow geometry analogous to pure shear to better understand the microscopic events within jammed materials during the straining process. Our quasi-2D system serves as an experimental model system of jamming and consists of oil-in-water emulsion droplets confined between two parallel plates. Using a technique we have developed, we can determine the forces between pairs of droplets in contact based on each droplet's deformation. By imaging the motion and deformation of the droplets during the flowing process, we quantify the microscopic events using spatiotemporal correlations in strain and stress. We study these spatiotemporal correlations at various droplet concentrations to understand how the microscopic events change as we approach the jamming point.   

Low-$k$ behavior in Structure Factor and Compressibility Factor for Monodisperse and Bidisperse Packings of Frictionless Spheres

One particular structural signature of jamming transition has emerged in studies of large systems: \emph{hyperuniformity}, which is the supression of the long wavelength density fluctuations. Also, it has been observed an unusual linear dependence ($S(k)\sim k$) of the structure factor in the low $k$ limit, in monodisperse systems. The small wavenumber region of the static structure factor $S(k)$ for monodisperse systems and the compressibility factor $\theta(k)$ for bidisperse mixtures, are investigated for jammed packings of frictionless spheres with Hooke and Hertz force model, using a high precision data analysis. We have found that the zero-wavenumber intercept $S(k=0)$ and $\theta(k=0)$, as a function of the pressure, are non-zero constant, revealing a finite compressibility. This behavior is relatively insensitive to the force model but shows a dependence on the bidispersity. We have studied also zero-temperature Lennard-Jones glasses which exhibit a finite compressibility that depend weakly on the density of the glass.   

Jamming and Unjamming of the Rigid Amorphous Fraction

Semicrystalline polymers obey a three-phase model comprising crystalline, mobile amorphous (MAF), and rigid amorphous fractions (RAF) as an interphase. Using quasi-isothermal temperature modulated differential scanning calorimetry (QI-TMDSC), we investigate the formation behavior of these fractions in poly(trimethylene terephthalate), PTT. PTT was quasi-isothermally cooled step-wise from the melt which causes its crystalline fraction to be fixed below 451K, and RAF is determined as a function of temperature. For PTT, most of the RAF vitrifies between 451K and T$_{g }$step-by-step during QI cooling. With lamellar crystals acting as topological constrains, a model is proposed in which the vitrification and devitrification of RAF are interpreted using the concepts of ``jamming'' and ``unjamming.'' Constraints of the crystal surfaces reduce the mobility of the highly entangled polymer chains attached to the lamellae, and the layers which constitute RAF are formed one after another in the manner of successive jamming. In this way, several features of the RAF temperature dependence are explained for the first time, with implications in other research areas, such as topological constraints exerted on the polymer melt through effects of inclusions in polymer-based nanocomposites.\\[4pt] For support of this research, the authors thank the NSF, Polymers Program of the Division of Materials Research through DMR-0602473, and the MRI Program under DMR-0520655 for thermal analysis instrumentation. A portion of this work was conducted at the BNL, National Synchrotron Light Source, supported by the DoE. G. Georgiev thanks Assumption College for continuous research support.