Session T14: Disordered Systems, Glassy Dynamics, and Jamming I

Shear Induced Structural Relaxation in a Supercooled Colloidal Liquid

The rheology of dense amorphous materials under large shear strain is not fully understood, partly due to the difficulty of directly viewing the microscopic details of such materials. We use a colloidal suspension to simulate amorphous materials, and study the shear-induced structural relaxation with fast confocal microscopy. We quantify the plastic rearrangements of the particles in two ways. First, we consider ``non-affine mobility'' by subtracting the global linear applied strain from the particle motion. Second, we examine ``local deformation'' by subtracting the local linear apparent strain (as measured from the particle motion). We find these measures of plasticity are spatially heterogeneous, with localized regions where many particles are strongly rearranging by these measures. We examine the shapes of these regions and find them to be essentially isotropic, with no alignment in any particular direction.   

Complete Density Landscape for a Model Confined Liquid

We enumerate the complete jamming landscape for a system of hard discs with diameter $\sigma$ confined between walls having a separation $h$, such that $1.866 [Preview Abstract]

Influence of Flow Quench Rate on the Internal Stress and Aging Dynamics of a Repulsive Colloidal Glass

We investigate the dynamics of aging in a repulsive colloidal glass composed of charged clay particles in aqueous suspension. Dynamic rheological measurements show a power law evolution of the elastic modulus of the system with sample age, measured as time elapsed after the cessation of a rejuvenating shear flow. We show that the scaling exponent is dependent on the rate of flow cessation or the flow quench rate. Comparatively fast quenches lead to systems with a smaller elastic modulus and accelerated aging whereas slower quenches result in higher modulus but correspondingly less rapid aging. We apply a recently proposed technique to follow the dynamics of residual or internal elastic stresses immediately after the flow arrest and find striking parallels between the relaxation of these stresses and the aging of the system. These results indicate that the evolution of the slow dynamics is strongly coupled to the internal stress state of the system and point to the identification of the flow quench rate as a mechanical variable that characterizes the system's departure from equilibrium.   

Hydrogen-bond network dynamics in sugar-based glasses

Hydrophilic organic glasses composed of sugars and polysaccharides are known to stabilize proteins against aggregation and chemical degradation. It has long been supposed that, due to the long timescales involved in protein aggregation and chemical degradation in the glass, $\alpha $ relaxation processes essentially control the rate of degradation. We have shown that, although there may be $>$ 7 orders of magnitude in time separation, $\beta $ relaxation processes can dominate in influencing both chemical and physical degradation. Also, it is apparent that these $\beta $ processes are closely related to dynamics of the hydrogen-bond network in these glasses. In this presentation we will briefly discuss the phenomenology of protein degradation in sugar-based glasses, and also present details of work on developing a fluorescent probe for use as a sensor for dynamics of the hydrogen-bond network in these glasses.   

Density of states and soft modes of hard sphere colloidal glasses -- experimental observations.

Recent theories and simulations have predicted the presence of soft modes due to which the DOS of glassy materials does not go to zero at zero frequency. We obtain DOS of colloidal hard sphere suspensions from experimental data. The displacement fields of hard sphere colloidal suspensions were studied for a range of volume fractions near the glass transition using confocal microscope. Normal mode frequencies are then computed from the time averaged correlation matrix. The density of vibrational states obtained from normal mode analysis indeed reveals an excess of low frequency anomalous modes in the system. To understand the nature of the modes we analyse the displacement vector fields at various frequencies.   

XPCS Studies of Nanoparticle Motion within Glassy Polymer Melts

We report x-ray photon correlation spectroscopy (XPCS) experiments to investigate the motion of nanoscale gold particles within polystyrene (PS) melts of molecular weight between 2K and 48K g/mol. The particles, with radius of approximately 2 nm, are dispersed in a highly dilute concentration (volume fraction 0.0004) and are functionalized with PS chains to stabilize them against aggregation. At high temperature, the observed motion is diffusive, with a rate that follows a Vogel-Fulcher temperature dependence. When the melts are quenched to lower temperature, the XPCS results indicate hyper-diffusive motion that can be modeled as strain in the melt in response to localized stress relaxation. These dynamics evolve with time following the quench, suggesting that they are coupled to aging of the polymer. Our observation of this hyper-diffusive motion among such a dilute concentration of stable nanoparticles indicates that the particles act as passive tracers and the motion is an intrinsic property of quenched melts.   

Divergent four-point dynamic density correlation function of a glassy suspension

We use a diagrammatic formulation of the dynamics of interacting Brownian particles\footnote{G. Szamel, J. Chem. Phys. \textbf{127}, 084515 (2007).} to study a four-point dynamic density correlation function of a glassy colloidal suspension. We re-sum a class of diagrams which separate into two disconnected components upon cutting a single propagator. The resulting formula for the four-point correlation function can be expressed in terms of three-point functions closely related to the three-point susceptibility introduced by Biroli \textit{et al.}\footnote{G. Biroli \textit{et al.}, Phys. Rev. Lett. \textbf{97}, 195701 (2006).} and the standard two-point correlation function. We numerically evaluate the four-point function and the associated dynamic correlation length. Both the amplitude of the four-point function and the correlation length diverge at the mode-coupling transition.   

Self-Organized Criticality in Periodically-Sheared Sedimenting Suspensions

Suspensions of non-colloidal particles under slow periodic strain can undergo a dynamical phase transition from an active fluctuating state to an absorbing steady state at a critical volume fraction In the case of density-mismatched particles, sedimentation and shear-induced diffusion drive the system towards a self-organized critical state. The lengthscales and timescales associated with the dynamics of the active particle clusters sustained near the critical point are shown to follow power-law behavior via simulation of activated random walkers. Finite-size effects and excluded volume interactions are explored for sedimenting and neutrally buoyant, mono- and bi-disperse suspensions both by simulation and experiment.   

Heat transfer in model amorphous solids

We investigate heat transfer in model amorphous solids obtained from jammed packings of soft spheres. At the boson peak frequency, we find a sharp crossover from a weak-scattering regime, in which the energy diffusivity drops rapidly with frequency, to a strong-scattering regime, in which the diffusivity is nearly frequency-independent. We present a scaling analysis of how the crossover frequency shifts to zero as the system is decompressed towards the jamming transition. We show that the regime of flat diffusivity, invoked to explain the temperature dependence of the thermal conductivity of glasses, can arise from properties of the jamming transition.   

Structural response of a colloidal glass to local forcing

Video microscopy of glassy colloidal suspensions permits direct visualization of particle locations and trajectories, thereby providing an excellent experimental tool to aid our understanding of glasses and address current theories. We have conducted a series of experiments utilizing a bidisperse mixture of thermosensitive NIPA microgel spheres to study the structural response of a two-dimensional colloidal glass to point expansion. The packing fraction of the colloidal suspension is tuned from a liquid to a deeply jammed glass by varying the global temperature of the sample. Over this range of packing fractions, the response of the sample to point expansion is analyzed. In particular, an infrared laser tightly focused on the sample generates thermophoretic forces that lead to a point expansion in the colloidal glass. We track particle rearrangements and characterize the response as a function of packing fraction. These experiments take a step towards understanding the relationship between local structure and bulk properties of glass.   

Relaxation processes in polystyrene melts and ultra-thin films

By means of large-scale computer simulations we investigate relaxation processes in polystyrene melts and ultra-thin films. The local orientational mobility of the phenyl bonds is studied with the help of Legendre polynamials of the second-order P{\_}2(t). The spectral density of P{\_}2 (t) shows several distinctive peaks. They are caused by the large- scale motions of cooperative segments ($\alpha $ relaxation), smaller-scale structural dynamics ($\beta $ relaxation), and transient processes. Our simulations reveal that interfaces affect $\alpha -$ and $\beta $-relaxation processes differently. The most puzzling observation is a slight decrease in the structural relaxation time in the middle of the film, compared to that near the free surface. As expected, the $\alpha $-relaxation time is shorter near the free surface. The glass transition temperature, obtained from a plot of thickness versus temperature, decreases with decreasing film thickness, which is in agreement with an observed decrease in the $\alpha -$relaxation time. Surprisingly, the structural relaxation time is roughly the same for the bulk and for films. Our results will be compared with published experimental data.   

Changes in Local Structure and Dynamic Heterogeneity in an Aging Glass

Recent works have shown a connection between structure and dynamical heterogeneity in glass$^{12}$. However, a connection between structure and aging dynamics remains elusive. To this end, we study aging in a bidisperse suspension of soft spheres. Micron-sized temperature-sensitive NIPA particles are employed in two-dimensions, and directly observed with video microscopy. After quenching from liquid to glass, the fraction of particles with crystalline order within the first coordination shell increases with time. Particles that undergo irreversible rearrangements$^{2}$, the aspect of dynamic heterogeneity most closely linked to structural relaxation, are identified. Particles with local crystalline order are observed to be very unlikely to irreversibly rearrange, and therefore more stable. This increase in stable particle configurations leads to the slowing of dynamics that is characteristic of aging. [1] A. Widmer-Cooper, H. Perry, P. Harrowell, and D. R. Reichman, Nat Phys \textbf{4}, 711 (2008) [2] K. Watanabe and H. Tanaka, Physical Review Letters \textbf{100} (2008)   

Investigation of electron beam induced changes in glassy Ge$_{x}$Se$_{1-x}$ thin films

Global structures in network glasses are characterized by their connectedness or mean co-ordination number. As the number of these cross-links within a covalent network increases by compositional tuning these systems steadily evolve from being underconstrained (floppy) to an overconstrained (rigid) solid. Recently (Appl Phys Lett 93, 041107 (2008)) we exploited electron beams to write nanoscale surface motifs in Ge$_{0.2}$Se$_{0.8}$ thin films that are at the special Ge in Se composition lying in the immediate vicinity of the floppy to rigid stiffness transition. In order to investigate the nature of the surface reliefs we have employed selected area transmission electron microscopy (TEM) to probe the electron beam induced structural changes to the film. Films of thicknesses less than 150 nm were deposited by pulsed laser deposition directly onto a carbon film on a mica substrate. The glass film and carbon layer were then lifted off onto copper grids for the TEM studies. Extension of the electron beam driven studies to other compositions, as well as the effect of multiple beam overwrites on the surface reliefs and trenches in several Ge$_{x}$Se$_{1-x}$ compositions will also be presented.   

Periodic Lattices Near Isostaticity

Lattices in $d$ dimensions with with an average of $z=2d$ contacts per site are at the verge of mechanical stability and are called isostatic. Common isostatic lattices include the two-dimensional square and Kagome lattices as well as the three-dimensional cubic lattice with nearest-neighbor sites connected by central-force springs of spring constant $k$ and randomly packed spheres at random close packing at what is called point $J$. We calculate the phonon response functions and spectra of nearly isostatic square, cubic, and Kagome lattices in which springs of spring constant $k'$ connect next-nearest-neighbor sites. These lattices exhibit highly anisotropic modes at $k'=0$, among which are soft modes with one-dimensional dispersion in wavenumber, giving rise to a flat density of states as a function of frequency $\omega$. In the square lattice, these modes are shear acoustic phonons, whereas in the Kagome lattice, they are optical phonons. When $k'>0$, the low-energy modes crossover from acoustic phonons of the appropriate lattice symmetry for $\omega < \omega^* \sim\sqrt{k'}$ to the soft isostatic-like modes for $\omega>\omega^*$, and the density of states crosses over from Debye-like to flat. Static phonon response functions exhibit correlation lengths $\xi \sim 1/\sqrt{k'}$. We discuss the relation of these results to those for jammed systems near point $J$.   

Soft modes and elasticity of nearly isostatic lattices: randomness and dissipation

Isostatic periodic lattices, such as the square and kagome lattices in spatial dimension $d=2$, are systems at the onset of rigidity. They are marginally stable with coordination number $z=2d$, and they may exhibit a non-extensive number of soft modes that can be removed by adding an infinitesimal number of additional bonds. Randomly packed frictionless spheres at the jamming point J represent an important isostatic system that, because of its randomness, exhibits complexities beyond those of periodic systems. To study the effects of randomness on phonon response, propagation, and damping, we constructed model lattices near isostaticity by adding randomly distributed next-nearest and second-nearest neighbor bonds to the isostatic square and kagome lattices, respectively. We calculated a number of properties of these models using the CPA approximation and found them to resemble those of jammed solids near the point J. In particular, the phonon density of states crosses over from Debye-like at low frequency $\omega$ to the flat frequency-independent behavior of a one-dimensional systems at a characteristic frequency $\omega^*$ that scales as the density of additional random bonds $\Delta z$. The real and imaginary part of the effective random-bond spring constants become equal at $\omega^*$. We also identify a characteristic length that scales as $(\Delta z)^{-1}$.