Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session M42: Focus Session: Physics of Glasses and Viscous Liquids III |
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Sponsoring Units: DCP Chair: Patrick Charbonneau, Duke University Room: Hilton Baltimore Holiday Ballroom 3 |
Wednesday, March 20, 2013 8:00AM - 8:36AM |
M42.00001: High-dimensional surprises neat the glass and the jamming transitions Invited Speaker: Patrick Charbonneau The glass problem is notoriously hard and controversial. Even at the mean-field level, there is little agreement about how a fluid turns sluggish while exhibiting but unremarkable structural changes. It is clear, however, that the process involves self-caging, which provides an order parameter for the transition. It is also broadly assumed that this cage should have a Gaussian shape in the mean-field limit. Here we show that this ansatz does not hold, and explore its consequences. Non-Gaussian caging, for instance, persists all the way to the jamming limit of infinitely compressed hard spheres, which affects mechanical stability. We thus obtain new scaling relations, and establish clear mileposts for the emergence of a mean-field theory of jamming. [Preview Abstract] |
Wednesday, March 20, 2013 8:36AM - 8:48AM |
M42.00002: Microscopic theories of the structure and glassy dynamics of ultra-dense hard sphere fluids Ryan Jadrich, Kenneth Schweizer We construct a new thermodynamically self-consistent integral equation theory (IET) for the equilibrium metastable fluid structure of monodisperse hard spheres that incorporates key features of the jamming transition. A two Yukawa generalized mean spherical IET closure for the direct correlation function tail is employed to model the distinctive short and long range contributions for highly compressed fluids. The exact behavior of the contact value of the radial distribution function (RDF) and isothermal compressibility are enforced, as well as an approximate theory for the RDF contact derivative. Comparison of the theoretical results for the real and Fourier space structure with nonequilibrium jammed simulations reveals many similarities, but also differences as expected. The new structural theory is used as input into the nonlinear Langevin equation (NLE) theory of activated single particle dynamics to study the alpha relaxation time, and good agreement with recent experiments and simulations is found. We demonstrate it is crucial to accurately describe the very high wave vector Fourier space to reliably extract the dynamical predictions of NLE theory, and structural precursors of jamming play an important role in determining entropic barriers. [Preview Abstract] |
Wednesday, March 20, 2013 8:48AM - 9:00AM |
M42.00003: Beyond the mode-coupling theory: a perturbative diagrammatic approach Grzegorz Szamel, Elijah Flenner We analyze corrections to the mode-coupling theory of the glass transition, focusing on the self-consistent equation for the non-ergodicity parameter. We use a diagrammatic formulation of the dynamics of interacting Brownian particles\footnote{G. Szamel, J. Chem. Phys. 127, 084515 (2007)}. Our approach builds upon an earlier identification of a divergent contribution to a four-point correlation function\footnote{G. Szamel, Phys. Rev. Lett. 101, 205701 (2008)}. We find that diagrams similar to those generating the divergence of the four-point function lead to divergent corrections to the mode-coupling theory's prediction for the long time limit of the irreducible memory function. We propose and investigate a new equation for the non-ergodicity parameter that self-consistently includes the diagrams leading to the divergent corrections. [Preview Abstract] |
Wednesday, March 20, 2013 9:00AM - 9:12AM |
M42.00004: Shapes of dynamically heterogeneous regions in glassy fluids with attractive and repulsive interactions as revealed through anisotropic four-point correlation functions Elijah Flenner, Grzegorz Szamel We investigate the size and anisotropy of dynamically heterogeneous regions in glassy fluids with attractive and repulsive interactions. To this end we simulate a binary Lennard-Jones mixture and its Weeks-Chandler-Andersen truncation. We use a four-point correlation function $G_4(\vec{k},\vec{r};t)$, which depends on the angle between $\vec{k}$ and $\vec{r}$, and its associated structure factor $S_4(\vec{k},\vec{q};t)$, which depends on the angle $\theta$ between $\vec{k}$ and $\vec{q}$, to characterize the size and anisotropy of the dynamically correlated regions. In particular, $G_4(\vec{k},\vec{r};t)$ allows us to explore dynamic heterogeneities at shorter distances. In contrast, to investigate dynamic heterogeneities at longer distances we analyze the small $q$ behavior of $S_4(\vec{k},\vec{q};t)$ and obtain an anisotropic dynamic correlation length $\xi(\theta)$. We explore the dependence of dynamic heterogeneities at shorter and longer distances on the presence of attractive interactions. [Preview Abstract] |
Wednesday, March 20, 2013 9:12AM - 9:48AM |
M42.00005: Reversible and Irreversible Behavior of Glass-forming Materials from the Standpoint of Hierarchical Dynamical Facilitation Invited Speaker: Aaron Keys Using molecular simulation and coarse-grained lattice models, we study the dynamics of glass-forming liquids above and below the glass transition temperature. In the supercooled regime, we study the structure, statistics, and dynamics of excitations responsible for structural relaxation for several atomistic models of glass-formers. Excitations (or soft spots) are detected in terms of persistent particle displacements. At supercooled conditions, we find that excitations are associated with correlated particle motions that are sparse and localized, and the statistics and dynamics of these excitations are facilitated and hierarchical. Excitations at one point in space facilitate the birth and death of excitations at neighboring locations, and space-time excitation structures are microcosms of heterogeneous dynamics at larger scales. Excitation-energy scales grow logarithmically with the characteristic size of the excitation, giving structural-relaxation times that can be predicted quantitatively from dynamics at short time scales. We demonstrate that these same physical principles govern the dynamics of glass-forming systems driven out-of-equilibrium by time-dependent protocols. For a system cooled and re-heated through the glass transition, non-equilibrium response functions, such as heat capacities, are notably asymmetric in time, and the response to melting a glass depends markedly on the cooling protocol by which the glass was formed. We introduce a quantitative description of this behavior based on the East model, with parameters determined from reversible transport data, that agrees well with irreversible differential scanning calorimetry. We find that the observed hysteresis and asymmetric response is a signature of an underlying dynamical transition between equilibrium melts with no trivial spatial correlations and non-equilibrium glasses with correlation lengths that are both large and dependent upon the rate at which the glass is prepared. The correlation length corresponds to the size of amorphous domains bounded by excitations that remain frozen on the observation time scale, thus forming stripes when viewed in space and time. We elucidate properties of the striped phase and show that glasses of this type, traditionally prepared through cooling, can be considered a finite-size realization of the inactive phase formed by the s-ensemble in the space-time thermodynamic limit. [Preview Abstract] |
Wednesday, March 20, 2013 9:48AM - 10:00AM |
M42.00006: Dynamical Heterogeneity in Higher Dimensions: Kinetically Constrained Models YounJoon Jung, Soree Kim We use kinetically constrained models to investigate the dimensional dependence of dynamic heterogeneity in supercooled liquid systems. Higher dimensional generalizations of one dimensional East model and its variation with an embedded probe particle are used as a representative fragile liquid system. We first investigate how the breakdown of the Stokes-Einstein relation changes with the system dimensionality from $d=1$ up to $d=10$. The fractional scaling behavior $D\propto{\tau}^{-\xi}$ are observed, where $D$ and $\xi$ are the diffusion constant of the probe and the relaxation time of the liquid, respectively. The scaling exponent, $\xi$, decreases as the dimensionality increases. The decoupling between persistence and exchange times are also characterized as the dimensionality changes. Time and length scales of the dynamic heterogeneity are analyzed by calculating persistence functions and the dynamic susceptibility. Comparisons are made with respect to recent atomistic MD simulation results. [Preview Abstract] |
Wednesday, March 20, 2013 10:00AM - 10:12AM |
M42.00007: Dynamics in a meta-basin and its relation to $\beta$ relaxation in glass-forming liquids Chandan Dasgupta, Pranabjyoti Bhuyan A clear interpretation of the short-time $\beta$ relaxation of glass-forming liquids in terms of dynamics in the potential energy landscape is not yet available. We have studied the relation between dynamics in a meta-basin of the potential energy landscape and $\beta$ relaxation in a well-known glass-forming liquid - the Kob-Andersen binary mixture. Meta-basins are determined from the series of inherent structures obtained by minimizing the potential energy, starting from configurations obtained from a constant-temperature molecular dynamics (MD) simulation. The eigenvalues and eigenvectors of the Hessian matrices of the inherent structures in a meta-basin are then used to calculate various dynamical quantities in the harmonic approximation. We find that the results of the harmonic calculation begin to deviate from those obtained from MD simulations at time scales substantially shorter than the $\beta$ relaxation time corresponding to the plateau in the mean-square displacement versus time plot. The agreement between the results of our analysis of the dynamics in a meta-basin and those of MD simulations is found to extend to longer times when anharmonic effects are included in the analysis. A detailed comparison between these two set of results will be presented. [Preview Abstract] |
Wednesday, March 20, 2013 10:12AM - 10:24AM |
M42.00008: Universal Microstructure of Jammed Packings in Higher Dimensions Eric Corwin, Patrick Charbonneau, Francesco Zamponi Jammed packings' mechanical properties depend sensitively on their detailed local structure. We simulate the structure of jammed packings of frictionless spheres over a range of spatial dimensions $d$=3-10 using a variety of preparation protocols for both hard and soft spheres. We provide a complete characterization of the pair correlation close to contact and of the force distribution. We find that even as the density for jamming depends strongly on the packing protocol there nevertheless exist universal scaling relationships that hold true for all jammed packings. These relationships connect the behavior of particles participating in the mechanical structure of the packing and particles that bear no force but are almost in contact. [Preview Abstract] |
Wednesday, March 20, 2013 10:24AM - 11:00AM |
M42.00009: Ginzburg criterion for the glass transition Invited Speaker: Francesco Zamponi I will discuss the onset of slow relaxation in glassy systems by constructing a static replica field theory approach to the problem. At the mean field level, criticality in the four point correlation functions arises because of the presence of soft modes and I will present an effective replica field theory for these critical fluctuations. At the Gaussian level many physical quantities are obtained: the correlation length, the exponent parameter that controls the Mode-Coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions. A one-loop computation allows to identify the region in which the mean field Gaussian approximation is valid. The result is a Ginzburg criterion for the glass transition, which confirms that the upper critical dimension for the glass transition is d$=$8. Finally, I will present numerical results for hard spheres in dimension d ranging from 3 to 9 that support the analytical results. [Preview Abstract] |
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