Ratio of effective temperature to pressure controls the mobility of sheared hard spheres

Using molecular dynamics simulation, we calculate fluctuations and response for steadily sheared hard spheres over a wide range of packing fractions $\phi$ and shear strain rates $\gamma$, using two different methods to dissipate energy. To a good approximation, shear stress and density fluctuations are related to their associated response functions by a single effective temperature $T_{eff}$ that is equal to or larger than the kinetic temperature $T_{kin}$. We find a crossover in the relationship between the relaxation time $\tau$ and the the nondimensionalized effective temperature $T_{eff}/p\sigma^3$, where $p$ is the pressure and $\sigma$ is the sphere diameter. In the solid response regime, the behavior at fixed packing fraction satisfies $\tau\gamma\propto \exp(-cp\sigma^3/T_{eff})$, where $c$ depends weakly on $\phi$, suggesting that the average local yield strain is controlled by the effective temperature in a way that is consistent with shear transformation zone theory. In the fluid response regime, the relaxation time depends on $T_{eff}/p\sigma^3$ as it depends on $T_{kin}/p\sigma^3$ in equilibrium. This regime includes both near-equilibrium conditions where $T_{eff} ~ T_{kin}$ and far-from-equilibrium conditions where $T_{eff} \ne T_{kin}$. We discuss the implications of our results for systems with soft repulsive interactions.Comment: 9 pages, 6 figures. Major revision: added results and analysis for sheared inelastic hard spheres to complement the previous results for sheared thermostatted hard spheres, increasing the available range of $T_{eff}$ and strengthening the conclusions; added discussion of results relative to the jamming phase diagra

Jamming Phase Diagram, Effective Temperature, and Heterogeneous Dynamics of Model Glass-Forming Liquids

We establish that the behavior of fluids consisting of repulsive spheres under the combined effects of pressure p, temperature T, and applied shear stress s can be organized in a jamming phase diagram parameterized by the dimensionless quantities T/pd^3, s/p, and pd^3/e, where d is the diameter of the spheres and e is the interaction energy scale. The jamming phase diagram describes the three-dimensional parameter space as the product of an equilibrium plane at s/p=0 and a hard sphere plane at pd^3/e=0. Near the hard sphere plane, the jamming phase diagram is universal in the sense that material properties are insensitive to the details of the interaction potential. We demonstrate that within the universal regime, the conventional approach to the dynamic glass transition along a decreasing temperature trajectory is equivalent to the colloidal glass transition approach along an increasing pressure trajectory. Defining the dynamic glass transition by where a dimensionless relaxation time equals a large but arbitrary value, we measure a two-dimensional dynamic glass transition surface whose precise location depends on the choice of time scale but which always encloses the singular point at the origin, T/pd^3=s/p=pd^3/e=0. We show that at finite shear stress, the effective temperature Teff fluidizes the system in a similar way as the environment temperature T fluidizes the system in the absence of shear. We demonstrate that the dynamic glass transition surface is largely controlled a single parameter, the dimensionless effective temperature Teff/pd^3, that describes the competition between low frequency fluctuations and the confining pressure. Even well into the fluid portion of the jamming phase diagram, we show that relaxation is largely controlled by this single parameter, regardless of whether the fluctuations are created by temperature or shear. Finally, by investigating correlations in the dynamics as a function of length scale a and time scale t, we identify two types of pairs (a, t) over which the dynamics are maximally correlated, suggesting that kinetic heterogeneity is a general feature of dynamical crossovers and not necessarily an indication of an impending thermodynamic transition

Universal Jamming Phase Diagram in the Hard-Sphere Limit

We present a new formulation of the jamming phase diagram for a class of glass-forming fluids consisting of spheres interacting via finite-ranged repulsions at temperature $T$, packing fraction $\phi$ or pressure $p$, and applied shear stress $\Sigma$. We argue that the natural choice of axes for the phase diagram are the dimensionless quantities $T/p\sigma^3$, $p\sigma^3/\epsilon$, and $\Sigma/p$, where $T$ is the temperature, $p$ is the pressure, $\Sigma$ is the stress, $\sigma$ is the sphere diameter, $\epsilon$ is the interaction energy scale, and $m$ is the sphere mass. We demonstrate that the phase diagram is universal at low $p\sigma^3/\epsilon$; at low pressure, observables such as the relaxation time are insensitive to details of the interaction potential and collapse onto the values for hard spheres, provided the observables are non-dimensionalized by the pressure. We determine the shape of the jamming surface in the jamming phase diagram, organize previous results in relation to the jamming phase diagram, and discuss the significance of various limits.Comment: 8 pages, 5 figure

Activated dynamics and effective temperature in a steady state sheared glass

We conduct nonequilibrium molecular dynamics simulations to measure the shear stress, the average inherent structure energy, and the effective temperature $T_{eff}$ of a sheared model glass as a function of bath temperature $T$ and shear strain rate. For $T$ above the glass transition temperature $T_0$, the rheology approaches a Newtonian limit and $T_{eff}$ approaches $T$ as the strain rate approaches zero, while for $T<T_0$, the shear stress approaches a yield stress and $T_{eff}$ approaches a limiting value near $T_0$. In the shear-dominated regime at high $T$, high strain rate or at low $T$, we find that the shear stress and the average inherent structure energy each collapse onto a single curve as a function of $T_{eff}$. This indicates that $T_{eff}$ is controlling behavior in this regime.Comment: 4 pages, 2 figures. Revised to include additional data. Inherent structure energy results were included, and much of the shear transformation zone discussion was remove

Equivalence of glass transition and colloidal glass transition in the hard-sphere limit

We show that the slowing of the dynamics in simulations of several model glass-forming liquids is equivalent to the hard-sphere glass transition in the low-pressure limit. In this limit, we find universal behavior of the relaxation time by collapsing molecular-dynamics data for all systems studied onto a single curve as a function of $T/p$, the ratio of the temperature to the pressure. At higher pressures, there are deviations from this universal behavior that depend on the inter-particle potential, implying that additional physical processes must enter into the dynamics of glass-formation.Comment: 4 pages, 4 figure

Mapping the glassy dynamics of soft spheres onto hard-sphere behavior

We show that the dynamics of soft-sphere systems with purely repulsive interactions can be described by introducing an effective hard-sphere diameter determined using the Andersen-Weeks-Chandler approximation. We find that this approximation, known to describe static properties of liquids, also gives a good description of a dynamical quantity, the relaxation time, even in the vicinity of the glass transition.Comment: 5 pages, 3 figure

Common physical framework explains phase behavior and dynamics of atomic, molecular, and polymeric network formers

We show that the self-assembly of a diverse collection of building blocks can be understood within a common physical framework. These building blocks, which form periodic honeycomb networks and nonperiodic variants thereof, range in size from atoms to micron-scale polymers and interact through mechanisms as different as hydrogen bonds and covalent forces. A combination of statistical mechanics and quantum mechanics shows that one can capture the physics that governs the assembly of these networks by resolving only the geometry and strength of building-block interactions. The resulting framework reproduces a broad range of phenomena seen experimentally, including periodic and nonperiodic networks in thermal equilibrium, and nonperiodic supercooled and glassy networks away from equilibrium. Our results show how simple “design criteria” control the assembly of a wide variety of networks and suggest that kinetic trapping can be a useful way of making functional assemblies