Computing the viscosity of supercooled liquids

Abstract

We describe an atomistic method for computing the viscosity of highly viscous liquids based on activated state kinetics. A basin-filling algorithm allowing the system to climb out of deep energy minima through a series of activation and relaxation is proposed and first benchmarked on the problem of adatom diffusion on a metal surface. It is then used to generate transition state pathway trajectories in the potential energy landscape of a binary Lennard-Jones system. Analysis of a sampled trajectory shows the system moves from one deep minimum to another by a process that involves high activation energy and the crossing of many local minima and saddle points. To use the trajectory data to compute the viscosity we derive a Markov Network model within the Green-Kubo formalism and show that it is capable of producing the temperature dependence in the low-viscosity regime described by molecular dynamics simulation, and in the high-viscosity regime (10(2)-10(12) Pa s) shown by experiments on fragile glass-forming liquids. We also derive a mean-field-like description involving a coarse-grained temperature-dependent activation barrier, and show it can account qualitatively for the fragile behavior. From the standpoint of molecular studies of transport phenomena this work provides access to long relaxation time processes beyond the reach of current molecular dynamics capabilities. In a companion paper we report a similar study of silica, a representative strong liquid. A comparison of the two systems gives insight into the fundamental difference between strong and fragile temperature variations. We describe an atomistic method for computing the viscosity of highly viscous liquids based on activated state kinetics. A basin-filling algorithm allowing the system to climb out of deep energy minima through a series of activation and relaxation is proposed and first benchmarked on the problem of adatom diffusion on a metal surface. It is then used to generate transition state pathway trajectories in the potential energy landscape of a binary Lennard-Jones system. Analysis of a sampled trajectory shows the system moves from one deep minimum to another by a process that involves high activation energy and the crossing of many local minima and saddle points. To use the trajectory data to compute the viscosity we derive a Markov Network model within the Green-Kubo formalism and show that it is capable of producing the temperature dependence in the low-viscosity regime described by molecular dynamics simulation, and in the high-viscosity regime ͑10 2 -10 12 Pa s͒ shown by experiments on fragile glass-forming liquids. We also derive a mean-field-like description involving a coarse-grained temperature-dependent activation barrier, and show it can account qualitatively for the fragile behavior. From the standpoint of molecular studies of transport phenomena this work provides access to long relaxation time processes beyond the reach of current molecular dynamics capabilities. In a companion paper we report a similar study of ...

Formation, migration, and clustering of delocalized vacancies and interstitials at a solid-state semicoherent interface

“…Examples of such methods are temperature accelerated dynamics (TAD) 93 , the parallel replica method 94 , activation-relaxation techniques (ART) 95,96 and variants of algorithms where energy basins are filled by introducing artificial potentials, some of which are called metadynamics 97,98 and other hyperdynamics 99,100 .…”

Mapping strain rate dependence of dislocation-defect interactions by atomistic simulations

“…7. Although the original ABC algorithm (34) has been used here, significant improvements to the efficiency of the method (43) can enable the investigation of more complex microstructures such as grain boundaries and cracks. Comparing Figs.…”

“…The algorithm defined in Methods permits us to identify the dislocationobstacle interaction mechanism and the critical shear stresses under different strain rates and temperatures, and to extend to arbitrarily lower strain rates than those possible with traditional MD. In summary, the present approach combines the TST framework with the activation-relaxation algorithm known as ABC for sampling interaction pathways and energies (34)(35)(36)(37)(38). The simulation proceeds in time step increments.…”

“…Here we extend our formulation to predicting the mechanisms and kinetics of dislocation-defect interactions from atomistic simulations over a wide range of time scales including low strain rates. Our starting point is the sampling of interaction pathways and energies at the atomistic level using the ABC method (34)(35)(36)(37)(38). Combining the atomistic interaction pathways and energy barriers with TST, in what we now call ABC-T, enables us to span a wide range of time scales.…”

“…We apply this approach to the problem of an edge dislocation colliding with a cluster of self-interstitial atoms (SIAs) under shear deformation. Using an activation-relaxation algorithm [Kushima A, et al (2009) J Chem Phys 130:224504], we uncover a unique strain-ratedependent trigger mechanism that allows the SIA cluster to be absorbed during the process, leading to dislocation climb. Guided by this finding, we determine the activation barrier of the trigger mechanism as a function of shear strain, and use that in a coarsegraining rate equation formulation for constructing a mechanism map in the phase space of strain rate and temperature.…”