Understanding the viscosity of supercooled liquids and the glass transition through molecular simulations

Abstract

We discuss a potential energy landscape (PEL) approach to calculate the characteristically sluggish viscous behaviour of supercooled liquids. This phenomenon is central to the theoretical understanding of the liquid-to-glass transition, a long-standing challenge in non-equilibrium statistical mechanics of amorphous states of matter. Experimentally, the shear viscosity of supercooled glass-forming liquids shows strong variations with the quench temperature. In particular, two types of behaviour are observed, Arrhenius and highly super-Arrhenius. Conceptually, the molecular description of the structural and dynamical processes underpinning the viscosity behaviour has become a topic of interest because of general implications for the kinetics of slow relaxation in the glassy state. We regard the supercooled liquid as an assembly of interacting particles undergoing thermal fluctuations such that the system evolves in space and time by crossing a series of potential energy barriers. To find these barriers and their corresponding atomic configurations, we apply an energy landscape sampling algorithm that maps out the evolution trajectories in the form of alternating sequences of local energy minima and saddle points. The energy sequences and the atomic coordinates constitute a body of atomic-scale data which we then process using two distinct methods. One is based on an effective activation barrier extracted from the transition-state pathway data, and the other is based on the linear response theory of statistical mechanics. The former is heuristic by being more physically transparent, while the latter is theoretically more rigorous. Through these two complementary calculations, an understanding of the temperature variations of shear viscosities of supercooled liquids, as well as the nature of fragile and strong behaviour of the glass transition, emerges. Our calculation provides a molecular-level account of the viscosities of supercooled liquids in a unified and consistent manner without invoking ad hoc assumptions. Relative to the nature of the glass transition, the usefulness of the PEL perspective is demonstrated, along with the concept of crossover between strong and fragile behaviour. In terms of advancing atomistic simulation capability, we believe the time-scale limitations of traditional molecular dynamics may be significantly extended through the use of metadynamics algorithms for sampling transition-state pathways.

Keywords:

• Viscosity
• supercooled liquids
• glass transition
• molecular simulation
• glassy dynamics

Acknowledgements

This work is supported in part by the Project on Sustainability of Kuwait’s Built Environment of the MIT Center for Natural Resources and Environment and by the Basic Energy Sciences, US Department of Energy award DE-SC0002633, along with associations with the Concrete Sustainability Hub at MIT. I would like to acknowledge the collaboration of A. Kushima, X. Lin, J. Li, J. Eapen, X.-F. Qian, J. Mauro and P. Diep in the viscosity calculations described here, extensive discussions with A. S. Argon and J. S. Langer over the years, and with Y. Fan more recently, and the hospitality of the Kavli Institute of Theoretical Physics at UC Santa Barbara for two workshop programmes, the Physics of Glasses 2010 and Systems Far from Equilibrium 2014.

Disclosure statement

No potential conflict of interest was reported by the author.