Effects of random pinning on the potential energy landscape of a supercooled liquid.

We use energy landscape methods to investigate the response of a supercooled liquid to random pinning. We classify the structural similarity of different energy minima using a measure of overlap. This analysis reveals a correspondence between distinct particle packings (which are characterised via the overlap) and funnels on the energy landscape (which are characterised via disconnectivity graphs). As the number of pinned particles is increased, we find a crossover from glassy behavior at low pinning to a structure-seeking landscape at high pinning, in which all thermally accessible minima are structurally similar. We discuss the consequences of these results for theories of randomly pinned liquids. We also investigate how the energy landscape depends on the fraction of pinned particles, including the degree of frustration and the evolution of distinct packings as the number of pinned particles is reduced.

Pathways for diffusion in the potential energy landscape of the network glass former SiO2.

We study the dynamical behaviour of a computer model for viscous silica, the archetypal strong glass former, and compare its diffusion mechanism with earlier studies of a fragile binary Lennard-Jones liquid. Three different methods of analysis are employed. First, the temperature and time scale dependence of the diffusion constant is analysed. Negative correlation of particle displacements influences transport properties in silica as well as in fragile liquids. We suggest that the difference between Arrhenius and super-Arrhenius diffusive behaviour results from competition between the correlation time scale and the caging time scale. Second, we analyse the dynamics using a geometrical definition of cage-breaking transitions that was proposed previously for fragile glass formers. We find that this definition accurately captures the bond rearrangement mechanisms that control transport in open network liquids, and reproduces the diffusion constants accurately at low temperatures. As the same method is applicable to both strong and fragile glass formers, we can compare correlation time scales in these two types of systems. We compare the time spent in chains of correlated cage breaks with the characteristic caging time and find that correlations in the fragile binary Lennard-Jones system persist for an order of magnitude longer than those in the strong silica system. We investigate the origin of the correlation behaviour by sampling the potential energy landscape for silica and comparing it with the binary Lennard-Jones model. We find no qualitative difference between the landscapes, but several metrics suggest that the landscape of the fragile liquid is rougher and more frustrated. Metabasins in silica are smaller than those in binary Lennard-Jones and contain fewer high-barrier processes. This difference probably leads to the observed separation of correlation and caging time scales.

Defining and quantifying frustration in the energy landscape: Applications to atomic and molecular clusters, biomolecules, jammed and glassy systems.

The emergence of observable properties from the organisation of the underlying potential energy landscape is analysed, spanning a full range of complexity from self-organising to glassy and jammed systems. The examples include atomic and molecular clusters, a ß-barrel protein, the GNNQQNY peptide dimer, and models of condensed matter that exhibit structural glass formation and jamming. We have considered measures based on several different properties, namely, the Shannon entropy, an equilibrium thermodynamic measure that uses a sample of local minima, and indices that require additional information about the connections between local minima in the form of transition states. A frustration index is defined that correlates directly with key properties that distinguish relaxation behaviour within this diverse set. The index uses the ratio of the energy barrier to the energy difference with reference to the global minimum. The contributions for each local minimum are weighted by the equilibrium occupation probabilities. Hence we obtain fundamental insight into the connections and distinctions between systems that cover the continuum from efficient structure-seekers to landscapes that exhibit broken ergodicity and rare event dynamics.

Dynamics of a molecular glass former: Energy landscapes for diffusion in ortho-terphenyl.

Relaxation times and transport processes of many glass-forming supercooled liquids exhibit a super-Arrhenius temperature dependence. We examine this phenomenon by computer simulation of the Lewis-Wahnström model for ortho-terphenyl. We propose a microscopic definition for a single-molecule cage-breaking transition and show that, when correlation behaviour is taken into account, these rearrangements are sufficient to reproduce the correct translational diffusion constants over an intermediate temperature range in the supercooled regime. We show that super-Arrhenius behaviour can be attributed to increasing negative correlation in particle movement at lower temperatures and relate this to the cage-breaking description. Finally, we sample the potential energy landscape of the model and show that it displays hierarchical ordering. Substructures in the landscape, which may correspond to metabasins, have boundaries defined by cage-breaking transitions. The cage-breaking formulation provides a direct link between the potential energy landscape and macroscopic diffusion behaviour.