Simple glass-forming liquids: their definition, fragilities, and landscape excitation profiles

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Abstract
The `excitation profile' of a liquid is a measure of the rate per kelvin at which the liquid is driven by entropy generation to the top of its potential energy landscape. We argue that it determines the liquid fragility, and hence controls the canonical features of viscous liquid phenomenology. We seek to prove this using studies of simple glass formers. We recognize two types of simple glass former, molecularly simple and excitationally simple, and provide examples and characterization of each. In the first category we describe the systems , , and their binary solutions. The simplest case is only glass forming in emulsion form but solutions in up to 85% are found to be bulk glass formers. The fragility of each component is determined by the new `reduced-transition-width' measurement and found to be only 60% fragile versus 75% for the fragile liquid toluene and propylene carbonate. We infer that the mixed LJ (Lennard-Jones) system, whose landscape `excitation profile' has recently been determined by MD computer simulations, is only a moderately fragile liquid. For the increase in heat capacity at is used to `quantify' the energy landscape and establish the appropriate `excitation profile' for liquids of this fragility. The second type of simplicity is bestowed by the presence of a single dominant interaction in the system. The best cases are the covalent glass formers of the chalcogenide variety, e.g. Ge-Se, and Ge-As-Se, in which the breaking of angle-specific covalent bonds is the dominant excitation process. We show that in the ground-state bond lattice an extremum in the glass transition temperature occurs close to the theoretical rigidity percolation bond density of 2.4 bonds per particle where a fragility minimum is also found. Invoking a simple theoretical treatment of this bond lattice we find that the entropy of the elementary excitation is a minimum or zero at percolation, and the glass transition becomes a simple Schottky anomaly with kinetic arrest. The excitation profile predicted by this model seems similar to that found by the simulations for the molecularly simple glasses. The fragility of the liquid is, in this case, controlled by the entropy change in the elementary excitation process. Whether this excitation entropy is determined within the configurational or vibrational densitites of states is a key question. In either case, large values mean sharp excitation profiles which, due to cooperative effects near pure Ge, can become first-order liquid-liquid transitions.