Relationship between thermodynamics and dynamics of supercooled liquids
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[(a) and (b)] Excess entropy and diffusivity vs density obtained from molecular dynamics simulations of 1000 particles interacting via a “core-softened” potential (i.e., a Lennard-Jones potential plus a Gaussian repulsion; for details, see Ref. 15). Symbols are simulation data, and curves are guides to the eyes. The quantities are reported in reduced units of , , and , where is the Boltzmann constant, is the temperature, is the energy scale of the potential, is the number density, is the particle diameter, and is the particle mass. The excess entropy has been calculated using transition-matrix Monte Carlo simulations (Refs. 6 and 21). (c) Diffusivity vs excess entropy for the data shown in (a) and (b) along paths of constant (symbols). Symbols are simulation data, and lines reflect the form .
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Diffusivity vs excess entropy for different density states of a binary Lennard-Jones alloy (Refs. 12 and 18). Excess entropy has been obtained from the semiempirical free energy expression reported in Ref. 18, and diffusivity has been extracted from Fig. 3 in Ref. 18. The lines reflect the form . The inset shows the linear dependence between excess entropy and the inverse product of temperature and configurational entropy, , the latter extracted from Fig. 2 in Ref. 12. The quantities are reported in the same reduced units as in Fig. 1.
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