Melting/freezing transition in polydisperse Lennard-Jones system: Remarkable agreement between predictions of inherent structure, bifurcation phase diagram, Hansen-Verlet rule and Lindemann criteria

摘要

We use polydispersity in size as a control parameter to explore certainaspects of melting and freezing transitions in a system of Lennard-Jonesspheres. Both analytical theory and computer simulations are employed toestablish a potentially interesting relationship between observed terminalpolydispersity in Lennard-Jones polydisperse spheres and prediction of the samein the integral equation based theoretical analysis of liquid-solid transition.As we increase polydispersity, solid becomes inherently unstable because of thestrain built up due to the size disparity. This aspect is studied here bycalculating the inherent structure (IS) calculation. With polydispersity atconstant volume fraction we find initially a sharp rise of the average ISenergy of the crystalline solid until transition polydispersity, followed by across over to a weaker dependence of IS energy on polydispersity in theamorphous state. This cross over from FCC to amorphous state predicted by ISanalysis agrees remarkably well with the solid-liquid phase diagram (withextension into the metastable phase) generated by non-linear integral equationtheories of freezing. Two other well-known criteria of freezing/meltingtransitions, the Hansen-Verlet rule of freezing and the Lindemann criterion ofmelting are both shown to be remarkably in good agreement with the above twoestimates. Together they seem to indicate a small range of metastability in theliquid-solid transition in polydisperse solids.