Renaissance of Bernal's random close packing and hypercritical line in the theory of liquids

摘要: We review the scientific history of random close packing (RCP) equal spheres, advocated by J D Bernal as a more plausible alternative to non-ideal gas or imperfect crystal structural model simple liquids. After decades neglect, computer experiments are revealing central role for RCP in theory These demonstrate that amorphous state hard spheres can be well defined, is reproducible, and has thermodynamic status metastable ground state. Further evidence from simulations square-well liquids indicates an extended terminates supercooled liquid coexistence line, suggesting likewise real A phase diagram involving percolation boundaries been proposed which there no merging phases, critical singularity assumed van der Waals. Rather, continuously spans all temperatures, but above dividing line on Gibbs density surface, it bounded transition separated colloidal supercritical mesophase. The colloidal-like inversion mesophase changes gas-in-liquid liquid-in-gas identified with hypercritical Bernal. therefore argue statistical should start reference rather than ideal gas. Future experimental priorities (i) find liquids, (ii) explore microscopic structures mesophase, (iii) determine how these change liquid, especially across Bernal's line. theoretical priority geometrical RCP. Only then might we explain coincident values fraction Buffon's constant, residual entropy Boltzmann's constant.