Hypotheses in phase transition theories: “What is ‘liquid’?”

Abstract

Theories predicting thermodynamic properties that describe liquid phase transitions and critical phenomena have resulted in the award of three Nobel prizes in physics: (i) “Continuity of Gaseous and Liquid States” hypothesis of van der Waals [1910], (ii) “Critical Point Universality” hypothesis embodied in the renormalization group (RG) theory of Wilson [1982], and (iii) “Topological Defect Melting” hypothesis that 2D-crystal-liquid states exhibit ‘hexatic’ phases in KTHNY theory [Kosterlitz et al. 2016]. All three hypotheses are invalidated by the reality of experimental results and raise a fundamental question first posed by Barker and Henderson in 1976: “What is liquid”. A single Gibbs phase, that includes triple-point (Tt) liquid, extends over the whole fluid density range to temperatures above the Boyle temperature (TB). Below TB, above the critical temperature Tc, predominantly gas- and liquid-like states are bounded by a narrow colloidal ‘supercritical mesophase’ with constant rigidity (ω = (dp/dρ)T). The liquid phase also becomes colloidal at the onset of pre-freezing growth and percolation of crystallites in a narrow density range below freezing density for all T > Tt. Whereas the Boyle line (RT = p/ρ) defines a crystalline ground state, a rigidity line, RT = ω, interpolates to an amorphous ground-state akin to random close packing (RCP) at T = 0. All states of gas, liquid, and crystals, are present in the stable ‘liquid phase’ and, are represented in thermodynamic p-T states all along the rigidity line. For 2D liquid–crystal coexistence in constrained computer models, the KTHNY theory describes a non-equilibrium fracture process. Hetero-phase fluctuations, leading to percolation transitions, have been misconstrued as “hexatic” in 2D, as also have 2-phase coexistence states, that are homogeneous in the absence of gravity.