Abstract :
The heat capacity of the equilibrium state, Cp,liq, of nine liquids has been interpolated along a stretched sigmoid-shape path from its known value above Tg to its zero value at 0 K. The entropy of the equilibrium liquid, Sliq also decreases along a sigmoid-shape path tending to zero at 0 K, and the enthalpy remains finite, as is the case for two crystal forms of the same material with zero entropy and different energies at 0 K. This is in contrast with the vanishing of the configurational entropy, Sconf, at T>0 K expected at an unobservable thermodynamic transition in an equilibrium liquid. The plot of the difference between Sglass and Sliq against T shows a broad peak in our interpolation. Its significance is discussed in terms of the structural relaxation, and relevance to both the entropy theory and the conjectured thermodynamic transition. It is also shown that the entropy theory does not naturally lead to an abrupt decrease in Cp of an equilibrium liquid at T>0 K. Moreover, the conjecture of an underlying thermodynamic transition in an equilibrium liquid, which the current theories have attempted to explain, is itself a result of, (i) the approximations, which made the original entropy formalism consistent with a liquid’s viscosity data, and (ii) the assumptions later built into the theory’s modification in which it was related to the critical phenomenon. The original entropy formalism does not conflict with the proposed sigmoid-shape curve of Cp,liq in a temperature plane. The broad peak in (dCp,liq/dT) at a certain T still relates a liquid’s thermodynamics to its transport properties, and this relation can be reconciled with the observed approximate fit of the empirical, Vogel–Fulcher–Tammann equation to a liquid’s transport properties only after its Sconf is available. Sconf is neither equal to the excess entropy nor proportional to it, the latter because the anharmonic contribution does not increase in proportion to the number of accessible configurations.
