In thermodynamics, the Frenkel line is a proposed boundary on the phase diagram of a supercritical fluid, separating regions of qualitatively different behavior.
[1] Fluids on opposite sides of the line have been described as "liquidlike" or "gaslike", and exhibit different behaviors in terms of oscillation, excitation modes, and diffusion.
Although this approach allows explanation of many principal features of fluids, in particular the liquid-gas phase transition, it fails to explain other important issues such as, for example, the existence in liquids of transverse collective excitations such as phonons.
This approach is based on postulation of some similarity between crystals and liquids, providing insight into many important properties of the latter: transverse collective excitations, large heat capacity, and so on.
From the discussion above, one can see that the microscopic behavior of particles of moderate and high temperature fluids is qualitatively different.
[4][5] The exact criterion defining the Frenkel line is the one based on a comparison of characteristic times in fluids.
The second characteristic time corresponds to the shortest period of transverse oscillations of particles within the fluid,
When these two time scales are roughly equal, one cannot distinguish between the oscillations of the particles and their jumps to another position.
There exist several approximate criteria to locate the Frenkel line on the pressure-temperature plane.
The second criterion is based on the fact that at moderate temperatures, liquids can sustain transverse excitations, which disappear upon heating.
The isochoric heat capacity per particle of a monatomic liquid near the melting line is close to
Therefore, at the Frenkel line, where transverse excitations vanish, the isochoric heat capacity per particle should be