Collective modes and thermodynamics of the liquid state

Abstract

Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids, with the historical tradition of hydrodynamic description as the starting point. We review different approaches to liquids as well as recent experimental and theoretical work, and propose that liquids do not need classifying in terms of their proximity to gases and solids or any categorizing for that matter. Instead, they are a unique system in their own class with a notably mixed dynamical state in contrast to pure dynamical states of solids and gases. We start with explaining how the first-principles approach to liquids is an intractable, exponentially complex problem of coupled non-linear oscillators with bifurcations. This is followed by a reduction of the problem based on liquid relaxation time τ representing non-perturbative treatment of strong interactions. On the basis of τ , solid-like high-frequency modes are predicted and we review related recent experiments. We demonstrate how the propagation of these modes can be derived by generalizing either hydrodynamic or elasticity equations. We comment on the historical trend to approach liquids using hydrodynamics and compare it to an alternative solid-like approach. We subsequently discuss how collective modes evolve with temperature and how this evolution affects liquid energy and heat capacity as well as other properties such as fast sound. Here, our emphasis is on understanding experimental data in real, rather than model, liquids. Highlighting the dominant role of solid-like high-frequency modes for liquid energy and heat capacity, we review a wide range of liquids: subcritical low-viscous liquids, supercritical state with two different dynamical and thermodynamic regimes separated by the Frenkel line, highly-viscous liquids in the glass transformation range and liquid-glass transition. We subsequently discuss the fairly recent area of liquid-liquid phase transitions, the area where the solid-like properties of liquids have become further apparent. We then discuss gas-like and solid-like approaches to quantum liquids and theoretical issues that are similar to the classical case. Finally, we summarize the emergent view of liquids as a unique system in a mixed dynamical state, and list several areas where interesting insights may appear and continue the extraordinary liquid story.

Simple liquids’ quasiuniversality and the hard-sphere paradigm

“…In honor of this it has been suggested to term the (blurred) line delimiting the genuine liquid phase from the more gas-like phase the 'Frenkel line' [13,14,22] (see, however, also [23]). This Topical Review focuses on the The colored region is where quasiuniversality applies for many simple liquids, i.e.…”

“…not too far from the melting line. At these state points (delimited by the so-called Frenkel line [13,14]) many properties like density, specific heat, enthalpy, etc, are closer to those of the solid phase than to those of the gas phase. (b) Density-temperature phase diagram with the same states colored.…”

“…genuine liquid phase between the Frenkel line and the freezing line (colored in figure 1), defining the 'ordinary' liquid phase for which properties like density, energy, specific heat, compressibility, heat conductivity, etc, are closer to their solid than to their gas values [14,22,24].…”

Thermodynamic scaling of vibrational dynamics and relaxation

“…where ω D ∼ 10 13 rad/s is the Debye frequency [35]. Rattling, a manifestation of the vibrational dynamics, occurs in a soft cage so that the fast mobility is in principle affected by both local aspects, like cage geometry or local rearrangements, as well as extended collective properties like elasticity [35][36][37][38][39][40][41].…”

“…The temporary trapping and subsequent escape mechanisms lead to large fluctuations around the averaged dynamical behavior with strong heterogeneous dynamics [1,2] and non-exponential relaxation [42]. The presence of rattling and escape processes in liquids and relationships between them were first proposed by Maxwell [43] and Frenkel [44][45][46], see a recent review [35]. Other early investigations [47,48] and recent theoretical [49][50][51][52][53][54][55][56][57][58][59][60] studies addressed the rattling process in the cage to understand the structural relaxation -the escape process -gaining support from numerical [36,37,56, and experimental [84][85][86][87] works on glassforming liquids.…”