BTFFH

Some binary mixtures, such as specific alcohol-alkane mixtures or even water-tbutanol, exhibit two humps "camel back" shaped Kirkwood-Buff integrals (KBIs). This is in sharp contrast with the usual KBIs of binary mixtures having a single extremum. This extremum is interpreted as the region of maximum concentration fluctuations, usually occurs in binary mixtures presenting appreciable micro-segregation, and corresponds to where the mixture exhibits a percolation of the two species domains. In this paper, it is shown that two extrema occur in binary mixtures when one species forms "meta-particle" aggregates, the latter acts as a meta-species, and they have their own concentration fluctuations, hence their own KBI extremum. This "meta-extremum" occurs at a low concentration of the aggregate-forming species (such as alcohol in alkane) and is independent of the other usual extremum observed at mid-volume fraction occupancy. These systems are a good illustration of the concept of the duality between concentration fluctuations and micro-segregation.

The Kirkwood-Buff theory is a cornerstone of the statistical mechanics of liquids and solutions. It relates volume integrals over the radial distribution function, so-called Kirkwood-Buff integrals (KBIs), to particle number fluctuations and thereby to various macroscopic thermodynamic quantities such as the isothermal compressibility and partial molar volumes. Recently, the field has seen a strong revival with breakthroughs in the numerical computation of KBIs and applications to complex systems such as bio-molecules. One of the main emergent results is the possibility to use the finite volume KBIs as a tool to access finite volume thermodynamic quantities. The purpose of this Perspective is to shed new light on the latest developments and discuss future avenues.