Recent progress in the statistical mechanics of solutions through Kirkwood-Buff integrals and related approaches
CECAM-FR-MOSER, CECAM-FR-RA, Maison Internationale, Dijon, France
The accurate description of density and concentration fluctuations is essential for the understanding of complex systems, mixtures and solutions. Fluctuations directly relate to thermodynamic properties such as partial molar volumes and -enthalpies, derivatives of chemical potentials, and isothermal compressibility . Particle number fluctuations can be expressed as volume integrals over the pair distribution function (PDF), so-called Kirkwood-Buff integrals (KBI) , which provide a link between thermodynamic data and nanoscale structural properties . KBI theory is an exact theory, valid for any solution or mixture in thermodynamic equilibrium, and it is widely used in physical chemistry and biochemistry. Until recently, however, for systems of great structural complexity and/or long-range correlations, KBIs could not be obtained accurately from molecular simulation because of severe finite size errors in (i) the long-range part of the PDF and (ii) its integration over volume. For both problems, efficient solutions have been proposed in the last few years. Ganguly et al.  and Cortes et al.  have devised new finite size corrections of the PDF that are considerably more accurate than all previous schemes . Krüger et al.  have shown that the slow convergence of the volume integrals is because the standard integral truncation is unphysical. They have developed the correct finite volume generalization of KBI theory and fast converging extrapolations to the infinite volume limit. These conceptual breakthroughs have triggered a vivid activity in KB theory [8, 9, 10], which has been applied to ionic solutions , biological molecules, force field development , multicomponent fluids .
It is expected that the scope of KBI theory and concentration fluctuations will keep growing in coming years, with new applications to critical phenomena, ionic liquids, nematic phases, solid solutions etc. This will bring about new theoretical challenges such as the handling of long-range correlations, anisotropy, and internal degrees of freedom in molecules that will be discussed in the workshop.
Various other recent approaches in statistical mechanics of liquids and solutions will also be discussed, such as the combination of molecular simulations for the short-range part of the PDF with an approximate solution of the Ornstein-Zernike integral equations for the long-range part. In this respect, the recent combination of Monte-Carlo results with the hypernetted-chain approach has proved particularly successfully .
The calculation of accurate local thermodynamic properties from these approaches (fluctuation and/or KBI), was used to better understand the size dependence of thermodynamic properties and the link between structure of matter and thermodynamics from microscopic, mesoscopic to macroscopic scales. A consequence of these findings was to show the coherence between the concentration fluctuation/KBI approach, the Gibb’s thermodynamic of surfaces and the thermodynamics of small systems (nanothermodynamics) by T. H. Hill [14, 15].
From a practical point of view, the approaches offer new theoretical tools to investigate thermodynamic properties from the knowledge of the behavior of small numbers of individual elements or particles. In that sense it is well adapted to extract accurate thermodynamic properties from first principal calculations or from the simulation of heavy systems like biological systems or colloids. These points will be presented and discussed in the workshop. Another application is the analysis of images from microscopy that also will be addressed in the workshop.
Given the new insights and fast progress in the field over the last few years, there is now a strong need to bring together the leading researchers in order to discuss the strengths and limitations of the various approaches. The workshop will be a great opportunity to discuss the state of the art and future developments and to generate new ideas both for further progress in methodology and novel applications.
Antoine Carof (Université de Lorraine) - Organiser
Peter Kruger (Department of Materials Science, Graduate School of Engineering, Chiba University, Chiba, Japan.) - Organiser
Thomas Niehaus (Université Claude Bernard Lyon 1) - Organiser
Jean-Marc Simon (Université de Bourgogne) - Organiser
Thijs J.H. Vlugt (Delft University of Technology, ) - Organiser
Dick Bedeaux (NTNU) - Organiser
Sondre Schnell (Norwegian University of Science and Technology) - Organiser