The Solution Chemistry of Mixing States Probed via Fluctuations: a Direct Description of Inhomogeneity in Mixing

Abstract

Radial distribution functions are commonly used to represent the structures of solutions, which represent the probability of finding another atom in the shell at a distance r from the atom of interest. This method has been used to study the structures of many non-crystalline materials. However, the information gained in this method is microscopic, and is limited to the first or second nearest neighbors from the featured atom. The present author proposed a completely different method to describe the solution structure by expressing the inhomogeneity in distribution of atoms and molecules and in concentration as “density fluctuation” and “concentration fluctuation”, respectively; namely the structure of a solution is described in terms of the “mixing state” or “mixing scheme.” This paper introduces density fluctuation and concentration fluctuation, as well as Kirkwood-Buff Integrals. Fluctuations of solutions become more pronounced in the mesoscale region. The relationship with solution thermodynamics, which represents the macroscopic limit, is also discussed. The features and cautions of experiments to measure the fluctuations are described. Finally, as analytical examples, temperature and concentration dependences of mixing schemes for two solution systems with upper critical and lower critical solution temperatures are presented.

Volume viscosity and ultrasonic relaxation of ethanol–water mixtures studied by molecular dynamics simulations

“…The presence of the q = 0 peak has been reported experimentally by means of small-angle X-ray or neutron scattering, and ascribed to the concentration fluctuation. 33 The q = 0 limit of wcc q j j ð Þ gives the thermodynamic concentration fluctuation of an open system as…”

“…The concentration mode defined by eqn (14) is proportional to those used in the analysis of small-angle X-ray or neutron scattering 32,33 as is described in Section S3 of the ESI †…”

“…The presence of the q = 0 peak has been reported experimentally by means of small-angle X-ray or neutron scattering, and ascribed to the concentration fluctuation. 33 The q = 0 limit of gives the thermodynamic concentration fluctuation of an open system aswhere N stands for the total number of molecules in the system, and the left-hand side of eqn (18) is related to the osmotic compressibility. The small-angle X-ray scattering experiment performed by Nishikawa and Iijima showed that the water–ethanol mixture at 293 K exhibits a peak of the concentration fluctuation at x E = 0.4, and its maximum value is about 1.0.…”

A method for determining the density fluctuations of supercritical fluids absolutely based on small-angle scattering experiments and application to supercritical methanol

“…To evaluate fluctuations in the mixing state of binary solutions, comparisons with thermodynamic quantities or standard liquid samples have been employed for the scattering-intensity normalization. [37][38][39] Water is commonly used as a standard sample. Considering the application of this procedure to the present experiment, it is concerned that unintentional mixing of the standard liquid with the sample fluids because the present type of experiment has to be performed without disassembling the sample container to keep the path length constant.…”