Methanol-ethanol “ideal” mixtures as a test ground for the computation of Kirkwood-Buff integrals

Abstract

Mixtures of 1-alkanols are a textbook example of the concept of ideal mixtures. Yet, such mixtures have a very strong local order due to the hydrogen bonding interactions, with a strong tendency for chain formation. Despite this apparent non-ideality, the Kirkwood-Buff integrals of such system exhibit near ideal behaviour. This dual property can be used to test the calculations of the Kirkwood-Buff integrals in a controlled mixing situation, and clarify many points, in particular the statistical problems that can be encountered. By studying the methanol-ethanol mixtures, we uncover an interesting physical asymmetry between low methanol and low ethanol concentrations, which can produce statistical artifacts in the calculation of Kirkwood-Buff integrals, illustrating and exemplifying some of the difficulties encountered in such calculations. Finally, liquid state integral equations results for these mixtures are reported. They help demonstrate that thermodynamic ideality hides complex correlations and microscopic non-ideality.

The influence of charge ordering in the microscopic structure of monohydroxy alcohols

“…aibj (k) (also called total structure factor S (T) ab (k) in our previous papers [22,40]) is defined as:…”

Camel back shaped Kirkwood-Buff Integrals

“…The so-called Kirkwood-Buff integrals (KBI) [1,2] are defined as the integrals of the species-species pair correlation functionsG ab = 1 Ω ´dX 1 dX 2 [g ab (X 1 , X 2 ) − 1] where X i is the set of position, and if required, the orientations, of molecule i, where a and b designates the species indexes (Ω = V ω 2 , where ω is the angular integral, equal to 4π or 8π 2 , depending on the symmetry of the molecules). It can be shown [3,4] that this integral is identical to that involving the pair correlation between any two atoms belonging to each molecules. Following this, the KBI are more simply defined as…”

“…were x b is the mole fraction of component b, Vc is the partial molar volume of component c (c = a or b), V is the molar volume, χ T is the isothermal compressibility (with T the temperature and k B the Boltzmann constant) and D is related to the concentration fluctuations and given by D = x i ∂βµ i ∂x i T P (4) where µ i is the chemical component of species i and β = 1/k B T is the Boltzmann factor. Fig.…”

Connecting density fluctuations and Kirkwood-Buff integrals for finite-size systems

“…This connection between local structure and thermodynamics is particularly useful in computational softmatter studies where KBI are widely used to evaluate isothermal compressibilities, partial molar volumes and derivatives of chemical potentials [2][3][4][5]. In particular, applications of KBI include the investigation of the thermodynamics of complex molecular mixtures [6][7][8][9][10][11][12], solvation of macromolecules [13][14][15][16][17][18][19][20], multicomponent diffusion in liquids [21,22], protein self-assembly and aggregration [23,24], Hofmeister ion chemistry [25], identification of nanostructures in water solutions of ionic liquids [26] and the parameterisation of atomistic [27][28][29][30] and coarse-grained [31,32] force fields. Recently, KBI have been applied to compute isothermal compressibilities of prototypical crystals [33,34], showing unprecedented flexibility and range of applicability.…”