Kirkwood-Buff integration: A promising route to entropic properties?

Abstract

Kirkwood-Buff integration (KBI) is implemented into the massively-parallel molecular simulation tool ms2 and assessed by molecular dynamics simulations of binary liquid mixtures. The formalism of Krüger et al. (P. Krüger et al., J. Phys. Chem. Lett. 4: 235-238, 2013) that adopts NVT ensemble data to the μVT ensemble is employed throughout. Taking advantage of its linear scaling with inverse system size, the extrapolation to the thermodynamic limit is analyzed. KBI are calculated with standard radial distribution functions (RDF) and two corrected RDF forms. Simulations in the NVT ensemble are carried out in the entire composition range for four Lennard-Jones mixtures, studying system size dependence by varying N = 4000, 8000 and 16000 molecules. Moreover, four mixtures of "real" components are considered with N = 4000. Thermodynamic factor, partial molar volumes and isothermal compressibility are calculated from KBI and compared with benchmark data from NpT ensemble simulations. The assessment shows that the formalism of Krüger et al. greatly improves KBI and that extrapolation is important, particularly for smaller systems.

Diffusion in multicomponent aqueous alcoholic mixtures

“…Because the Fick and Maxwell–Stefan approaches describe the same process, there is a straightforward relation between the according coefficients given by the so-called thermodynamic factor. In this work, equilibrium molecular dynamics simulation and the Green–Kubo formalism were employed to obtain the Maxwell–Stefan diffusion coefficient and Kirkwood–Buff integration 23 , 24 to sample the thermodynamic factor consistently on the basis of the chosen force field model.…”

“…However, the thermodynamic factor can be also sampled directly by molecular simulation, e.g. with Kirkwood–Buff integration 24 , 28 or free energy perturbation methods, to obtain the composition dependence of the chemical potential 21 , 29 . For the sake of consistency, the thermodynamic factor was calculated here with Kirkwood–Buff integration as described in preceding work 12 , 23 .…”

Fick diffusion coefficients via molecular dynamics: An alternative approach in the Fourier domain

“…Density and thermodynamic factor results It is also noteworthy that the choice of this methodology for the calculation of the thermodynamic factor is due to the fact that it arguably surmounts finite-size effects, commonly observed in the resolution of Kirkwood-Buff integrals in the canonical ensemble by means of radial distribution functions. [26][27][28][29][30]49 Figure 2 illustrates the effect of the simulation box size on the determination of the static structure factor for a CO 2 +n-octane mixture with…”

“…However, these approaches are highly susceptible to finite-size effects of the simulation box, and KB-integrals may not converge even for simple molecular systems. 26,27 There are several recent attempts in the literature to increase the convergence of such integrals for the calculation of the socalled KB coefficients and of thermodynamic factors, [27][28][29]…”

Kirkwood-Buff integrals from molecular simulation

“…A practical approach to deal with finite-size effects was proposed by Krüger and co-workers [35,37] where an expression for KB integrals for finite volumes was derived. The method of Krüger and co-workers [34,35,37,38] has been used in many studies [6,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. According to Hill's thermodynamics of small systems [56,57] (also called nanothermodynamics), KB integrals for finite volumes scale with the inverse of the characteristic length scale of the small system and this scaling can be extrapolated to the thermodynamic limit (i.e to KB integrals as defined by Kirkwood and Buff).…”