Abstract
Kirkwood-Buff (KB) integrals provide a connection between microscopic properties and thermodynamic properties of multicomponent fluids. The estimation of KB integrals using molecular simulations of finite systems requires accounting for finite size effects. In the small system method, properties of finite subvolumes with different sizes embedded in a larger volume can be used to extrapolate to macroscopic thermodynamic properties. KB integrals computed from small subvolumes scale with the inverse size of the system. This scaling was used to find KB integrals in the thermodynamic limit. To reduce numerical inaccuracies that arise from this extrapolation, alternative approaches were considered in this work. Three methods for computing KB integrals in the thermodynamic limit from information of radial distribution functions (RDFs) of finite systems were compared. These methods allowed for the computation of surface effects. KB integrals and surface terms in the thermodynamic limit were computed for Lennard–Jones (LJ) and Weeks–Chandler–Andersen (WCA) fluids. It was found that all three methods converge to the same value. The main differentiating factor was the speed of convergence with system size L. The method that required the smallest size was the one which exploited the scaling of the finite volume KB integral multiplied by L. The relationship between KB integrals and surface effects was studied for a range of densities.
Highlights
Using knowledge of the molecular structure of liquids to predict their macroscopic behavior is important for several applications [1,2,3,4,5]
KB integrals in the thermodynamic limit G∞ are obtained using the three different approaches discussed earlier
These parameters define the thermodynamic state of the system
Summary
Using knowledge of the molecular structure of liquids to predict their macroscopic behavior is important for several applications [1,2,3,4,5]. To accurately estimate Gα∞β, it is possible to use KB integrals of finite and open subvolumes V embedded in larger reservoirs. In this way, the grand-canonical ensemble, in which KB integrals in the thermodynamic limit were derived, is mimicked. According to Hill’s thermodynamics of small systems, properties of open embedded subvolumes scale with the inverse size of the subvolumes [13,14]. This applies to KB integrals of finite subvolumes, GV αβ [10,12]
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