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.

The Kirkwood–Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a reservoir. Using molecular simulation of finite systems, KB integrals can be computed either from density fluctuations inside such subvolumes, or from integrals of radial distribution functions (RDFs). Here, based on the second approach, we establish a framework to compute KB integrals for subvolumes with arbitrary convex shapes. This requires a geometric function w(x) which depends on the shape of the subvolume, and the relative position inside the subvolume. We present a numerical method to compute w(x) based on Umbrella Sampling Monte Carlo (MC). We compute KB integrals of a liquid with a model RDF for subvolumes with different shapes. KB integrals approach the thermodynamic limit in the same way: for sufficiently large volumes, KB integrals are a linear function of area over volume, which is independent of the shape of the subvolume.

We study the adsorption of carbon dioxide at a graphite surface using the new Small System Method, and find that for the temperature range between 300 K and 550 K most relevant for CO₂ separation; adsorption takes place in two distinct thermodynamic layers defined according to Gibbs. We calculate the chemical potential and the activity coefficient of both layers directly from the simulations. Based on thermodynamic relations, the entropy and enthalpy of the CO₂ adsorbed layers are also obtained. Their values indicate that there is a trade-off between entropy and enthalpy when a molecule chooses for one of the two layers. The first layer is a densely packed monolayer of relatively constant excess density with relatively large repulsive interactions and negative enthalpy. The second layer has an excess density varying with the temperature, an activity coefficient, which also indicates repulsion, but to a much smaller degree than in the first layer. Results for activity coefficients, entropies and enthalpies can be used to model transport through and along graphitic membranes for carbon dioxide separation purposes.