Adsorption of an Ideal Gas on a Small Spherical Adsorbent

Kirkwood-Buff integrals: From fluctuations in finite volumes to the thermodynamic limit

The Kirkwood-Buff theory is a cornerstone of the statistical mechanics of liquids and solutions. It relates volume integrals over the radial distribution function, so-called Kirkwood-Buff integrals (KBIs), to particle number fluctuations and thereby to various macroscopic thermodynamic quantities such as the isothermal compressibility and partial molar volumes. Recently, the field has seen a strong revival with breakthroughs in the numerical computation of KBIs and applications to complex systems such as bio-molecules. One of the main emergent results is the possibility to use the finite volume KBIs as a tool to access finite volume thermodynamic quantities. The purpose of this Perspective is to shed new light on the latest developments and discuss future avenues.

Legendre-Fenchel transforms capture layering transitions in porous media

We have investigated the state of a nanoconfined fluid in a slit pore in the canonical and isobaric ensembles. The systems were simulated with molecular dynamics simulations. The fluid has a transition to a close-packed structure when the height of the slit approaches the particle diameter. The Helmholtz energy is a non-convex function of the slit height if the number of particles does not exceed that of one monolayer. As a consequence, the Legendre transform cannot be applied to obtain the Gibbs energy. The Gibbs energy of a non-deformable slit pore can be transformed into the Helmholtz energy of a deformable slit pore using the Legendre-Fenchel transform. The Legendre-Fenchel transform corresponds to the Maxwell construction of equal areas.

Small size effects in open and closed systems: What can we learn from ideal gases about systems with interacting particles?

Small systems have higher surface area-to-volume ratios than macroscopic systems. The thermodynamics of small systems therefore deviates from the description of classical thermodynamics. One consequence of this is that properties of small systems can be dependent on the system's ensemble. By comparing the properties in grand canonical (open) and canonical (closed) systems, we investigate how a small number of particles can induce an ensemble dependence. Emphasis is placed on the insight that can be gained by investigating ideal gases. The ensemble equivalence of small ideal gas systems is investigated by deriving the properties analytically, while the ensemble equivalence of small systems with particles interacting via the Lennard-Jones or the Weeks-Chandler-Andersen potential is investigated through Monte Carlo simulations. For all the investigated small systems, we find clear differences between the properties in open and closed systems. For systems with interacting particles, the difference between the pressure contribution to the internal energy, and the difference between the chemical potential contribution to the internal energy, are both increasing with the number density. The difference in chemical potential is, with the exception of the density dependence, qualitatively described by the analytic formula derived for an ideal gas system. The difference in pressure, however, is not captured by the ideal gas model. For the difference between the properties in the open and closed systems, the response of increasing the particles' excluded volume is similar to the response of increasing the repulsive forces on the system walls. This indicates that the magnitude of the difference between the properties in open and closed systems is related to the restricted movement of the particles in the system. The work presented in this paper gives insight into the mechanisms behind ensemble in-equivalence in small systems, and illustrates how a simple statistical mechanical model, such as the ideal gas, can be a useful tool in these investigations.