The paper entitled Small Size Effects in Open and Closed Systems: What Can We Learn from Ideal Gases about Systems with Interacting Particles? has been published in the Journal of Chemical Physics.
Small systems have higher surface area-to-volume ratios than macroscopic systems. 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. 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.
The system we use to investigate these effects has been illustrated in the figure below. This is a cubic simulation box with surface energy “U” experienced by particles closer than a distance “d” from each wall. Particles close to the sides (light blue regions) experience a potential energy contribution of “U”, while particles close to the edges (medium blue regions) experience a potential energy contribution of 2″U”, and particles close to the corners (dark blue regions) experience a potential energy contribution of 3″U”.
For all 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 increasing with system size and 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 main person behind the work has been PhD candidate Vilde Bråten , with contributions also from Sondre K. Schnell and Dick Bedeaux.