Calculating Thermodynamic Properties from Fluctuations at Small Scales

Abstract

We show how density and energy fluctuations of small nonperiodic systems embedded in a reservoir can be used to determine macroscopic thermodynamic properties like the enthalpy density and the thermodynamic correction factor. For mixtures, the same formalism leads to a very convenient method to obtain so-called total correlation function integrals, also often referred to as Kirkwood-Buff integrals. Using finite size scaling, the properties obtained for small systems can be extrapolated to the macroscopic system limit provided that the system is sufficiently far from the critical point. As derived in our previous work (Chem. Phys. Lett. 2011, 504, 199-201), the finite size scaling is significant and depends on 1/L, where L is the length of the small system in one dimension. By considering a reservoir with an ensemble of embedded small systems, we can use the scaling arising from surface effects to determine properties for macroscopic systems by extrapolation. We demonstrate this method for the WCA and LJ fluids, as well a for a heterogeneous system, i.e., argon adsorbed in silicalite-1 zeolite.

Partial molar enthalpies and reaction enthalpies from equilibrium molecular dynamics simulation

“…Our previous MD simulations of small systems [18][19][20][21][22] confirm this behavior. In practice, extrapolation to 1/L → 0 can easily be performed as the scaling in 1/L is usually leading.…”

“…The thermodynamic limit is obtained from linear extrapolation of the quantity calculated from Eq. (19) in small systems, see early with 1/L 18 , we calculated (∂N i /∂H ) T ,V ,μ j , and inverted its value in the thermodynamic limit. The results are plotted as a function of the composition in Fig.…”

“…The method considers small subsystems in a large reservoir (i.e., the simulation box), and uses the construction of Hill 17 to compute thermodynamic properties in the thermodynamic limit from small-scale fluctuations. The method largely expands the work on small systems by Schnell et al [18][19][20][21][22] The subsystem refers to an open volume (or area element) with a linear size of the order of 1-10 molecular diameters, inside a much larger simulation box (a reservoir). We will derive how energy and particle fluctuations inside the subsystem can be used to obtain thermodynamic properties in the grandcanonical ensemble.…”

“…In MD simulations, it can be computed using the "small system method" developed by Schnell and co-workers by calculating energy and particle number fluctuations in randomly positioned subsystems inside the simulation box. 18,19 At this stage it is important to note that fluctuations inside small subsystems strongly depend on the size of the subsystem. There is a general theorem 26,27 due to Hadwiger that implies that every extensive thermodynamic variable (e.g., X) in a system where the interaction potentials have a finite range has the following form:…”

“…This enables us to obtain the thermodynamic limit value of property X/V = A b . [18][19][20][21] More specifically, for the enthalpy we can write…”