Abstract
We present a new method for computing chemical potential differences of macroscopic systems by sampling fluctuations in small systems. The small system method, presented by Schnell et al. [Schnell et al., J. Phys. Chem. B, 2011, 115, 10911], is used to create small embedded systems from molecular dynamics simulations, in which fluctuations of the number of particles are sampled. The sampled fluctuations represent the Boltzmann distributed probability of the number of particles. The overlapping region of two such distributions, sampled from two different systems, is used to compute their chemical potential difference. Since the thermodynamics of small systems is known to deviate from the classical thermodynamic description, the particle distributions will deviate from the macroscopic behavior as well. We show how this can be utilized to calculate the size dependence of chemical potential differences and eventually extract the chemical potential difference in the thermodynamic limit. The macroscopic chemical potential difference is determined with a relative error of 3% in systems containing particles that interact through the truncated and shifted Lennard-Jones potential. In addition to computing chemical potential differences in the macroscopic limit directly from molecular dynamics simulation, the new method provides insights into the size dependency that is introduced to intensive properties in small systems.
Highlights
Properties available from molecular simulations (MD) can be sorted in two categories: mechanical properties and thermal properties.[1]
The purpose of the first section of the results is to investigate the performance of the overlapping distribution methods (ODMs) in small systems compared to how well it performs in a periodic system
The second section contains a description on how the system method (SSM) is combined with the ODM to compute the size dependence of chemical potential differences
Summary
Properties available from molecular simulations (MD) can be sorted in two categories: mechanical properties and thermal properties.[1]. We will show how the ODM can be used to extract the chemical potential difference of two small grand canonical systems, directly from two MD simulations at different densities. It is possible to utilize the chemical potential differences in the subsystems to obtain the chemical potential difference for the total simulation boxes, that is, in the macroscopic limit When investigating these distributions, one must keep in mind that they are calculated in small nonperiodic systems, which means that their thermodynamic properties will deviate from the classical macroscopic behavior. We use cubic simulation boxes containing 27,000 particles at three different number densities, ρ = 0.70, ρ = 0.72, and ρ = 0.74 An in-house MC code and cross-checked with the TREND equation of state (EOS) provided by Thol et al.[50]
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