Local Grand Canonical Monte Carlo Simulation Method for Confined Fluids

Abstract

We describe a new local grand canonical Monte Carlo method to treat fluids in pores in chemical equilibrium with a reference bulk. The method is applied to Lennard-Jones particles in pores of different geometry and is shown to be much more accurate and efficient than other techniques such as traditional grand canonical simulations or Widom’s particle insertion method. It utilizes a penalty potential to create a gas phase, which is in equilibrium with a more dense liquid component in the pore. Grand canonical Monte Carlo moves are employed in the gas phase, and the system then maintains chemical equilibrium by “diffusion” of particles. This creates an interface, which means that the confined fluid needs to occupy a large enough volume so that this is not an issue. We also applied the method to confined charged fluids and show how it can be used to determine local electrostatic potentials in the confined fluid, which are properly referenced to the bulk. This precludes the need to determine the Donnan potential (which controls electrochemical equilibrium) explicitly. Prior approaches have used explicit bulk simulations to measure this potential difference, which are significantly costly from a computational point of view. One outcome of our analysis is that pores of finite cross-section create a potential difference with the bulk via a small but nonzero linear charge density, which diminishes as ∼1/ln­(L), where L is the pore length.

Chemical Potential and Thermodynamic Properties of Self-Assembled Monolayers: A Method of External Fields in a Monte Carlo Simulation

“…Variation of the external potential shifts the gas–solid equilibrium resulting in changing the pressure and the chemical potential of the crystal, which provides valuable information on its thermodynamic properties. As stated in the Introduction, the efficiency of this technique has been demonstrated many times on examples of 3D liquids and solids, ,,,, crystalline monolayers on the graphite surface, − and the adsorbed phase in pores. − , Probably, the only shortcoming of the external potential method appears when the crystal to be analyzed is substantially rigid. In this case, a very small density of the coexisting gas phase causes a significant relative uncertainty in its value.…”

“…As stated in the Introduction, the efficiency of this technique has been demonstrated many times on examples of 3D liquids and solids, 40,44,45,54,55 crystalline monolayers on the graphite surface, 50−53 and the adsorbed phase in pores. [41][42][43]46 Probably, the only shortcoming of the external potential method appears when the crystal to be analyzed is substantially rigid. In this case, a very small density of the coexisting gas phase causes a significant relative uncertainty in its value.…”

“…To overcome this difficulty, some tricks have been proposed that artificially make the transition reversible. − Such a technique can be applied in molecular simulations of fluids uniformly distributed over the simulation cell. Another way called the Monte Carlo phase switch method has also been proposed by Wilding and co-workers. , Some methods have been developed for the two-phase system explicitly accounting for the interface. − There is also a group of methods that share the idea of a non-uniform external potential in the simulation cell. − Some of those consider finite pores where the adsorption potential gradually reduces toward the pore ends, − , while others explore the simulation cell with soft repulsive walls. , In both cases, the non-uniform potential splits the system into dense and gas phases. The latter allows for a reliable evaluation of the chemical potential by a standard Widom test particle insertion method .…”

“…37−39 There is also a group of methods that share the idea of a nonuniform external potential in the simulation cell. 40−46 Some of those consider finite pores where the adsorption potential gradually reduces toward the pore ends, [40][41][42][43]46 while others explore the simulation cell with soft repulsive walls. 44,45 In both cases, the non-uniform potential splits the system into dense and gas phases.…”

Boundary-Monte Carlo Method for Neutral and Charged Confined Fluids

“…As has already been discussed, one technical goal in any GCMC scheme to simulate highly coupled fluids, such as dense RTILs, is to increase the acceptance rates of insertion and deletion moves. In the l-GCMC method, 54 this problem was resolved to some extent by performing local GCMC simulations in a gas or at least a lower-density fluid. The low-density fluid is created by the use of a penalty potential, ϕ pen (r), and chemical equilibrium with the dense "fluid of interest" is maintained by allowing free diffusion of particles throughout the simulated volume.…”