Diffusion under Confinement: Hydrodynamic Finite-Size Effects in Simulation

Abstract

We investigate finite-size effects on diffusion in confined fluids using molecular dynamics simulations and hydrodynamic calculations. Specifically, we consider a Lennard-Jones fluid in slit pores without slip at the interface and show that the use of periodic boundary conditions in the directions along the surfaces results in dramatic finite-size effects, in addition to that of the physically relevant confining length. As in the simulation of bulk fluids, these effects arise from spurious hydrodynamic interactions between periodic images and from the constraint of total momentum conservation. We derive analytical expressions for the correction to the diffusion coefficient in the limits of both elongated and flat systems, which are in excellent agreement with the molecular simulation results except for the narrowest pores, where the discreteness of the fluid particles starts to play a role. The present work implies that the diffusion coefficients for wide nanopores computed using elongated boxes suffer from finite-size artifacts which had not been previously appreciated. In addition, our analytical expression provides the correction to be applied to the simulation results for finite (possibly small) systems. It applies not only to molecular but also to all mesoscopic hydrodynamic simulations, including Lattice-Boltzmann, Multiparticle Collision Dynamics or Dissipative Particle Dynamics, which are often used to investigate confined soft matter involving colloidal particles and polymers.

Revising the Concept of Pore Hierarchy for Ionic Transport in Carbon Materials for Supercapacitors

“…It is worth mentioning that structurally C meso is an inverse replica of SBA-15 mesoporous silica [22] in which the pore network possesses a 1D channel architecture (Figure 1b). [34] Again the impedance spectroscopy-based approaches of Ahuja and Armstrong show good agreement with those diffusivities obtained by PFG NMR. [33] Similar processing applied to the data in Figure 3a results in the diffusion coefficients D ̸ ̸ (9 × 10 −11 m 2 s −1 for TEA + , 12 × 10 −11 m 2 s −1 for BF 4 − ) and D ⊥ (≤4 × 10 −12 m 2 s −1 for TEA + and BF 4 − ), which can be assigned to the diffusion parallel and perpendicularly to the orientation of primary carbon nanorods.…”

“…It is worth noting that D is about an order of magnitude slower than for bulk ionic diffusivities, probably due to imperfections in the arrangements of nanorods and/or confinement-induced hydrodynamic changes in the direction parallel to the nanorods surface. [34] Again the impedance spectroscopy-based approaches of Ahuja and Armstrong show good agreement with those diffusivities obtained by PFG NMR. However, the diffusion anisotropy in C meso is not accessible via these approaches.…”

Molecular dynamics study of nanoconfined TIP4P/2005 water: how confinement and temperature affect diffusion and viscosity

“…2.3. Then, we derived a confined Stokes-Einstein relation, taking into account the influence of the (stressfree) confining walls, based on a previous expression derived for no-slip walls [85]. Viscosity can also be estimated through this confined Stokes-Einstein relation, although this expression could fail at low temperatures, similarly to its bulk counterpart.…”

“…However, the case of confined systems is quite different and has been less explored. In planar confinement, assuming a no-slip boundary condition on the walls, Simonnin et al [85] have computed analytically the effect of liquid height d and box lateral size L on the diffusion coefficient. Here we would like to emphasize that, while the effect of the finite lateral size L is purely a limit of the simulation, the confinement height d has a real physical effect.…”

Large effect of lateral box size in molecular dynamics simulations of liquid-solid friction

“…Although the use of periodic boundary conditions can, in some aspects, efficiently mimic a macroscopic system, finite size effects can still impact the measured quantities. For instance, the self-diffusion coefficient strongly depends on the size of the simulation box because of hydrodynamic interactions with periodic images, an effect well captured by continuum hydrodynamics [53][54][55][56]. In slab simulations, two types of finite size effects should be considered.…”