Lattice Boltzmann electrokinetics simulation of nanocapacitors

Abstract

We propose a method to model metallic surfaces in Lattice Boltzmann Electrokinetics simulations (LBE), a latticebased algorithm rooted in kinetic theory which captures the coupled solvent and ion dynamics in electrolyte solutions. This is achieved by a simple rule to impose electrostatic boundary conditions, in a consistent way with the location of the hydrodynamic interface for stick boundary conditions. The proposed method also provides the local charge induced on the electrode by the instantaneous distribution of ions under voltage. We validate it in the low voltage regime by comparison with analytical results in two model nanocapacitors: parallel plate and coaxial electrodes. We examine the steady-state ionic concentrations and electric potential profiles (and corresponding capacitance), the timedependent response of the charge on the electrodes, as well as the steady-state electro-osmotic profiles in the presence of an additional, tangential electric field. The LBE method further provides the time-dependence of these quantities, as illustrated on the electro-osmotic response. While we do not consider this case in the present work, which focuses on the validation of the method, the latter readily applies to large voltages between the electrodes, as well as to timedependent voltages. This work opens the way to the LBE simulation of more complex systems involving electrodes and metallic surfaces, such as sensing devices based on nanofluidic channels and nanotubes, or porous electrodes. arXiv:1907.04732v1 [physics.comp-ph]

Axisymmetric Stokes flow due to a point-force singularity acting between two coaxially positioned rigid no-slip disks

“…Prime examples include the ionic transport and electrokinetics in small-scale capacitors (Marini Bettolo Marconi & Melchionna 2012; Thakore & Hickman 2015; Babel, Eikerling & Löwen 2018; Asta et al. 2019), electrochemomechanical energy conversion in microfluidic channels (Daiguji et al. 2004), and the rheology of droplets, capsules or cells in constricted/structured microchannels (Park & Dimitrakopoulos 2013; Le Goff et al.…”

Molecular Simulation of Electrode-Solution Interfaces

“…At the same continuous level of description, extensions of the mean-field Poisson-Boltzmann theory have been proposed to capture the e↵ects of electrostatic correlations and excluded volume or solvent polarization [4,5] on the structure and capacitance of the EDL, with a low computational cost compatible with routine use in engineering applications. Even the charging dynamics can be investigated at this level [6], even though the e↵ects of ionic correlations or of the coupling with the solvent dynamics are more accurately described by mesoscopic simulations with explicit or implicit ions [7][8][9][10]. At the other extreme, quantum calculations, usually based on electronic Density Functional Theory (even though Quantum Monte Carlo can now provide even more accurate results e.g.…”

“…Understanding and discovery can be accelerated by use of atomistic simulations up to the large nanometer scale (e.g., 100 nm) in comparison with experiment [9][10][11][12][13][14][15] . The Interface force field (IFF), for example, contains Lennard-Jones parameters for facecentered cubic (fcc) metals to simulate bulk solids, aqueous interfaces, and multiphase materials with polymers and biomacromolecules 9,10 .…”

“…Understanding and discovery can be accelerated by use of atomistic simulations up to the large nanometer scale (e.g., 100 nm) in comparison with experiment [9][10][11][12][13][14][15] . The Interface force field (IFF), for example, contains Lennard-Jones parameters for facecentered cubic (fcc) metals to simulate bulk solids, aqueous interfaces, and multiphase materials with polymers and biomacromolecules 9,10 . The parameters reproduce the density, surface tension, and anisotropy of surface energies of (h k l) facets, as well as the mechanical properties in excellent agreement with experiments, even better than some DFT methods 16 .…”

Blessing and Curse: How a Supercapacitor’s Large Capacitance Causes its Slow Charging

“…This discrepancy comes as no surprise as the above σ(t) applies to planar electrodes: this model does not account for the huge surface area and for the ion transport through the porous structure of the supercapacitor electrodes. Simple extensions of the flat electrode setup were discussed, such as spherical and cylindrical electrodes [19,30] and a single cylindrical pore in contact with a reservoir [9]. Several theoretical works focused on the charging dynamics of porous electrodes [31][32][33][34][35][36][37].…”