Correction to “Simulation of an Electrical Double Layer Model with a Low Dielectric Layer between the Electrode and the Electrolyte”

Correction to “Simulation of an Electrical Double Layer Model with a Low Dielectric Layer between the Electrode and the Electrolyte

Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

<p>Explicit analytical expressions are presented for the density derivative, ∂<i>g</i>_HS(<i>R</i>; ρ)/∂ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for <i>R</i> ≤ 6σ, where σ is the hard-sphere diameter and ρ = (<i>N</i>/<i>V</i>)σ³ is the reduced density, where <i>N</i> is the number of particles and <i>V</i> is the volume. A FORTRAN program is provided for the implementation of these for <i>R</i> ≤ 6σ, which includes code for the calculation of <i>g</i>_HS(<i>R</i>; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past <i>R</i> = 6σ. Our expressions are numerically tested against exact results.</p

Impurity effects on ionic-liquid-based supercapacitors

<p>Small amounts of an impurity may affect the key properties of an ionic liquid and such effects can be dramatically amplified when the electrolyte is under confinement. Here the classical density functional theory is employed to investigate the impurity effects on the microscopic structure and the performance of ionic-liquid-based electrical double-layer capacitors, also known as supercapacitors. Using a primitive model for ionic species, we study the effects of an impurity on the double layer structure and the integral capacitance of a room temperature ionic liquid in model electrode pores and find that an impurity strongly binding to the surface of a porous electrode can significantly alter the electric double layer structure and dampen the oscillatory dependence of the capacitance with the pore size of the electrode. Meanwhile, a strong affinity of the impurity with the ionic species affects the dependence of the integral capacitance on the pore size. Up to 30% increase in the integral capacitance can be achieved even at a very low impurity bulk concentration. By comparing with an ionic liquid mixture containing modified ionic species, we find that the cooperative effect of the bounded impurities is mainly responsible for the significant enhancement of the supercapacitor performance.</p

Solvent Effect on the Pore-Size Dependence of an Organic Electrolyte Supercapacitor

Organic electrolytes such as tetraethylammonium tetrafluoroborate dissolved in acetonitrile (TEA-BF₄/ACN) are widely used in commercial supercapacitors and academic research, but conflicting experimental results have been reported regarding the dependence of surface-area-normalized capacitance on the pore size. Here we show from a classical density functional theory the dependence of capacitance on the pore size from 0.5 to 3.0 nm for a model TEA-BF₄/ACN electrolyte. We find that the capacitance–pore size curve becomes roughly flat after the first peak around the ion diameter, and the peak capacitance is not significantly higher than the large-pore average. We attribute the invariance of capacitance with the pore size to the formation of an electric double-layer structure that consists of counterions and highly organized solvent molecules. This work highlights the role of the solvent molecules in modulating the capacitance and reconciles apparently conflicting experimental reports

Cavity correlation and bridge functions at high density and near the critical point: a test of second-order Percus–Yevick theory

<p>Cavity correlation functions, pair correlation functions, and bridge functions for the Lennard-Jones fluid are calculated from first Percus–Yevick (PY) theory and second-order Percus– Yevick (PY2) theory, molecular dynamics, and grand canonical Monte Carlo techniques. We find that the PY2 theory is significantly more accurate than the PY theory, especially at high density and near the critical point. The pair correlation function near the critical point has the expected slowly decaying long-range behaviour. However, we do not observe any long-range behaviour in the bridge function for the state points near the critical point we have simulated. However, we do note that the bridge function, which is usually negative near <i>r</i> = 0, becomes positive as <i>r</i> → 0. This behaviour is seen for the bridge functions computed from both PY2 and molecular dynamics, but not from PY.</p