arXiv subjects

Dirk Gillespie

Publications and source records attributed to Dirk Gillespie.

10 recordsLinked to original sources

arXiv2026

The interplay of cation/anion and monovalent/divalent selectivity in negatively charged nanopores: local charge inversion and anion leakage

The anomalous mole fraction effect (AMFE) is widely regarded as a hallmark of calcium versus monovalent ion selectivity in negatively charged pores. While AMFE is well understood in highly cation-selective narrow ion channels, its microscopic origin in wide synthetic nanopores, where anions may also contribute to transport, remains less clear. Here, we use a reduced Nernst-Planck + Local Equilibrium Monte Carlo framework to study ionic transport in a negatively charged PET nanopore, with particular emphasis on how the modeling of surface carboxyl (COO$^{-}$) groups influences charge inversion, ionic currents, and AMFE. We systematically compare fixed point-charge models and explicit-particle representations of surface oxygens and identify two controlling parameters: the distance of closest approach (DCA) between ionic charges and pore charges and grid spacing that modulates localization (while keeping average surface charge constant). By fitting pore diffusion coefficients to three experimental conductance points, we reproduce the entire experimental AMFE curve as well as anion leakage in CaCl$_2$ seen in experiments and molecular dynamics simulations. Remarkably, vastly different microscopic models of the surface groups yield indistinguishable device-level conductance curves when the DCA is matched, despite substantial differences in local Ca$^{2+}$ concentration profiles. Our results demonstrate that AMFE in wide nanopores is governed by a delicate interplay between charge inversion, anion leakage, and ionic mobility, underlying that in wide pores monovalent vs.\ divalent cation selectivity is modulated by cations vs.\ anion selecivity.

cond-mat.mes-hall↗

arXiv2022

Individual ion species chemical potentials in the Mean Spherical Approximation

The Mean Spherical Approximation (MSA) is a commonly-used thermodynamic theory for computing the energetics of ions in the primitive model (i.e., charged hard-sphere ions in a background dielectric). For the excess chemical potential, however, the early MSA formulations (which were widely adopted) only included the terms needed to compute the mean excess chemical potential (or the mean activity coefficient). Other terms for the chemical potential $\mu_i$ of individual species $i$ were not included because they sum to $0$ in the mean chemical potential. Here, we derive these terms to give a complete MSA formulation of the chemical potential. The result is a simple additive term for $\mu_i$ that we show is a qualitative improvement over the previous MSA version. In addition, our derivation shows that the MSA's assumption of global charge neutrality is not strictly necessary, so that the MSA is also valid for systems close to neutrality.

cond-mat.stat-mech↗

arXiv2021

Impedance response of ionic liquids in long slit pores

We study the dynamics of ionic liquids in a thin slit pore geometry. Beginning with the classical and dynamic density functional theories for systems of charged hard spheres, an asymptotic procedure leads to a simplified model which incorporates both the accurate resolution of the ion layering (perpendicular to the slit pore wall) and the ion transport in the pore length. This reduced-order model enables qualitative comparisons between different ionic liquids and electrode pore sizes at low numerical expense. We derive semi-analytical expressions for the impedance response of the reduced-order model involving numerically computable sensitivities, and obtain effective finite-space Warburg elements valid in the high and low frequency limits. Additionally, we perform time-dependent numerical simulations to recover the impedance response as a cross-validation step. We investigate the dependence of the impedance response on system parameters and the choice of density functional theory used. The inclusion of electrostatic effects beyond mean-field qualitatively changes the dependence of the characteristic response time on the pore width. We observe peaks in the response time as a function of pore width, with height and location depending on the potential difference imposed. We discuss how the calculated dynamic properties can be used together with equilibrium results to optimise ionic liquid supercapacitors for a given application.

cond-mat.soft↗

arXiv2019

Scaling Behavior of Bipolar Nanopore Rectification with Multivalent Ions

We present a scaling behavior of a rectifying bipolar nanopore as a function of the parameter $ξ=R_{\mathrm{P}}/(λz_{\mathrm{if}})$, where $R_{\mathrm{P}}$ is the radius of the pore, $λ$ is the characteristic screening length of the electrolyte filling the pore, and $z_{\mathrm{if}}=\sqrt{z_{+}|z_{-}|}$ is a scaling factor that makes scaling work for electrolytes containing multivalent ions ($z_{+}$ and $z_{-}$ are cation and the anion valences). By scaling we mean that the rectification of the pore (defined as the ratio of currents in the forward and reversed biased states) depends on pore radius, concentration, $c$, and ion valences via the parameter $ξ$ implicitly. This feature is based on the fact that rectification depends on the voltage-sensitive appearance of depletion zones that, in turn, depend on the relation of $R_{\mathrm{P}}$ to the rescaled screening length $λz_{\mathrm{if}}$. In this modeling study, we use the Poisson-Nernst-Planck (PNP) theory and a particle simulation method, the Local Equilibrium Monte Carlo (LEMC). The latter can compute ion correlations that are ignored in the mean-field treatment of PNP and that are very important for multivalent ions (we show results for 1:1, 2:1, 3:1, and 2:2 electrolytes). In addition to the $z_{\mathrm{if}}$ factor, we show that one must choose a screening length appropriate to the system, in our case the Debye length for $λ$ for PNP and the screening length given by the Mean Spherical Approximation for LEMC.

cond-mat.mes-hall↗

arXiv2019

Multiscale analysis of the effect of surface charge pattern on a nanopore's rectification and selectivity properties: from all-atom model to Poisson-Nernst-Planck

We report a multiscale modeling study for charged cylindrical nanopores using three modeling levels that include (1) an all-atom explicit-water model studied with molecular dynamics (MD), and reduced models with implicit water containing (2) hard-sphere ions studied with the Local Equilibrium Monte Carlo simulation method (computing ionic correlations accurately), and (3) point ions studied with Poisson-Nernst-Planck (PNP) theory (mean-field approximation). We show that reduced models are able to reproduce device functions (rectification and selectivity) for a wide variety of charge patterns; that is, reduced models are useful in understanding the mesoscale physics of the device (i.e., how the current is produced). We also analyze the relationship of the reduced implicit-water models with the explicit-water model and show that diffusion coefficients in the reduced models can be used as adjustable parameters with which the results of the explicit- and implicit-water models can be related. We find that the values of the diffusion coefficients are sensitive to the net charge of the pore, but are relatively transferable to different voltages and charge patterns with the same total charge.

cond-mat.mes-hall↗

arXiv2017

A systematic Monte Carlo simulation study of the primitive model electrical double layer over an extended range of concentrations, electrode charges, cation diameters and valences

The purpose of this study is to provide data for the primitive model of the electrical double layer, where ions are modeled as charged hard spheres, the solvent as an implicit dielectric background (with dielectric constant $ε= 78.5$), and the electrode as a smooth, uniformly charged, hard wall. We use canonical and Grand Canonical Monte Carlo simulations to compute the concentration profiles, from which the electric field and electrostatic potential profiles are obtained by solving Poisson's equation. We report data for an extended range of parameters including 1:1, 2:1, and 3:1 electrolytes at concentrations $c=0.0001-1$ M near electrodes carrying surface charges up to $σ=\pm 0.5$ Cm$^{-2}$. The anions are monovalent with a fixed diameter $d_{-}=3$ Å, while the charge and diameter of cations are varied in the range $z_{+}=1$, 2, 3 and $d_{+}=1.5$, 3, 6, and 9 Å (the temperature is $298.15$ K). We provide all the raw data in the Supporting Information.

cond-mat.soft↗

arXiv2017

Multiscale modeling of a rectifying bipolar nanopore: explicit-water versus implicit-water simulations

In a multiscale modeling approach, we present computer simulation results for a rectifying bipolar nanopore on two modeling levels. In an all-atom model, we use explicit water to simulate ion transport directly with the molecular dynamics technique. In a reduced model, we use implicit water and apply the Local Equilibrium Monte Carlo method together with the Nernst-Planck transport equation. This hybrid method makes the fast calculation of ion transport possible at the price of lost details. We show that the implicit-water model is an appropriate representation of the explicit-water model when we look at the system at the device (i.e., input vs.\ output) level. The two models produce qualitatively similar behavior of the electrical current for different voltages and model parameters. Looking at details of concentration and potential profiles, we find profound differences between the two models. These differences, however, do not influence the basic behavior of the model as a device because they do not influence the $z$-dependence of the concentration profiles which are the main determinants of current. These results then address an old paradox: how do reduced models, whose assumptions should break down in a nanoscale device, predict experimental data? Our simulations show that reduced models can still capture the overall device physics correctly, even though they get some important aspects of the molecular-scale physics quite wrong; reduced models work because they include the physics that is necessary from the point of view of device function. Therefore, reduced models can suffice for general device understanding and device design, but more detailed models might be needed for molecular level understanding.

cond-mat.mes-hall↗

arXiv2013

Dynamic Monte Carlo simulation of coupled transport through a narrow multiply-occupied pore

Dynamic Monte Carlo simulations are used to study coupled transport (co-transport) through sub-nanometer-diameter pores. In this classic Hodgkin-Keynes mechanism, an ion species uses the large flux of an abundant ion species to move against its concentration gradient. The efficiency of co-transport is examined for various pore parameters so that synthetic nanopores can be engineered to maximize this effect. In general, the pore must be narrow enough that ions cannot pass each other and the charge of the pore large enough to attract many ions so that they exchange momentum. Co-transport efficiency increases as pore length increases, but even very short pores exhibit co-transport, in contradiction to the usual perception that long pores are necessary. The parameter ranges where co-transport occurs is consistent with current and near-future synthetic nanopore geometry parameters, suggesting that co-transport of ions may be a new application of nanopores.

cond-mat.soft↗

arXiv2009

An Efficient Algorithm for Classical Density Functional Theory in Three Dimensions: Ionic Solutions

Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids of charged, hard spheres that uses $\mathcal{O}(N\log N)$ operations and $\mathcal{O}(N)$ memory, where $N$ is the number of grid points. This system-size scaling is significant because of the very large $N$ required for three-dimensional systems. The algorithm uses fast Fourier transforms (FFT) to evaluate the convolutions of the DFT Euler-Lagrange equations and Picard (iterative substitution) iteration with line search to solve the equations. The pros and cons of this FFT/Picard technique are compared to those of alternative solution methods that use real-space integration of the convolutions instead of FFTs and Newton iteration instead of Picard. For the hard-sphere DFT we use Fundamental Measure Theory. For the electrostatic DFT we present two algorithms. One is for the \textquotedblleft bulk-fluid\textquotedblright functional of Rosenfeld [Y. Rosenfeld. \textit{J. Chem. Phys.} 98, 8126 (1993)] that uses $\mathcal{O}(N\log N)$ operations. The other is for the \textquotedblleft reference fluid density\textquotedblright (RFD) functional [D. Gillespie et al., J. Phys.: Condens. Matter 14, 12129 (2002)]. This functional is significantly more accurate than the bulk-fluid functional, but the RFD algorithm requires $\mathcal{O}(N^{2})$ operations.

physics.chem-ph↗

arXiv2005

On the Physics of Size Selectivity

We demonstrate that two mechanisms used by biological ion channels to select particles by size are driven by entropy. With uncharged particles in an infinite cylinder, we show that a channel that attracts particles is small-particle selective and that a channel that repels water from the wall is large-particle selective. Comparing against extensive density-functional theory calculations of our model, we find that the main physics can be understood with surprisingly simple bulk models that neglect the confining geometry of the channel completely.

cond-mat.soft↗