arXiv subjects

Mathijs Janssen

Publications and source records attributed to Mathijs Janssen.

At least 19 recordsLinked to original sources

arXiv2026

Modeling electrolytes in nanopores by Monte Carlo simulations and the Bazant--Storey--Kornyshev model

We study electrolyte-filled cylindrical nanopores through Monte Carlo (MC) simulations and the Bazant--Storey--Kornyshev model, for different ionic valencies, sizes, and bulk concentrations, pore radii and surface charge densities. Our model accounts for finite ion size through a Stern layer and we use de~Souza and Bazant's mechanical equilibrium principle to derive a boundary condition for the outer Helmholtz plane. For 1:1 electrolytes and moderate surface charge densities, we find that both the classical Poisson--Boltzmann--Stern (PB--Stern) and our Bazant--Storey--Kornyshev--Boltzmann--Stern (BSKB--Stern) model fit MC data well---for 2:1 and 3:1 electrolytes, the BSKB--Stern outperforms the PB-Stern model. Conversely, the BSKB--Stern model poorly fits MC data in other scenarios. First, BSKB--Stern does not capture drying and apparent like-charge attraction in 3:1 electrolytes and small surface charge densities. Second, BSKB--Stern only fits MC data for finely-tuned ionic diameters; for other ionic diameters, the ionic charge densities show oscillations or extended near-surface regions caused by ionic packing and strong Coulomb interactions, not captured by the BSKB--Stern model.

physics.chem-ph↗

arXiv2026

The impedance of a charged flat-plate electric double-layer capacitor

We calculate the impedance of a flat-plate electric double-layer (EDL) capacitor by means of Finite Element Method simulations of modified Poisson--Nernst--Planck equations. In Nyquist representation, the impedance spectra show a slanted line at intermediate frequencies if the capacitor is biased by a voltage, $U_\mathrm{bias}\neq 0$, or if the cation and anion diffusion coefficients differ, $D_-\neq D_+$. By inspecting the concentration perturbations in the relevant frequency range, we confirm that the slanted line is in both cases related to ambipolar salt diffusion. On the basis of our impedance data, we disprove two previously made claims: 1) that the width $R_\mathrm{sl}$ of the slanted-line region represents an EDL resistance; and 2) that the slope $k_\mathrm{sl}$ of the slanted line is a measure of the ratio of the diffusion and charging time scales, $\tau_\mathrm{diff}/\tau_\mathrm{c}$. For the quantitative analysis of flat-electrode EDL capacitor impedance, we propose instead two equivalent circuits, for the cases $D_-\neq D_+$ and $U_\mathrm{bias}\neq 0$. These two cases give rise to antisymmetric and symmetric salt perturbations, which are best described by a Warburg short and Warburg open element, respectively. From our circuit analysis, we obtain quantitative relations that link the Warburg prefactors to the ambipolar diffusion coefficient, the chemical capacitance of the bulk electrolyte, and the differential charge efficiency of the EDLs. We thus provide a theoretical framework that explains why the width of the slanted line saturates at large biases, why it vanishes for large ion packing fractions, and how the system's overall capacitance is limited by the finite amount of ions in a closed system.

physics.chem-ph↗

arXiv2025

Basic requirements for potential differences across solid--fluid interfaces

At model water--vapor and water--solid interfaces, molecular ordering leads to charge oscillations and, thereby, to a spatially varying electrostatic potential. Atomistic simulations indicate that such ordering leads to an electric potential difference $\chi$, the surface potential, of about $-0.5\,\mathrm{V}$ across the first few molecular layers. Here, we calculate surface potentials at interfaces between a simple model fluids and a solid, with Molecular Dynamics simulations. The fluids are made up of either diatomic, dipolar molecules or a single Lennard-Jones particle with a dipole moment. All fluids show some structuring near the interface, but charge oscillations and a non-zero surface potential are present only for asymmetric molecules (unequal diameters of the atoms) or molecules with an off-center dipole. We condense this finding into the criterion that the geometric and dipolar centers of a molecule must differ for the fluid to exhibit a surface potential. Remarkably, while the solid--fluid interaction strength strongly affects the magnitude of charge oscillations, it hardly affects the potential drop $\chi$. Further, our results demonstrate that changing the diameter of the smaller atom can flip the sign of the surface potential, thus highlighting the importance of steric effects.

physics.chem-ph↗

arXiv2025

Faradaic and capacitive charging of an electrolyte-filled pore in response to a small applied potential

Electrochemical devices often charge both through Faradaic reactions and electric double layer formation. Here, we study these coupled processes in a model system of a long electrolyte-filled pore subject to a small suddenly-applied potential, close to the equilibrium potential $\Psi^\text{eq}$ at which there is no net Faradaic charge transfer. Specifically, we solve the coupled Poisson-Nernst-Planck and Frumkin-Butler-Volmer equations by asymptotic approximations, using the pore's small inverse aspect ratio as the small parameter. In the early-time limit, the reaction-diffusion equations yield an extended Faradaic transmission line model that includes a voltage source, $\Psi_\text{eq}$, biasing the Faradaic reactions, captured by the resistance $R_F$. In the long-time limit, the model exhibits a nontrivial potential of zero charge, $\Psi_\text{pzc} = \Psi_\text{eq}[1 - \hat{Z}(0)/R_F]$, where $\hat{Z}(0)$ is the experimentally accessible zero-frequency impedance of the system. This expression provides a new means to experimentally measure the Faradaic contribution to $\Psi_\text{pzc}$.

cond-mat.stat-mech↗

arXiv2025

Charging dynamics of electric double layer capacitors including beyond-mean-field electrostatic correlations

Electric double layer (EDL) formation underlies the functioning of supercapacitors and several other electrochemical technologies. Here, we study how the EDL formation near two flat blocking electrodes separated by $2L$ is affected by beyond-mean-field Coulombic interactions, which can be substantial for electrolytes of high salt concentration or with multivalent ions. Our model combines the Nernst-Planck and Bazant-Storey-Kornyshev (BSK) equations; the latter is a modified Poisson equation with a correlation length $\ell_c$. In response to a voltage step, the system charges exponentially with a characteristic timescale $\tau$ that depends nonmonotonically on $\ell_c$. For small $\ell_c$, $\tau$ is given by the BSK capacitance times a dilute electrolyte's resistance, in line with [Zhao, Phys. Rev. E 84, 051504 (2011)]; here, $\tau$ decreases with increasing $\ell_c$. Increasing the correlation length beyond $\ell_c\approx L^{2/3}\lambda_D^{1/3}$, with $\lambda_D$ the Debye length, $\tau$ reaches a minimum, rises as $\tau\propto \lambda_D\ell_c/D$, and plateaus at $\tau=4L^2/(\pi^2 D)$. Our results imply that strongly correlated, strongly confined electrolytes - ionic liquids in the surface force balance apparatus, say - move slower than predicted so far.

physics.chem-ph↗

arXiv2024

Convection can enhance the capacitive charging of porous electrodes

Charge transport in porous electrodes is foundational for modern energy storage technologies like supercapacitors, fuel cells, and batteries. Supercapacitors in particular rely solely on storing energy in charged pores. Here, we simulate the charging of a single electrolyte-filled pore using the modified Poisson-Nernst-Planck and Navier-Stokes equations. We find that electroconvection can substantially speed up the charging dynamics. We uncover the fundamental mechanism of electroconvection during pore charging through an analytical model that predicts the induced flow field and the electric current arising due to convection. Our findings suggest that convection is especially important in the limit of slender pores with thin electric double layers, and becomes significant beyond a certain threshold voltage that is an inherent electrolyte property.

cond-mat.soft↗

arXiv2024

Crowding-Regulated Binding of Divalent Biomolecules

Macromolecular crowding affects biophysical processes as diverse as diffusion, gene expression, cell growth, and senescence. Yet, there is no comprehensive understanding of how crowding affects reactions, particularly multivalent binding. Herein, we use scaled particle theory and develop a molecular simulation method to investigate the binding of monovalent to divalent biomolecules. We find that crowding can increase or reduce cooperativity--the extent to which the binding of a second molecule is enhanced after binding a first molecule--by orders of magnitude, depending on the sizes of the involved molecular complexes. Cooperativity generally increases when a divalent molecule swells and then shrinks upon binding two ligands. Our calculations also reveal that, in some cases, crowding enables binding that does not occur otherwise. As an immunological example, we consider Immunoglobulin G-antigen binding and show that crowding enhances its cooperativity in bulk but reduces it when an Immunoglobulin G binds antigens on a surface.

cond-mat.soft↗

arXiv2023

Water, not salt, causes most of the Seebeck effect of nonisothermal aqueous electrolytes

When two electrolyte-immersed electrodes have different temperatures, a voltage $\Delta \psi$ can be measured between them. This electrolyte Seebeck effect is usually explained by cations and anions flowing differently in thermal gradients. However, our molecular dynamics simulations of aqueous electrolytes reveal a large temperature-dependent potential drop $\chi$ near blocking electrodes caused by water layering and orientation. The difference in surface potentials at hot and cold electrodes is more important to the Seebeck effect than ionic thermodiffusion, $\Delta \psi \sim \chi_{\rm hot}-\chi_{\rm cold}$.

physics.chem-ph↗

arXiv2023

Equivalent circuit and continuum modeling of the impedance of electrolyte-filled pores

Batteries, supercapacitors, and several other electrochemical devices charge by accumulating ions in the pores of electrolyte-immersed porous electrodes. The charging of such devices has long been interpreted using equivalent circuits and the partial differential equations these give rise to. Here, we discuss the validity of the transmission line (TL) circuit and equation for modeling a single electrolyte-filled pore in contact with a reservoir of resistance $R_{r}$. The textbook derivation of the pore-reservoir impedance $R_r+Z_p$ from the TL equation does not correctly account for ionic current conservation at the pore-reservoir interface. However, correcting this shortcoming leads to the same impedance. We also show that the pore impedance $Z_p$ can be derived directly from the TL circuit, bypassing the TL equation completely. The TL circuit assumes equipotential lines in an electrolyte-filled pore to be straight, which is not the case near the pore entrance and end. To determine the importance of these regions, we numerically simulated the charging of pores of different lengths $\ell_p$ and radii $\varrho_p$ through the Poisson-Nernst-Planck equations. We find that pores with aspect ratios beyond $\ell_p/\varrho_p\gtrapprox5$ have impedances in good agreement with $Z_p$.

cond-mat.soft↗

arXiv2023

Optimising nanoporous supercapacitors for heat-to-electricity conversion

Innovative ways of harnessing sustainable energy are needed to meet the world's ever-increasing energy demands. Supercapacitors may contribute, as they can convert waste heat to electricity through cyclic charging and discharging at different temperatures. Herein, we use an analytically-solvable model of a cylindrical pore filled with a single file of ions to identify optimal conditions for heat-to-electricity conversion with supercapacitors. We consider Stirling and Ericsson-like charging cycles and show that the former or latter yields more work when a supercapacitor operates under charge or voltage limitations, respectively. Both cycles yield the most work for pores almost as narrow as the size of the ions they contain, as is the case for energy storage with supercapacitors. In contrast to energy storage, which can be maximised by ionophobic pores, such pores do not yield the best heat-to-electricity conversion, independently of the applied potential. Instead, we find that for a given pore size, a moderately ionophilic pore harvests more work than ionophobic and strongly ionophilic pores.

cond-mat.soft↗

arXiv2022

Direct numerical simulations of the modified Poisson-Nernst-Planck equations for the charging dynamics of cylindrical electrolyte-filled pores

Understanding how electrolyte-filled porous electrodes respond to an applied potential is important to many electrochemical technologies. Here, we consider a model supercapacitor of two blocking cylindrical pores on either side of a cylindrical electrolyte reservoir. A stepwise potential difference $2\Phi$ between the pores drives ionic fluxes in the setup, which we study through the modified Poisson-Nernst-Planck equations, solved with finite elements. We focus our discussion on the dominant timescales with which the pores charge and how these timescales depend on three dimensionless numbers. Next to the dimensionless applied potential $\Phi$, we consider the ratio $R/R_b$ of the pore's resistance $R$ to the bulk reservoir resistance $R_b$ and the ratio $r_{p}/\lambda$ of the pore radius $r_p$ to the Debye length $\lambda$. We compare our data to theoretical predictions by Aslyamov and Janssen ($\Phi$), Posey and Morozumi ($R/R_b$), and Henrique, Zuk, and Gupta ($r_{p}/\lambda$). Through our numerical approach, we delineate the validity of these theories and the assumptions on which they were based.

cond-mat.soft↗

arXiv2022

ELECTRODE: An electrochemistry package for atomistic simulations

Constant potential methods (CPM) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics (MD). They have been successfully used, for example, to realistically model the behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and batteries. The CPM models conductive electrodes by updating charges of individual electrode atoms according to the applied electric potential and the (time-dependent) local electrolyte structure. Here we present a feature-rich CPM implementation, called ELECTRODE, for the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), which includes a constrained charge method and a thermo-potentiostat. The ELECTRODE package also contains a finite-field approach, multiple corrections for non-periodic boundary conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi model for using non-ideal metals as electrodes. We demonstrate the capabilities of this implementation for a parallel-plate electrical double-layer capacitor, for which we have investigated the charging times with the different implemented methods and found an interesting relationship between water and ionic dipole relaxations. To prove the validity of the one-dimensional correction for the long-range electrostatics, we estimated the vacuum capacitance of two co-axial carbon nanotubes and compared it to structureless cylinders, for which an analytical expression exists. In summary, the ELECTRODE package enables efficient electrochemical simulations using state-of-the-art methods, allowing one to simulate even heterogeneous electrodes. Moreover, it allows unveiling more rigorously how electrode curvature affects the capacitance with the one-dimensional correction.

physics.chem-ph↗

arXiv2022

Analytical solution to the Poisson-Nernst-Planck equations for the charging of a long electrolyte-filled slit pore

We study the charging dynamics of a long electrolyte-filled slit pore in response to a suddenly applied potential. In particular, we analytically solve the Poisson-Nernst-Planck (PNP) equations for a pore for which $\lambda_D\ll H\ll L$, with $\lambda_D$ the Debye length and $H$ and $L$ the pore's width and length. For small applied potentials, we find the time-dependent potential drop between the pore's surface and its center to be in complete agreement with a prediction of the celebrated transmission line model. For moderate to high applied potentials, prior numerical work showed that charging slows down at late times; Our analytical model reproduces and explains such biexponential charge buildup.

cond-mat.soft↗

arXiv2021

Transmission line circuit and equation for an electrolyte-filled pore of finite length

I discuss the strong link between the transmission line (TL) equation and the TL circuit model for the charging of an electrolyte-filled pore of finite length. In particular, I show how Robin and Neumann boundary conditions to the TL equation, proposed by others on physical grounds, also emerge in the TL circuit subject to a stepwise potential. The pore relaxes with a timescale $\tau$, an expression for which consistently follows from the TL circuit, TL equation, and from the pore's known impedance. An approximation to $\tau$ explains the numerically determined relaxation time of the stack-electrode model of Lian et al. [Phys. Rev. Lett. 124, 076001 (2020), arXiv:1911.09924].

physics.chem-ph↗

arXiv2021

Reversible heat production during electric double layer buildup depends sensitively on the electrolyte and its reservoir

Several modern technologies for energy storage and conversion are based on the screening of electric charge on the surface of porous electrodes by ions in an adjacent electrolyte. This so-called electric double layer (EDL) exhibits an intricate interplay with the electrolyte's temperature that was the focus of several recent studies. In one of them, Janssen et al. [Phys. Rev. Lett. 119, 166002 (2017)] experimentally determined the ratio $\mathcal{Q}_\text{rev}/W_\text{el}$ of reversible eat flowing into a supercapacitor during an isothermal charging process and the electric work applied therein. To rationalize that data, here, we determine $\mathcal{Q}_\text{rev}/W_\text{el}$ within different models of the EDL using theoretical approaches like density functional theory (DFT) as well as molecular dynamics simulations. Applying mainly the restricted primitive model, we find quantitative support for a speculation of Janssen et al. that steric ion interactions are key to the ratio $\mathcal{Q}_\text{rev}/W_\text{el}$. Here, we identified the entropic contribution of certain DFT functionals, which grants direct access to the reversible heat. We further demonstrate how $\mathcal{Q}_\text{rev}/W_\text{el}$ changes when calculated in different thermodynamic ensembles and processes. We show that the experiments of Janssen et al. are explained best by a charging process at fixed bulk density, or in a "semi-canonical" system. Finally, we find that $\mathcal{Q}_\text{rev}/W_\text{el}$ significantly depends on parameters as pore and ion size, salt concentration, and valencies of the cat- and anions of the electrolyte. Our findings can guide further heat production measurements and can be applied in studies on, for instance, nervous conduction, where reversible heat is a key element.

cond-mat.soft↗

arXiv2020

On the time-dependent electrolyte Seebeck effect

Single-ion Soret coefficients $\alpha_{i}$ characterize the tendency of ions in an electrolyte solution to move in a thermal gradient. When these coefficients differ between cations and anions, an electric field can be generated. For this so-called electrolyte Seebeck effect to occur, the different thermodiffusive fluxes need to be blocked by boundaries -- electrodes, for example. Local charge neutrality is then broken in the Debye-length vicinity of the electrodes. Confusingly, many authors point to these regions as the source of the thermoelectric field yet ignore them in derivations of the time-dependent Seebeck coefficient $S(t)$, giving a false impression that the electrolyte Seebeck effect is purely a bulk phenomenon. Without enforcing local electroneutrality, we derive $S(t)$ generated by a binary electrolyte with arbitrary ionic valencies subject to a time-dependent thermal gradient. Next, we experimentally measure $S(t)$ for five acids, bases, and salts near titanium electrodes. For the steady state we find $S\approx2~\mathrm{mV~K}^{-1}$ for many electrolytes, roughly one order of magnitude larger than predictions based on literature $\alpha_{i}$. We fit our expression for $S(t)$ to the experimental data, treating the $\alpha_{i}$ as fit parameters, and also find larger-than-literature values, accordingly.

physics.chem-ph↗

arXiv2019

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

The development of novel electrolytes and electrodes for supercapacitors is hindered by a gap of several orders of magnitude between experimentally measured and theoretically predicted charging timescales. Here, we propose an electrode model, containing many parallel stacked electrodes, that explains the slow charging dynamics of supercapacitors. At low applied potentials, the charging behavior of this model is described well by an equivalent circuit model. Conversely, at high potentials, charging dynamics slow down and evolve on two relaxation time scales: a generalized $RC$ time and a diffusion time, which, interestingly, become similar for porous electrodes. The charging behavior of the stack-electrode model presented here helps to understand the charging dynamics of porous electrodes and qualitatively agrees with experimental time scales measured with porous electrodes.

physics.chem-ph↗

arXiv2019

Curvature affects electrolyte relaxation: studies of spherical and cylindrical electrodes

With two minimal models, I study how electrode curvature affects the response of electrolytes to applied electrostatic potentials. For flat electrodes, Bazant et al. [Phys. Rev. E. 70, 021506 (2004)] popularized the "RC" timescale $\lambda_{\textrm{D}} L/D$, with $\lambda_{\textrm{D}}$ being the Debye length, $2L$ the electrode separation, and $D$ the ionic diffusivity. For thin electric double layers near concentric spherical and coaxial cylindrical electrodes, I show here that equivalent circuit models again predict the correct ionic relaxation timescales. Importantly, these timescales explicitly depend on both electrode radii, not simply on their difference.

physics.chem-ph↗