arXiv subjects

Mathijs Janssen

Publications and source records attributed to Mathijs Janssen.

27 records · Page 2Linked to original sources

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 $λ_{\textrm{D}} L/D$, with $λ_{\textrm{D}}$ 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↗

arXiv2019

Driving an electrolyte through a corrugated nanopore

We characterize the dynamics of a $z-z$ electrolyte embedded in a varying-section channel. In the linear response regime, by means of suitable approximations, we derive the Onsager matrix associated to externally enforced gradients in electrostatic potential, chemical potential, and pressure, for both dielectric and conducting channel walls. We show here that the linear transport coefficients are particularly sensitive to the geometry and the conductive properties of the channel walls when the Debye length is comparable to the channel width. In this regime, we found that one pair of off-diagonal Onsager matrix elements increases with the corrugation of the channel transport, in contrast to all other elements which are either unaffected by or decrease with increasing corrugation. Our results have a possible impact on the design of blue-energy devices as well as on the understanding of biological ion channels through membranes

cond-mat.soft↗

arXiv2019

Transient response of an electrolyte to a thermal quench

We study the transient response of an electrolytic cell subject to a small, suddenly applied temperature increase at one of its two bounding electrode surfaces. An inhomogeneous temperature profile then develops, causing, via the Soret effect, ionic rearrangements towards a state of polarized ionic charge density $q$ and local salt density $c$. For the case of equal cationic and anionic diffusivities, we derive analytical approximations to $q, c$, and the thermovoltage $V_{T}$ for early ($t\llτ_{T}$) and late ($t\ggτ_{T}$) times as compared to the relaxation time $τ_{T}$ of the temperature. We challenge the conventional wisdom that the typically large Lewis number, the ratio $a/D$ of thermal to ionic diffusivities, of most liquids implies a quickly reached steady-state temperature profile onto which ions relax slowly. Though true for the evolution of $c$, it turns out that $q$ (and $V_{T}$) can respond much faster. Particularly when the cell is much bigger than the Debye length, a significant portion of the transient response of the cell falls in the $t\llτ_{T}$ regime, for which our approximated $q$ (corroborated by numerics) exhibits a density wave that has not been discussed before in this context. For electrolytes with unequal ionic diffusivities, $V_{T}$ exhibits a two-step relaxation process, in agreement with experimental data of Bonetti et al. [J. Chem. Phys. 142, 244708 (2015)].

physics.chem-ph↗

arXiv2018

Transient dynamics of electric double-layer capacitors: Exact expressions within the Debye-Falkenhagen approximation

We revisit a classical problem of theoretical electrochemistry: the response of an electric double layer capacitor (EDLC) subject to a small, suddenly applied external potential. We solve the Debye-Falkenhagen equation to obtain exact expressions for key EDLC quantities: the ionic charge density, the ionic current density, and the electric field. In contrast to earlier works, our results are not restricted to the long-time asymptotics of those quantities. The solutions take the form of infinite sums whose successive terms all decay exponentially with increasingly short relaxation times. Importantly, this set of relaxation times is the same among all aforementioned EDLC quantities; this property is demanded on physical grounds but not generally achieved within approximation schemes. The scaling of the largest relaxation timescale $τ_{1}$, that determines the long-time decay, is in accordance with earlier results: depending on the Debye length, $λ_{D}$, and the electrode separation, $2L$, it amounts to $τ_{1}\simeqλ_{D} L/D$ for $L\ggλ_{D}$, and $τ_{1} \simeq 4 L^2/(π^2 D)$ for $L\llλ_{D}$, respectively (with $D$ being the ionic diffusivity).

physics.chem-ph↗

arXiv2017

Coulometry and Calorimetry of Electric Double Layer Formation in Porous Electrodes

Coulometric measurements on salt-water-immersed nanoporous carbon electrodes reveal, at a fixed voltage, a charge decrease with increasing temperature. During far-out-of-equilibrium charging of these electrodes, calorimetry indicates the production of both irreversible Joule heat and reversible heat, the latter being associated with entropy changes during electric double layer (EDL) formation in the nanopores. These measurements grant experimental access --for the first time-- to the entropic contribution of the grand potential; for our electrodes, this amounts to roughly 25% of the total grand potential energy cost of EDL formation at large applied potentials, in contrast with point-charge model calculations that predict 100%. The coulometric and calorimetric experiments show a consistent picture of the role of heat and temperature in EDL formation and provide hitherto unused information to test against EDL models.

physics.chem-ph↗

arXiv2017

Reversible heating in electric double layer capacitors

A detailed comparison is made between different viewpoints on reversible heating in electric double layer capacitors. We show in the limit of slow charging that a combined Poisson-Nernst-Planck and heat equation, first studied by d'Entremont and Pilon [J. Power Sources {\bf 246}, 887 (2014)], recovers the temperature changes as predicted by the thermodynamic identity of Janssen, Härtel, and van Roij [Phys. Rev. Lett. {\bf 113}, 268501 (2014)], and disagrees with the approximative model of Schiffer, Linzen, and Sauer [J. Power Sources {\bf 160}, 765 (2006)] that predominates the literature.

cond-mat.soft↗

arXiv2016

Harvesting vibrational energy with liquid-bridged electrodes: thermodynamics in mechanically and electrically driven RC-circuits

We theoretically study a vibrating pair of parallel electrodes bridged by a (deformed) liquid droplet, which is a recently developed microfluidic device to harvest vibrational energy. The device can operate with various liquids, including liquid metals, electrolytes, as well as ionic liquids. We numerically solve the Young-Laplace equation for all droplet shapes during a vibration period, from which the time-dependent capacitance follows that serves as input for an equivalent circuit model. We first investigate two existing energy harvesters (with a constant and a vanishing bias potential), for which we explain an open issue related to their optimal electrode separations, which is as small as possible or as large as possible in the two cases, respectively. Then we propose a new engine with a time-dependent bias voltage, with which the harvested work and the power can be increased by orders of magnitude at low vibration frequencies and by factors 2-5 at high frequencies, where frequencies are to be compared to the inverse RC-time of the circuit.

physics.comp-ph↗

arXiv2015

Fundamental measure theory for the electric double layer: implications for blue-energy harvesting and water desalination

Capacitive mixing (CAPMIX) and capacitive deionization (CDI) are promising candidates for harvesting clean, renewable energy and for the energy efficient production of potable water, respectively. Both CAPMIX and CDI involve water-immersed porous carbon (supercapacitors) electrodes at voltages of the order of hundreds of millivolts, such that counter-ionic packing is important for the electric double layer (EDL) which forms near the surface of these porous materials. Thus, we propose a density functional theory (DFT) to model the EDL, where the White-Bear mark II fundamental measure theory functional is combined with a mean-field Coulombic and a mean spherical approximation-type correction to describe the interplay between dense packing and electrostatics, in good agreement with molecular dynamics simulations. We discuss the concentration-dependent potential rise due to changes in the chemical potential in capacitors in the context of an over-ideal theoretical description and its impact on energy harvesting and water desalination. Compared to less elaborate mean-field models our DFT calculations reveal a higher work output for blue-energy cycles and a higher energy demand for desalination cycles.

cond-mat.soft↗

arXiv2015

Boosting capacitive blue-energy and desalination devices with waste heat

We show that sustainably harvesting 'blue' energy from the spontaneous mixing process of fresh and salty water can be boosted by varying the water temperature during a capacitive mixing process. Our modified Poisson-Boltzmann calculations predict a strong temperature dependence of the electrostatic potential of a charged electrode in contact with an adjacent aqueous 1:1 electrolyte. We propose to exploit this dependence to boost the efficiency of capacitive blue engines, which are based on cyclically charging and discharging nanoporous supercapacitors immersed in salty and fresh water, respectively [D. Brogioli, Phys. Rev. Lett. 103, 058501 (2009)]. We show that the energy output of blue engines can be increased by a factor of order two if warm (waste-heated) fresh water is mixed with cold sea water. Moreover, the underlying physics can also be used to optimize the reverse process of capacitive desalination of water.

cond-mat.stat-mech↗