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Poisson-Nernst-Planck charging dynamics of an electric double layer capacitor: symmetric and asymmetric binary electrolytes
Authors:
Ivan Palaia,
Adelchi J. Asta,
Megh Dutta,
Patrick B. Warren,
Benjamin Rotenberg,
Emmanuel Trizac
Abstract:
A parallel plate capacitor containing an electrolytic solution is the simplest model of a supercapacitor, or electric double layer capacitor. Using both analytical and numerical techniques, we solve the Poisson-Nernst-Planck equations for such a system, describing the mean-field charging dynamics of the capacitor, when a constant potential difference is abruptly applied to its plates. Working at c…
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A parallel plate capacitor containing an electrolytic solution is the simplest model of a supercapacitor, or electric double layer capacitor. Using both analytical and numerical techniques, we solve the Poisson-Nernst-Planck equations for such a system, describing the mean-field charging dynamics of the capacitor, when a constant potential difference is abruptly applied to its plates. Working at constant total number of ions, we focus on the physical processes involved in the relaxation and, whenever possible, give its functional shape and exact time constants. We first review and study the case of a symmetric binary electrolyte, where we assume the two ionic species to have the same charges and diffusivities. We then relax these assumptions and present results for a generic strong (i.e. fully dissociated) binary electrolyte. At low electrolyte concentration, the relaxation is simple to understand, as the dynamics of positive and negative ions appear decoupled. At higher electrolyte concentration, we distinguish several regimes. In the linear regime (low voltages), relaxation is multi-exponential, it starts by the build-up of the equilibrium charge profile and continues with neutral mass diffusion, and the relevant time scales feature both the average and the Nernst-Hartley diffusion coefficients. In the purely nonlinear regime (intermediate voltages), the initial relaxation is slowed down exponentially due to increased capacitance, while bulk effects become more and more evident. In the fully nonlinear regime (high voltages), the dynamics of charge and mass are completely entangled and, asymptotically, the relaxation is linear in time. We finally discuss non-ideal behavior in real capacitors and provide conditions for which mean-field is expected to hold.
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Submitted 18 August, 2025; v1 submitted 14 March, 2023;
originally announced March 2023.
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Charging dynamics of electric double layer nanocapacitors in mean-field
Authors:
Ivan Palaia,
Adelchi J. Asta,
Megh Dutta,
Patrick B. Warren,
Benjamin Rotenberg,
Emmanuel Trizac
Abstract:
An electric double layer capacitor (EDLC) stores energy by modulating the spatial distribution of ions in the electrolytic solution that it contains. We determine the mean-field time scales for planar EDLC relaxation to equilibrium, after a potential difference is applied. We tackle first the fully symmetric case, where positive and negative ionic species have same valence and diffusivity, and the…
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An electric double layer capacitor (EDLC) stores energy by modulating the spatial distribution of ions in the electrolytic solution that it contains. We determine the mean-field time scales for planar EDLC relaxation to equilibrium, after a potential difference is applied. We tackle first the fully symmetric case, where positive and negative ionic species have same valence and diffusivity, and then the general, more complex, asymmetric case. Depending on applied voltage and salt concentration, different regimes appear, revealing a remarkably rich phenomenology relevant for nanocapacitors.
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Submitted 2 June, 2025; v1 submitted 2 January, 2023;
originally announced January 2023.
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Cell Dynamic Simulations of Diblock Copolymer/Colloid Systems
Authors:
Javier Diaz,
Marco Pinna,
Andrei Zvelindovsky,
Adelchi Asta,
Ignacio Pagonabarraga
Abstract:
The presence of nanoparticles in a diblock copolymer leads to changes in the morphology and properties of the matrix and can produce highly organized hybrid materials. The resulting material properties depend not only on the polymer composition but also on the size, shape, and surface properties of the colloids. The dynamics of this kind of systems using a hybrid mesoscopic approach has been studi…
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The presence of nanoparticles in a diblock copolymer leads to changes in the morphology and properties of the matrix and can produce highly organized hybrid materials. The resulting material properties depend not only on the polymer composition but also on the size, shape, and surface properties of the colloids. The dynamics of this kind of systems using a hybrid mesoscopic approach has been studied in this work. A continuum description for the polymer is used, while colloids are individually resolved. The method allows for a variable preference of the colloids, which can have different sizes, to the different components the block copolymer is made of. The impact that the nanoparticle preference for either, both, or none of the blocks has on the collective properties of nanoparticle-block copolymer composites can be analyzed. Several experimental results are reproduced covering colloid-induced phase transition, particles' placement within the matrix, and the role of incompatibilities between colloids and monomers.
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Submitted 29 May, 2018;
originally announced May 2018.