Supercapacitors are electrochemical devices which store energy by ion adsorption on the surface of a porous carbon. They are characterized by high power delivery. The use of nanoporous carbon to increase their energy density should not hinder their fast charging. However, the mechanisms for ion transport inside electrified nanopores remain largely unknown. Here we show that the diffusion is characterized by a hierarchy of time scales arising from ion confinement, solvation, and electrosorption effects. By combining electrochemistry experiments with molecular dynamics simulations, we determine the in-pore conductivities and diffusion coefficients and their variations with the applied potential. We show that the diffusion of the ions is slower by 1 order of magnitude compared to the bulk electrolyte. The desolvation of the ions occurs on much faster time scales than electrosorption.

Capacitive mixing (CapMix) and capacitive deionization (CDI) are currently developed as alternatives to membrane-based processes to harvest blue energy-from salinity gradients between river and sea waterand to desalinate water-using charge-discharge cycles of capacitors. Nanoporous electrodes increase the contact area with the electrolyte and hence, in principle, also the performance of the process. However, models to design and optimize devices should be used with caution when the size of the pores becomes comparable to that of ions and water molecules. Here, we address this issue by simulating realistic capacitors based on aqueous electrolytes and nanoporous carbide-derived carbon (CDC) electrodes, accounting for both their complex structure and their polarization by the electrolyte under applied voltage. We compute the capacitance for two salt concentrations and validate our simulations by comparison with cyclic voltammetry experiments. We discuss the predictions of Debye-Hückel and Poisson-Boltzmann theories, as well as modified Donnan models, and we show that the latter can be parametrized using the molecular simulation results at high concentration. This then allows us to extrapolate the capacitance and salt adsorption capacity at lower concentrations, which cannot be simulated, finding a reasonable agreement with the experimental capacitance. We analyze the solvation of ions and their confinement within the electrodes-microscopic properties that are much more difficult to obtain experimentally than the electrochemical response but very important to understand the mechanisms at play. We finally discuss the implications of our findings for CapMix and CDI, both from the modeling point of view and from the use of CDCs in these contexts.

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When an ionic liquid adsorbs onto a porous electrode, its ionic arrangement is deeply modified due to a screening of the Coulombic interactions by the metallic surface and by the confinement imposed upon it by the electrode's morphology. In particular, ions of the same charge can approach at close contact, leading to the formation of a superionic state. The impact of an electrified surface placed between two liquid phases is much less understood. Here we simulate a full supercapacitor made of the 1-butyl-3-methylimidazolium hexafluorophosphate and nanoporous graphene electrodes, with varying distances between the graphene sheets. The electrodes are held at constant potential by allowing the carbon charges to fluctuate. Under strong confinement conditions, we show that ions of the same charge tend to adsorb in front of each other across the graphene plane. These correlations are allowed by the formation of a highly localized image charge on the carbon atoms between the ions. They are suppressed in larger pores, when the liquid adopts a bilayer structure between the graphene sheets. These effects are qualitatively similar to the recent templating effects which have been reported during the growth of nanocrystals on a graphene substrate.

The numerical resolution of the Vlasov equation is usually performed by particle methods (PIC) which consist in approximating the plasma by a finite number of particles. The trajectories of these particles are computed from the characteristic curves given by the Vlasov equation, whereas selfconsistent fields are computed on a mesh of the physical space. This method allows to obtain satisfying results with a relatively small number of particles. However, it is well known that, in some cases, the numerical noise inherent to the particle method becomes too important to have an accurate description of the distribution function in phase space. To remedy to this problem, methods discretizing the Vlasov equation on a mesh of phase space have been proposed [2,5,6].The major drawback of Vlasov methods using a uniform and fixed mesh is that their numerical cost is high, which makes them rather inefficient when the dimension of phase-space grows. For this reason we are investigating a method using an adaptive mesh. The adaptive method is overlayed to a classical semi-Lagrangian method which is based on the conservation of the distribution function along particle trajectories. The phase-space grid is updated using a multiresolution technique.The model we consider throughout this paper is the nonrelativistic Vlasov equation coupled self-consistently with Poisson's equation. It readsthe self electric field E is computed from Poisson's equationsThe magnetic field is external and considered to be known. In the present work, we have chosen to introduce a phase-space mesh which can be refined or derefined adaptively in time. For this purpose, we use a technique based on multiresolution analysis which is in the same spirit as the methods developed in particular by S. Bertoluzza [1], A. Cohen et al. [3] and M. Griebel and F. Koster [4]. We represent the distribution function on a wavelet basis at different scales. We can then compress it by eliminating coefficients which are small and accordingly remove the associated mesh points. Another specific feature of our method is that we use an advection in physical and velocity space forward in time to predict the useful grid points for the next time step, rather than restrict ourselves to the neighboring points. This enables us to use a much larger time step, as in the semi-Lagrangian method the time step is not limited by a Courant condition. Once the new mesh is predicted, the semi-Lagrangian methodology is used to compute the new values of the distribution function at the predicted mesh points, using an interpolation based on the wavelet decomposition of the old distribution function. The mesh is then refined again by performing a wavelet transform, and eliminating the points associated to small coefficients. This paper is organized as follows : we shall first present the context of multiresolution analysis for adaptive simulations, then describe the adaptive semi-Lagrangian method and validate our method on typical simulation in beam physics.

Applied electrochemistry plays a key role in many technologies, such as Li-ion batteries, fuel cells, supercapacitors, solar cells, etc. It is therefore at the core of many research programs all over the world. However, fundamental electrochemical investigations remain scarce. In particular, electrochemistry is among the fields for which the gap between theory and experiment is the largest. From the computational point of view, there is no classical molecular dynamics (MD) software devoted to the simulation of electrochemical systems while other fields such as biochemistry or material science have dedicated tools. "MetalWalls" (MW), a MD code dedicated to electrochemistry, fills this gap. Its main originality is the inclusion of a series of methods which allow a constant electrical potential to be applied to the electrode materials. It also allows the simulation of bulk liquids or solids using the polarizable ion model and the aspherical ion model. MW is designed to be used on high-performance computers and it has already been employed in a number of scientific publications. It was for example used to study the charging mechanism of supercapacitors, nanoelectrowetting and water desalination devices.

Nanoconfinement generally leads to a drastic effect on the physical and chemical properties of ionic liquids. Here we investigate how the electrochemical reactivity in such media may be impacted inside of nanoporous carbon electrodes. To this end, we study a simple electron transfer reaction using molecular dynamics simulations. The electrodes are held at constant electric potential by allowing the atomic charges on the carbon atoms to fluctuate. We show that the Fe/Fe couple dissolved in an ionic liquid exhibits a deviation with respect to Marcus theory. This behavior is rationalized by the stabilization of a solvation state of the Fe cation in the disordered nanoporous electrode that is not observed in the bulk. The simulation results are fitted with a recently proposed two solvation state model, which allows us to estimate the effect of such a deviation on the kinetics of electron transfer inside of nanoporous electrodes.

Over the past decades, the specific surface area and the pore size distribution have been identified as the main structural features that govern the performance of carbon-based supercapacitors. As a consequence, graphene nanostructures have been identified as strong candidates for maximizing their capacitance. However, this hypothesis could not be thoroughly tested