In recent experiments (Chmiola et al 2006 Science 313 1760; Largeot et al 2008 J. Am. Chem. Soc. 130 2730) an anomalous increase of the capacitance with a decrease of the pore size of a carbon-based porous electric double-layer capacitor has been observed. We explain this effect by image forces which exponentially screen out the electrostatic interactions of ions in the interior of a pore. Packing of ions of the same sign becomes easier and is mainly limited by steric interactions. We call this state 'superionic' and suggest a simple model to describe it. The model reveals the possibility of a voltage-induced first order transition between a cation(anion)-deficient phase and a cation(anion)-rich phase which manifests itself in a jump of capacitance as a function of voltage.

Having smaller energy density than batteries, supercapacitors have exceptional power density and cyclability. Their energy density can be increased using ionic liquids and electrodes with sub-nanometer pores, but this tends to reduce their power density and compromise the key advantage of supercapacitors. To help address this issue through material optimization, here we unravel the mechanisms of charging sub-nanometer pores with ionic liquids using molecular simulations, navigated by a phenomenological model. We show that charging of ionophilic pores is a diffusive process, often accompanied by overfilling followed by de-filling. In sharp contrast to conventional expectations, charging is fast because ion diffusion during charging can be an order of magnitude faster than in bulk, and charging itself is accelerated by the onset of collective modes. Further acceleration can be achieved using ionophobic pores by eliminating overfilling/de-filling and thus leading to charging behavior qualitatively different from that in conventional, ionophilic pores.

This paper focuses on the choice of the optimal pore size and the effect of pore size dispersion, which is important for the rational design of nanoporous supercapacitors. Optimization of the pore size of nanoporous carbon electrodes is discussed in terms of the maximal stored energy density. By applying a previously developed theory, and supporting it by newly performed experiments, we find that the energy density is a non-monotonic function of the pore size of monodisperse porous electrodes. The 'optimal' pore size that provides the maximal energy density increases with increasing operating voltage and saturates at high voltages. We also analyse how the pore size distribution affects the voltage dependent capacitance and the stored energy density, and show that the latter is maximized for monodisperse electrodes.

Recently observed anomalous properties of ionic-liquid-based nanoporous supercapacitors [C. Largot et al., J. Am. Chem. Soc., 2008, 130, 2730-2731] have attracted much attention. Here we present Monte Carlo simulations of a model ionic liquid in slit-like metallic nanopores. We show that exponential screening of the electrostatic interactions of ions inside a pore, as well as the image-charge attraction of ions to the pore surface, lead to the 'anomalous' increase of the capacitance with decreasing the pore width. The simulation results are in good agreement with the experimental data. The capacitance as a function of voltage is almost constant for low voltages and vanishes above a certain threshold voltage. For very narrow pores, these two regions are separated by a peak. With increase of the pore size the peak turns into a bump and disappears for wide pores. This effect, related to a specific character of the voltage-induced filling of nanopores with counterions at high densities, is yet to be verified experimentally.

We discuss nonlinear effects and efficiency of charge storage in supercapacitors with nanoporous electrodes and ionic liquids, and demonstrate that to maximize the stored energy, it may be beneficial to create 'obstacles' or 'difficulties' in charging.This can be achieved by making thermodynamically unfavourable conditions for ions inside nanopores, or more favourable outside. We show by means of Monte Carlo simulations that such 'ionophobic' pores store energy more efficiently and can provide equivalent or even better energy capacity. Since the recent analysis predicts much faster charging of ionophobic nanopores, we conclude that such pores offer a much better option for simultaneous energy/power optimization.Keywords: Ionic liquids, energy storage, optimization, nanopores, capacitance, supercapacitors Conceptual Insights. Supercapacitors emerge as a promising green alternative to batteries. They store energy via fast charge accumulation in nano-thick ionic layers at the electrode/electrolyte interface.The stored energies are relatively low for microporous electrodes with wide pores, and electrodes with ultranarrow 1-2nm sized pores are used to increase the energy density. However, such narrow pores are detrimental to the rate of charging/discharging and hence power density, the high value of which is one of the most important advantages of supercapacitors over batteries. We explore here a hypothesis how this problem can be overcome by creating 'ionophobic' pores with low or vanishing amount of an ionic liquid inside them at no applied voltage. Counter-intuitively, our analysis shows that such ionophobic nanopores can store not less but often more energy than the conventional ionophilic pores. Nanopores empty in a non-polarized state have also been shown to charge with much faster rate. This suggests a challenging task and an exciting opportunity for material scientists to engineer nanoporous electrodes for supercapacitors that can fulfil two dreams simultaneously -high energy and power densities, up to now considered as mutually exclusive.

An improved mean-field model used earlier (J. Phys.: Condens. Matter 2011, 23, 022201) to explain the anomalous increase of capacitance in nanoporous supercapacitors is extended to the study of charging dynamics. We find that charging of initially empty (i.e., ionic liquid-phobic) pores proceeds in a front-like way, while charging of filled (i.e., ionophilic) pores is diffusive; in both cases, however, the accumulated charge grows as a square root of time. We also discuss two-step complementary optimization of porous electrodes for supercapacitors. In a first step, the optimal pore width is chosen to maximize the stored energy density; in a second step, the optimal pore depth/length (that is, electrode's thickness) is chosen to satisfy the requirement on charging times. In addition, the use of "nanoporous channels" in a "multilayered" configuration is suggested to decrease the volume and to increase the capacitance, stored energy, and power density of a supercapacitor.

Nanoporous supercapacitors attract much attention as green energy storage devices with remarkable cyclability and high power and energy densities. However, their use in high-frequency applications is limited by relatively slow charging processes, while accelerating charging without compromising the energy storage still remains a challenging task. Here, we study in detail the charging and discharging behavior of nanoporous supercapacitors with narrow pores, which provide exceptionally high capacitances and stored energy densities. We scrutinize the dynamic modes of charging, revealing, in particular, a transient formation of crowded and dilute ionic-liquid phases inside the pores, which leads to co-ion trapping and correspondingly slow charging. We show how trapping can be circumvented by applying a slow voltage sweep, and we demonstrate that it can accelerate the overall charging process considerably if the sweep rate is chosen appropriately. While one might be tempted to apply a similar strategy to discharging, we find that the best discharge rates are obtained when the voltage is switched off in a step-like fashion, whereby the optimal charge and discharge times differ a few-fold. We unveil the scaling laws for such optimal quantities, which allow one to predict quantitatively the charging behavior for realistically long pores. On the basis of our findings, we propose an optimal charge-discharge cycle and elaborate on optimization strategies.

We study the normal and lateral effective critical Casimir forces acting on a spherical colloid immersed in a critical binary solvent and close to a chemically structured substrate with alternating adsorption preference. We calculate the universal scaling function for the corresponding potential and compare our results with recent experimental data [Soyka F., Zvyagolskaya O., Hertlein C., Helden L., and Bechinger C., Phys. Rev. Lett., 101, 208301 (2008)]. The experimental potentials are properly captured by our predictions only by accounting for geometrical details of the substrate pattern for which, according to our theory, critical Casimir forces turn out to be a sensitive probe. Introduction. -The confinement of a fluctuating medium generates effective forces acting on its boundaries. A particularly interesting realization of this general principle is provided by the confinement of concentration fluctuations of a binary liquid mixture upon approaching a critical demixing point at temperature T = T c in its bulk phase diagram [1]. Generically, the confining surfaces preferentially adsorb one of the two components of the binary liquid. This amounts to the presence of effective, symmetry-breaking surface fields favoring either positive [(+)] or negative [(−)] values of the scalar order parameter φ which is the difference between the local concentrations of the two species. The extension of the spatial region in the direction normal to the surfaces, within which the local structural properties of the fluid deviate from the bulk ones, is given by the bulk correlation length ξ , which diverges upon approaching the critical point as ξ (t → 0) = ξ