Overscreening in 1D lattice Coulomb gas model of ionic liquids

Overscreening in the charge distribution of ionic liquids at electrified interfaces is shown to proceed from purely electrostatic and steric interactions in an exactly soluble one dimensional lattice Coulomb gas model. Being not a mean-field effect, our results suggest that even in higher dimensional systems the overscreening could be accounted for by a more accurate treatment of the basic lattice Coulomb gas model, that goes beyond the mean field level of approximation, without any additional interactions.Comment: 4 pages 5 .eps figure

Drag forces on inclusions in classical fields with dissipative dynamics

We study the drag force on uniformly moving inclusions which interact linearly with dynamical free field theories commonly used to study soft condensed matter systems. Drag forces are shown to be nonlinear functions of the inclusion velocity and depend strongly on the field dynamics. The general results obtained can be used to explain drag forces in Ising systems and also predict the existence of drag forces on proteins in membranes due to couplings to various physical parameters of the membrane such as composition, phase and height fluctuations.Comment: 14 pages, 7 figure

Out of equilibrium thermal Casimir effect in a model polarizable material

Relaxation of the thermal Casimir or van der Waals force for a model dielectric medium is investigated. We start with a model of interacting polarization fields with a dynamics that leads to a frequency dependent dielectric constant of the Debye form. In the static limit the usual zero frequency Matsubara mode component of the Casimir force is recovered. We then consider the out of equilibrium relaxation of the van der Waals force to its equilibrium value when two initially uncorrelated dielectric bodies are brought into sudden proximity. It is found that the spatial dependence of the out of equilibrium force is the same as the equilibrium one but it has a time dependent amplitude, or Hamaker coefficient, which increases in time to its equilibrium value. The final relaxation to the equilibrium value is exponential in systems with a single or finite number of polarization field relaxation times. However, in systems, such as those described by the Havriliak-Negami dielectric constant, with a broad distribution of relaxation times, we observe a much slower power law decay to the equilibrium value.Comment: 15 pages RevTex, 4 figure

Mean first-passage times of non-Markovian random walkers in confinement

The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the efficiency of processes as varied as diffusion-limited reactions, target search processes or spreading of diseases. Most methods to determine the FPT properties in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects can not be neglected. Examples of non Markovian dynamics include single-file diffusion in narrow channels or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics \cite{turiv2013effect}, dense soft colloids or viscoelastic solution. Here, we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean FPT of a Gaussian non-Markovian random walker to a target point. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the trajectory of the random walker in the future of the first-passage event, which are shown to govern the FPT kinetics.This analysis is applicable to a broad range of stochastic processes, possibly correlated at long-times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes including the emblematic case of the Fractional Brownian Motion in one or higher dimensions. These results show, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.Comment: Submitted version. Supplementary Information can be found on the Nature website : http://www.nature.com/nature/journal/v534/n7607/full/nature18272.htm

Ionic liquids at electrified interfaces

Until recently, “room-temperature” (<100–150 °C) liquid-state electrochemistry was mostly electrochemistry of diluted electrolytes(1)–(4) where dissolved salt ions were surrounded by a considerable amount of solvent molecules. Highly concentrated liquid electrolytes were mostly considered in the narrow (albeit important) niche of high-temperature electrochemistry of molten inorganic salts(5-9) and in the even narrower niche of “first-generation” room temperature ionic liquids, RTILs (such as chloro-aluminates and alkylammonium nitrates).(10-14) The situation has changed dramatically in the 2000s after the discovery of new moisture- and temperature-stable RTILs.(15, 16) These days, the “later generation” RTILs attracted wide attention within the electrochemical community.(17-31) Indeed, RTILs, as a class of compounds, possess a unique combination of properties (high charge density, electrochemical stability, low/negligible volatility, tunable polarity, etc.) that make them very attractive substances from fundamental and application points of view.(32-38) Most importantly, they can mix with each other in “cocktails” of one’s choice to acquire the desired properties (e.g., wider temperature range of the liquid phase(39, 40)) and can serve as almost “universal” solvents.(37, 41, 42) It is worth noting here one of the advantages of RTILs as compared to their high-temperature molten salt (HTMS)(43) “sister-systems”.(44) In RTILs the dissolved molecules are not imbedded in a harsh high temperature environment which could be destructive for many classes of fragile (organic) molecules

Phase diagram of a bulk 1d lattice Coulomb gas

The exact solution, via transfer matrix, of the simple one dimensional lattice Coulomb gas (1d LCG) model can reproduce peculiar features of ionic liquid capacitors, such as overscreening, layering, and camel- and bell-shaped capacitance curves. Using the same transfer matrix method, we now compute the bulk properties of the 1d LCG in the constant voltage ensemble. We unveil a phase diagram with rich structure exhibiting a low density disordered and high density ordered phases, separated by a first order phase transition at low temperature; the solid state at full packing can be ordered or not, depending on the temperature. This phase diagram, which is strikingly similar to its three dimensional counterpart, also sheds light on the behaviour of the confined system