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The electric double layer (EDL) formed around charged nanostructures at the liquid-solid interface determines their electrochemical activity and influences their electrical and optical polarizability. We experimentally demonstrate that restructuring of the EDL at the nanoscale can be detected by dark-field scattering microscopy. Temporal and spatial characterization of the scattering signal demonstrates that the potentiodynamic optical contrast is proportional to the accumulated charge of polarisable ions at the interface and its time derivative represents the nanoscale ionic current. The material-specificity of the EDL formation is used in our work as a label-free contrast mechanism to image nanostructures and perform spatially-resolved cyclic voltametry on ion current density of a few attoamperes, corresponding to the exchange of only a few hundred ions.
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A simple non-local theoretical model is developed considering concentrated ionic surfactant solutions as regular ones. Their thermodynamics is described by the Cahn-Hilliard theory coupled with electrostatics. It is discovered that unstable solutions possess two critical temperatures, where the temperature coefficients of all characteristic lengths are discontinuous. At temperatures below the lower critical temperature ionic surfactant solutions separate into thin layers of oppositely charged liquids spread across the whole system and the electric potential is strictly periodic. At temperatures between the two critical temperatures separation can occur only near the solution surface thus leading to an oscillatory-decaying electric double layer. At temperatures above the higher critical temperature as well as in stable solutions there is no separation and the electric potential decays exponentially.
Modulating the electric potential on a conducting electrode is presented to generate an optical contrast for scattering microscopy that is sensitive to both surface charge and local topography. We dub this method Electric-Double-Layer-Modulation microscopy. We numerically compute the change in the local ion concentration that is the origin of this optical contrast for three experimentally relevant geometries: nanosphere, nanowire, and nanohole. In absence of plasmonic effects and physical absorption, the observable optical contrast is proportional to the derivative of the ion concentration with respect to the modulated potential. We demonstrate that this derivative depends on the size of the object and, less intuitively, also on its surface charge. This dependence is key to measuring the surface charge, in an absolute way, using this method. Our results help to identify the experimental conditions such as dynamic range and sensitivity that will be necessary for detecting the elementary charge jumps. We conclude that the nanohole is the most suitable geometry among these three for achieving elementary charge sensitivity.
Anisotropic colloidal particles constitute an important class of building blocks for self-assembly directed by electrical fields. The aggregation of these building blocks is driven by induced dipole moments, which arise from an interplay between dielectric effects and the electric double layer. For particles that are anisotropic in shape, charge distribution, and dielectric properties, calculation of the electric double layer requires coupling of the ionic dynamics to a Poisson solver. We apply recently proposed methods to solve this problem for experimentally employed colloids in static and time-dependent electric fields. This allows us to predict the effects of field strength and frequency on the colloidal properties.
This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration and conductivity is accounted for, while in the other model it is not. A spectral element method is used to discretise the model equations and it is found that the error convergence rate with respect to the number of elements is faster compared to a finite difference method. The increased accuracy of the spectral element approach means that, for a similar level of solution accuracy, the model simulation computing time is approximately 50% of that of the finite difference method. This suggests that the spectral element model could be used for control and state estimation purposes. For a typical supercapacitor charging profile, the numerical solutions from both models closely match experimental voltage and current data. However, when the electrolyte is dilute or where there is a long charging time, a noticeable difference between the numerical solutions of the two models is observed. Electrical impedance spectroscopy simulations show that the capacitance of the two models rapidly decreases when the frequency of the perturbation current exceeds an upper threshold.
We induce surface carrier densities up to $sim7cdot 10^{14}$cm$^{-2}$ in few-layer graphene devices by electric double layer gating with a polymeric electrolyte. In 3-, 4- and 5-layer graphene below 20-30K we observe a logarithmic upturn of resistance that we attribute to weak localization in the diffusive regime. By studying this effect as a function of carrier density and with ab-initio calculations we derive the dependence of transport, intervalley and phase coherence scattering lifetimes on total carrier density. We find that electron-electron scattering in the Nyquist regime is the main source of dephasing at temperatures lower than 30K in the $sim10^{13}$cm$^{-2}$ to $sim7 cdot 10^{14}$cm$^{-2}$ range of carrier densities. With the increase of gate voltage, transport elastic scattering is dominated by the competing effects due to the increase in both carrier density and charged scattering centers at the surface. We also tune our devices into a crossover regime between weak and strong localization, indicating that simultaneous tunability of both carrier and defect density at the surface of electric double layer gated materials is possible.
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