The electric double layer at high surface potentials: The influ- ence of excess ion polarizability

By including excess ion polarizability into Poisson-Boltzmann theory, we show that the decrease in differential capacitance with voltage, observed for metal electrodes above a threshold potential, can be understood in terms of thickening of the double layer due to ion-induced polarizability-holes in water. We identify a new length which controls the role of excess ion polarizability in the double layer, and show that when this is comparable to the size of the effective Debye layer, ion polarizability can significantly influence the properties of the double layer. Near a charged surface in contact with an electrolyte, attracted counterions and depleted coions form a layer that electrically screens the interfacial charge, rendering the so-called double layer electrically neutral. The counterion layer is loosely associated with the charged surface, under the influence of both the attractive and repulsive Coulomb force and thermal motion. The double layer has been studied extensively due to its importance within a wide number of areas e.g. colloid science, electrochemistry, and geophysics. Much attention has been devoted to the low and moderate surface potential regime, where established Gouy-Chapman-Stern (GCS) models [1–3] can quantitatively explain most experimental results. However, the double layer is also a key ingredient in applications such as supercapacitors [4] and microfluidic devices [5], which often operate at surface potentials much larger than the thermal voltage (kBT/e = 25mV, where e is the fundamental unit of charge). The behavior of double layers at such high voltages is not well understood, and experimentally available quantities, such as the electroosmotic mobility and the differential capacitance, deviate from established models based on GCS theory [1–3, 6]. Many experimental observations in the high surface potential regime can be qualitatively explained by including ionic excluded volume interactions into Poisson-Boltzmann theory, either by a lattice approximation [6–8] or by the more accurate BMCSL equation of state [6, 9, 10]. However, quantitative agreement between theory and experimental data is in most cases only obtained with unphysically large ion sizes [6], suggesting that other effects are equally or more important. In this Letter, we study ions in water near planar electrodes at a surface potential ψ0, including not only excluded volume, but also the excess ion polarizbility, i.e. the change of the water polarizability due to the presence of an ion [11]. Due to excess ion polarizability, an additional dielectrophoretic force is exerted on the ions [12], which becomes comparable to the bare Coulomb force for large electric fields. The model without excluded volume interactions was first published in its present form in Ref. 11 and analyzed in more detail in Ref. 13. Similar models were used to describe excess polarizability effects in bulk electrolytes [14] and in double layers with charged polymers [15]. Studies of excess polarizability in the double layer dates back to the papers by Gouy [16], Frumkin [17], and Butler [18], who examined the influence of neutral molecules on the differential capacitance. The influence of excess ion polarizability on the differential capacitance was first studied by Bikerman [7]. The model used by Bikerman includes how excess ion polarizability changes the chemical potential of the ions, and due to lack of computational power, he restricted the study to the asymptotic behavior for weak and strong electric fields. It is also well known that excess polarizability also influence the dielectric constant [19], and a complete model of excess ion polarizability must capture both these effects, as done in Refs. [11, 13]. The main result of this Letter is the finding that excess ion polarizability can explain the experimentally observed increase of the double layer at surface potentials larger than a certain threshold ψα, for bulk packing fractions below v0. We find an analytic expression for ψα, and show that when