Emergence of a Stern Layer from the Incorporation of Hydration Interactions into the Gouy–Chapman Model of the Electrical Double Layer

Abstract

In one of the most commonly used phenomenological descriptions of the electrical double layer, a charged solid surface and a diffuse region of mobile ions are separated from each other by a thin charge-depleted Stern layer. The Stern layer acts as a capacitor that improves the classical Gouy-Chapman model by increasing the magnitude of the surface potential and limiting the maximal counterion concentration. We show that very similar Stern-like properties of the diffuse double layer emerge naturally from adding a nonelectrostatic hydration repulsion to the electrostatic Coulomb potential. The interplay of electrostatic attraction and hydration repulsion of the counterions and the surface leads to the formation of a diffuse counterion layer that remains well separated from the surface. In addition, hydration repulsions between the ions limit and control the maximal ion concentration and widen the width of the diffuse double layer. Our mean-field model, which we express in terms of electrostatic and hydration potentials, is physically consistent and conceptually similar to the classical Gouy-Chapman model. It allows the incorporation of ion specificity, accounts for hydration properties of charged surfaces, and predicts Stern layer properties, which we analyze in terms of the effective size of the hydrated counterions.

Determination of Surface Potential and Electrical Double-Layer Structure at the Aqueous Electrolyte-Nanoparticle Interface

“…7). Local maxima are predicted at finite separations from the interfaces that we interpret to be the formation of Stern-like layers [57], where d Stern is chosen to be the maximum in n þ ðxÞ (inset of Fig. 7).…”

“…Moreover, such forces are responsible for the formation of the Stern layer. To capture such behavior, we employ a recent model [55][56][57] that adds a hydration repulsion between cations in the form of a Yukawa potential, ðU h =k B TÞ ¼ bl h expðκl h − κrÞ=r, to the Coulomb potential that is at the core of the classical PoissonBoltzmann model. Here, k B is the Boltzmann constant, T the absolute temperature, κ −1 ¼ 0.3 nm is the decay length of the water ordering [53], and b is a constant that specifies the hydration interaction to equal k B T=b at a cation-cation distance r ¼ l h .…”

Osmotic pressure of permeable ionic microgels: Poisson-Boltzmann theory and exact statistical mechanical relations in the cell model

“…(23), noting that ∂g/∂u = n ′ f (u)ψ(u), integrating by parts, and making use of Eqs. (20) and (21), we obtain…”

BMIm[OH] Catalyzed Rapid, Mild and Improved Protocol for the Synthesis of 3‐Hydroxy‐3‐(nitroalkyl)indolin‐2‐one Derivatives in Water

“…The possible mechanistic pathway proposed for the synthesis of 3‐hydroxy‐3‐(nitromethyl)‐2‐oxindole derivative is shown in Figure . Here, we reasoned that the imidazolium core of the basic ionic liquid BMIm[OH] interacts with the surfactant SDS to form stern layer ( A ) . The role of SDS basically is to making hydrophobic cores by the formation of the micellar that helps the solubility of substrate.…”