Discreteness-of-Charge Adsorption Micropotentials

Abstract

A convenient general method for calculating potentials and fields arising from planar arrays of discrete adions under a variety of imaging conditions is described and illustrated. Adions are perfectly imaged by one conducting plane (single imaging) and are also imaged by a dielectric constant discontinuity at a plane on their other side. The method employs only solutions of the single imaging problem, is readily applied without a computer, and is pertinent to the usual electrolyte compact layer adjoining either an electrode or a dielectric material, which may be air. The single image solutions used in calculating more complex imaging results may be exact values obtained from a previous rather complicated approach, or for ease in calculation, may frequently be approximate but quite accurate values calculated by a simple method described herein. Using the exact approach, one can calculate, for the full range of the dielectric reflection parameter, fields and potentials along any line perpendicular to the conducting plane. Here we are primarily concerned with potentials and fields along the line through a removed adion, and the approximate single imaging solution is especially useful. Although we apply the method to regular hexagonal arrays, in the ....' " 1 latter case it is equally apphcable to arrays described by. Grahame s partla ly smeared, cut-off model for single imaging. Some comparison with the results of this model is presented. In addition to calculating and illustrating the variation of field and potential within the compact layer and the adjoining dielectric medium, we have examined in detail the difference between the micropotential and the macropotential for many different imaging situations. The present study includes the previously treated single conductive plane imaging and also the (infinite) conductive-conductive imaging situations as special cases. It is found that special care is needed to describe the latter situation by the present model. Finally, the effect of possible conductive imaging by the electrolyte diffuse layer is considered qualitatively.The system we shall consider in this paper is the electrolyte compact double layer (1). We shall assume it consists of a monolayer of ions (effective charge zve and average surface charge density qz) bounded on one side by a plane interface which we shall call the electrode-surface plane (ESP), generally (but not always) associated with an adsorbing conductor, and on the other side by an imaginary plane marking the points of closest approach of the charge centroids of ions in the electrolyte, or diffuse layer. The plane of closest approach is known as the outer Helmholtz plane (OHP), and the plane passing through the charge centroids of the adions in the monolayer is the inner Helmholtz plane (IHP). We shall define to be the distance between the OHP and the IHP and ~ to be the IHP-ESP separation; d ---/9 + "r is therefore the total thickness of the compact layer. REGION

Discreteness of Charge and Ion Association Effects on Electroactive Self-Assembled Monolayers

“…Alternatively, a more appropriate description of the electrostatic interactions that take place in a SAM is obtained through the hexagonal array model of Barlow and Macdonald. , Within this model, redox centers are represented by an hexagonal distribution of point charges embedded in a dielectric medium with relative permittivity ε a and thickness γ + β. This dielectric slab is bounded by a metallic wall on one side and by the diffuse layer on the other.…”

“…This model gives a simple analytical expression to evaluate the discreteness of charge potential, but its applicability is restricted to low coverages of the redox centers. An alternative approach can be derived from the work of Barlow and Macdonald , on ion adsorption at electrode surfaces. They assumed that charged groups are located on a regular hexagonal array and considered different imaging conditions at the electrode surface and the electrolyte solution.…”

Open Circuit Potential Changes upon Protonation/Deprotonation of ω‐Functionalized Alkanethiols on Au: Determination of Surface pK1/2 in Aqueous and Non‐Aqueous System

“…This potential difference between metal and PAD depends on the dielectric constant of SAM, thickness of SAM and charges at terminal groups, which is similar to capacitor . It is worth to mention that discreteness‐of‐charge contribution might be considered, which is caused by the interaction between the surrounding charges and images on a charged adsorbed molecules . In spite of possible perturbation , potential difference is related monotonically to the charge state of SAM by protonation/deprotonation indicating that the charge state of terminal groups monotonically increases/decreases V oc depending on the polarity of charge and charge density …”

“…15 It is worth to mention that discreteness-of-charge contribution might be considered, which is caused by the interaction between the surrounding charges and images on a charged adsorbed molecules. [16][17][18][19][20] In spite of possible perturbation , potential difference is related monotonically to the charge state of SAM by protonation/deprotonation indicating that the charge state of terminal groups monotonically increases/decreases V oc depending on the polarity of charge and charge density. 15 To examine the V oc dependence on the degree of protonation/deprotonation, 16-mercaptohexadecanoic acid (MHA) and 11-Amino-1-undecanethiol (AUT)-modified Au were served as model system to represent the negatively and positively charged functional groups, respectively.…”

Bromide Electrosorption on Liquid Gallium: A Typical Example of Halide Electrosorption from Aqueous Solutions and Its Modeling

“…Ionic adsorption on mercury from aqueous solutions has been examined very thoroughly, − and interpretations based on models accounting for discreteness-of-charge effects have been provided. − Despite the pioneering work by Frumkin, Bagotskaya, et al − aiming at extending adsorption measurements from mercury to liquid gallium, there are very few papers concerning ionic adsorption on this metal. The main reason for this is the narrow potential range within which this metal is electroinactive.…”