Dale A. Huckaby

A model for sequential first-order phase transitions occurring in the underpotential deposition of metals

Abstract A model for the underpotential deposition of metals that occurs in stages is introduced. In this model the deposition takes place as a sequence of first order phase transitions of the adsorbate. In this application we study the underpotential deposition of Cu on a Au(111) surface in the presence of sulfate ions. The voltammogram of the deposition shows two sharp spikes which are reproduced by our model.

Underpotential deposition of Cu on Au(111): implications of the HB model

Abstract A model for the underpotential deposition of Cu on Au(111) in the presence of bisulfate ions has recently been proposed. In this model it was assumed that the bisulfate ions formed a √3 × √3 template. This template leaves a honeycomb lattice of free sites for the adsorption of copper. The clear implication is that the first peak corresponds to two-thirds of a monolayer of Cu. The second peak corresponds to the replacement of the bisulfate by copper in the adlayer. We showed also that the broad foot of the first peak is due to a second-order hard-hexagon-like transition, which has been seen experimentally. The interpretation, based on scanning tunneling microscopy and low energy electron diffraction observations, that the first peak corresponds to only one-third of a monolayer, is consistent with our model if it is the bisulfate ion that is actually seen in those experiments. In the present work we discuss further refinements of this theory. We show that, from the dimensions of the bisulfate ion, an oxygen atom protrudes 1.84 A above the plane of copper adsorption and the hydrogen atom of the bisulfate protrudes 2.13 A. For the same geometry on a clean Au(111) surface, the bisulfate layer should stand about 4.1 A above the surface. However, scanning tunneling microscopy cannot measure absolute heights, and therefore both cases appear as a √3 × √3 overlayer. The dependence of the peak position on concentration is also discussed using a recently developed theory of kinetic effects.

Phase transitions at electrode interfaces

Abstract A general statistical mechnical model of the adsorption of ions at the electrode interface is presented. The three-dimensional adsorption model is equivalent to a two-dimensional lattice gas. The adsorption isotherm for a single ion is given in terms of Pade approximants for the high and low fugacity limits. This formalism is applied to the case of the underpotential deposition of copper onto gold(111). The spikes in the voltammogram of this deposition are viewed as resulting from a first order phase transition on a honeycomb lattice followed by a first order phase transition on a triangular lattice. This model is extended by incorporating the coadsorption of (bi)sulfate with copper and by considering longer range interactions between adatoms using the mean neighbor approximation. The model voltammograms agree quite well with the experimental ones.

Phase transitions at liquid–solid interfaces: Padé approximant for adsorption isotherms and voltammograms

A Pade approximant that is the natural extension of Langmuir’s adsorption isotherm is used to study the adsorption in the liquid–solid interface. The coefficients of this approximant are generated by a recursion relation and can be computed from the fugacity series in closed form. We apply this approximant to the underpotential deposition of metals on an electrode, and obtain voltammograms that show the sharp spikes seen in recent experiments.

Exact results for the adsorption of a dense fluid onto a triangular lattice of sticky sites

A discussion of exact results for the interface between a dense fluid of molecules with a spherical hard core of diameter σ and a triangular lattice of sticky sites with spacing d on a wall with hard repulsive potential is given. When σ≤d and first neighbors attract, there is a first order transition when the stickiness parameter λ, singlet wall density ρ01(0), and pair correlation function g02(d) satisfy λρ01(0)[g02(d)]3=1. If d<σ< 7/8 d, and further neighbors do not interact, the model is equivalent to the hard hexagon model solved by Baxter. In this case there is a second order phase transition between an ordered 7/8 × 7/8 phase and a disordered one.

An extended hexagon model for Cu underpotential deposition on Au(111)

The hard hexagon adsorption isotherm of Baxter and Joyce was previously used in a statistical model for the underpotential deposition (upd) of Cu on Au(111). This model gave a plausible physical picture of Cu upd on Au(111) and was able to reproduce the gross features of the voltammogram. In the present work the hexagon model is extended to include a mean field treatment of the adsorbate interactions. Using this extended hexagon model, coupled adsorption isotherms for copper and sulfate ions are obtained and solved numerically. These isotherms yield theoretical quartz microbalance curves which compare well with the experimental ones. The model voltammogram reproduces the experimental voltammogram including the finer details of the broad foot region.

An exactly solvable model ternary solution with three-body interactions

We consider a three-component model of rodlike molecules AA, BB, and AB, confined to the bonds of the honeycomb or three-coordinated Bethe lattice, and with three-body interactions between the molecular ends near a common lattice site. The model is equivalent to an Ising model on an associated lattice and has been previously transformed first to an Ising model on an intermediate lattice then to a standard Ising model on the original honeycomb or Bethe lattice. The exact coexistence curves for phase separation have been previously calculated for weak three-body interactions. In the present paper the same transformations are used for the case of strong three-body interactions, the difference being that in this case the Ising parameters on the intermediate lattice are complex. Exact, closed-form expressions are obtained for the two-phase coexistence surface in temperature-composition space. The exact coexistence curves are drawn for various values of a reduced three-body coupling constant and the reduced temperature. It is proved there is no phase separation in the model on these lattices if the reduced three-body coupling constant is sufficiently large.

Exact solution of a three-component system on the honeycomb lattice

A model three-component system is considered in which the bonds of a honeycomb lattice are covered by rodlike molecules of typesAA, BB, andAB. The ends of molecules near a common lattice site interact with energiesɛAA,ɛBB, andɛAB. The model is equivalent to an Ising model on the 3–12 lattice. Exact results are obtained for the two-phase coexistence curves in the isothermal composition plane.

Free energy of the fcc and hcp lattices under first- and second-neighbor harmonic interactions

Abstract The harmonic contribution to the high-temperature expansion of the Helmholtz free energy was calculated for the hcp and fcc lattices for an arbitrary analytic central pair potential with interactions extending to first and second neighbors. The numerical method used was not the usual extrapolation based upon a sampling of points in the first Brillouin zone but rather an extrapolation of the properties of finite crystals to the thermodynamic limit ( N → ∞).

Shapes of voltammogram spikes explained as resulting from the effects of finite electrode crystal sizes

We study the voltammogram spikes of the underpotential deposition at electrode surfaces that correspond to first-order phase transitions. The shape of symmetric spikes is approximated by the function cosh−2. In order to explain this spike shape microscopically, which is our main concern, we observe that an electrode surface consists of many small crystals. A voltammogram spike is then interpreted as an averaged result of the finite-size effects occurring in each of these crystals. This view also allows us to comment on asymmetry in the voltammogram spikes. Our analysis is based on the rigorous statistical mechanical techniques of the Pirogov–Sinai theory. For the sake of simplicity, we model the deposition process by the one-component lattice gas. We apply the results to the underpotential deposition of Cu on Pt(111) in a sulfuric acid medium, and find very good agreement with experiment.