S. H. Liu

An iterated three-layer model of the double layer with permanent dipoles

There does not exist a theory of the ionic double layer at a completely blocking metal electrode in liquid electrolytes which is adequate in the charge/potential region where ions and solvent molecules begin to approach saturated conditions. Under these conditions, a continuum theory, such as that of Gouy and Chapman (GC), becomes entirely inadequate. Here the problem is attacked in a semi-discrete way by first partitioning the space charge region into layers parallel to the planar blocking electrode. Each layer is part of a cubic lattice with lattice-site spacing determined by the pure solvent concentration. Lattice sites may be occupied by ions of either sign or by solvent molecules, taken as spheres having a permanent dipole moment. The solvent molecule finite-length dipoles are then approximated by slabs of constant point-dipole polarization. Thus each of the planes parallel to the electrode is a locus of ion centers, and the polarization is accounted for by equal and opposite charge layers equidistant on either side of an ionic charge layer. The mean polarization and ionic concentration in each three-layer region are determined self-consistently by free energy minimization, and electrostatic equations are employed to couple the electrical conditions in one layer to those adjacent. This ion-dipole model (IDM) is solved self-consistently for arbitrary molarity in two regimes: the weak-field situation where the electrode charge approaches zero, and the arbitrary field-strength regime. In the first case, an, exact, closed-form solution is obtained which reduces to that of GC in the appropriate limit, but numerical analysis is required in the second situation. The present treatment provides a more realistic account of the electrical effects of discrete solvent dipoles than do those treatments, such as the GC model, which represent them entirely by a background, non-saturable, or even saturable, bulk dielectric constant. Here polarization saturation enters naturally in a fully self-consistent way Thus although dipoles line up with the field in high-field regions, they tend to be displaced by ions of a given sign in the layers immediately adjacent to the blocking, electrode, reducing the net polarization. A simpler model, more directly appropriate for single crystals than for liquids, the layered lattice gas model (LLM), retains layering but represents the permanent dipolar polarization by a non-saturable continuum bulk dielectric constant; it is thus intermediate between the IDM and the GCM. Predictions of the three, models are compared with Grahames experimental differential capacitance results for NaF in the low-field region. The IDM is found to be much superior to either the LMM or the GCM. Many results are presented for the three models in the arbitrary field region. One of the most striking is that the IDM alone yields a strong oscillation in potential versus distance away from the blocking electrode, as first predicted by Kirkwood and Poirier for layered ionic structures.

Interlayer pairing and c-axis versus ab-plane gap anisotropy in high-Tc superconductors

Abstract Interlayer BCS-like pairing in nearly two-dimensional superconductors with N =1, 2 conducting layers per unit cell is investigated. For N =1, the singlet Δ s and triplet Δ t , order parameters have identical T c s ( T cs = T ct ) and magnitudes, and the gap is isotropic. For N = 2, T cs ⩾ T ct and | Δ s |⩾ Δ t . In region I of the parameters, the gap is anisotropic and nodeless for T T cs . In region II, the gap has nodes near T cs but is nodeless at low T . In a magnetic field, non-unitary states are possible. For N = 1 (2), intra-and interlayer pairing are completely (essentially) incompatible.

THEORY OF THE AC RESPONSE OF ROUGH INTERFACES

It has been known for six decades that the small signal ac impedance of the interface between a blocking electrode and an aqueous or solid electrolyte frequently contains a constant-phase-angle (CPA) element whose impedance has the frequency dependence according to Z ∝ (jω)−η, where 0 < η < 1. In recent years it has been shown experimentally that the exponent η is related to the roughness of the interface, with η approaching 1 when the interface is made increasingly smooth. We propose that the CPA originates from the fractal geometry of the rough interface, and derive on the basis of a number of models that η = 3 - ds, where ds is the fractal dimension of the interface.

Crossover from real space to intraband pairing in the copper oxide superconductors

Abstract We have investigated BCS-like models of layered superconductors with N = 2 conducting layers per unit cell, both in the real space or discrete layer representation, and in the band representation with interband pairing projected out. The single quasiparticles are assumed to propagate as free particles within the conducting layers with effective masses m 1 and m 2 , and tunnel between neighboring layers with matrix elements J 1 and J 2 ,respectively. Intralayer pairing with strengths δ 01 , δ 02 and interlayer pairing with strengths δ 1 , δ 2 are both considered. for all such processes, J 1 and J 2 are pairbreaking parameters for interband pairing. The transition temperatures for real space and intraband pairing are compared, and a crossover from real space to intraband pairing occurs as the interlayer hopping is increased. This crossover usually occurs when J max / gw c ≈ 1, where J max is the maximum interlayer tunneling matrix element, and ω c is the BCS cutoff energy for the appropriate pairing process, but can sometimes occur for smaller J max values.

Change of island density due to multi-channels of adatom diffusion

Recent experimental studies on surfactant-assisted thin film growth indicate that there is a strong possibility that adatoms can diffuse both on top of and under the surfactant layer. We present here a model of growth to study the effects of multi-channels of diffusion on the island density. We find that there can be four different regimes as temperature of growth increases from low to very high values. We find that there is a scaling relation of island density with deposition flux and temperature in each regime. The transition temperatures are found to be connected to the system parameters such as barriers to diffusion.

Electronic structure of the hypothetical electrode material PtWO3

Abstract We have calculated the energy bands and the density of electronic states of the hypothetical solid PtWO3. The results confirm that the electronic structure of this material is very similar to that of Pt metal, and this may be the reason for the high electrocatalytic activity of certain Pt contaminated sodium tungsten bronze electrodes.

Density of states and tunneling characteristics of layered superconductors

We have studied the structure of the density-of-states (DOS) curves and tunneling characteristics of layered superconductors with two distinct layers in a unit cell. In general, the peaks of the DOS curves do not correspond to energy gaps of each layer, but depend on the gaps and the interlayer hopping strengths in a complex manner. This makes the interpretation of tunneling data of layered superconductors much less straightforward than isotropic superconductors. Our simulated tunneling characteristics bear certain resemblance to experimental results.

Energy gap structure and tunneling characteristics of layered superconductors

The authors have analyzed the energy gaps and density-of-states (DOS) of layered superconductors with two inequivalent layers in a unit cell along the c-axis. In the physically interesting parameter range where the interlayer hopping strengths of the quasiparticles are comparable to the critical temperature, the peaks in the DOS curve do not correspond to the order parameters (OP`s) of each layer, but depend on the OP`s and the interlayer hopping strengths in a complex manner. In contrast to a BCS superconductor, the DOS of layered systems have logarithmic singularities. The simulated tunneling characteristics bear close resemblance to experimental results.

A Fractal Model for Charge Diffusion Across a Rough Interface

It would appear to be a simple matter to describe the process of charge transfer across the interface between two substances (e.g., electrode and electrolyte): there is ohmic resistance in each material and a capacitance across the interface.

A fast and accurate method for the calculation of orbital susceptibility and form factor of paramagnetic transition metals

Abstract We describe a new method for calculating the orbital contribution to the susceptibility and neutron magnetic form factor of paramagnetic transition metals. The method has been developed by us over the past four years, and the computational details and results will be published elsewhere. In this paper we discuss the theoretical issues, which include a justification of the basic approximation and the estimate of errors. It is shown that it gives reliable results for the size of the susceptibility and the overall shape of the form factor, but is probably not sufficiently accurate to account for the anisotropy in the orbital moment distribution.