Charge storage in nanotubes: the case of a 2-1 electrolyte

We consider a 2-1 electrolyte in contact with a narrow nanotube, which only allows one-dimensional storage along the axis. The asymmetry does not allow an a priori definition of the potential of zero charge; instead, the natural reference is the electrode potential at which both ions have the same electrochemical potential; the value of the latter can serve as a measure of ionophilicity. Near this potential, ionophobic tubes are filled with a dilute gas, ionophilic tubes are filled with a one-dimensional solid containing about the same number of the divalent ions and the monovalent counterions, a structure that is stabilized by a strong screening of the Coulomb interaction by an induced counter charge on the walls of the tube. The filling of the tube by the application of an electrode potential exhibits a complicated pattern of interactions between the two kinds of ions.Comment: 7 pages, 6 figure

Efimov universality with Coulomb interaction

The universal properties of charged particles are modified by the presence of a long-range Coulomb interaction. We investigate the modification of Efimov universality as a function of the Coulomb strength using the Gaussian expansion method. The resonant short-range interaction is described by Gaussian potentials to which a Coulomb potential is added. We calculate binding energies and root mean square radii for the three- and four-body systems of charged particles and present our results in a generalised Efimov plot. We find that universal features can still be discerned for weak Coulomb interaction, but break down for strong Coulomb interaction. The root-mean-square radius plateaus at increasingly smaller values for strong Coulomb interaction and the probablity distributions of the states become more concentrated inside the Coulomb barrier. As an example, we apply our universal model to nuclei with an alpha-cluster substructure. Our results point to strong non-universal contributions in that sector.Comment: 18 pages, 9 figures, final version (with small orthographical corrections

Universal physics of bound states of a few charged particles

We study few-body bound states of charged particles subject to attractive zero-range/short-range plus repulsive Coulomb interparticle forces. The characteristic length scales of the system at zero energy are set by the Coulomb length scale $D$ and the Coulomb-modified effective range $r_{\mathrm{eff}}$. We study shallow bound states of charged particles with $D\gg r_{\mathrm{eff}}$ and show that these systems obey universal scaling laws different from neutral particles. An accurate description of these states requires both the Coulomb-modified scattering length and the effective range unless the Coulomb interaction is very weak ($D\to \infty$). Our findings are relevant for bound states whose spatial extent is significantly larger than the range of the attractive potential. These states enjoy universality -- their character is independent of the shape of the short-range potential.Comment: 8 pages, 6 figures, extended discussion, results unchanged, to appear in Phys. Lett.

Electron Transfer Reaction Through an Adsorbed Layer

We consider electron transfer from a redox to an electrode through and adsorbed intermediate. The formalism is developed to cover all regimes of coverage factor, from lone adsorbate to monolayer regime. The randomness in the distribution of adsorbates is handled using coherent potential approximation. We give current-overpotential profile for all coverage regimes. We explictly analyse the low and high coverage regimes by supplementing with DOS profile for adsorbate in both weakly coupled and strongly coupled sector. The prominence of bonding and anti-bonding states in the strongly coupled adsorbates at low coverage gives rise to saddle point behaviour in current-overpotential profile. We were able to recover the marcus inverted region at low coverage and the traditional direct electron transfer behaviour at high coverage

Nanoscale electrochemistry of sp2 carbon materials: from graphite and graphene to carbon nanotubes

Carbon materials have a long history of use as electrodes in electrochemistry, from (bio)electroanalysis to applications in energy technologies, such as batteries and fuel cells. With the advent of new forms of nanocarbon, particularly, carbon nanotubes and graphene, carbon electrode materials have taken on even greater significance for electrochemical studies, both in their own right and as components and supports in an array of functional composites. With the increasing prominence of carbon nanomaterials in electrochemistry comes a need to critically evaluate the experimental framework from which a microscopic understanding of electrochemical processes is best developed. This Account advocates the use of emerging electrochemical imaging techniques and confined electrochemical cell formats that have considerable potential to reveal major new perspectives on the intrinsic electrochemical activity of carbon materials, with unprecedented detail and spatial resolution. These techniques allow particular features on a surface to be targeted and models of structure–activity to be developed and tested on a wide range of length scales and time scales. When high resolution electrochemical imaging data are combined with information from other microscopy and spectroscopy techniques applied to the same area of an electrode surface, in a correlative-electrochemical microscopy approach, highly resolved and unambiguous pictures of electrode activity are revealed that provide new views of the electrochemical properties of carbon materials. With a focus on major sp2 carbon materials, graphite, graphene, and single walled carbon nanotubes (SWNTs), this Account summarizes recent advances that have changed understanding of interfacial electrochemistry at carbon electrodes including: (i) Unequivocal evidence for the high activity of the basal surface of highly oriented pyrolytic graphite (HOPG), which is at least as active as noble metal electrodes (e.g., platinum) for outer-sphere redox processes. (ii) Demonstration of the high activity of basal plane HOPG toward other reactions, with no requirement for catalysis by step edges or defects, as exemplified by studies of proton-coupled electron transfer, redox transformations of adsorbed molecules, surface functionalization via diazonium electrochemistry, and metal electrodeposition. (iii) Rationalization of the complex interplay of different factors that determine electrochemistry at graphene, including the source (mechanical exfoliation from graphite vs chemical vapor deposition), number of graphene layers, edges, electronic structure, redox couple, and electrode history effects. (iv) New methodologies that allow nanoscale electrochemistry of 1D materials (SWNTs) to be related to their electronic characteristics (metallic vs semiconductor SWNTs), size, and quality, with high resolution imaging revealing the high activity of SWNT sidewalls and the importance of defects for some electrocatalytic reactions (e.g., the oxygen reduction reaction). The experimental approaches highlighted for carbon electrodes are generally applicable to other electrode materials and set a new framework and course for the study of electrochemical and interfacial processes

Electron tunneling between two electrodes mediated by a molecular wire containing a redox center

We derive an explicit expression for the quantum conductivity of a molecular wire containing a redox center, which is embedded in an electrochemical environment. The redox center interacts with the solvent, and the average over the solvent configurations is performed numerically. Explicit calculations have been performed for a chain of three atoms. When the redox center interacts strongly with neighboring electronic levels, the current-potential curves show interesting features like rectification, current plateaus and negative differential resistance. Electronic spectroscopy of intermediate states can be performed at constant small bias by varying the electrochemical potential of the wire

The rate of electron-transfer reactions in the diffusive limit

A simple electron-transfer reaction is treated in the diffusive limit, in which the motion of the solvent is governed by the Smoluchowski equation. The electronic transition probability is calculated from the Landau-Zener expression. The rate constant of the reaction is calculated as a function of the strength of the electronic interaction between the reactants. For weak interactions, the rate is the same as that obtained form first-order perturbation theory. For strong interactions, solvent dynamics is rate-determining. The calculations presented here bridge these two limits.Проста реакція електронного переносу розглядається в дифузійній границі, в якій рух розчинника описується рівнянням Смолуховського. Імовірність електронного переходу розраховується з виразу Ландау-Зенера. Константа реакції розрахована як функція сили електронної взаємодії між реактантами. Для слабких взаємодій ступінь реакції співпадає з виразом, отриманим в першому наближенні теорії збурень. Для сильних взаємодій динаміка розчинника визначається ступенем реакції. Представлені розрахунки поєднують обидві границі

Double layer of Platinum Electrodes: Non-Monotonic Surface Charging Phenomena and Negative Double Layer Capacitance

In this study, the refined double layer model of platinum electrodes accounts for chemisorbed oxygen species, oriented interfacial water molecules and ion size effects in solution. It results in a non-monotonic surface charging relation and a peculiar capacitance vs. potential curve with a maximum and maybe negative-defined values in the potential regime of oxide-formation. &nbsp

Considerations for an Ac Dipole for the LHC

Following successful experience at the BNL AGS, FNAL Tevatron, and CERN SPS, an AC Dipole will be adopted at the LHC for rapid measurements of ring optics. This paper describes some of the parameters of the AC dipole for the LHC, scaling from performance of the FNAL and BNL devices.Comment: proceedings of the 2007 Particle Accelerator Conferenc