Richard P. Buck

Numerical solution of the Nernst-Planck and poisson equation system with applications to membrane electrochemistry and solid state physics

Abstract An efficient finite difference simulation procedure for the steady state and transient solution of the Nernst-Planck and Poisson equation system is presented. The procedure is general and extremely efficient, containing refinements in time and distance scaling. The implicitly-formulated non-linear equations are solved with an iterative Newton-Raphson technique. The derivation is presented in sufficient detail for the reader to directly formulate similar computer codes. Steady state solutions, transient responses, and impedance-frequency responses are presented for a number of examples from the fields of membrane electrochemistry and solid state physics.

Kinetics of bulk and interfacial ionic motion: microscopic bases and limits for the nernst—planck equation applied to membrane systems

Abstract Criticisms of, limitations on, and alternatives to the Nernst—Planck equation for ionic transport are outlined in the context of motion into and through liquids, gels, ion-exchanger membranes, ionic crystals and polycrystalline materials, mainly in connection with their use as membranes. The origin of the equation from the point of view of Langevin and Onsager, and contributions of Schlogl provide a basis for discussion of limitations on applications to non-homogeneous materials. The surprising usefulness and wide applicability are demonstrated using correlations for diverse cases including coupled transport, association (ion pairing and clustering), adsorption and concentrated electrolytes. Some microscopic models for the friction coefficient, based on hole theory of liquid transport and vacancy transport in crystals are discussed in terms of atomic properties. These models were picked because they relate easily to the macroscopic Nernst—Planck equation. An attempt to show similarities of transport in liquid, semi-solid and crystalline membranes, and thereby to show why the Nernst—Planck equation seems to apply so widely, may fail to satisfy some specialists. Many complicated and subtle phenomena are discussed tersely and discussions rely on heuristic theories. New material on kinetic boundary conditions, slow ion exchange and ionic overpotential is presented.

Interpretation of Finite‐Length‐Warburg‐Type Impedances in Supported and Unsupported Electrochemical Cells with Kinetically Reversible Electrodes

The origin of finite-length-Warburg-type impedances in supported and unsupported systems is examined within a common framework and with reference to previous exact and approximate results. While close agreement is found between an approximate treatment based on bulk electroneutrality and an exact solution of the Nernst-Planck-Poisson equation system for unsupported systems of many Debye length thicknesses with rapid electrode reaction kinetics, the approximate treatment is unjustified when the electrode reaction is slow or the electrode separation is less than or comparable to the Debye length.

Flexible (Kapton-based) microsensor arrays of high stability for cardiovascular applications

The design, fabrication and performance characteristics of Kapton-based planar mini and semimicro potentiometric sensors with an Ag/AgCl or a quinhydrone-based redox internal reference electrode are described. The ion-selective membranes cast from conventional and various modified PVC matrices and containing different pH-sensitive ionophores are ranked on the basis of their performances in hostile environments. The adhesive bonding strength of the different PVC membranes to the polyimide-coated Kapton substrate was quantitatively evaluated as a function of fabrication procedure and sample solution contact. The long-term stability of the electrodes was characterized by the alterations of the analytical parameters of the sensors over a period of time, as well as by determining the resistance changes of their sensing membranes.

Recent Advances in Pharmaceutical Analysis with Potentiometric Membrane Sensors

Abstract The development and applications of ion-selective membrane electrodes continue to provide excitement in expanding areas of analytical chemistry, including analytical pharmaceutical research and analysis, because these sensors offer the advantages of simple design, construction, and manipulation, reasonable selectivity, fast response time, applicability to colored and turbid solutions, and possible interfacing with automated and computerized systems. The combination of membrane sensors with flow injection analysis (FIA) for the determination of various organic ions of biological interest (e.g., drugs) is a new promising area with many applications. This review covers the material that is of interest to those who deal with ion-selective electrodes in organic and pharmaceutical analysis.

Diffusion-migration impedances for finite, one-dimensional transport in thin layer and membrane cells: an analysis of derived electrical quantities and equivalent circuits

This paper presents analytical solutions for diffusion-migration impedances of four systems that can serve as a basis for analysis of redox membrane-coated electrode and electrolyte-bathed membrane cells. Two extreme cases have classical analogues: symmetric cells with constant numbers of carriers, such as Ag|AgNO3|Ag with and without excess supporting electrolyte, and asymmetric cells with variable numbers of carriers, such as Na(Hg)|NaCl|Pt,Cl2 with and without excess supporting electrolyte. Transmission line equivalent circuits are derived and analyzed. Time constants for impedances and responses under voltage steps are compared.

CHEMICALLY MODIFIED ELECTRODES: RECOMMENDED TERMINOLOGY AND DEFINITIONS

Chemically modified electrodes (CMEs) comprise a relatively modern approach to electrode systems that finds utility in (1) a wide spectrum of basic electrochemical investigations, including the relationship of heterogeneous electron transfer and chemical reactivity to electrode surface chemistry, electrostatic phenomena at electrode surfaces, and electron and ionic transport phenomena in polymers, and (2) the design of electrochemical devices and systems for applications in chemical sensing, energy conversion and storage, molecular electronics, electrochromic displays, corrosion protection, and electro-organic syntheses. Compared with other electrode concepts in electrochemistry, the distinguishing feature of a CME is that a generally thin film of a selected chemical is bonded or coated onto the electrode surface to endow the electrode with the chemical, electrochemical, optical, electrical, transport, and other desirable properties of the film in a rational, chemically designed manner. In this report, we have attempted to identify and define the most widely used terminology in the growing field of CMEs and to recommend a particular term in cases where a multiplicity of terms has arisen over the past several years or where previously defined terms have taken on broadened meanings for the special cases of CMEs. It is expected that additional terms will be added to this lexicon in the future as new research directions evolve.

Microfabricated amperometric creatine and creatinine biosensors

Miniaturized enzyme electrodes for determination of creatine and creatinine in serum are described. The creatine sensor is based on a bienzyme sequence, involving creatine amidinohydrolase (CI) and sarcosine oxidase (SO). For the creatinine sensor a third enzyme, creatinine amidohydrolase (CA), is added. The signals of both sensors are based on the oxidation of the hydrogen peroxide formed in the enzymatic layer to yield currents proportional to the concentration of creatine or creatinine in the sample solution. For the optimization of enzyme loadings several macro-size electrodes were tested. Crosslinking with glutaraldehyde was selected as the immobilization method for the enzymatic system. The substrate for the miniaturized sensors is a polyimide foil, on which film structures are built using well established microelectronic techniques. Biosensors based on this planar, thin and thick film technology, have shown extended linear range (up to 2 mM), good sensitivity and operational stability (at least 3 months) when tested in buffer solutions. A cellulose acetate inner membrane in combination with a polyurethane outer membrane significantly reduces in vitro response of the biosensors to common interferences such as ascorbic acid, uric acid and acetaminophen. The creatine and creatinine microfabricated sensors were tested in control human serum samples, where the detection limit was 20 μM and 30 μM, respectively. The experimental values are in agreement with the assigned values for creatinine in the control samples.

Ion selective electrodes, potentiometry, and potentiometric titrations

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Simple hierarchical impedance functions for asymmetric cells: Thin-layer cells and modified electrodes

Abstract The main result is a closed-form solution for concentration profiles, currents, potential distributions and impedances when electrons (polarons) and counter-ions have different transference numbers. Two cases are treated in detail and illustrated with the new Laplace inversion program: a single uni-univalent salt asymmetric cell and the related modified electrode with fixed positive sites, mobile electrons and counter-ions. The first case is a model of redox polymers with counter-anions. The second case is the metal redox center as the fixed site with mobile counter-ions, which illustrates a more complex stoichiometry. Methods for adding the isolated processes of bulk (geometric, high frequency) charging, interfacial kinetics, adsorption/reaction and ion pair or complex formation/dissociation to the total impedance function are emphasized. The nonlinearities of the continuity equation can be written in ways that cover both electron diffusion and electron hopping. The nonlinear effects can be minimized because certain time-dependent terms occur as ratios in the canonical single-species flux equations. In this proposal, based on extensive examples in the literature, the total impedance can be understood without generating the large complicated equations which occur when all processes are written into a single theory.