Electrodes are modified with polymer films to grant novel permeability. Often, redox probes partition from solution into film and are electrolyzed at the electrode. This creates a flux of probe into the polymer film and a flux of electrolyzed probe out of the polymer film. Transport of the probe through the film is governed by diffusion and migration, mathematically described from the Nernst-Planck equation as J_{i}=-D_{i}((∂C_{i}(x,t))/(∂x))-((z_{i}F)/(RT))D_{i}C_{i}(x,t)((∂Φ(x,t))/(∂x)) where x is the distance from the electrode, t is time, C_{i}(x,t) is space and time dependant concentration of the probe i, z_{i} is the charge of the probe i, F is Faraday's constant, R is the gas constant, T is absolute temperature, J_{i} is the flux of the probe i, D_{i} is the diffusion constant of the probe i and Φ(x,t) is the space and time dependant potential. In most natural systems, charge accumulation is not appreciably noticed, the system behaves in such a way that a charged ion is neutralized by a counterion. This is called electroneutrality and is mathematically represented by Laplace's condition on the potential, ((∂²Φ)/(∂x²))=0. In some systems, it is not clear if counterions are readily available to neutralize an ion. In such a system, there may not be electroneutrality, giving Poisson's equation to replace Laplace's condition as ((∂²Φ)/(∂x²))=-(F/ɛ)∑_{i}z_{i}C_{i}(x,t) where ɛ is the relative permittivity. The addition of Poisson's condition makes the system nonsolvable. In addition, the magnitude of F/ɛ creates difficulty simulating the system using standard techniques. The first system investigated determines the concentration and potential profiles over the polymer membrane of a fuel cell without electroneutrality. In some systems, the probes can not easily diffuse around each other, certain polymer film environments prevent such a swap of location as diffusion is commonly thought to occur. A more generalized form of the Nernst-Planck equation describes spatially varying diffusion coefficient as J=-D(x,t)((∂C(x,t))/(∂x))-((zF)/(RT))D(x,t)C(x,t)((∂Φ(x,t))/(∂x)). D(x,t) is space and time dependent diffusion, usually thought of with a physical diffusion term and an ion hopping term. The second system this thesis investigates is a modified electrode system where electron hopping is responsible for a majority of the probe transport within the film. Lastly, the beginnings of a method are presented to easily determine the physical diffusion rate of a probe within a modified electrode system based on known system parameters.

The concepts of electroneutrality coupling and electron-hopping, which are useful for the incorporation of functional components and transportation of electrons, were applied in this project. Discrete layered structures were fabricated by sequential electropolymerization to modulate the performances of formate biosensors. Different types of layers, with or without enzyme, were successfully grown on the electrode surface. The presence of the enzyme (formate dehydrogenase), co-factor (B-nicotinamide adenine dinucleotide) and an electron mediator in the polypyrrole film was verified by scanning electron microscopy, chronopotentiometry, cyclic voltammetry and amperometric measurements. Monolayer, bilayer and trilayer formate biosensors were successfully fabricated for different analytical purposes. The utilisation of the biosensing membrane for the reliable batch and FIA determination of formate based on a amperometric mode of detection are explored. Electron mediators such as ferrocyanide, Prussian Blue, ferrocene and ferrocene carboxylic acid were incorporated into the polypyrrole film to lower the required applied potential for amperometric sensing and to maintain the conductivity and stability of the polypyrrole backbone. The application of artificial neural networks (ANN) to overcome the problem of reusability and reproducibilty in a nonlinear and complicated dynamic system is also considered. The resulting system was trained with a new neural network based software package, Turbo Neuron, for prediction of the concentration of formate, based on the entire collected data, which contain the history of the detection experiments. The proposed integrated ANN conducting polymer biosensor enables the determination of formate concentration, both online and in real time / Doctor of Philosophy (PhD)

Electrolytic solutions contain mobile ions that can pass current, and are essential components of any solution-phase electrochemical system. The Nernst–Planck–Poisson equations describe the electrodynamics and transport dynamics of electrolytic solutions. This thesis applies modern numerical and mathematical techniques in order to solve these equations, and hence determine the behaviour of electrochemical systems involving charge transport. The following systems are studied: a liquid junction where a concentration gradient causes charge transport; an ideally polarisable electrode where an applied potential difference causes charge transport; and an electrochemical cell where electrolysis causes charge transport. The nanometre Debye length and nanosecond Debye time scales are shown to control charge separation in electrolytic solutions. At equilibrium, charge separation is confined to within a Debye length scale of a charged electrode surface. Non-equilibrium charge separation is compensated in solution on a Debye time scale following a perturbation, whereafter electroneutrality dictates charge transport. The mechanism for the recovery of electroneutrality involves both migration and diffusion, and is non-linear for larger electrical potentials. Charge separation is an extremely important consideration on length scales comparable to the Debye length. The predicted features of capacitive charging and electrolysis at nanoelectrodes are shown to differ qualitatively from the behaviour of larger electrodes. Nanoscale charge separation can influence the behaviour of a larger system if it limits the overall rate of mass transport or electron transfer. This thesis advocates the use of numerical methods to solve the Nernst–Planck–Poisson equations, in order to avoid the simplifying approximations required by traditional analytical methods. As this thesis demonstrates, this methodology can reveal the behaviour of increasingly elaborate electrochemical systems, while illustrating the self-consistency and generality of fundamental theories concerning charge transport.

Electrodialysis performance strongly depends on the boundary layer near ion exchange membranes. The thickness of the boundary layer has not been clearly evaluated due to its substantial fluctuation around the spacer geometry. In this study, the boundary layer thickness was defined with three statistical parameters: the mean, standard deviation, and correlation coefficient between the two boundary layers facing across the spacer. The relationship between the current and potential under conditions of the competitive transport between mono- and di-valent cations was used to estimate the statistical parameters. An uncertainty model was developed for the steady-state ionic transport in a two-dimensional cell pair. Faster ionic separations were achieved with smaller means, greater standard deviations, and more positive correlation coefficients. With the increasing flow velocity from 1.06 to 4.24 cm/s in the bench-scale electrodialyzer, the best fit values for the mean thickness reduced from 40 to less than 10 μm, and the standard deviation was in the same order of magnitude as the mean. For the partitioning of mono- and di-valent cations, a CMV membrane was examined in various KCl and CaCl₂ mixtures. The equivalent fraction correlation and separation factor responded sensitively to the composition of the mixture; however, the selectivity coefficient was consistent over the range of aqueous-phase ionic contents between 5 and 100 mN and the range of equivalent fractions of each cation between 0.2 and 0.8. It was shown that small analytic errors in measuring the concentration of the mono-valent cation are amplified when estimating the selectivity coefficient. To minimize the effects of such error propagation, a novel method employing the least square fitting was proposed to determine the selectivity coefficient. Each of thermodynamic factors, such as the aqueous- and membrane-phase activity coefficients, water activity, and standard state, was found to affect the magnitude of the selectivity coefficient. The overlimiting current, occurring beyond the electroneutral limit, has not been clearly explained because of the difficulty in solving the singularly perturbed Nernst-Planck-Poisson equations. The steady-state Nernst-Planck-Poisson equations were converted into the Painlevé equation of the second kind (P[subscript II] equation). The converted model domain is explicitly divided into the space charge and electroneutral regions. Given this property, two mathematical formulae were proposed for the limiting current and the width of the space charge region. The Airy solution of the P[subscript II] equation described the ionic transport in the space charge region. By using a hybrid numerical scheme including the fixed point iteration and Newton Raphson methods, the P[subscript II] equation was successfully solved for the ionic transport in the space charge and electroneutral regions as well as their transition zone. Above the limiting current, the sum of the ionic charge in the aqueous-phase electric double layer and in the space charge region remains stationary. Thus, growth of the space charge region involves shrinkage of the aqueous-phase electric double layer. Based on this observation, a repetitive mechanism of expansion and shrinkage of the aqueous-phase electric double layer was suggested to explain additional current above the limiting current. / text