Diffusion, drift and their interrelation through volume density

International audienceThe evolution of the understanding of the mass transport phenomena in solids and liquids reduce the gap between these continua and allow for the unification of phenomenological models. We consider the central Darken problem of the choice of the coordinate axes for diffusion. Namely, the definition of this mode of motion and the method how diffusion displacement is defined and measured. In our analysis we extensively use the Euler's and Liouville theorems. We derive the formula of volume density conservation, i.e., the volume continuity equation. This fundamental formula defines the volume-fixed frame of reference in the multicomponent, solid, gas and liquid solutions. The volume fixed frame of reference is self-consistent with the foundations of linear irreversible thermodynamics except recognizing the need to add volume density to the usual list of extensive physical properties undergoing transport in every continuum. Proposed modifications are self-consistent with the literature dating back to Onsager, the experiments of Kirkendall, their interpretation by Darken and recent generalized formulations. It will be shown that the method can be used in mechano-chemistry and electro-mechano-chemistry

Computer simulations of electrodiffusion problems based on Nernst-Planck and Poisson equations

A numerical procedure based on the method of lines for time-dependent electrodiffusion transport has been developed. Two types of boundary conditions (Neumann and Dirichlet) are considered. Finite difference space discretization with suitably selected weights based on a non-uniform grid is applied. Consistency of this method and the method put forward by Brumleve and Buck are analysed and compared. The resulting stiff system of ordinary differential equations is effectively solved using the RADAU5, RODAS and SEULEX integrators. The applications to selected electrochemical systems: liquid junction, bi-ionic case, ion selective electrodes and electrochemical impedance spectroscopy have been demonstrated. In the paper we promote the use of the full form of the Nernst-Planck and Poisson (NPP) equations, that is including explicitly the electric field as an unknown variable with no simplifications like electroneutrality or constant field assumptions. An effective method of the numerical solution of the NPP problem for arbitrary number of ionic species and valence numbers either for a steady state or a transient state is shown. The presented formulae - numerical solutions to the NPP problem - are ready to be implemented by anyone. Moreover, we make the resulting software freely available to anybody interested in using it. (C) 2012 Elsevier B.V. All rights reserved

Electrochemical Impedance Spectroscopy (EIS) of ion sensors Direct modeling and inverse problem solving using the Nernst-Planck-Poisson (NPP) model and the HGS(FP) optimization strategy

The Nernst-Planck-Poisson (NPP) model is used to numerically simulate electrochemical impedance spectra (EIS) of ion-selective electrodes (ISEs). By using the Hierarchical Genetic Strategy with real number encoding (HGS(FP)) the reverse problem is solved. The NPP-HGS(FP) method allows estimation of physicochemical parameters of ISEs with plastic membranes, which is illustrated here by using NPP-HGS(FP) for obtaining the values of the diffusion coefficients of ions in the ISE membrane phase.The NPP-HGS(FP) method allows calculation of the most accurate solution of the inverse problem and can be effectively used to facilitate the process of finding the parameters for optimal ISE performance.The method presented here not only allows for interpretation of the EIS spectra but also for accounting for the mechanism of the processes occurring at the interface in terms of physicoelectrochemically valid concepts. (C) 2011 Elsevier B.V. All rights reserved

Novel Strategy for Finding the Optimal Parameters of Ion Selective Electrodes

The detection limit (DL) of an analytical method determines the range of its applicability. For ion selective electrodes (ISE) used in potentiometric measurements, this parameter can vary by several orders of magnitude depending on the inner solution concentrations or the time of measurement. The detection limit of ISE can be predicted using the Nernst-Planck-Poisson model (NPP), as a general approach to the description of the time-dependent electro-diffusion processes. To find the optimal parameters, we need to formulate the inverse electro-diffusion problem. In this work, we combine the Nernst-Planck-Poisson model with the Hierarchical Genetic Strategy with real number encoding (HGS-FP). We use the HGS-FP method to approximate inner solution concentrations as well as the measuring time that provide a linear dependence of the membrane potential over the widest concentration range. We show that the HGS-FP method allows us to find the solution of the inverse problem. The presented calculations show a great future potential of the NPP method combined with the HGS-FP strategy

Modeling Non Equilibrium Potentiometry to Understand and Control Selectivity and Detection Limit

The majority of present theoretical interpretations of ion-sensor response focus on phase boundary potentials. They assume electroneutrality and equilibrium or steady-state, thus ignoring electrochemical migration and time-dependent effects, respectively. These theoretical approaches, owing to their idealizations, make theorizing on ion distributions and electrical potentials in space and time domains impossible. Moreover, they are in conflict with recent experimental reports on ion-sensors, in which both kinetic (time-dependent) discrimination of ions to improve selectivity, and non-equilibrium transmembrane ion-transport for lowering detection limits, are deliberately used.For the above reasons, the Nernst-Planck-Poisson (NPP) equations are employed here to model the non-equilibrium response in a mathematically congruent manner. In the NPP model, electroneutrality and steady-state/equilibrium assumptions are abandoned. Consequently, directly predicting and visualizing the selectivity and the low detection limit variability over time, as well as the influence of other parameters, i.e. ion diffusibility, membrane thickness and permittivity, and primary to interfering ion concentration ratios on ion-sensor responses, are possible. Additionally, the NPP allows for solving the inverse problem i.e. searching for optimal sensor properties and measurement conditions via target functions and hierarchical modeling. The conditions under which experimentally measured selectivity coefficients are true (unbiased) and detection limits are optimized are demonstrated, and practical conclusions relevant to clinical measurements and bioassays are derived

Breakthrough in Modeling of Electrodiffusion Processes; Continuation and Extensions of the Classical Work of Richard Buck

In 1978 Brumleve and Buck published an important paper [1] pertaining to numerical modeling of electrodiffusion. At the time their approach was not immediately recognized and followed. However, it has changed since the beginning of 21st century. The approach of Brumleve and Buck based on Nernst-Planck-Poisson (NPP) equations is utilized to model transient behavior of various electrochemical processes. Multi-layers and reactions allow extending applications to selectivity and low detection limit with time variability, influence of parameters (ion diffusivities, membrane thickness, permittivity, rate constants), and ion interference on ion-sensor responses. Solution of NPP inverse problem allows for optimizing sensor properties and measurement environment. Conditions under which experimentally measured selectivity coefficients are true (unbiased) and detection limit is optimized are demonstrated. Impedance spectra obtained directly from NPPs are presented. Modeling durability and diagnosis of reinforced concrete is presented. Chlorides transport in concrete is modeled using NPPs and compared to other solutions

Ghosts of other stories: a synthesis of hauntology, crime and space

Criminology has long sought to illuminate the lived experience of those at the margins. More recently, there has been a turn toward the spatial in the discipline. This paper sets out an analytical framework that synthesizes spatial theory with hauntology. We demonstrate how a given space's violent histories can become embedded in the texts that constitute it and the language that describes it. The art installation ‘Die Familie Schneider’ is used as an example of how the incorporation of social trauma can lead to the formation of a spatial “crypt”. Cracking open this “crypt” allows us to draw out Derrida's notion of the specter within the context of a “haunted” city space