Bartłomiej Wierzba

Three-dimensional interdiffusion under stress field in Fe-Ni-Cu alloys

We present the method of solving the mechanochemical transport problem in multicomponent solid solutions, namely, the method of quantitative description of the interdiffusion (ID) under the stress field. We postulate that the velocities appearing in the momentum balance equation should be the drift and diffusion velocity. The energy, momentum, and mass transport are diffusion controlled, and the diffusion fluxes of the components are given by the Nernst-Planck formulas. The diffusion depends on the chemical potential gradient and on the stress that can be induced solely by the diffusion as well as by the boundary conditions. The key results lie in the interpretation of the Navier-Lamé equation for the deformed regular crystal, where the concentrations are not uniform and ID occurs. The presented coupling of the Darken and CALPHAD methods with the momentum balance equation allows for quantitative analysis of the transport processes occurring on entirely different time scales. It is shown that the proposed method is effective for modeling transport processes in Fe-Ni-Cu alloys. We demonstrate the case of ID in a planar plate, and predict slower penetration and accumulation. The experimental results confirm theoretical predictions.

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 electrodiffusion 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.

The Stress Field Induced Diffusion

The mathematical description of the mass transport in multicomponent solution is presented. Model base on Darken concept of the drift velocity. In order to present an example of the real system we restrict analysis to an isotropic solid and liquids for which Navier equation holds. The diffusion of components depends on the chemical potential gradients and on the stress that can be induced by the diffusion and by the boundary and/or initial conditions. In such quasi-continuum the energy, momentum and mass transport are diffusion controlled and the fluxes are given by the Nernst-Planck formulae. It is show that the Darken method combined with Navier equations is valid for solid solutions as well as multi component liquids.