טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentElad Doron
SubjectMathematical Modeling of Concentrated Electrolyte Solutions
DepartmentDepartment of Applied Mathematics
Supervisor Professor Nir Gavish


Abstract

Concentrated electrolyte solutions are key components in many biological systems, such as ion channels and active sites of enzymes, and are examined for a broad range of applications, such as dye sensitized solar cells, fuel cells, batteries, and super-capacitors.   Such solutions consist of positive and negative ions, which are dissolved in a solvent, forming a concentrated solution.  A common feature in all the aforementioned applications is the presence of a charged surface that attracts ions with an opposite charge and repels ions with the same charge. This results in the rearrangement of the ion distribution in the solution and in the formation of a few nanometers-long region next to the charged surface in which there is an excess of oppositely charged ions, screening the surface charge.


The theoretical description of electrolytes goes back to the 1890's with the formulation of the Poisson-Nernst-Planck (PNP) framework, known to be accurate for dilute electrolyte solutions under the influence of a moderately charged surface. Extensive research efforts were invested during the last century in extending the PNP approach to concentrated electrolyte solutions. Nevertheless, recent experimental observations show qualitative features that are beyond the scope of all existing generalized-PNP models. These phenomena include bulk self-assembly and underscreening, which affect the interfacial dynamics and the transport in these systems.

In the first part of this thesis, we present a thermodynamically consistent, unified framework for electrolyte solutions that captures the behavior of both dilute and concentrated electrolyte solutions. In contrast to all generalized-PNP models, the models from which the starting point of this study stems are models for ionic liquids with an explicit account of the solvent density. The resulting model captures the aforementioned phenomena, and, by using tools from pattern formation theory, reveals their underlying mathematical origin.

In the second part of this thesis, we examine steady-state solutions of the PNP equations in finite domains and the dependence of the arising solutions on natural parameters, such as the applied voltage on the surface and the domain size. By using singular perturbation theory, we derive an approximate solution for the steady-state equation, and then use this approximation to classify the parameter space into regions of confined domains, regions of large domains, and regions of infinite domains, where the domain size is so large that it can be accurately approximated by an infinite domain size.  The results are validated with numerical simulations.