Date of Award
Master of Science (MS)
William R. Harrell
In this thesis, nanofluidic diodes were studied theoretically using fundamental physics as a basis. A comprehensive theory was constructed for ion current rectification (ICR) in nanofluidic systems, written from an engineering and physics perspective. The primary goal of this work was to clarify the fundamental theory of ICR through the interpretation and consideration of various literature sources on the topic, which often use contradictory definitions and simplifications. New figures were created for this research to more effectively convey and clarify vital concepts such as electric double layers (EDL), and included multiple definitions to compare different theoretical approaches. Lastly, a simulation was written to apply our developed theory by numerically modeling the electric potential profile in a nanofluidic diode of asymmetric ion concentration. The simulation results were interpreted to help visualize the formation of EDL in the system, and to conceptualize the mechanisms producing ICR. Three main types of nanofluidic diodes were identified by their characteristic asymmetries and studied in-depth: asymmetry in fixed wall charge, asymmetry in ion concentration, and asymmetry in channel diameter. Foundational electrostatic physics equations, such as the Poisson-Boltzmann equation and Ohm’s law, were derived and manipulated to produce important equations describing electric potential and ion current conductivity in nanofluidic systems. Several of these – the Debye-Hückel approximation of the Poisson-Boltzmann equation, the Debye screening length equation, and the Grahame equation – were later used in the simulation of electric potential profiles. Building on fundamental concepts, the Poisson-Nernst-Planck (PNP) equations were shown to describe the sources of ion movement in nanofluidics in the form of a self-consistent set of coupled mean-field equations. Utilizing these equations and employing electric potential and ion current conductivity relationships, the three main types of nanofluidic diodes were analyzed to examine their sources of ICR, and each was explained through molecular-level behavioral considerations at different applied voltages. Based on the theory developed to explain ICR, a theoretical causal chain for ICR was identified. To visualize asymmetrical electrostatic impact, which is the foundational requirement for ICR to be present in a nanofluidic system, electric potential profiles were simulated for a nanofluidic diode of asymmetric ion concentration. Using the Grahame equation and the Debye length equation to substitute values into the Debye-Hückel approximation, the electric potential was numerically calculated for the example system in equilibrium, forward bias and reverse bias. The simulation results qualitatively agreed with similar models from the literature which were obtained through PNP and analytical methods. Analysis of our simulation results using the theory we developed revealed the importance of an electric potential well which forms near one opening of the nanochannel. This “trench” causes ion accumulation, which increases that ion’s conductivity. Applying forward voltage bias results in this high conductivity at the ions’ entrance, while reverse bias results in the high conductivity at the ions’ exit. Thus, forward bias is characterized by greater ion flux into the channel than out of it, increasing overall ion concentration in the channel and promoting higher ion current through the system. Reverse bias is characterized by greater ion flux out of the channel than into it, decreasing overall ion concentration in the channel and suppressing ion current through the system. Asymmetry in electrostatic impact is therefore sufficient to explain ion current rectification in nanofluidic diodes, and the simulation results were used to illustrate this theoretical discussion.
Proctor, Julia Ellen, "Theory of Ion Transport and Ion Current Rectification in Nanofluidic Diodes" (2021). All Theses. 3619.