Electrokinetics of nanochannels and porous membranes with dynamic surface charges

The present thesis deals with fundamental aspects of mass-transport in the context of nanofluidics. One of the goals is to obtain a fundamental understanding of the working principles of nanofluidic mass-transport which can be applied in a macroscopic setting. To this end, we have developed a model framework that combines electrostatics, ionic transport, hydrodynamics, bulk solution equilibrium chemistry, and surface equilibrium chemistry. As detailed below, we use our model framework to analyze and interpret nanofluidic experiments and for theoretical predictions of novel nanofluidic phenomena.
First, we investigate how the surface dissociation constants and Stern layer capacitance depend on the local environment in terms of surface coating. Thus, we study the behavior of both bare and cyanosilane coated silica nanochannels subjected to two independent experiments. One experiment is particularly interesting because it relies on capillary filling, so it avoids the use of external forcing such as electric fields. Basically, during the filling of nanochannels by capillary action, the advancing electrolyte is titrated by deprotonation from the surface. This is observed using the pH-sensitive fluorescent dye fluorescein. The method relies on the large surface-to-volume ratio in the nanochannel and is thus a great example of a novel nanofluidic technique. Additionally, these measurements are complemented by current-monitoring in which an externally driven electro-osmotic (EO) flow velocity is used to estimate the zeta potential of the wall. Together, the two experiments provide independent data that are interpreted using our model framework. Solving the model self-consistently, while adjusting the low-value surface dissociation constant and the Stern capacitance, we obtain their dependence on the local surface condition in terms of surface coating.
Second, we investigate the streaming current resulting from an applied pressure difference in bare and surface-coated silica nanochannels. The channels have a low aspect ratio. Thus, we develop an effective boundary condition for the surface chemistry and apply our model in the 2-D cross section. Theoretically, we use our model to investigate the effects of corners in nanochannels on the electrochemical properties of the surface. As above, the streaming-current measurements are supplemented by current-monitoring data, and our model predicts both streaming current and EO flow velocity using only parameters from the literature. Moreover, over 48 hours there is a steady rise in the streaming current which we ascribe to silica dissolution. Using our model, we estimate the dissolution rate as a function of buffer type and surface condition.
Third, in bare silica nanochannels, our model predicts a hitherto unnoticed minimum in the electrical conductance as the salt concentration decreases. Our model predicts the behavior of the minimum in the conductance for different conditions including CO₂ content, supporting buffer type, and nanochannel height. Notably, we find that the conductance minimum is mainly caused by hydronium ions, and in our case almost exclusively due to carbonic acid generated from the dissolution of CO₂ from the atmosphere. We carry out delicate experiments and measure the conductance of silica nanochannels as a function of decreasing salt concentration. The measurements conform with the model prediction, both for a pure salt buffer and a buffer with extra hydronium ions added, in this case through HCl. In any case, the model prediction is supported by the appearance of the conductance minimum in several independent studies in the literature.
Fourth, we use our model to predict a novel phenomenon called currentinduced membrane discharge (CIMD) to explain over-limiting current in ionexchange membranes. The model is based on dynamic surface charges in the membrane in equilibrium with the buffer. However, here we take the next step and consider strong out-of-equilibrium transport across the membrane. Our model predicts large pH variations in the electrodialysis system that in turn lowers the ion-selectivity of the membrane by protonation reactions. This opens up for significant over-limiting current. We use our model to investigate the dependence on reservoir concentration and pH. Even without fluid flow, CIMD predicts overlimiting current and even a suppression of the extended space charge layer and thus a suppression of the electro-osmotic instability. Future work will include comparison with experimental data which is a delicate procedure that requires much attention to the comparability between the conditions in the model and in the experiment.
Finally, we make a small digression and study induced-charge electro-osmosis (ICEO) and the validity of common EO slip formulae as a function of a finite Debye screening length and the system geometry (here the metal-strip height). The slip models are strictly only valid in the limit of a vanishing screening length. Compared to a full boundary-layer resolving model, we show surprisingly large deviations even for relatively thin screening layers. Both slip models are based on the classical Helmholtz–Smoluchowski expression, and while one assumes a static screening layer, the other takes surface conduction into account.