Downloaded from orbit.dtu.dk on: Oct 06, 2021 Electrokinetics of nanochannels and porous membranes with dynamic surface charges Andersen, Mathias Bækbo Publication date: 2012 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Andersen, M. B. (2012). Electrokinetics of nanochannels and porous membranes with dynamic surface charges. Technical University of Denmark. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Electrokinetics of nanochannels and porous membranes with dynamic surface charges Mathias Bækbo Andersen PhD thesis, 31 March 2012 Advisor: Prof Henrik Bruus Copyright © 2012 Mathias Bækbo Andersen All Rights Reserved Technical University of Denmark Department of Micro- and Nanotechnology Building 345 East, DK-2800 Kongens Lyngby, Denmark Phone +45 45255700, Fax +45 45887762 [email protected] http://www.nanotech.dtu.dk https://sites.google.com/site/baekbo Abstract The present thesis deals with fundamental aspects of mass-transport in the con- text 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 equilib- rium 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 in- teresting 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 measure- ments 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 inter- preted 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 pres- sure 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 mea- surements are supplemented by current-monitoring data, and our model predicts iv 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 cur- rent 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 con- ditions 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 current- induced membrane discharge (CIMD) to explain over-limiting current in ion- exchange 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 sig- nificant over-limiting current. We use our model to investigate the dependence on reservoir concentration and pH. Even without fluid flow, CIMD predicts over- limiting 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. Resumé Denne afhandling omhandler grundlæggende aspekter ved masse-transport i na- nofluidik. Et af målene er at opnå en grundlæggende forståelse af de gældende principper for nanofluidisk masse-transport, som så kan anvendes i makroskopiske systemer. Til dette formål har vi udviklet en model der kombinerer elektrosta- tik, ion transport, hydrodynamik, ligevægtskemi i opløsning og ligevægtskemi på overflader. Som beskrevet nedenfor bruger vi vores model til at analysere og fortolke nanofluidik eksperimenter og til at lave teoretiske forudsigelser af nye nanofluidiske fænomener. For det første undersøger vi hvordan ligevægtskonstanter og Stern-kapacitans afhænger af det lokale overflademiljø i form af overfladebelægning. Vi studerer både rene og cyanosilane-belagte silika nanokaneler i to uafhængige eksperimen- ter. Et eksperiment er særligt interessant, idet det bygger på kapillærfyldning, så brugen af eksterne drivfelter, såsom elektriske felter, undgås. Kort sagt bliver elek- trolytten titreret af silika væggen under kapillærfyldningen. Vi observerer dette ved at anvende et pH-følsomt fluorescerende farvestof kaldet fluorescein. Metoden afhænger af det store overflade-til-volumen forhold i nanokanelen og er således et godt eksempel på en nyskabende nanofluidisk teknik. Disse kapillærfyldninger er derudover suppleret med strøm-overvågnings forsøg, hvori en eksternt drevet elektro-osmotisk (EO) strømning anvendes til at estimere zeta potentialet på væg- gen. Tilsammen giver de to eksperimenter uafhængig data, der fortolkes ved hjælp af vores model. Modellen løses selv-konsistent, medens værdien af ligevægtskon- stanten og Stern kapacitansen optimeres. Således får vi belyst disse parametres afhængighed af den lokale tilstand på overfladen i form af overfladebelægning. For det andet undersøger vi advektionsstrøm afledt af en påført trykforskel i rene og overfladebelagte silika nanokaneler. Kanalerne har et forhold mellem højde og bredde tæt på een. Vi har derfor udviklet en effektiv randbetingelse for overfladekemien og anvendt vores model i det 2-dimensionelle tværsnit. Vi bruger vores model til teoretisk at undersøge effekten af hjørner i nanokaneler på de elektrokemiske overfladeegenskaber. Som ovenfor er de advektionsstrømmålin- gerne suppleret med strøm-overvågnings forsøg og vores model forudsiger både advektionsstrømmen og EO strømningen kun ved brug af parametre fra littera- turen. Desuden er der i løbet af 48 timer en støt stigning i advektionsstrømmen, vi som vi tilskriver opløsning af silikaen. Ved brug af vores model estimerer vi op- løsningshastigheden som funktion af elektrolyt art