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Prospects of Observing Ionic Coulomb Blockade in Artificial Ion entropy Perspective Prospects of Observing Ionic Coulomb Blockade in Artificial Ion Confinements Andrey Chernev, Sanjin Marion and Aleksandra Radenovic * Laboratory of Nanoscale Biology, Institute of Bioengineering, School of Engineering, EPFL, 1015 Lausanne, Switzerland; andrey.chernev@epfl.ch (A.C.); sanjin.marion@epfl.ch (S.M.) * Correspondence: aleksandra.radenovic@epfl.ch Received: 9 November 2020; Accepted: 11 December 2020; Published: 18 December 2020 Abstract: Nanofluidics encompasses a wide range of advanced approaches to study charge and mass transport at the nanoscale. Modern technologies allow us to develop and improve artificial nanofluidic platforms that confine ions in a way similar to single-ion channels in living cells. Therefore, nanofluidic platforms show great potential to act as a test field for theoretical models. This review aims to highlight ionic Coulomb blockade (ICB)—an effect that is proposed to be the key player of ion channel selectivity, which is based upon electrostatic exclusion limiting ion transport. Thus, in this perspective, we focus on the most promising approaches that have been reported on the subject. We consider ion confinements of various dimensionalities and highlight the most recent advancements in the field. Furthermore, we concentrate on the most critical obstacles associated with these studies and suggest possible solutions to advance the field further. Keywords: nanofluidics; ionic Coulomb blockade; 2D materials; nanopores; nanotubes; angstrom slits 1. Introduction In the past fifteen years, various artificial nanofluidic platforms have become highly compelling for fundamental studies of physical phenomena and numerous practical applications where the transport of the confined ions plays a crucial role [1,2]. Among the most exciting practical applications are power generation [3–7], filtration, and molecular separation [8–10]. The last five years have witnessed remarkable progress in the fabrication of nanofluidic devices, enabling researchers to develop artificial nanofluidic systems with the confinement of one to a few water molecules (below 1 nm) [11]. Such nanofluidic platforms have been realized in zero-dimensional (0D), 1D, or 2D geometry [7,12–14] (Figure1 ). These platforms exhibit giant permeability and ion selectivity comparable to biological ion channels, excluding anions and macromolecules, and closely mimic functionalities previously observed only in biological channels. Superb selectivity of the sodium/calcium family of channels has fascinated scientists due to its physiological relevance and underlying physical mechanism [15–17]. A simplified electrostatic and Brownian dynamics model of the prototypical model Ca2+ or Na+ channel has been used in describing its conduction and selectivity [18], echoing the phenomenology of Coulomb blockade [17]. The term ionic Coulomb blockade (ICB) was suggested first as a counterpart of the electronic Coulomb blockade (ECB) by Krems and Di Ventra [19]. Confinement below 1 nm dictates a departure from the mean-field assumptions as the correlations between the ions and finite-size effects cannot be neglected and complicates the insight into the ionic charge transfer at the nanoscale [17,20,21]. Entropy 2020, 22, 1430; doi:10.3390/e22121430 www.mdpi.com/journal/entropy Entropy 2020, 22, 1430 2 of 14 Entropy 2018, 20, x 2 of 14 FigureFigure 1. 1. DifferentDifferent geometries geometries are are considered considered for for confined confined nanofluidic nanofluidic systems systems from from two two-dimensional‐dimensional (2D)(2D) nanoslits toto 1D 1D nanowires nanowires and and quantum quantum dot-like dot‐like nanopores nanopores in the in atomically the atomically thin material thin material matrix, matrix,i.e., 2D i.e., nanopores. 2D nanopores. ArtificialArtificial nanofluidic nanofluidic devices devices developed developed for for single single-ion‐ion conductivity conductivity measurements measurements provide provide a a uniqueunique opportunity opportunity to to test test the the proposed proposed models models and and reveal reveal the the many many-body‐body effects effects in in ionic ionic systems. systems. ThisThis perspective perspective article article aims aims to todiscuss discuss practical practical challenges challenges in verifying in verifying the models the models that evoke that evoke ionic Coulombionic Coulomb blockade blockade in a invariety a variety of settings of settings that that are arenow now available available due due to to recent recent progress progress in in nanofabricationnanofabrication [12,22,23]. [12,22,23]. Furthermore, Furthermore, it it also also provides provides suggestions suggestions for for the the integration integration of of additional additional approachesapproaches suchsuch as as modulation modulation of theof the charges, charges, pressure, pressure, pH, ionic pH, strength,ionic strength, temperature, temperature, and potential and potentialin the range in the not range attainable not attainable on lipid bilayers. on lipid bilayers. AsAs suggested suggested initially, initially, ionic ionic Coulomb Coulomb blockade blockade is is based based on on the the relation relation of of ion ion kinetic kinetic and and barrier barrier energiesenergies and and manifests manifests as as the the nonlinear transport of ions. This This behavior behavior was was later later experimentally experimentally observed in atomically thin, sub-nanometer-sized molybdenum disulfide (MoS ) nanopores [13]. observed in atomically thin, sub‐nanometer‐sized molybdenum disulfide (MoS22) nanopores [13]. AlthoughAlthough theoreticaltheoretical models models predict predict ICB ICB and and suggest suggest particular particular conditions conditions to reveal to the reveal effect the [17 ,20effect,24], [17,20,24],irrefutable irrefutable experimental experimental observation observation of this phenomenon of this phenomenon is still challenging. is still challenging. The reason The forreason that foris a that whole is a set whole of issues set of that issues have that to have be taken to be into taken account into account before considering before considering this complex this complex process. process.The most The critical most issues critical that issues could that mask could ICB mask observation ICB observation are related are to therelated fact thatto the ionic fact transport that ionic is transportmeasured is at measured room temperatures, at room temperatures, causing large causing charge fluctuations, large charge which fluctuations, leads to which the increased leads to noise, the increasedand instability noise, of theand nanofluidic instability devices.of the nanofluidic Together with devices. regular Together wetting and with contamination regular wetting challenges and contaminationin nanofluidics challenges [25], we can in arguenanofluidics that the [25], ionic we systems’ can argue nonlinear that the current-voltage ionic systems’ nonlinear characteristics current are‐ voltageinsufficient characteristics to prove the are ICB insufficient effect. Unlike to prove in thethe caseICB effect. of ECB Unlike [26], there in the are case still of no ECB convincing [26], there data are stillshowing no convincing conductance data oscillations showing conductance or single-ion oscillations devices. or single‐ion devices. Therefore,Therefore, it it is is essential essential to to critically critically assess assess the the suitability suitability of of different different nanofluidic nanofluidic platforms platforms for for thethe observation observation of of ICB ICB and and propose propose novel novel solutions solutions that that will willallow allow us to us untangle to untangle the role the of role the issues of the mentionedissues mentioned above. above. New Newgeometries geometries like likenanopores nanopores in 2D in 2Dmaterials, materials, single single-digit‐digit nanotubes nanotubes and and angstromangstrom slits playplay a a key key role role and and are are essential essential in verifying in verifying the di thefferent different parameters parameters required required to observe to observeICB reproducibly. ICB reproducibly. The complex The complex nature ofnature ionic of transport ionic transport can be consideredcan be considered with di ffwitherent different settings settingsand thus and allow thus direct allow observation direct observation of experimental of experimental parameter parameter variation variation such as pore such length, as pore diameter, length, diameter,access resistance, access resistance, surface charge, surface gating charge, voltage gating temperature, voltage temperature, and many and others many [27 ].others [27]. Entropy 2020, 22, 1430 3 of 14 2. Prerequisites for Ionic Coulomb Blockade The basic prerequisites for ionic Coulomb blockade are shared with its electronic counterpart [28,29]. The geometrical requirement for ICB to occur is represented by two reservoirs with charge carriers, in our case ions, with a channel in between with a large resistance to ion transport at least in one direction [17,19,20,24]. More specifically, the channel has to provide the type of confinement that allows ions to dwell inside of it as it was suggested originally [15]. Ion transport between the two reservoirs is inhibited due to strong Coulomb interactions and an ion dwelling at or near the channel, so that there is a limit on the possible charge, which can be transferred between the two sides of the chamber [17,19,20,24]. When the energy barrier for ions to enter the channel, and subsequently traverse it, is larger than the system’s
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