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Ionic Coulomb blockade as a fractional Wien effect

DOI:10.1038/s41565-019-0425-y
Authors:
Nikita Kavokine
Nikita Kavokine
Nikita Kavokine
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Sophie Marbach at Ecole Normale Supérieure de Paris
Sophie Marbach
Alessandro Siria at French National Centre for Scientific Research
Alessandro Siria
Lyderic Bocquet at Ecole Normale Supérieure de Paris
Lyderic Bocquet
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Abstract and Figures

Recent advances in nanofluidics have allowed the exploration of ion transport down to molecular-scale confinement, yet artificial porins are still far from reaching the advanced functionalities of biological ion machinery. Achieving single ion transport that is tunable by an external gate—the ionic analogue of electronic Coulomb blockade—would open new avenues in this quest. However, an understanding of ionic Coulomb blockade beyond the electronic analogy is still lacking. Here, we show that the many-body dynamics of ions in a charged nanochannel result in quantized and strongly nonlinear ionic transport, in full agreement with molecular simulations. We find that ionic Coulomb blockade occurs when, upon sufficient confinement, oppositely charged ions form ‘Bjerrum pairs’, and the conduction proceeds through a mechanism reminiscent of Onsager’s Wien effect. Our findings open the way to novel nanofluidic functionalities, such as an ion pump based on ionic Coulomb blockade, inspired by its electronic counterpart.
Brownian dynamics simulations of ionic CB in a nanochannel a, Sketch of ions confined in a gated nanochannel. The tunable surface charge Q acts as a gate—it is equivalent to a voltage applied to an electrode, which is capacitively coupled to the channel. b, Setting for the Brownian dynamics simulations: the ions have quasi-1D Coulomb interactions, with the electric field confined in the channel over a characteristic length ξ. c, The ionic current through the channel, at fixed applied electric field (E = 1 kBT e⁻¹ nm⁻¹), shows peaks at discrete values of the surface charge. d, The neutralizing charge N(Q)—the total positive charge that screens the negative surface charge—increases in steps as a function of Q. The dashed line shows the mean-field prediction obtained from the equilibrium solution of the PNP equations (Supplementary Section 1.5), which is in complete disagreement with the simulations. e, Ionic current as a function of the applied electric field at fixed surface charge (Q = −1.7). A strongly nonlinear behaviour is observed. The parameters are thermal length xT = 0.09 nm, ξ = 3.5 nm and salt concentration ρ0 = 0.44 M. Error bars in c–e represent the standard deviation of the mean (smaller than the symbol size in d, e).
Brownian dynamics simulations of ionic CB in a nanochannel a, Sketch of ions confined in a gated nanochannel. The tunable surface charge Q acts as a gate—it is equivalent to a voltage applied to an electrode, which is capacitively coupled to the channel. b, Setting for the Brownian dynamics simulations: the ions have quasi-1D Coulomb interactions, with the electric field confined in the channel over a characteristic length ξ. c, The ionic current through the channel, at fixed applied electric field (E = 1 kBT e⁻¹ nm⁻¹), shows peaks at discrete values of the surface charge. d, The neutralizing charge N(Q)—the total positive charge that screens the negative surface charge—increases in steps as a function of Q. The dashed line shows the mean-field prediction obtained from the equilibrium solution of the PNP equations (Supplementary Section 1.5), which is in complete disagreement with the simulations. e, Ionic current as a function of the applied electric field at fixed surface charge (Q = −1.7). A strongly nonlinear behaviour is observed. The parameters are thermal length xT = 0.09 nm, ξ = 3.5 nm and salt concentration ρ0 = 0.44 M. Error bars in c–e represent the standard deviation of the mean (smaller than the symbol size in d, e).
… 
Analytical theory for the fractional Wien effect mechanism of ionic CB a, Schematic representation of Onsager’s Wien effect and of the fractional Wien effect. Both correspond to nonlinearities in the current–voltage characteristic due to the electric field dependence of the dissociation rate of ion pairs. b, Schematic setting for the study of out-of-equilibrium Bjerrum pair dynamics. The main ingredient is the computation of the mean escape time of an ion from the potential created by an effective charge q. c, Neutralizing charge N(Q) as a function of surface charge. d, Positive ion current, at fixed applied electric field (E = 1 kBT e⁻¹ nm⁻¹), as a function of surface charge. e, Current–voltage characteristic at fixed surface charge, corresponding to a conductance peak (Q = −1.7). Inset, enlarged view of the region of small applied electric field. In c–e, dots are simulation results, while the solid line is the theoretical prediction from equations (5) and (8). The Wien effect theory shows quantitative agreement with simulations. Error bars represent the standard deviation of the mean.
Analytical theory for the fractional Wien effect mechanism of ionic CB a, Schematic representation of Onsager’s Wien effect and of the fractional Wien effect. Both correspond to nonlinearities in the current–voltage characteristic due to the electric field dependence of the dissociation rate of ion pairs. b, Schematic setting for the study of out-of-equilibrium Bjerrum pair dynamics. The main ingredient is the computation of the mean escape time of an ion from the potential created by an effective charge q. c, Neutralizing charge N(Q) as a function of surface charge. d, Positive ion current, at fixed applied electric field (E = 1 kBT e⁻¹ nm⁻¹), as a function of surface charge. e, Current–voltage characteristic at fixed surface charge, corresponding to a conductance peak (Q = −1.7). Inset, enlarged view of the region of small applied electric field. In c–e, dots are simulation results, while the solid line is the theoretical prediction from equations (5) and (8). The Wien effect theory shows quantitative agreement with simulations. Error bars represent the standard deviation of the mean.
… 
Conditions for observation of ionic CB a, Neutralizing charge N(Q) as a function of the surface charge Q, as obtained from Brownian dynamics simulations (dots) and the full theoretical prediction from Supplementary equation (32) (solid line), at different salt concentrations c. CB steps disappear as the salt concentration is increased. The parameters are chosen here as xT = 0.18 nm and ξ = 7 nm. b, ‘Phase diagram’ for CB. The colour scale shows, as an assessment of the ‘strength’ of ionic CB, the steepness of the steps in the neutralizing charge N(Q). It is defined as 1 − 1/maximum slope of a step and varies between 0 (no CB) and 1 (full CB). The axes correspond to the channel radius (in terms of the dimensionless quantity xT∕ξ=R2∕2ℓBξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_{\mathrm{T}}/\xi = R^2/2\ell _{\mathrm{B}}\xi$$\end{document}) and to the dimensionless bulk salt concentration ρ0ξ³. On the right panel, the fraction of ion pairs in the channel is plotted as a function of xT/ξ, at bulk concentration 0.1 M. Ion pairing is a prerequisite for ionic CB; that is, CB occurs when the salt behaves as a weak electrolyte.
Conditions for observation of ionic CB a, Neutralizing charge N(Q) as a function of the surface charge Q, as obtained from Brownian dynamics simulations (dots) and the full theoretical prediction from Supplementary equation (32) (solid line), at different salt concentrations c. CB steps disappear as the salt concentration is increased. The parameters are chosen here as xT = 0.18 nm and ξ = 7 nm. b, ‘Phase diagram’ for CB. The colour scale shows, as an assessment of the ‘strength’ of ionic CB, the steepness of the steps in the neutralizing charge N(Q). It is defined as 1 − 1/maximum slope of a step and varies between 0 (no CB) and 1 (full CB). The axes correspond to the channel radius (in terms of the dimensionless quantity xT∕ξ=R2∕2ℓBξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_{\mathrm{T}}/\xi = R^2/2\ell _{\mathrm{B}}\xi$$\end{document}) and to the dimensionless bulk salt concentration ρ0ξ³. On the right panel, the fraction of ion pairs in the channel is plotted as a function of xT/ξ, at bulk concentration 0.1 M. Ion pairing is a prerequisite for ionic CB; that is, CB occurs when the salt behaves as a weak electrolyte.
… 
Ionic-CB-based ion pump a, Schematic of the ion pump inspired by its electronic counterpart and time dependence of the variable surface charges Qi(t). The 125 variable charges are placed every 5 nm, and periodic boundary conditions are used. b, Positive ion current resulting from the pump operation (with no applied electric field), at xT = 0.1 nm (CB regime) and xT = 2 nm (no CB), as obtained from Brownian dynamics, as a function of the pump amplitude ΔQ. The current is normalized by I(1 ion), which is the current resulting from one ion moving at a velocity of 5 nm per 10 ns. Error bars represent the standard deviation of the mean.
Ionic-CB-based ion pump a, Schematic of the ion pump inspired by its electronic counterpart and time dependence of the variable surface charges Qi(t). The 125 variable charges are placed every 5 nm, and periodic boundary conditions are used. b, Positive ion current resulting from the pump operation (with no applied electric field), at xT = 0.1 nm (CB regime) and xT = 2 nm (no CB), as obtained from Brownian dynamics, as a function of the pump amplitude ΔQ. The current is normalized by I(1 ion), which is the current resulting from one ion moving at a velocity of 5 nm per 10 ns. Error bars represent the standard deviation of the mean.
… 
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Articles
https://doi.org/10.1038/s41565-019-0425-y
Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité,
Paris, France. *e-mail: lyderic.bocquet@ens.fr
Ionic transport is key to numerous processes, from neurotransmis-
sion to ultrafiltration1–4. Over the past decade, it has been exten-
sively investigated in biological systems, evidencing advanced
functionalities such as high selectivity, ionic pumping and elec-
trical or mechanical gating5–7. However, it is only recently that
experimental progress in nanoscience has allowed the fabrication
of artificial pores with controlled material properties and channel-
or slit-like geometries. These new systems have reached unprec-
edented nanometre- and even angström-scale confinements8–11, yet
they are still far from exhibiting the same functions as biological
ionic machines.
At these scales, ion transport is usually described by the Poisson–
Nernst–Planck (PNP) framework2, which couples ion diffusive
dynamics to electric interactions. Although it may account for
nonlinear (for example, diode-type) effects2, the PNP framework is
intrinsically continuum and mean field. Building bio-inspired func-
tions, however, may require control of transport at the single ion
level, which is out of the reach of a mean-field description. Single
charge transport in fact echoes the canonical Coulomb blockade
(CB) phenomenon, which has been thoroughly explored in nano-
electronics. CB is typically observed in a single electron transistor:
under fixed bias, the current between source and drain peaks at
quantized values of the gating voltage12. The origins of this effect
stem from the many-body Coulomb interactions between electrons
and from the discreteness of the charge carriers13. Similar physi-
cal ingredients are at play in a nanoscale channel filled with a salt
solution (Fig. 1a): the ions also interact via Coulombic forces, and a
variable surface charge on the channel walls can play the role of the
gating voltage. One may therefore expect to observe an ‘ionic CB’,
namely peaks in the ionic conductance of a nanochannel at quan-
tized values of its surface charge. It is thus of interest that molecular
dynamics simulations14–17 and experiments18–20 have shown what
might be indirect signatures of ionic CB (although in the absence
of a gating voltage), and conductance gating by a surface charge
has been demonstrated in simulations of a biological ion channel
model21,22. These observations remain surprising, because ionic
systems in water at room temperature have specific features con-
trasting with electronic systems that may preclude the occurrence
of ionic CB. Beyond the absence of quantum effects, the fact that
ions are of both signs— while electrons are only negative—results
in Debye screening, which is expected to greatly weaken the many-
body interaction. It remains unclear under which conditions these
aspects may suppress ionic transport quantization.
Although pioneering analytical efforts have translated the results
established for electrons13 to the ionic case22–24, a general theory
for ionic CB, incorporating the unique features of ionic systems in
contrast to their electronic counterparts, is still lacking. We develop
such a theory in this Article.
Model definition and numerical results
Our theory is based on a simple but general model of a nanochan-
nel which confines ions in one dimension (Fig. 1a). The channel
has radius R and length
≫LR
, as opposed to nanopores which have
length L ≈ R. The nanochannel is filled with water, which under
confinement exhibits a priori an anisotropic dielectric permittivity
ϵ
(refs. 25,26), and it is embedded in a membrane with low permit-
tivity
ϵm
(whenever needed, we use
ϵ=2
m
). Under such conditions
(Fig. 1b), the electric field lines produced by an ion stay confined
inside the channel over a characteristic length ξ (ref. 27). This leads
to a stronger Coulomb interaction than in the bulk solution, which
is well described by the exponential potential
ξ
=ξ−∣ ∣∕
Vx kTxe() (1
)
x
B
T
This introduces a thermal length xT (ref. 28), which quantifies the
strength of the interaction. We detail in Supplementary Section 3
how the parameters ξ and xT are related to the channel geometry
and to the various dielectric constants. If the permittivity of con-
fined water is assumed to be the same as in the bulk, one has ξ ≈ 7R
and
=∕ℓx R 2
T2B
, where
ℓ= .07nm
B
is the Bjerrum length in bulk
water. We shall use these relations in the following, keeping in mind
that taking into account the anisotropic permittivity would result in
a stronger interaction for a given confinement.
A charge is imposed on the confining surface and acts as a gate
on the system; here, we reduce the surface charge to a point-like
charge Q. The ions interact between themselves and with the sur-
face charge through the potential given in equation (1); depending
on conditions, an electric field E may be applied along the channel.
Ionic Coulomb blockade as a fractional Wien effect
Nikita Kavokine , Sophie Marbach , Alessandro Siria and Lydéric Bocquet *
Recent advances in nanofluidics have allowed the exploration of ion transport down to molecular-scale confinement, yet arti-
ficial porins are still far from reaching the advanced functionalities of biological ion machinery. Achieving single ion transport
that is tunable by an external gate—the ionic analogue of electronic Coulomb blockade—would open new avenues in this quest.
However, an understanding of ionic Coulomb blockade beyond the electronic analogy is still lacking. Here, we show that the
many-body dynamics of ions in a charged nanochannel result in quantized and strongly nonlinear ionic transport, in full agree-
ment with molecular simulations. We find that ionic Coulomb blockade occurs when, upon sufficient confinement, oppositely
charged ions form ‘Bjerrum pairs’, and the conduction proceeds through a mechanism reminiscent of Onsager’s Wien effect.
Our findings open the way to novel nanofluidic functionalities, such as an ion pump based on ionic Coulomb blockade, inspired
by its electronic counterpart.
NATURE NANOTECHNOLOGY | VOL 14 | JUNE 2019 | 573–578 | www.nature.com/naturenanotechnology 573
The Nature trademark is a registered trademark of Springer Nature Limited.
... Water notably becomes anisotropic, with a dielectric constant ε ⊥ ∼ 2 in the direction of confinement -while other directions remain unaffected, with ε ∼ 80. Overall, one should typically replace ε w by √ ε ⊥ ε in Eqs. (3) and (4) 31,39 . Hence, modifications to the dielectric properties of water at the nanoscale generally result in stronger electrostatic effects. ...
... In particular, this phenomenon replicates the physics of voltage-gated ion channels, and its modelization has opened the way for the design of solid-state channels with key properties. Examples include a single-ion pump (see Fig. 3A) 39 and ionic memristors (see Fig. 3B) 31 . On the experimental side, voltage-gating was observed in both short pores and 2D slit-like channels (see Fig. 3B and C) 32,40 . ...
... • Nanofluidic machines: In terms of circuitry, we believe that gated channels discussed in Section II are the building blocks which offer some of the most promising perspectives 32,39,57 . They potentially allow to control ion transport at the molecular level, through the use of 'switches' on the surface of the pores -playing a role similar to transistors in electronics. ...
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Nanofluidics, the field interested in flows at the smallest scales, has grown at a fast pace, reaching an ever finer control of fluidic and ionic transport at the molecular level. Still, artificial pores are far from reaching the wealth of functionalities of biological channels that regulate sensory detection, biological transport and neurostransmission - all while operating at energies comparable to thermal noise. Here, we argue that artificial ionic machines can be designed by harnessing the entire wealth of phenomena available at the nanoscales and exploiting techniques developped in various fields of physics. As they are generally based on solid-state nanopores, rather than soft membranes and proteins, they should in particular aim at taking advantage of their specific properties such as their electronic structure or their ability to interact with light. These observations call for the design of new ways of probing nanofluidic systems. Nanofluidics is now at the crossroads, there are new avenues to build complex ionic machines and this may allow to develop new functionalities inspired by Nature.
View
... The corresponding effective Coulomb interactions are stronger than in bulk water, their strength increasing with decreasing channel width 1 . In channels with diameters smaller than about 2 nm, these were predicted to cause strong ionic correlations, which in turn result in Bjerrum pairing and ion-exchange phase transitions [8][9][10]12 , leading to deviations from Ohm's law transport in the form of Wien effect conduction 13 and Coulomb-blockade-like phenomena 11,13 . The concept of reinforced Coulomb interactions due to a dielectric contrast was later extended to a twodimensional nano-slit geometry 14 , where it was found to produce even more striking non-linear ion transport: under the effect of an electric field, the ions may undergo a dynamical phase transition and assemble into dense clusters termed Bjerrum polyelectrolytes [14][15][16] . ...
... We find that, in all but the perfect metal cases, the measured current displays a non-linear dependence on the applied electric field and the channel conductance is hindered with respect to the Ohm's law prediction: this is a signature of the second Wien effect. The Wien effect has been historically known to govern the conduction in weak electrolytes; it has recently been predicted to occur as well in strong electrolytes when confined in nanoscale channels, because oppositely charged ions form Bjerrum pairs due to the reinforced Coulomb interactions in confinement 13,14 . In refs. ...
... In refs. 13,14 , the Wien effect was studied in the case of insulating channel walls. Here, we find that the Wien effect can persist even in the presence of electronic screening and the magnitude of the effect can be tuned by the channel wall's electronic properties. ...
View
... We first assume for simplicity that the channel is filled with water that has isotropic dielectric permittivity w = 80, and that it is embedded in an insulating medium with much lower permittivity m (for a lipid membrane 6 , m ∼ 2). The effective Coulomb interaction V (x) between two monovalent ions separated by a distance x on the channel axis can be computed exactly by solving Poisson's equation 7,11,12 . A simple approximate expression can be obtained for ...
... Here, we detail the analytical solution for the partition function of a 1D Coulomb gas-like system that was first introduced in ref. 12 . We set k B T = 1 until the end of Sec. ...
... We may check that the prefactor in Eq. (46) is the correct one by evaluating analytically the expression in Eq. (26) in the low concentration limit z T ≡ zx T 1. An analytical expansion of the function χ(k) in powers of z T was derived in ref. 12 ...
Ion filling of a one-dimensional nanofluidic channel in the interaction confinement regime
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Ion transport measurements are widely used as an indirect probe for various properties of confined electrolytes. It is generally assumed that the ion concentration in a nanoscale channel is equal to the ion concentration in the macroscopic reservoirs it connects to, with deviations arising only in the presence of surface charges on the channel walls. Here, we show that this assumption may break down even in a neutral channel, due to electrostatic correlations between the ions arising in the regime of interaction confinement, where Coulomb interactions are reinforced due to the presence of the channel walls. We focus on a one-dimensional channel geometry, where an exact evaluation of the electrolyte's partition function is possible with a transfer operator approach. Our exact solution reveals that in nanometre-scale channels, the ion concentration is generally lower than in the reservoirs, and depends continuously on the bulk salt concentration, in contrast to conventional mean-field theory that predicts an abrupt filling transition. We develop a modified mean-field theory taking into account the presence of ion pairs that agrees quantitatively with the exact solution and provides predictions for experimentally-relevant observables such as the ionic conductivity. Our results will guide the interpretation of nanoscale ion transport measurements.
View
... In particular, this phenomenon replicates the physics of voltage-gated ion channels, and its modelization has opened the way for the design of solid-state channels with key properties. Examples include a single-ion pump (see Fig. 3A) 32 and ionic memristors (see Fig. 3B) 24 . On the experimental side, voltage-gating was observed in both short pores and 2D slit-like channels (see Fig. 3B and C) 25,33 . ...
... • In terms of circuitry, we believe that gated channels discussed in Section II are the building blocks which offer some of the most promising perspectives 25,32,49 . They potentially allow to control ion transport at the molecular level, through the use of 'switches' on the surface of the pores. ...
... Voltage-gated nanofluidic channels. A Schematic design of a single-ion pump, as suggested by ref.32 . Several electrodes are placed along the surface of a nanotube, each bearing a local charge, with which an ion of opposite sign can pair up. ...
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View
... example, to discuss the capacitance of nanoporous systems [19][20][21] . The lattice models may be taken to the continuum limit, and the resulting path integral solutions have been used to discuss various ion-exchange phase transitions that arise in the presence of fixed discrete charges inside the channel 9,22,23 and the ionic Coulomb blockade phenomenon 13 . Such models are particularly rich theoretically, as they support a mapping to non-Hermitian quantum mechanics 24 . ...
... We first assume for simplicity that the channel is filled with water that has isotropic dielectric permittivity w = 80, and that it is embedded in an insulating medium with much lower permittivity m (for a lipid membrane 7 , m ∼ 2). The effective Coulomb interaction V (x) between two monovalent ions separated by a distance x on the channel axis can be computed exactly by solving Poisson's equation 8,12,13 . A simple approximate expression can be obtained for ...
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... New functionalities in nanoscale fluid transport have been achieved by exploiting analogies with condensed matter phenomena. The analogy between surface charge in a nanochannel and doping in a semiconductor [1] has led to the development of nanofluidic diodes [2,3] and transistors [4]; the similarity between ionic and electronic Coulomb interactions [5] allows for ionic Coulomb blockade [6][7][8][9]. More recently, it has been suggested thatbeyond mere analogies-nanofluidic transport can directly couple to electronic effects within the channel wall, as the solid-liquid interface can host fluctuation-induced electromagnetic phenomena [10,11]: energy and momentum transfer mediated by interfacial charge fluctuations. ...
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... Almost identical nonlinear σ-E relations were reported in the studies of strongly correlated ionic conductance, referring to the Onsager-Wien effect. 27,28 It is interesting to nd the simple mathematical form of Merz's law ting well in describing the nonlinear effect in ionic conductance. ...
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Full-text available
  • Mar 2018
A discrete electrostatic/diffusion model has been developed to describe the selective permeation of ion channels, based on ionic Coulomb blockade (ICB) and quantised dehydration (QD). It has been applied to describe selectivity phenomena measured in the bacterial NaChBac sodium channel and some of its mutants. Site-directed mutagenesis and the whole-cell patch-clamp technique were used to investigate how the value $Q_f$ of the fixed charge at the selectivity filter (SF) affected both valence and alike-charge selectivity. The new ICB/QD model predicts that increasing ${Q_f}$ should lead to a shift of selectivity sequences towards larger ion sizes and charges, a result that agrees with the present experiments and with earlier work. Comparison of the model with experimental data provides evidence for an {\it effective charge} $Q_f^*$ at the SF that is smaller in magnitude than the nominal $Q_f$ corresponding to the charge on the isolated protein residues. Furthermore, $Q_f^*$ was different for aspartate and glutamate charged rings and also depended on their position within the SF. It is suggested that protonation of the residues within the restricted space is an important factor in significantly reducing the effective charge of the EEEE ring. Values of $Q_f^*$ derived from experiments on the anomalous mole fraction effect (AMFE) agree well with expectations based on the ICB/QD model and have led to the first clear demonstration of the expected ICB oscillations in Ca$^{2+}$ conduction as a function of the fixed charge. Pilot studies of the dependence of Ca$^{2+}$ conduction on pH are consistent with the predictions of the model.
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Surface effects on ionic Coulomb blockade in nanometer-size pores
Article
Full-text available
  • Nov 2017
Ionic Coulomb blockade in nanopores is a phenomenon that shares some similarities but also differences with its electronic ounterpart. Here, we investigate extensively this phenomenon using all-atom molecular dynamics of ionic transport through nanopores of about one nanometer in diameter and up to several nanometers in length. Our goal is to better understand the role of atomic roughness and structure of the pore walls in facilitating ionic Coulomb blockade. Our numerical results reveal the following general trends. First, the nanopore selectivity changes with its diameter, and the nanopore position in the membrane influences the current strength. Second, the ionic transport through the nanopore takes place in a hopping-like fashion over a set of discretized states caused by local electric fields due to membrane atoms. In some cases, this creates a slow-varying ``crystal-like'' structure of ions inside the nanopore. Third, while at a given voltage, the resistance of the nanopore depends on its length, the slope of this dependence appears to be independent of the molarity of ions. An effective kinetic model that captures the ionic Coulomb blockade behavior observed in MD simulations is formulated.
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Gated Water Transport Through Graphene Nanochannels: From Ionic Coulomb Blockade to Electroosmotic Pump
Article
Full-text available
  • Jul 2017
Understanding and controlling water or ion transport in nanochannels plays an important role in further unravelling the transport mechanism of biological membrane channels and designing functional nanofluidic devices. In this work, molecular dynamics simulations were conducted to investigate water and ion transport in graphene nanochannels. Similar to electron coulomb blockade phenomenon observed in quantum dots, we discovered an ionic coulomb blockade phenomenon in our graphene nanochannels, and another two ion transport modes were also proposed to rationalize the observed phenomena under different electric field intensities. Furthermore, based on this blockade phenomenon we found that the Open and Closed state of the graphene nanochannels for water transport could be switched according to external electric field intensities, and electroosmotic flow could further enhance the water transport. These findings might have potential applications in designing and fabricating controllable valves in lab-on-chip nanodevices.
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Ionic Coulomb blockade and anomalous mole fraction effect in NaChBac bacterial ion channels
Article
Full-text available
  • Dec 2016
Background. The selectivity of biological cation channels is defined by a short, narrow selectivity filter, having a negative net fixed charge Qf. Voltage gated bacterial channels (NaChBac and some others) are frequently used in biophysics as simplified models of mammalian calcium and sodium channels. We report an experimental, analytic and numerical study of the effects of Qf and bulk ionic concentrations of Ca2+ and Na+ on conduction and selectivity of NaChBac channels, wild type and Qf-varied mutants. Methods. Site-directed mutagenesis and voltage clamp recordings were used to investigate the Na+/Ca2+ selectivity, divalent blockade and anomalous mole fraction effect (AMFE) for different NaChBac wild type/mutants channels and the properties dependence on Qf. Experimental results were compared with Brownian dynamics simulations and with analytic predictions of the ionic Coulomb blockade (ICB) model, which was extended to encompass bulk concentration effects. Results. It was shown that changing of Qf from –4e (for LESWAS wild type) to –8e (for LEDWAS mutant) leads to strong divalent blockade of the Na+ current by micromolar amounts of Ca2+ ions, similar to the effects seen in mammalian calcium channels. The BD simulations revealed a concentration-related logarithmic shift of the conduction bands. These results were shown to be consistent with ICB model predictions. Conclusions. The extended ICB model explains the experimental (divalent blockade and AMFE) and simulated (multi-ion bands and their concentration-related shifts) selectivity phenomena of NaChBac channel and its charge-varied mutants. These results extend the understanding of ion channel selectivity and may also be applicable to biomimetic nanopores with charged walls.
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Single-layer MoS2 nanopores as nanopower generators
Article
Full-text available
  • Jul 2016
Making use of the osmotic pressure difference between fresh water and seawater is an attractive, renewable and clean way to generate power and is known as 'blue energy'. Another electrokinetic phenomenon, called the streaming potential, occurs when an electrolyte is driven through narrow pores either by a pressure gradient or by an osmotic potential resulting from a salt concentration gradient. For this task, membranes made of two-dimensional materials are expected to be the most efficient, because water transport through a membrane scales inversely with membrane thickness. Here we demonstrate the use of single-layer molybdenum disulfide (MoS2) nanopores as osmotic nanopower generators. We observe a large, osmotically induced current produced from a salt gradient with an estimated power density of up to 10(6) watts per square metre-a current that can be attributed mainly to the atomically thin membrane of MoS2. Low power requirements for nanoelectronic and optoelectric devices can be provided by a neighbouring nanogenerator that harvests energy from the local environment-for example, a piezoelectric zinc oxide nanowire array or single-layer MoS2 (ref. 12). We use our MoS2 nanopore generator to power a MoS2 transistor, thus demonstrating a self-powered nanosystem.
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Statistical Theory of Selectivity and Conductivity in Biological Channels
Article
Full-text available
  • Apr 2016
We present an equilibrium statistical-mechanical theory of selectivity in biological ion channels. In doing so, we introduce a grand canonical ensemble for ions in a channel's selectivity filter coupled to internal and external bath solutions for a mixture of ions at arbitrary concentrations, we use linear response theory to find the current through the filter for small gradients of electrochemical potential, and we show that the conductivity of the filter is given by the generalized Einstein relation. We apply the theory to the permeation of ions through the potassium selectivity filter, and are thereby able to resolve the long-standing paradox of why the high selectivity of the filter brings no associated delay in permeation. We show that the Eisenman selectivity relation follows directly from the condition of diffusion-limited conductivity through the filter. We also discuss the effect of wall fluctuations on the filter conductivity.
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Anomalously low dielectric constant of confined water
Article
  • Jun 2018
Water's surface dielectric Theoretical studies predict that the inhibition of rotational motion of water near a solid surface will decrease its local dielectric constant. Fumagalli et al. fabricated thin channels in insulating hexagonal boron nitride on top of conducting graphene layers (see the Perspective by Kalinin). The channels, which varied in height from 1 to 300 nanometers, were filled with water and capped with a boron nitride layer. Modeling of the capacitance measurements made with an atomic force microscope tip revealed a surface-layer dielectric constant of 2, compared with the bulk value of 80 for water. Science , this issue p. 1339 ; see also p. 1302
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Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins
Article
  • Aug 2017
Fast water transport through carbon nanotube pores has raised the possibility to use them in the next generation of water treatment technologies. We report that water permeability in 0.8-nanometer-diameter carbon nanotube porins (CNTPs), which confine water down to a single-file chain, exceeds that of biological water transporters and of wider CNT pores by an order of magnitude. Intermolecular hydrogen-bond rearrangement, required for entry into the nanotube, dominates the energy barrier and can be manipulated to enhance water transport rates. CNTPs block anion transport, even at salinities that exceed seawater levels, and their ion selectivity can be tuned to configure them into switchable ionic diodes. These properties make CNTPs a promising material for developing membrane separation technologies.
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Water Dielectric Effects in Planar Confinement
Article
We investigate the dielectric profile of water confined between two planar polar walls using atomistic molecular dynamics simulations. For a water slab thickness below 1 nm the dielectric response is highly asymmetric: while the parallel component slightly increases compared to bulk, the perpendicular one decreases drastically due to anticorrelated polarization of neighboring water molecules. We demonstrate the importance of the dielectric contribution due to flexible polar headgroups and derive an effective dielectric tensorial box model suitable for coarse-grained electrostatic modeling.
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Molecular transport through capillaries made with atomic-scale precision
Article
  • Sep 2016
Nanometre-scale pores and capillaries have long been studied because of their importance in many natural phenomena and their use in numerous applications1. A more recent development is the ability to fabricate artificial capillaries with nanometre dimensions, which has enabled new research on molecular transport and led to the emergence of nanofluidics2, 3, 4. But surface roughness in particular makes it challenging to produce capillaries with precisely controlled dimensions at this spatial scale. Here we report the fabrication of narrow and smooth capillaries through van der Waals assembly5, with atomically flat sheets at the top and bottom separated by spacers made of two-dimensional crystals6 with a precisely controlled number of layers. We use graphene and its multilayers as archetypal two-dimensional materials to demonstrate this technology, which produces structures that can be viewed as if individual atomic planes had been removed from a bulk crystal to leave behind flat voids of a height chosen with atomic-scale precision. Water transport through the channels, ranging in height from one to several dozen atomic planes, is characterized by unexpectedly fast flow (up to 1 metre per second) that we attribute to high capillary pressures (about 1,000 bar) and large slip lengths. For channels that accommodate only a few layers of water, the flow exhibits a marked enhancement that we associate with an increased structural order in nanoconfined water. Our work opens up an avenue to making capillaries and cavities with sizes tunable to ångström precision, and with permeation properties further controlled through a wide choice of atomically flat materials available for channel walls.
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