Ionic Coulomb blockade information

Ionic Coulomb blockade (ICB)^[1][2] is an electrostatic phenomenon that appears in ionic transport through mesoscopic electro-diffusive systems (artificial nanopores^[1][3] and biological ion channels^[2]) and manifests itself as oscillatory dependences of the conductance on the fixed charge ${\displaystyle Q_{\rm {f}}}$ in the pore^[2] ( or on the external voltage ${\displaystyle V}$, or on the bulk concentration ${\displaystyle c_{\rm {b}}}$^[1]).

ICB represents an ion-related counterpart of the better-known electronic Coulomb blockade (ECB) that is observed in quantum dots.^[4][5] Both ICB and ECB arise from quantisation of the electric charge and from an electrostatic exclusion principle and they share in common a number of effects and underlying physical mechanisms. ICB provides some specific effects related to the existence of ions of different charge ${\displaystyle q=ze}$ (different in both sign and value) where integer ${\displaystyle z}$ is ion valence and ${\displaystyle e}$ is the elementary charge, in contrast to the single-valence electrons of ECB (${\displaystyle z=-1}$).

ICB effects appear in tiny pores whose self-capacitance ${\displaystyle C_{\rm {s}}}$ is so small that the charging energy of a single ion ${\displaystyle \Delta E=z^{2}e^{2}/(2C_{s})}$becomes large compared to the thermal energy per particle ( ${\displaystyle \Delta E\gg k_{\rm {B}}T}$). In such cases there is strong quantisation of the energy spectrum inside the pore, and the system may either be “blockaded” against the transportation of ions or, in the opposite extreme, it may show resonant barrier-less conduction,^[6][2] depending on the free energy bias coming from ${\displaystyle Q_{\rm {f}}}$, ${\displaystyle V}$, or ${\displaystyle \log {c_{\rm {b}}}}$.

The ICB model claims that ${\displaystyle Q_{\rm {f}}}$ is a primary determinant of conduction and selectivity for particular ions, and the predicted oscillations in conductance and an associated Coulomb staircase of channel occupancy vs ${\displaystyle Q_{\rm {f}}}$^[2] are expected to be strong effects in the cases of divalent ions (${\displaystyle z=2}$) or trivalent ions (${\displaystyle z=3}$).

Some effects, now recognised as belonging to ICB, were discovered and considered earlier in precursor papers on electrostatics-governed conduction mechanisms in channels and nanopores.^{[7][8][9][10][11]}

The manifestations of ICB have been observed in water-filled sub-nanometre pores through a 2D ${\displaystyle {\ce {MoS2}}}$ monolayer,^[3] revealed by Brownian dynamics (BD) simulations of calcium conductance bands in narrow channels,^[2][12] and account for a diversity of effects seen in biological ion channels.^[2] ICB predictions have also been confirmed by a mutation study of divalent blockade in the NaChBac bacterial channel.^[13]