Competition between Born solvation, dielectric exclusion, and Coulomb attraction in spherical nanopores

Abstract

The recent measurement of a very low dielectric constant, , of water confined in nanometric slit pores leads us to reconsider the physical basis of ion partitioning into nanopores. For confined ions in chemical equilibrium with a bulk of dielectric constant b > , three physical mechanisms, at the origin of ion exclusion in nanopores, are expected to be modified due to this dielectric mismatch: dielectric exclusion at the water-pore interface (with membrane dielectric constant, m < ), the solvation energy related to the difference in Debye-Hückel screening parameters in the pore, κ, and in the bulk κ b , and the classical Born solvation self-energy proportional to −1 − −1 b . Our goal is to clarify the interplay between these three mechanisms and investigate the role played by the Born contribution in ionic liquid-vapor (LV) phase separation in confined geometries. We first compute analytically the potential of mean force (PMF) of an ion of radius R i located at the center of a nanometric spherical pore of radius R. Computing the variational grand potential for a solution of confined ions, we then deduce the partition coefficients of ions in the pore versus R and the bulk electrolyte concentration ρ b . We show how the ionic LV transition, directly induced by the abrupt change of the dielectric contribution of the PMF with κ, is favored by the Born self-energy and explore the decrease of the concentration in the pore with both in the vapor and liquid states. Phase diagrams are established for various parameter values and we show that a signature of this phase transition can be detected by monitoring the total osmotic pressure as a function of R. For charged nanopores, these exclusion effects compete with the electrostatic attraction that imposes the entry of counterions into the pore to enforce electroneutrality. This study will therefore help in deciphering the respective roles of the Born self-energy and dielectric mismatch in experiments and simulations of ionic transport through nanopores.

Ionic Conductance of Carbon Nanotubes: Confronting Literature Data with Nanofluidic Theory

“…The basic mean-field type transport model adopted here to study the conductance of CNTs incorporates, as is usual in this context, nanopore (electrostatic) surface charge effects and includes contributions from ionic electrical migration, electro-osmosis, and fluid slip. This model does not, however, integrate certain mechanisms that may be important in ionic partitioning into nanopores (and have already been included at least in part in nanofiltration modeling). − These additional, generally ion specific, mechanisms go beyond the commonly employed Poisson–Boltzmann mean field theory and include steric exclusion and ion self-energy effects. − …”

“…The Born self-energy contribution depends sensitively on ionic charge and radius as well as the dielectric mismatch between the nanopore-confined electrolyte and the external reservoir (bulk) one. ,, The dielectric self-energy depends on ion charge and the dielectric mismatch between the nanopore confined electrolyte and the surrounding medium constituted by the CNT and its matrix − (Figure a). Because this external medium usually has low dielectric constant, the dielectric self-energy contribution should be strongly repulsive for tight CNTs.…”

“…More generally, the influence on conductance of a spatially varying dielectric constant that arises in the presence of an electrolyte confined in a nanopore needs to be further assessed . Additional self-energy effects arise from Debye–Hückel type ionic correlations related to differences in ionic solvation between the electrolyte in the pore and in the bulk. − Furthermore, the importance of ion pairing and ionic polarizability in transport through CNTs needs to be further investigated, especially their role in nanopore conductance. The role and importance of the theoretically predicted ionic “liquid–vapor” phase separation − on nanopore conductance remains an open question and very likely requires targeted simulation and experimental studies before clear answers can be provided.…”

Influence of the Quantum Capacitance on Electrolyte Conductivity through Carbon Nanotubes

“…Our nanoconfined electrolyte model is based on an accurate approximate mean-field description suitable for point ions that interact solely through electrostatic interactions. ,, As such, it does not include specific ion effects. Such effects have been studied numerically using Molecular Dynamics simulations that reveal structured radial profiles for water and ion concentrations, where counterions are closer to the pore wall than co-ions. − Other specific effects are chemical binding with the CNT, Born self-energy barrier, and dielectric jumps. , The role of these two last effects will be studied in a future work. Furthermore, we use a numerical DOS computed using the tight-binding method (which matches with the approximate theoretical DOS for V g ≤ 1 V) and assume no additional geometrical capacitance.…”

“…Such effects have been studied numerically using Molecular Dynamics simulations that reveal structured radial profiles for water and ion concentrations, where counterions are closer to the pore wall than coions. 35−37 Other specific effects are chemical binding with the CNT, 38 Born self-energy barrier, 39 and dielectric jumps. 40,41 The role of these two last effects will be studied in a future work.…”