Résumé
Fundamental understanding of ionic transport at the nanoscale is essential for developing biosensors based on nanopore technology and new generation high-performance nanofiltration membranes for separation and purification applications. Furthermore the number of precise conductance measurements of electrolytes in nanopores, made of single-walled carbon nanotubes (SWCNTs), is quickly growing.To clarify the dominant mechanisms at play and facilitate the characterization of such systems, we developed a mesoscopic model for the electrolyte conductivity in nanopores that focuses on the interaction between ions and the pore surface [1,2]. The model considers explicitly ion advection by electro-osmotic flow, fluid slippage at the pore surface, and the nature of the surface charge. In particular, we consider a charge-regulation mechanism, i.e. a surface charge density which is modulated by the reservoir pH and the salt concentration [1,3].This approach permits us to catalog the different possible transport regimes and propose an explanation for the wide variety of currently known experimental behavior for the conductance versus reservoir salt concentration. Hence, by fitting the experimental conductance data obtained with NaCl or KCl electrolytes in single nanometric hydrophobic pores made in track-etched membranes [2] or with SWCNTs [3,4], we are able to infer the values of the surface charge densities and the slip lengths. In particular the sublinear dependence of the conductance on the salt concentration observed in recent experiments points toward a charge-regulation mechanism and a possible strong influence of slippage, which leads to a novel 2/3 power law behavior . Furthermore, in some cases, a voltage activated behavior is observed and is accounted for by the presence of local energy barriers along or at the ends of the nanotube. Finally, we discuss theoretically the influence on the electrolyte conductance of the lower value of the water dielectric constant in this extreme confinement [5] and of the dielectric jump at the nanopore surface [6]. By properly including these effects in the ionic chemical potential, we show that they might play a central role when these dielectric constants are very different [7]. References[1] M. Manghi et al., Phys. Rev. E, 98, 012605 (2018)[2] S. Balme et al. Scientific Rep., 5, 10135 (2015)[3] E. Secchi et al., Phys. Rev. Lett. 116, 154501 (2016)[4] K. Yazda, et al., Nanoscale, 9, 11976 (2017)[5] Fumagalli et al. Science 369, 1339 (2018)[6] S. Buyukdagli, M. Manghi, J. Palmeri, Phys. Rev. Lett., 105, 158103 (2010)[7] T. Hennequin, M. Manghi, J. Palmeri, Physical Review E 104 (4), 044601 (2021) https://doi.org/10.1103/PhysRevE.104.044601