The Dukhin number as a scaling parameter for selectivity in the infinitely long nanopore limit: Extension to multivalent electrolytes

• DOI: 10.1016/j.molliq.2022.119072
• Publication Date: 2022-04-06T15:24:17Z
• Authors: Zsófia Sarkadi; Dávid Fertig; Mónika Valiskó; Dezső Boda
• Keywords: Chemical Physics (physics.chem-ph); QC03 Heat. Thermodinamics / hőtan; Condensed Matter - Mesoscale and Nanoscale Physics; Statistical Mechanics (cond-mat.stat-mech); FOS: Physical sciences; QC06 Physics of condensed matter / szilárdtestfizika; 02 engineering and technology; QD02 Physical chemistry / fizikai kémia; Condensed Matter - Soft Condensed Matter; 01 natural sciences; 3. Good health; Physics - Chemical Physics; Mesoscale and Nanoscale Physics (cond-mat.mes-hall); 0103 physical sciences; Soft Condensed Matter (cond-mat.soft); termodinamika; 0210 nano-technology; Condensed Matter - Statistical Mechanics

Scaling of the behavior of a nanodevice means that the device function (selectivity, in this work) is a unique function of a scaling parameter that is an appropriate combination of the device parameters. Although nanopores facilitate the transport of ions through a membrane of finite length if the pore is long compared to the pore radius, we deal with an important limiting case, the infinitely long nanopore (nanotube). While in our previous study (Sarkadi et al., J. Chem. Phys. 154 (2021) 154704.) we showed that the Dukhin number is an appropriate scaling parameter in the nanotube limit for 1:1 electrolytes, in this work we obtain the Dukhin number from first principles on the basis of the Poisson-Boltzmann (PB) theory and generalize it to electrolytes containing multivalent ions as well. We show that grand canonical Monte Carlo simulations for charged hard spheres in an implicit solvent give results that are similar to those obtained from the PB theory with deviations that are the consequences of ionic correlations (including finite size of ions) beyond the mean-field level of the PB theory. Such a deviation occurs when charge inversion is present, in 2:2 and 3:1 electrolytes, for example.