Spiers Memorial Lecture: Towards understanding of iontronic systems: electroosmotic flow of monovalent and divalent electrolyte through charged cylindrical nanopores.

In many practical applications, ions are the primary charge carrier and must move through either semipermeable membranes or through pores, which mimic ion channels in biological systems. In analogy to electronic devices, the "iontronic" ones use electric fields to induce the charge motion. However, unlike the electrons that move through a conductor, motion of ions is usually associated with simultaneous solvent flow. A study of electroosmotic flow through narrow pores is an outstanding challenge that lies at the interface of non-equilibrium statistical mechanics and fluid dynamics. In this paper, we will review recent works that use dissipative particle dynamics simulations to tackle this difficult problem. We will also present a classical density functional theory (DFT) based on the hypernetted-chain approximation (HNC), which allows us to calculate the velocity of electroosmotic flows inside nanopores containing 1 : 1 or 2 : 1 electrolyte solution. The theoretical results will be compared with simulations. In simulations, the electrostatic interactions are treated using the recently introduced pseudo-1D Ewald summation method. The zeta potentials calculated from the location of the shear plane of a pure solvent are found to agree reasonably well with the Smoluchowski equation. However, the quantitative structure of the fluid velocity profiles deviates significantly from the predictions of the Smoluchowski equation in the case of charged pores with 2 : 1 electrolyte. For low to moderate surface charge densities, the DFT allows us to accurately calculate the electrostatic potential profiles and the zeta potentials inside the nanopores. For pores with 1 : 1 electrolyte, the agreement between theory and simulation is particularly good for large ions, for which steric effects dominate over the ionic electrostatic correlations. The electroosmotic flow is found to depend very strongly on the ionic radii. In the case of pores containing 2 : 1 electrolyte, we observe a reentrant transition in which the electroosmotic flow first reverses and then returns to normal as the surface change density of the pore is increased.

Effects of electrostatic coupling and surface polarization on polyelectrolyte brush structure.

In this work, we perform molecular dynamics simulations to study a spherical polyelectrolyte brush. We explore the effects of surface polarization and electrostatic coupling on brush size and distribution of counterions. The method of image charges is considered to take into account surface polarization, considering a metallic, an unpolarizable, and a dielectric nano-core. It is observed that, for all cases, a moderate shrinking-swelling effect appears with an increase in the electrostatic coupling parameter. This effect occurs under high Manning ratios. The curves relating the average size of polyelectrolyte brush as a function of coupling show a minimum. The results show that the grafting density of polyelectrolytes on the nano-core surface plays an important role in the polarization effect. We consider a modified Poisson-Boltzmann theory to describe the counterion profiles around the brush in the case of unpolarizable nano-cores and weak electrostatic coupling.

Reversal of Electroosmotic Flow in Charged Nanopores with Multivalent Electrolyte.

We study the reversal of electroosmotic flow in charged cylindrical nanopores containing multivalent electrolyte. Dissipative particle dynamics is used to simulate the hydrodynamics of the electroosmotic flow. The electrostatic interactions are treated using 3D Ewald summation, corrected for a pseudo-one-dimensional geometry of the pore. We observe that, for sufficiently large surface charge density, condensation of multivalent counterions leads to the reversal of the pore's surface charge. This results in the reversal of electroosmotic flow. Our simulations show that the Smoluchowski equation is able to quantitatively account for the electroosmotic flow through the nanopore, if the shear plane is shifted from the position of the Stern contact surface.

Electroosmotic Flow Grows with Electrostatic Coupling in Confining Charged Dielectric Surfaces.

In this work, the effects of polarization of confining charged planar dielectric surfaces on induced electroosmotic flow are investigated. To this end, we use dissipative particle dynamics to model solvent and ionic particles together with a modified Ewald sum method to model electrostatic interactions and surfaces polarization. A relevant difference between counterions number density profiles, velocity profiles, and volumetric flow rates obtained with and without surface polarization for moderate and high electrostatic coupling parameters is observed. For low coupling parameters, the effect is negligible. An increase of almost 500% in volumetric flow rate for moderate/high electrostatic coupling and surface separation is found when polarizable surfaces are considered. The most important result is that the increase in electrostatic coupling substantially increases the electroosmotic flow in all studied range of separations when the dielectric constant of electrolytes is much higher than the dielectric constant of confining walls. For the higher separation simulated, an increase of around 340% in volumetric flow rate when the electrostatic coupling is increased by a factor of two orders of magnitude is obtained.

Correction: Electroosmosis as a probe for electrostatic correlations.

Correction for 'Electroosmosis as a probe for electrostatic correlations' by Ivan Palaia et al., Soft Matter, 2020, 16, 10688-10696, DOI: 10.1039/D0SM01523G.

Electroosmosis as a probe for electrostatic correlations.

We study the role of ionic correlations on the electroosmotic flow in planar double-slit channels, without salt. We propose an analytical theory, based on recent advances in the understanding of correlated systems. We compare the theory with mean-field results and validate it by means of dissipative particle dynamics simulations. Interestingly, for some surface separations, correlated systems exhibit a larger flow than predicted by mean-field. We conclude that the electroosmotic properties of a charged system can be used, in general, to infer and weight the importance of electrostatic correlations therein.

Electroosmotic Flow in Polarizable Charged Cylindrical Nanopores.

We present a simulation method to study electroosmotic flow in charged nanopores with dielectric contrast between their interior and the surrounding medium. To perform simulations, we separate the electrostatic energy into the direct Coulomb and the polarization contributions. The polarization part is obtained using periodic Green functions and can be expressed as a sum of fast converging modified Bessel functions. On the other hand, the direct Coulomb part of the electrostatic energy is calculated using fast converging three-dimensional (3D) Ewald summation method, corrected for a pseudo one-dimensional (1D) geometry. The effects of polarization are found to be particularly important for systems with multivalent counterions and narrow nanopores. Depending on the surface charge density, polarization can increase the volumetric flow rate by 200%. For systems with 3:1 electrolyte, we observe that there is a saturation of the volumetric flow rate. In this case, for polarizable pores, the flow rate is 100% higher than for nonpolarizable pores.