Conditions for electroneutrality breakdown in nanopores

Donnan equilibrium in charged slit-pores from a hybrid nonequilibrium molecular dynamics/Monte Carlo method with ions and solvent exchange

Ion partitioning between different compartments (e.g., a porous material and a bulk solution reservoir), known as Donnan equilibrium, plays a fundamental role in various contexts such as energy, environment, or water treatment. The linearized Poisson-Boltzmann (PB) equation, capturing the thermal motion of the ions with mean-field electrostatic interactions, is practically useful to understand and predict ion partitioning, despite its limited applicability to conditions of low salt concentrations and surface charge densities. Here, we investigate the Donnan equilibrium of coarse-grained dilute electrolytes confined in charged slit-pores in equilibrium with a reservoir of ions and solvent. We introduce and use an extension to confined systems of a recently developed hybrid nonequilibrium molecular dynamics/grand canonical Monte Carlo simulation method ("H4D"), which enhances the efficiency of solvent and ion-pair exchange via a fourth spatial dimension. We show that the validity range of linearized PB theory to predict the Donnan equilibrium of dilute electrolytes can be extended to highly charged pores by simply considering renormalized surface charge densities. We compare with simulations of implicit solvent models of electrolytes and show that in the low salt concentrations and thin electric double layer limit considered here, an explicit solvent has a limited effect on the Donnan equilibrium and that the main limitations of the analytical predictions are not due to the breakdown of the mean-field description but rather to the charge renormalization approximation, because it only focuses on the behavior far from the surfaces.

Local electroneutrality breakdown for electrolytes within varying-section nanopores

We determine the local charge dynamics of a [Formula: see text] electrolyte embedded in a varying-section channel. By means of an expansion based on the length scale separation between the axial and transverse direction of the channel, we derive closed formulas for the local excess charge for both, dielectric and conducting walls, in 2D (planar geometry) as well as in 3D (cylindrical geometry). Our results show that, even at equilibrium, the local charge electroneutrality is broken whenever the section of the channel is not homogeneous for both dielectric and conducting walls as well as for 2D and 3D channels. Interestingly, even within our expansion, the local excess charge in the fluid can be comparable to the net charge on the walls. We critically discuss the onset of such local electroneutrality breakdown in particular with respect to the correction that it induces on the effective free energy profile experienced by tracer ions.

Essence of the Giant Reduction of Power Density in Osmotic Energy Conversion in Porous Membranes: Importance of Testing Area

Harvesting osmotic energy through nanofluidic devices with diverse materials has received considerable attention in recent years. Often, a small testing area on a membrane was chosen to assess its power performance by calculating power density as output power per effective area. Since the choice of this testing area is arbitrary, and it is usually quite small, the result obtained can be too optimistic. There is a need to come up with a common standard so that the performance of a device/membrane can be assessed reasonably. In this study, we systematically investigate the power density as a function of testing area in nanoporous anodic-aluminum-oxide membranes. Through changing the aperture size of substrates, we clearly show that the obtained power density decreases drastically with increasing testing area. For instance, the power density acquired from the testing area of μm2-scale can be five orders of magnitude larger than that from the pristine membrane of cm2-scale. We also advance simulations by building a 3D model to simulate osmotic-driven ion transport in the multichannel system. The result of modeling agrees with our experimental observation that the power density decreases with increasing number of channels, and the ionic concentration profile reveals that the concentration polarization becomes serious as the number of channels increases. Our result highlights the importance of effective area on testing the power performance in nanofluidic devices.

Electrical Conductance of Charged Nanopores

A nanopore's response to an electrical potential drop is characterized by its electrical conductance, . For the last two decades, it has been thought that at low electrolyte concentrations, , the conductance is concentration-independent such that . It has been recently demonstrated that surface charge regulation changes the dependency to , whereby the slope typically takes the values α = 1/3 or 1/2. However, experiments have observed slopes of 2/3 and 1 suggesting that additional mechanisms, such as convection and slip-lengths, appear. Here, we elucidate the interplay between three mechanisms: surface charge regulation, convection, and slip lengths. We show that the inclusion of convection does not change the slope, and when the effects of hydrodynamic slip are included, the slope is doubled. We show that when all effects are accounted for, α can take any value between 0 and 1 where the exact value of the slope depends on the material properties. This result is of utmost importance in designing any electro-kinetically driven nanofluidic system characterized by its conductance.