A molecular simulation study on the role of ion sizes and dielectric images in near-surface ion distribution far from the strong coupling limit

Quantifying uncertainty in nanofiltration transport models for enhanced metals recovery

To decarbonize our global energy system, sustainably harvesting metals from diverse sourcewaters is essential. Membrane-based processes have recently shown great promise in meeting these needs by achieving high metal ion selectivities with relatively low water and energy use. An example is nanofiltration, which harnesses steric, dielectric, and Donnan exclusion mechanisms to perform size- and charge-based fractionation of metal ions. To further optimize nanofiltration systems, multicomponent models are needed; however, conventional methods necessitate large amounts of data for model calibration, introduce substantial uncertainty into the characterization process, and often yield poor results when extrapolated. In this work, we develop a new computational architecture to alleviate these concerns. Specifically, we develop a framework that: (1) reduces the data requirement for model calibration to only charged species measurements; (2) eliminates uncertainty propagation problems present in conventional characterization processes; (3) enables exploration of pH optimization for enhancing metal ion selectivities; and (4) enables uncertainty quantification to assess the sensitivity of partition coefficients and ion driving forces to learned pore size distributions. Our framework captures eight independent datasets comprising over 500 measurements to within ±15%. Our studies also suggest that the expectation-maximization algorithm can effectively learn pore size distributions and that optimizing pH can improve metal ion selectivities by a factor of 3-10×. Our findings also reveal that image charges appear to play a less pronounced role in dielectric exclusion under the studied conditions and that ion driving forces are more sensitive to pore size distributions than partition coefficients.

On the physics of both surface overcharging and charge reversal at heterophase interfaces

A series of Monte Carlo simulations are employed to reveal the physics of both surface overcharging and charge reversal at a negatively charged dielectric interface exposed to a bulk solution containing a +2:−1 electrolyte in the absence and presence of a monovalent salt.

Ionic asymmetry and solvent excluded volume effects on spherical electric double layers: a density functional approach

In this article, we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry, and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids [J. Chem. Phys. 124, 154506 (2006); Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)]. It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilize a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the mean spherical approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry, and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that predicted by the Stern model.

Electric double layer force between charged surfaces: effect of solvent polarization

In this paper, we develop a theory to delineate the consequences of finite solvent polarization in electric double layer interaction or the osmotic pressure between two similar or oppositely charged surfaces. We use previously published Langevin-Bikerman equations to calculate this electric double layer interaction force or the osmotic pressure between the charged surfaces. The osmotic pressure between oppositely charged surfaces is found to be much larger than that between similarly charged surfaces, and for either case, the influence of solvent polarization ensures a larger pressure than that predicted by the Poisson-Boltzmann (PB) model. We derive distinct scaling relationships to explain the increase of the pressure as a function of the separation between the surfaces, the solvent polarizability, and the number density of water molecules. Most importantly, we demonstrate that our theory can successfully reproduce the experimental results of interaction force between similar and oppositely charged surfaces, by accounting for the large under-prediction made by the corresponding PB model.

Inversion of membrane surface charge by trivalent cations probed with a cation-selective channel

We demonstrate that the cation-selective channel formed by gramicidin A can be used as a reliable sensor for studying the multivalent ion accumulation at the surfaces of charged lipid membranes and the "charge inversion" phenomenon. In asymmetrically charged membranes with the individual leaflets formed from pure negative and positive lipids bathed by 0.1 M CsCl solutions the channel exhibits current rectification, which is comparable to that of a typical n/p semiconductor diode. We show that even at these highly asymmetrical conditions the channel conductance can be satisfactorily described by the electrodiffusion equation in the constant field approximation but, due to predictable limitations, only when the applied voltages do not exceed 50 mV. Analysis of the changes in the voltage-dependent channel conductance upon addition of trivalent cations allows us to gauge their interactions with the membrane surface. The inversion of the sign of the effective surface charge takes place at the concentrations, which correlate with the cation size. Specifically, these concentrations are close to 0.05 mM for lanthanum, 0.25 mM for hexaamminecobalt, and 4 mM for spermidine.