Heterogeneous surface charge confining an electrolyte solution

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.

Structure of electrolyte solutions at nonuniformly charged surfaces on a variety of length scales

The structures of dilute electrolyte solutions close to nonuniformly charged planar substrates are systematically studied within the entire spectrum of microscopic to macroscopic length scales by means of a unified classical density functional theory approach. This is in contrast to previous investigations, which are applicable either to short or to long length scales. It turns out that interactions with microscopic ranges, e.g., due to the hard cores of the fluid molecules and ions, have a negligible influence on the formation of nonuniform lateral structures of the electrolyte solutions. This partly justifies the Debye-Hückel approximation schemes applied in previous studies of that system. In general, a coupling between the lateral and the normal fluid structures leads to the phenomenology that, upon increasing the distance from the substrate, fewer details of the lateral nonuniformities contribute to the fluid structure, such that ultimately only large-scale surface features remain relevant. It can be expected that this picture also applies to other fluids characterized by several length scales.

Electrolytes in regimes of strong confinement: surface charge modulations, osmotic equilibrium and electroneutrality

In the present work, we study an electrolyte solution confined between planar surfaces with nanopatterned charged domains, which has been connected to a bulk ionic reservoir. The system is investigated through an improved Monte Carlo (MC) simulation method, suitable for simulation of electrolytes in the presence of modulated surface charge distributions. We also employ a linear approach in the spirit of the classical Debye-Hückel approximation, which allows one to obtain explicit expressions for the averaged potentials, ionic profiles, effective surface interactions and the net ionic charge confined between the walls. Emphasis is placed on the limit of strongly confined electrolytes, in which case local electroneutrality in the inter-surface space might not be fulfilled. In order to access the effects of such a lack of local charge neutrality on the ion-induced interactions between surfaces with modulated charge domains, we consider two distinct model systems for the confined electrolyte: one in which a salt reservoir is explicitly taken into account via the osmotic equilibrium with an electrolyte of fixed bulk concentration, and a second one in which the equilibrium with a charge neutral ionic reservoir is implicitly considered. While in the former case the osmotic ion exchange might lead to non-vanishing net charges, in the latter model charge neutrality is enforced through the appearance of an implicit Donnan potential across the charged interfaces. A strong dependence of the ion-induced surface interactions on the employed model system is observed at all surface separations. These findings strongly suggest that due care is to be taken while choosing among different scenarios to describe the ion exchange in electrolytes confined between charged surfaces, even in cases when the monopole (non zero net charge) surface contributions are absent.