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

Abstract

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); 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. © 2014 AIP Publishing LLC. [http://dx

Polar-solvation classical density-functional theory for electrolyte aqueous solutions near a wall

“…Therefore, the residual contributions to the direct correlation function are still approximated within MSA. This mixing version of FM DFT, which reproduces the accurate HS Carnahan-Starling equation of state and MSA DCFs for residual contributions, has been often used in the calculation of ionic fluids properties [5,6,27]. …”

“…This is because a significant part of the interaction energy is spent aligning so many intervening strong water dipoles. Additionally, the high water concentration is responsible for the strong ionic layering formation [5–7]. Consequently, modeling water molecules at experimentally known concentration, molecule size, and dipolar moment is a prerequisite to accurately describing these phenomena.…”

“…Moreover, the weighted density approximation (WDA) [19] and, subsequently, the most powerful fundamental measure theory (FMT) [20] and its modified versions [21–23] were developed to estimate the corresponding hard-sphere contributions to the potential of mean force. For instance, PB-MSA-WDA DFT was used to study the ionic atmosphere near a planar wall [24–26], whereas PB-MSA-FMT DFT was employed to investigate the ionic atmosphere outside spherical macroions [5], outside cylindrical DNA biomolecules [6], and near a planar wall [27–32]. One of the main advantages of FMT DFT over WDA DFT is that FMT DFT is able to accurately describe hard-sphere liquids at high concentration including those representing solvent molecules.…”

“…One of the main advantages of FMT DFT over WDA DFT is that FMT DFT is able to accurately describe hard-sphere liquids at high concentration including those representing solvent molecules. In particular, the so-called white bear II (WBII) version of FMT [23,33] has been shown to be accurate in describing inhomogeneous fluids, mainly near solid subtracts [5,6] and, therefore, it is the approach considered in this article to calculate the pure hard-sphere (HS) contributions to the structural and thermodynamical properties of the ionic electrical double layers near a uniformly charged hard wall.…”

“…In pursuit of this challenge, we introduce in this article a polar-solvation classical density-functional theory (PSCDFT) to calculate the equilibrium ionic and dipole density profiles of a refined ion-dipole electrolyte aqueous solution model. This is a straightforward extension of the unpolar-solvation classical functional density-functional theory (USCDFT) recently introduced by Marucho and collaborators [5,6] to describe symmetric solutes immersed in unpolar electrolyte aqueous solutions. USCDFT predictions on spherical and cylindrical solutes were validated numerically and experimentally.…”