Ionic size effects on the Poisson-Boltzmann theory

Abstract

In this paper, we develop a simple theory to study the effects of ionic size on ionic distributions around a charged spherical particle. We include a correction to the regular Poisson-Boltzmann equation in order to take into account the size of ions in a mean-field regime. The results are compared with Monte Carlo simulations and a density functional theory based on the fundamental measure approach and a second-order bulk expansion which accounts for electrostatic correlations. The agreement is very good even for multivalent ions. Our results show that the theory can be applied with very good accuracy in the description of ions with highly effective ionic radii and low concentration, interacting with a colloid or a nanoparticle in an electrolyte solution.

Connecting energetics to dynamics in particle growth by oriented attachment using real-time observations

“…Thus, to understand the interactions responsible for both the negligible barrier below 1 nm and the attractive interactions and torques beyond 5 nm, it is necessary to employ theoretical frameworks capable of probing both short-and long-range interactions that are mediated by the solution. Complexities in the experimental parameters, namely the extremely small separations, reduced dielectric contrast due to methanol, and the mixed valency of the ions comprising the electrolyte, complicate extraction of specific molecular information from molecular simulations and input to simple dielectric theories for calculating particle interactions [49][50][51] . Consequently, we chose to consider the granularity of solvent and ions in the context of classical density functional theory (cDFT) which can access both limits 52 .…”

Modified Poisson-Boltzmann theory for polyelectrolytes in monovalent salt solutions with finite-size ions

“…This occurs for example for multivalent ion species [73,74], localized charges [74], or large ion sizes [25,75]. It is worth mentioning that previous successful attempts to consider the finite size of ions in PB type models exist [25,28,31,76]. Additionally, for small ion diameters at low salt concentrations, some significant deviations between the LPB theory and CG-MD simulations ion distributions rise.…”

“…In this case, significant deviations, in practice positional correlations, are induced by steric packing considerations rising from the size and elevated concentration of the ions. Such steric and positional correlations due to the finite size and strong electrostatic correlations result in layered ion organization in the vicinity of highly charged PEs [28]. Beyond this any meanfield approach can be expected to fail when charge correlations become significant.…”

“…Specifically, mean-field models fail to account for molecular level structure and PE charge distribution deviations from the assumed cylindrical symmetry [8,24]. Ion size can be effectively accounted for in the models [25][26][27][28] and also chemical specificity of the ions can be partially considered for by modifying the interaction potentials, see e.g. Refs.…”

Nonlinear electrostatics: the Poisson–Boltzmann equation

“…We will focus on (5) in the present paper for this double layer. In this case again because of system symmetry ()  x and ()  x reduce to functions of just x (the coordinate orthogonal to the charged wall), the full Laplacian can be replaced by 22 There is also a large literature on theories going beyond primitive model PB 9,61,67,70,71,88,89,91,101,[110][111][112] by including ion-ion correlations, finite ionic size and molecular structure of the solvent (assumed above to be water), nonuniformities of the wall charges, additional intermolecular and wall forces. We do not discuss these improvements here, nor do we discuss the quantum generalization of classical PB theory, but we indicate in the references some quantum discussions [51][52][53][54][55][56][57][58]62 .…”