Poisson-Boltzmann model of electrolytes containing uniformly charged spherical nanoparticles

Structural and electrostatic properties between pH-responsive polyelectrolyte brushes studied by augmented strong stretching theory

In this paper, we study electrostatic and structural properties between pH-responsive polyelectrolyte brushes by using a strong stretching theory accounting for excluded volume interactions, the density of polyelectrolyte chargeable sites and the Born energy difference between the inside and outside of the brush layer.In a free energy framework, we obtain self-consistent field equations to determine electrostatic properties between two pH-responsive polyelectrolyte brushes. We elucidate that in the region between two pH-responsive polyelectrolyte brushes, electrostatic potential at the centerline and osmotic pressure increase not only with excluded volume interaction, but also with density of chargeable sites on a polyelectrolyte molecule. Importantly, we clarify that when two pH-responsive polyelectrolyte brushes approach each other, the brush thickness becomes short and that a large excluded volume interaction and a large density of chargeable sites yield the enhanced contract of polyelectrolyte brushes. In addition, we also demonstrate how the influence of such quantities as pH, the number of Kuhn monomers, the density of charged sites, the lateral separation between adjacent polyelectrolyte brushes, Kuhn length on the electrostatic and structural properties between the two polyelectrolyte brushes is affected by the exclusion volume interaction. Finally, we investigate the influence of Born energy difference on the thickness of polyelectrolyte brushes and the osmotic pressure between two pH-responsive polyelectrolyte brushes.

Nanoparticles: From synthesis to applications and beyond

In modern-day research, nanoparticles (size < 100nm) are an indispensable tool for various applications, especially in the field of biomedicine. Although enormous efforts have been made to understand the properties and specificities of nanoparticles, many questions are still not answered and the new ones arise. In this review we summarize current trends in the nanoparticle synthesis and characterization and interpret the stability of nanoparticles in various media from aqueous solutions to biological milieu important for the in vitro and in vivo studies. To get more detailed insight into nanoparticle charging properties and interactions of nanoparticles with interfaces the theoretical models are presented. Finally, the overview of nanoparticle applications is given and the future prospects are discussed.

Accurate Determination of the Quantity and Spatial Distribution of Counterions around a Spherical Macroion

The accurate distribution of countercations (Rb⁺ and Sr²⁺ ) around a rigid, spherical, 2.9-nm size polyoxometalate cluster, {Mo₁₃₂ }^42- , is determined by anomalous small-angle X-ray scattering. Both Rb⁺ and Sr²⁺ ions lead to shorter diffuse lengths for {Mo₁₃₂ } than prediction. Most Rb⁺ ions are closely associated with {Mo₁₃₂ } by staying near the skeleton of {Mo₁₃₂ } or in the Stern layer, whereas more Sr²⁺ ions loosely associate with {Mo₁₃₂ } in the diffuse layer. The stronger affinity of Rb⁺ ions towards {Mo₁₃₂ } than that of Sr²⁺ ions explains the anomalous lower critical coagulation concentration of {Mo₁₃₂ } with Rb⁺ compared to Sr²⁺ . The anomalous behavior of {Mo₁₃₂ } can be attributed to majority of negative charges being located at the inner surface of its cavity. The longer anion-cation distance weakens the Coulomb interaction, making the enthalpy change owing to the breakage of hydration layers of cations more important in regulating the counterion-{Mo₁₃₂ } interaction.

Incorporation of ion and solvent structure into mean-field modeling of the electric double layer

An electric double layer forms when the small mobile ions of an electrolyte interact with an extended charged object, a macroion. The competition between electrostatic attraction and translational entropy loss of the small ions results in a diffuse layer of partially immobilized ions in the vicinity of the macroion. Modeling structure and energy of the electric double layer has a long history that has lead to the classical Poisson-Boltzmann theory and numerous extensions that account for ion-ion correlations and structural ion and solvent properties. The present review focuses on approaches that instead of going beyond the mean-field character of Poisson-Boltzmann theory introduce structural details of the ions and the solvent into the Poisson-Boltzmann modeling framework. The former include not only excluded volume effects but also the presence of charge distributions on individual ions, spatially extended ions, and internal ionic degrees of freedom. The latter treat the solvent either explicitly as interacting Langevin dipoles or in the form of effective non-electrostatic interactions, in particular Yukawa interactions, that are added to the Coulomb potential. We discuss how various theoretical models predict structural properties of the electric double layer such as the differential capacitance and compare some of these predictions with computer simulations.

Note: Density functional theory for uniformly charged hard-sphere ions

The density function theory has been proposed for studying the structural properties of electrolytes containing uniformly charged hard-spherical ions. The calculated result shows good agreement with the corresponding Monte Carlo simulation data of Bohinc et al. [J. Chem. Phys. 145, 234901 (2016)]. The results confirm that the attraction between like-charged planar surfaces is the results of the intra-ionic correlation and depends strongly on the charge distribution of hard-sphere ions.

Two-Dimensional Electric Double Layer Structure with Heterogeneous Surface Charge

In this work we present a systematic study of the lateral (parallel to the wall) and normal (perpendicular to the wall) nanostructure of the electric double layer at a heterogeneous interface between two regions of different surface charges, often found in nanoscale electrochemical devices. Specifically, classical density functional theory (DFT) is used to probe a cation concentration range of 10 mM to 1 M, for valences of +1, + 2, and +3, and a diameter range of 0.15-0.9 nm over widely varying surface charges (between -0.15 and +0.15 C/m²). The DFT results predict significant lateral and normal nanostructure in the form of ion concentration oscillations. These results are directly compared with those from Poisson-Boltzmann theory, showing significant deviation between the two theories, not only in the concentration profiles, but also in the sign of the electrostatic potential.