Understanding Depletion Induced Like-Charge Attraction from Self-Consistent Field Model

Abstract

Abstract. The interaction force between likely charged particles/surfaces is usually repulsive due to the Coulomb interaction. However, the counterintuitive like-charge attraction in electrolytes has been frequently observed in experiments, which has been theoretically debated for a long time. It is widely known that the mean field PoissonBoltzmann theory cannot explain or predict this anomalous feature since it ignores many-body properties. In this paper, we develop efficient algorithm and perform the force calculation between two interfaces using a set of self-consistent equations which properly takes into account the electrostatic correlation and the dielectric-boundary effects. By solving the equations and calculating the pressure with the Debye-charging process, we show that the self-consistent equations could be used to study the attraction between like-charge surfaces from weak-coupling to mediate-coupling regime, and that the attraction is due to the electrostatics-driven entropic force which is significantly enhanced by the dielectric depletion of mobile ions. A systematic investigation shows that the interaction forces can be tuned by material permittivity, ionic size and valence, and salt concentration, and that the like-charge attraction exists only for specific regime of these parameters. 82.45.Un, 64.70.pv, 82.60.Lf PACS:

Microscopic insights into the efficiency of capacitive mixing process

“…Inside these micropores, where the average pore size is less than or comparable with one Debye length in electrolyte solution, the overlapping of the EDL should be taken into account . Toward this issue, several models have been developed including the MPB employed in this work . Nevertheless, we note that for the carbon electrode used in Capmix the most abundant pores are typically less than 10 nm in diameter, and thus the fully developed EDLs were attempted .…”

“…31 Toward this issue, several models 32,33 have been developed including the MPB employed in this work. 34 Nevertheless, we note that for the carbon electrode used in Capmix the most abundant pores are typically less than 10 nm in diameter, 11,12,35 and thus the fully developed EDLs were attempted. [11][12][13]21 These models can be expected to properly capture the essentials of the CDLE mechanism although in reality the pores will be neither parallel nor equally sized.…”

A modified Poisson–Nernst–Planck model with excluded volume effect: theory and numerical implementation

“…One common approach is to add an excess chemical potential to the potential of mean force. Such a correction is able to address the excluded volume effect [7,13,[20][21][22][23][24][25]34,35,41,43,45,48,49,52], dielectric effects [9,32,40,44], and ion-ion correlations [39,53]. For instance, the excluded volume effect is included by considering the entropy of solvent molecules, giving rise to a model with nonlinearly modified mobilities [25,43,49].…”

Modified Poisson--Nernst--Planck Model with Accurate Coulomb Correlation in Variable Media

“…To overcome these difficulties, asymptotic expansions of the self energy by taking the ionic size as a small parameter. The resulting modified PB/PNP equations or similar versions had been used by different authors to investigate important physical features such as the double layer structure and like-charge attraction [39][40][41][42]. With the asymptotic self-energy expression, we find the connection between the chemical potential and self energy, so that the modified PNP equation can preserve a simple form and satisfy a proper energy dissipation law thus a weak formuation.…”