Novel anomalies for like-charged attraction between curved surfaces and formulation of a hydrogen bonding style mechanism

Shiqi Zhou

doi:10.1063/1.4794798

Abstract

For the first time, the classical density functional theory (DFT) is numerically solved in three- and two-dimensional spaces for a two sphere model of electrostatic interactions between two spherical nanoscale colloids immersed in a primitive model electrolyte solution. Two scientific anomalies are found that (i) contrary to what is often asserted that presence of multivalent counter ion is necessary to induce a like-charge attraction (LCA), univalent counter ion also induces the LCA only if bulk electrolyte concentration and colloid surface charge are high enough, and (ii) although the LCA in general becomes stronger with the bulk electrolyte concentration, adverse effects unexpectedly occur if the colloid surface charge quantity rises sufficiently. In addition, effects of counter ion and co-ion diameters in eliciting the LCA are first investigated and several novel phenomena such as monotonic and non-monotonic dependence of the LCA well depth on the counter ion diameter in different colloid surface charge zones are confirmed. Based these findings, a hydrogen bonding style mechanism is suggested and surprisingly, by appealing to fairly common-sense concepts such as bond energy, bond length, number of hydrogen bonds formed, and counter ion single-layer saturation adsorption capacity, self-consistently explains origin of the LCA between two spherical nanoscale particles, and all phenomena previously reported and observed in this study.

Highlights

A quantitative description of electrostatic interactions (EI) among colloid particles in electrolyte solution is essential to understand many phenomena in colloid science.[1]
The EI between two spherical colloids is calculated based on the pioneering DLVO theory,[2] foundation of which is a postulate of additivity of a dispersion interaction and the EI, and the latter, a topic of this work, is calculated as pair interaction in an infinite electrolyte reservoir using the Poisson equation with ion density distribution characterized in terms of a Boltzmann statistics
System energy changes induced by different configurations of counter ions located on two face-to-face planar surfaces are depicted in Fig. 1(a), and serve to validate an intuitive assumption underlying the present mechanism for the like-charge attraction (LCA) phenomena

Summary

Introduction

A quantitative description of electrostatic interactions (EI) among colloid particles in electrolyte solution is essential to understand many phenomena in colloid science.[1]. The DLVO theory has been criticized over decades from a statistical mechanics viewpoint.[3] The main arguments, which go against validity of the DLVO theory, are the finite ion-size and electrostatic correlation effect ignored by the Boltzmann statistics, a linearization approximation of the PB equation, and the Derjaguin approximation[4] incurred to estimate forces between two spherical colloids by using an interaction between two flat surfaces. Most of the experimental investigations of colloid EI to date are directed to systems where characteristic size of the object is much larger than the interaction length scale, and this has its historical reason since main instruments in intermolecular and surface force measurements measure the interaction between two large mica sheets (radius of curvature ∼1 cm).[6] It is a well known fact that for large colloids the Derjaguin approximation applies. The EPMF between two small colloids remain less understood; they are relevant to polymers, biological molecules, and other nanoscale colloids

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Results

Conclusion