Like-Charge Attraction between Metal Nanoparticles in a1∶1Electrolyte Solution

Abstract

We calculate the force between two spherical metal nanoparticles of charge Q 1 and Q 2 in a dilute 1:1 electrolyte solution. Numerically solving the non-linear Poisson-Boltzmann equation, we find that metal nanoparticles with the same sign of charge can attract one another. This is fundamentally different from what is found for likecharged, non-polarizable, colloidal particles, the two body interaction potential for which is always repulsive inside a dilute 1:1 electrolyte. Furthermore, existence of like-charge attraction between spherical metal nanoparticles is even more surprising in view of the result that such attraction is impossible between parallel metal slabs, showing the fundamental importance of curvature. To overcome a slow convergence of the numerical solution of the full non-linear Poisson-Boltzmann equation, we developed a modified Derjaguin approximation which allows us to accurate and rapidly calculate the interaction potential between two metal nanoparticles, or between a metal nanoparticle and a phospholipid membrane.

Interfacial solvation can explain attraction between like-charged objects in aqueous solution

“…Note that under the relevant experimental conditions, corrections such as those arising from ion correlations, finite ion size and charge density fluctuations are not sufficient to render the screened repulsion attractive at long range [20][21][22] . The problem has thus far evaded satisfactory explanation and continues to attract great theoretical interest 23 .…”

Charge regulation radically modifies electrostatics in membrane stacks

“…The charge regulation mechanism, described originally in the 1920's [1] and later developed by Kirkwood and Schumaker [2], Marcus [3] and Lifson [4] has become a topic of considerable research interest in recent years [5][6][7][8][9]. Charge regulation refers to the situation in which the local charge on a solvated surface responds to changes in the environment, such as local pH, dielectric inhomogeneities, salt concentrations, etc.…”

Screened Coulomb interactions of general macroions with nonzero particle volume

“…For example, it was suggested that Janus spheres can be described by a collection of point charges [71]. My method becomes less accurate at small particle separations, like DLVO theory, where the surface potential and/or surface charge density become "polarized," which, however, can be reconciled with the Derjaguin approximation [43,66,72,73]. Furthermore, it is not possible to derive multibody interactions (of the form as in Ref.…”

“…As an outlook, I propose extending the theory with (manybody) charge regulation [51,73,[75][76][77] and renormalization [78][79][80][81] to incorporate more types of electrostatic boundary conditions and nonlinear screening, respectively. The expressions of this paper can then still be used with the bare charge replaced by an effective (renormalized) charge.…”