Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson–Boltzmann Framework: An Analytical Treatment

Abstract

This work considers the interaction of two dielectric particles of arbitrary shape immersed into a solvent containing a dissociated salt and assuming that the linearized Poisson–Boltzmann equation holds. We establish a new general spherical re-expansion result which relies neither on the conventional condition that particle radii are small with respect to the characteristic separating distance between particles nor on any symmetry assumption. This is instrumental in calculating suitable expansion coefficients for the electrostatic potential inside and outside the objects and in constructing small-parameter asymptotic expansions for the potential, the total electrostatic energy, and forces in ascending order of Debye screening. This generalizes a recent result for the case of dielectric spheres to particles of arbitrary shape and builds for the first time a rigorous (exact at the Debye–Hückel level) analytical theory of electrostatic interactions of such particles at arbitrary distances. Numerical tests confirm that the proposed theory may also become especially useful in developing a new class of grid-free, fast, highly scalable solvers.

Deconstructing Electrostatics of Functionalized Metal Nanoparticles from Molecular Dynamics Simulations

“…However, the behavior as a function of the ionic strength is finely described by λ D and A ( z̃ , R ϵ , λ D ). These results can be used in simplified representations of the NPs for coarse-grained molecular dynamics simulations, possibly including shape effects by means of recently proposed advanced analytic representations of the potentials. , …”

“…These results can be used in simplified representations of the NPs for coarsegrained molecular dynamics simulations, possibly including shape effects by means of recently proposed advanced analytic representations of the potentials. 55,56 In addition, we approximately evaluated the ζ-potentials as the values of ϕ on the SAS, whose average value is ∼exp(A(z, R ϵ , λ D )), showing its strong sensitivity to ionic strength. These results help interpret the literature data on electrostatic properties of metal NPs in saline solutions, which were extensively investigated.…”

Interaction of Nanoparticles in Electrolyte Solutions

“…The current state in this area is summarized by Kovalchuk et al To describe the interaction of nanoparticles, approximations are used at the joint calculation of forces, both electrostatic and London–van der Waals interactions, which are based on the Deryaguin approximation . Recently, the electrostatic interaction was considered without the Deryaguin approximation based on the exact solution of the linearized Poisson–Boltzmann equation. − New methods for the calculation of the strength of the London–van der Waals interaction were recently developed (see, for example, ref ). Below, an exact solution to the problem of the electrostatic interaction between nanoparticles based on the linearized Poisson–Boltzmann equation, which is supplemented by calculation of the London–van der Waals interaction force, is presented.…”

Biomolecular Electrostatic Phenomena: An Evergreen Field

“…Improvements to continuum models were discussed regarding a better prediction of water molecule distribution around negatively charged solutes, 17 and introducing better analytical estimates of the interaction energy of dielectric particles in a solvent obeying the linearized Poisson−Boltzmann equation. 18 The same solvent model was assumed in the development of an improved version of the TABI-PB solver. 19 Along the same lines, but following a different model, a coarse-grained version of ddCOSMO was presented as an efficient way to compute the solvation energy of large solutes within a polarizable continuum medium in a linear scaling computational time.…”

“…Approximately one-third of the contributions to this virtual special issue concerned methodological aspects, considered from many different points of view. Improvements to continuum models were discussed regarding a better prediction of water molecule distribution around negatively charged solutes, and introducing better analytical estimates of the interaction energy of dielectric particles in a solvent obeying the linearized Poisson–Boltzmann equation . The same solvent model was assumed in the development of an improved version of the TABI-PB solver .…”