Recent Developments in the Methods and Applications of Electrostatic Theory

[Image: see text] The review improves our understanding of how electrostatic interactions in the electrolyte, gas phase, and on surfaces can drive the fragmentation and assembly of particles. This is achieved through the overview of our advanced theoretical and computational modeling toolbox suitable for interpretation of experimental observations and discovery of novel, tunable assemblies and architectures. In the past decade, we have produced a significant, fundamental body of work on the development of comprehensive theories based on a rigorous mathematical foundation. These solutions are capable of accurate predictions of electrostatic interactions between dielectric particles of arbitrary size, anisotropy, composition, and charge, interacting in solvents, ionized medium, and on surfaces. We have applied the developed electrostatic approaches to describe physical and chemical phenomena in dusty plasma and planetary environments, in Coulomb fission and electrospray ionization processes, and in soft matter, including a counterintuitive but widespread attraction between like-charged particles. Despite its long history, the search for accurate methods to provide a deeper understanding of electrostatic interactions remains a subject of significant interest, as manifested by a constant stream of theoretical and experimental publications. While major international effort in this area has focused predominantly on the computational modeling of biocatalytic and biochemical performance, we have expanded the boundaries of accuracy, generality, and applicability of underlying theories. Simple solvation models, often used in calculating the electrostatic component of molecular solvation energy and polarization effects of solvent, rarely go beyond the induced dipole approximation because of computational costs. These approximations are generally adequate at larger separation distances; however, as particles approach the touching point, more advanced charged-induced multipolar descriptions of the electrostatic interactions are required to describe accurately a collective behavior of polarizable neutral and charged particles. At short separations, the electrostatic forces involving polarizable dielectric and conducting particles become nonadditive which necessitates further developments of quantitatively accurate many-body approaches. In applications, the electrostatic response of materials is commonly controlled by externally applied electric fields, an additional complex many-body problem that we have addressed most recently, both theoretically and numerically. This review reports on the most significant results and conclusions underpinning these recent advances in electrostatic theory and its applications. We first discuss the limitations of classical approaches to interpreting electrostatic phenomena in electrolytes and complex plasmas, leading to an extended analytical theory suitable for accurate estimation of the electrostatic forces in a dilute solution of a strong electrolyte. We then introduce the concept and numerical realization of many-body electrostatic theory focusing on its performance in selected experimental cases. These experiments underpin, among other applications, electrostatic self-assembly of two-dimensional lattice structures, melting of ionic colloidal crystals in an external electric field, and coalescence of charged clusters.