Coulomb energy of uniformly charged spheroidal shell systems

Dynamics of Rayleigh Fission Processes in ∼100 nm Charged Aqueous Nanodrops

Fission of micron-size charged droplets has been observed using optical methods, but little is known about fission dynamics and breakup of smaller nanosize droplets that are important in a variety of natural and industrial processes. Here, spontaneous fission of individual aqueous nanodrops formed by electrospray is investigated using charge detection mass spectrometry. Fission processes ranging from formation of just two progeny droplets in 2 ms to production of dozens of progeny droplets over 100+ ms are observed for nanodrops that are charged above the Rayleigh limit. These results indicate that Rayleigh fission is a continuum of processes that produce progeny droplets that vary widely in charge, mass, and number.

Shape control of deformable charge-patterned nanoparticles

Deformable nanoparticles (NPs) offer unprecedented opportunities as dynamic building blocks that can spontaneously reconfigure during assembly in response to environmental cues. Designing reconfigurable materials based on deformable NPs hinges on an understanding of the shapes that can be engineered in these NPs. We solve for the low-energy shapes of charge-patterned deformable NPs by using molecular dynamics-based simulated annealing to minimize a coarse-grained model Hamiltonian characterized with NP elastic and electrostatic energies subject to a volume constraint. We show that deformable spherical NPs of radius 50 nm whose surface is tailored with octahedrally distributed charged patches and double-cap charged patches adapt their shape differently in response to changes in surface charge coverage and ionic strength. We find shape transitions to rounded octahedra, faceted octahedra, faceted bowls, oblate spheroids, spherocylinders, dented beans, and dimpled rounded bowls. We demonstrate that similar shape transitions can be achieved in deformable NPs of different sizes. The effects of counterion condensation on the free-energetic drive associated with the observed deformations are examined via Manning model calculations that utilize simulation-derived estimates for the NP Coulomb energy under salt-free conditions. The charge-pattern-based shape control of deformable NPs has implications for the design of responsive nanocontainers and for assembling reconfigurable materials whose functionality hinges on the shape-shifting properties of their nanoscale building blocks.

Charged elastic rings: deformation and dynamics

We report the counter-intuitive instability of charged elastic rings, and the persistence of sinusoidal deformations in the lowest-energy configurations by the combination of high-precision numerical simulations and analytical perturbation calculation. We also study the dynamical evolution of the charged ring under random disturbance, and reveal the modulation of the dominant frequencies by the electrostatic force. The purely mechanical analysis of the classical ring system presented in this work yields insights into the subtlety of long-range forces in the organization and dynamics of matter.

Designing Surface Charge Patterns for Shape Control of Deformable Nanoparticles

Designing reconfigurable materials based on deformable nanoparticles (NPs) hinges on an understanding of the energetically favored shapes these NPs can adopt. Using simulations, we show that hollow, deformable, patchy NPs tailored with surface charge patterns such as Janus patches, stripes, and polyhedrally distributed patches differently adapt their shape in response to changes in patterns and ionic strength, transforming into capsules, hemispheres, variably dimpled bowls, and polyhedra. The links between anisotropy in NP surface charge, shape, and the elastic energy density are discussed.

Computational studies of shape control of charged deformable nanocontainers

Biological matter is often compartmentalized by soft membranes that dynamically change their shape in response to chemical and mechanical cues. Deformable soft-matter-based nanoscale membranes or nanocontainers that mimic this behavior can be used as drug-delivery carriers that can adapt to evolving physiological conditions, or as dynamic building blocks for the design of novel hierarchical materials via assembly engineering. Here, we connect the intrinsic features of charged deformable nanocontainers such as their size, charge, surface tension, and elasticity with their equilibrium shapes for a wide range of solution conditions using molecular dynamics simulations. These links identify the fundamental mechanisms that establish the chemical and materials design control strategies for modulating the equilibrium shape of these nanocontainers. We show that flexible nanocontainers of radii ranging from 10-20 nm exhibit sphere-to-rod-to-disc shape transitions yielding rods and discs over a wide range of aspect ratio λ (0.3 < λ < 5). The shape transitions can be controlled by tuning salt and/or surfactant concentration as well as material elastic parameters. The shape changes are driven by reduction in the global electrostatic energy and are associated with dramatic changes in local surface elastic energy distributions. To illustrate the shape transition mechanisms, exact analytical calculations for idealized spheroidal nanocontainers in salt-free conditions are performed. Explicit counterion simulations near nanocontainers and associated Manning model calculations provide an assessment of the stability of observed shape deformations in the event of ion condensation.

Electrostatic interactions between spheroidal dielectric particles

Theory is developed to address the significant problem of electrostatic interactions between charged polarizable dielectric spheroids. The electrostatic force is defined by particle dimensions and charge, dielectric constants of the interacting particles and medium, and the interparticle separation distance; and it is expressed in the form of an integral over the particle surface. The switching behavior between like charge repulsion and attraction is demonstrated as depending on the ratio of the major and minor axes of spheroids. When the major and minor axes are equal, the theory yields a solution equivalent to that obtained for spherical particles. Limiting cases are presented for nonpolarizable spheroids, which describe the electrostatic behavior of charged rods, discs, and point charges. The developed theory represents an important step toward comprehensive understanding of direct interactions and mechanisms of electrostatically driven self-assembly processes.