A theory of interactions between polarizable dielectric spheres

The significance of multipole interactions for the stability of regular structures composed from charged particles

Identifying the forces responsible for stabilising binary particle lattices is key to the controlled fabrication of many new materials. Experiments have shown that the presence of charge can be integral to the formation of ordered arrays; however, a complete analysis of the forces responsible has not included many of the significant lattice types that may form during fabrication. A theory of many-body electrostatic interactions has been applied to six lattice stoichiometries, AB, AB2, AB3, AB4, AB5 and AB6, to show that induced multipole interactions can make a very significant (>80 %) contribution to the total lattice energy of arrays of charged particles. Particle radii ratios which favour global minima in electrostatic energy are found to be the same or a close match to those observed by experiment. Although certain lattice types exhibit local energy minima, the calculations show that many-body rather than two-body interactions are ultimately responsible for the structures observed by experiment. For a lattice isostructural with CFe4, a particle size ratio not previously observed is found to be particularly stable due to many-body effects.

Discrete Element Method Evaluation of Triboelectric Charging Due to Powder Handling in the Capsule of a DPI

The generation and accumulation of an electrostatic charge from handling pharmaceutical powders is a well-known phenomenon, given the insulating nature of most APIs (Active Pharmaceutical Ingredients) and excipients. In capsule-based DPIs (Dry Powder Inhalers), the formulation is stored in a gelatine capsule placed in the inhaler just before inhalation. The action of capsule filling, as well as tumbling or vibration effects during the capsule life cycle, implies a consistent amount of particle-particle and particle-wall contacts. A significant contact-induced electrostatic charging can then take place, potentially affecting the inhaler's efficiency. DEM (Discrete Element Method) simulations were performed on a carrier-based DPI formulation (salbutamol-lactose) to evaluate such effects. After performing a comparison with the experimental data on a carrier-only system under similar conditions, a detailed analysis was conducted on two carrier-API configurations with different API loadings per carrier particle. The charge acquired by the two solid phases was tracked in both the initial particle settling and the capsule shaking process. Alternating positive-negative charging was observed. Particle charging was then investigated in relation to the collision statistics, tracking the particle-particle and particle-wall events for the carrier and API. Finally, an analysis of the relative importance of electrostatic, cohesive/adhesive, and inertial forces allowed the importance of each term in determining the trajectory of the powder particles to be estimated.

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.

Manipulating Interactions between Dielectric Particles with Electric Fields: A General Electrostatic Many-Body Framework

We derive a rigorous analytical formalism and propose a numerical method for the quantitative evaluation of the electrostatic interactions between dielectric particles in an external electric field. This formalism also allows for inhomogeneous charge distributions, and, in particular, for the presence of pointlike charges on the particle surface. The theory is based on a boundary integral equation framework and yields analytical expressions for the interaction energy and net forces that can be computed in linear scaling cost, with respect to the number of interacting particles. We include numerical results that validate the proposed method and show the limitations of the fixed dipole approximation at small separation between interacting particles. The proposed method is also applied to study the stability and melting of ionic colloidal crystals in an external electric field.

Exact polarization energy for clusters of contacting dielectrics

The induced surface charges appear to diverge when dielectric particles form close contacts. Resolving this singularity numerically is prohibitively expensive because high spatial resolution is needed. We show that the strength of this singularity is logarithmic in both inter-particle separation and dielectric permittivity. A regularization scheme is proposed to isolate this singularity, and to calculate the exact cohesive energy for clusters of contacting dielectric particles. The results indicate that polarization energy stabilizes clusters of open configurations when permittivity is high, in agreement with the behavior of conducting particles, but stabilizes the compact configurations when permittivity is low.

Rigorous treatment of pairwise and many-body electrostatic interactions among dielectric spheres at the Debye-Hückel level

Electrostatic interactions among colloidal particles are often described using the venerable (two-particle) Derjaguin-Landau-Verwey-Overbeek (DLVO) approximation and its various modifications. However, until the recent development of a many-body theory exact at the Debye-Hückel level (Yu in Phys Rev E 102:052404, 2020), it was difficult to assess the errors of such approximations and impossible to assess the role of many-body effects. By applying the exact Debye-Hückel level theory, we quantify the errors inherent to DLVO and the additional errors associated with replacing many-particle interactions by the sum of pairwise interactions (even when the latter are calculated exactly). In particular, we show that: (1) the DLVO approximation does not provide sufficient accuracy at shorter distances, especially when there is an asymmetry in charges and/or sizes of interacting dielectric spheres; (2) the pairwise approximation leads to significant errors at shorter distances and at large and moderate Debye lengths and also gets worse with increasing asymmetry in the size of the spheres or magnitude or placement of the charges. We also demonstrate that asymmetric dielectric screening, i.e., the enhanced repulsion between charged dielectric bodies immersed in media with high dielectric constant, is preserved in the presence of free ions in the medium.

Granular ionic crystals in a small nutshell

Ordered two-dimensional arrangements of triboelectrically oppositely charged granular particles have been reported several times, but observations of bulk ordered binary granular particle packings are singular. We attribute this suppression of triboelectrically induced order to the concurrent behaviour of granular particles to pack densest due to gravity. We show that triboelectrically induced order robustly emerges in a container that does not allow for crystallization into a dense packing under gravity. It turns out that the triboelectrically ordered structure follows Pauling's predictions for atomic ionic crystals in many aspects, but also exhibits systematic deviations. We discuss how the emergence of order in an incommensurate container, the deviations from Pauling's predictions and the gravitational potential energy of the particles are connected.

Charge polarization near dielectric interfaces and the multiple-scattering formalism

Interfacial charge polarization is ubiquitous in systems with sharp dielectric contrast. Fully resolving the interfacial charges often relies on demanding numerical algorithms to solve the boundary value problem. The recent development of an analytical multiple-scattering formalism to solve the interfacial charge polarization problem for particles carrying monopolar, dipolar, and multipolar charges is reviewed. Every term produced in this formalism has a simple interpretation, and terms for spherical particles can be rapidly evaluated using an image-line construction. Several practical applications of this formalism are illustrated. A dielectric virial expansion for polarizable particles based on this formalism is also described. The origins of singular polarization charges for particles in close contact are explained and evaluated for both dielectric and conducting spheres.

Discrete and Continuum Models for the Salt in Crowded Environments of Suspended Charged Particles

Electrostatic forces greatly affect the overall dynamics and diffusional activities of suspended charged particles in crowded environments. Accordingly, the concentration of counter- or co-ions in a fluid-''the salt"-determines the range, strength, and order of electrostatic interactions between particles. This environment fosters engineering routes for controlling directed assembly of particles at both the micro- and nanoscale. Here, we analyzed two computational modeling schemes that considered salt within suspensions of charged particles, or polyelectrolytes: discrete and continuum. Electrostatic interactions were included through a Green's function formalism, where the confined fundamental solution for Poisson's equation is resolved by the general geometry Ewald-like method. For the discrete model, the salt was considered as regularized point-charges with a specific valence and size, while concentration fields were defined for each ionic species for the continuum model. These considerations were evolved using Brownian dynamics of the suspended charged particles and the discrete salt ions, while a convection-diffusion transport equation, including the Nernst-Planck diffusion mechanism, accounted for the dynamics of the concentration fields. The salt/particle models were considered as suspensions under slit-confinement conditions for creating crowded "macro-ions", where density distributions and radial distribution functions were used to compare and differentiate computational models. Importantly, our analysis shows that disparate length scales or increased system size presented by the salt and suspended particles are best dealt with using concentration fields to model the ions. These findings were then validated by novel simulations of a semipermeable polyelectrolyte membrane, at the mesoscale, from which ionic channels emerged and enable ion conduction.

Influence of dielectric inhomogeneities on the structure of charged nanoparticles in neutral polymer solutions

We study the structural characteristics of a system of charged nanoparticles in a neutral polymer solution while accounting for the differences in the dielectric constant between the particles, polymer and the solvent. We use a hybrid computational methodology involving a combination of single chain in mean-field simulations and the solution of the Poisson's equation for the electrostatic field. We quantify the resulting particle structural features in terms of radial distribution function among particles as a function of the dielectric contrast, particle charge, particle volume fraction and polymer concentration. In the absence of polymers, charged macroions experience increased repulsion with a lowering of the ratio of particle to solvent dielectric constant. The influence of the dielectric contrast between the particle and the solvent however diminishes with an increase in the particle volume fraction and/or its charge. In the presence of neutral polymers, similar effects manifest, but with the additional physics arising from the fact that the polymer-induced interactions are influenced by the dielectric contrast of the particle and solvent.

Dynamic simulations of many-body electrostatic self-assembly

Two experimental studies relating to electrostatic self-assembly have been the subject of dynamic computer simulations, where the consequences of changing the charge and the dielectric constant of the materials concerned have been explored. One series of calculations relates to experiments on the assembly of polymer particles that have been subjected to tribocharging and the simulations successfully reproduce many of the observed patterns of behaviour. A second study explores events observed following collisions between single particles and small clusters composed of charged particles derived from a metal oxide composite. As before, observations recorded during the course of the experiments are reproduced by the calculations. One study in particular reveals how particle polarizability can influence the assembly process.This article is part of the theme issue 'Modern theoretical chemistry'.

Surface Polarization Effects on Ion-Containing Emulsions

Surface polarization in ion-containing heterogeneous dielectric media such as cell media and emulsions is determined by and determines the positions of the ions. We compute the surface polarization self-consistently as the ions move and analyze their effects on the interactions between electro-neutral, ion-containing droplets using coarse-grained molecular dynamics simulations based on the true energy functional. For water droplets immersed in oil, the interdroplet interaction is attractive, and the surface polarization makes the major contribution. By contrast, for oil droplets in water, the ion-surface induced charge interaction is repulsive and counteracts the attraction between the ions, leading to a small attractive interaction between the droplets. This research improves our understanding of self-assembly in mixed phases such as metal extraction for recovering rare earth elements and nuclear waste as well as water purification.

Charging changes contact composition in binary sphere packings

Equal volume mixtures of small and large polytetrafluorethylene spheres are shaken in an atmosphere of controlled humidity which allows one to also control their tribocharging. We find that the contact numbers are charge dependent: As the charge density of the beads increases, the number of same-type contacts decreases and the number of opposite-type contacts increases. This change is not caused by a global segregation of the sample. Hence, tribocharging can be a way to tune the local composition of a granular material.

Influence of humidity on tribo-electric charging and segregation in shaken granular media

We study the effect of humidity on the charge accumulation of polymer granulates shaken vertically in a stainless steel container. This setup allows us to control the humidity level from 5% to 100%RH while performing automated charge measurements in a Faraday cup directly connected to the shaking container. We find that samples of approximately 2000 polymer spheres become highly charged at low humidity levels (<30%RH), but acquire almost no charge for humidity levels above 80%RH. The transition between these two regimes does depend on the material, as does the sign of the charge. For the latter we find a correlation with the contact angle of the polymer with only very hydrophilic particles attaining positive charges. We show that this humidity dependence of tribo-charging can be used to control segregation in shaken binary mixtures.

Computational immuno-biology for organ transplantation and regenerative medicine

Organ transplantation and regenerative medicine are adopted platforms that provide replacement tissues and organs from natural or engineered sources. Acceptance, tolerance and rejection depend greatly on the proper control of the immune response against graft antigens, motivating the development of immunological and genetical therapies that prevent organ failure. They rely on a complete, or partial, understanding of the immune system. Ultimately, they are innovative technologies that ensure permanent graft tolerance and indefinite graft survival through the modulation of the immune system. Computational immunology has arisen as a tool towards a mechanistic understanding of the biological and physicochemical processes surrounding an immune response. It comprehends theoretical and computational frameworks that simulate immuno-biological systems. The challenge is centered on the multi-scale character of the immune system that spans from atomistic scales, during peptide-epitope and protein interactions, to macroscopic scales, for lymph transport and organ-organ reactions. In this paper, we discuss, from an engineering perspective, the biological processes that are involved during the immune response of organ transplantation. Previous computational efforts, including their characteristics and visible limitations, are described. Finally, future perspectives and challenges are listed to motivate further developments.