Effective multipoles and Yukawa electrostatics in dressed molecule theory

Energy-Scaled Debye-Hückel Theory for the Electrostatic Solvation Free Energy in Size-Asymmetric Electrolyte Solutions

In this report, an energy-scaled Debye-Hückel theory is developed for fast and accurate evaluation of the electrostatic solvation free energy in size-asymmetric electrolyte solutions. A size-asymmetric electrolyte solution is mapped to a dielectric continuum medium with Debye-Hückel-like response. Based on the scaling relation of the electrostatic energy of a spherical ion in the small and large size limits, a Padé polynomial is used to interpolate the electrostatic energy at finite size. The Padé polynomial is further interpreted as the electrostatic energy of an effective Debye-Hückel mean field model, depicted by a modified Debye parameter and a surface charge density due to the size asymmetry of the solvent ions. This theory can distinguish the electrostatic energies and the electrostatic solvation free energies of solutes with the same size but opposite charges. Application to charged hard and charged soft spheres demonstrates the accuracy of our approach.

Far-Field Electrostatic Signatures of Macromolecular 3D Conformation

In solution as in vacuum, the electrostatic field distribution in the vicinity of a charged object carries information on its three-dimensional geometry. We report on an experimental study exploring the effect of molecular shape on long-range electrostatic interactions in solution. Working with DNA nanostructures carrying approximately equal amounts of total charge but each in a different three-dimensional conformation, we demonstrate that the geometry of the distribution of charge in a molecule has substantial impact on its electrical interactions. For instance, a tetrahedral structure, which is the most compact distribution of charge we tested, can create a far-field effect that is effectively identical to that of a rod-shaped molecule carrying half the amount of total structural charge. Our experiments demonstrate that escape-time electrometry (ETe) furnishes a rapid and facile method to screen and identify 3D conformations of charged biomolecules or molecular complexes in solution.

Opto-Electrostatic Determination of Nucleic Acid Double-Helix Dimensions and the Structure of the Molecule–Solvent Interface

A DNA molecule is highly electrically charged in solution. The electrical potential at the molecular surface is known to vary strongly with the local geometry of the double helix and plays a pivotal role in DNA–protein interactions. Further out from the molecular surface, the electrical field propagating into the surrounding electrolyte bears fingerprints of the three-dimensional arrangement of the charged atoms in the molecule. However, precise extraction of the structural information encoded in the electrostatic “far field” has remained experimentally challenging. Here, we report an optical microscopy-based approach that detects the field distribution surrounding a charged molecule in solution, revealing geometric features such as the radius and the average rise per basepair of the double helix with up to sub-Angstrom precision, comparable with traditional molecular structure determination techniques like X-ray crystallography and nuclear magnetic resonance. Moreover, measurement of the helical radius furnishes an unprecedented view of both hydration and the arrangement of cations at the molecule–solvent interface. We demonstrate that a probe in the electrostatic far field delivers structural and chemical information on macromolecules, opening up a new dimension in the study of charged molecules and interfaces in solution.

The intimate relationship between the dielectric response and the decay of intermolecular correlations and surface forces in electrolytes

A general, exact theory for the decay of interactions between any particles immersed in electrolytes, including surface forces between macroscopic bodies, is derived in a self-contained, physically transparent manner. It is valid for electrolytes at any density, including ionic gases, molten salts, ionic liquids, and electrolyte solutions with molecular solvent at any concentration. The ions, the solvent and any other particles in the system can have any sizes, any shapes and arbitrary internal charge distributions. The spatial propagation of the interactions in electrolytes has several decay modes with different decay lengths that are given by the solutions, κν, ν = 1, 2,…, to a general equation for the screening parameter κ; an equation that describes the dielectric response. There can exist simultaneous decay modes with plain exponential decay and modes with damped oscillatory exponential decay, as observed experimentally and theoretically. In the limit of zero ionic density, the decay length 1/κν of the mode with the longest range approaches the Debye length 1/κD. The coupling between fluctuations in number density and charge density, described by the density-charge correlation function HNQ(r), makes all decay modes of pair correlations and interaction free energies identical to those of the screened electrostatic potential, and hence they have the same values for the screening parameters. The density-density and charge-charge correlation functions, HNN(r) and HQQ(r), also have these decay modes. For the exceptional case of charge-inversion invariant systems, HNQ(r) is identically zero for symmetry reasons and HNN(r) and HQQ(r) have, instead, decay modes with different decay lengths.

From discrete to continuous description of spherical surface charge distributions

The importance of electrostatic interactions in soft matter and biological systems can often be traced to non-uniform charge effects, which are commonly described using a multipole expansion of the corresponding charge distribution. The standard approach when extracting the charge distribution of a given system is to treat the constituent charges as points. This can, however, lead to an overestimation of multipole moments of high order, such as dipole, quadrupole, and higher moments. Focusing on distributions of charges located on a spherical surface - characteristic of numerous biological macromolecules, such as globular proteins and viral capsids, as well as of inverse patchy colloids - we develop a novel way of representing spherical surface charge distributions based on the von Mises-Fisher distribution. This approach takes into account the finite spatial extension of individual charges, and leads to a simple yet powerful way of describing surface charge distributions and their multipole expansions. In this manner, we analyze charge distributions and the derived multipole moments of a number of different spherical configurations of identical charges with various degrees of symmetry. We show how the number of charges, their size, and the geometry of their configuration influence the behavior and relative importance of multipole magnitudes of different order. Importantly, we clearly demonstrate how neglecting the effect of charge size leads to an overestimation of high-order multipoles. The results of our work can be applied to construct analytical models of electrostatic interactions and multipole expansion of charged particles in diverse soft matter and biological systems.

Alternating strings and clusters in suspensions of charged colloids

We report the formation of alternating strings and clusters in a binary suspension of repulsive charged colloids with double layers larger than the particle size. Within a binary cell model we include many-body and charge-regulation effects under the assumption of a constant surface potential, and consider their repercussions on the two-particle interaction potential. We find that the formation of induced dipoles close to a charge-reversed state may explain the formation of these structures. Finally, we will touch upon the formation of dumbbells and small clusters in a one-component system, where the effective electrostatic interaction is always repulsive.

Decay behavior of screened electrostatic surface forces in ionic liquids: the vital role of non-local electrostatics

General theory for dense electrolytes shows why both plain exponential and oscillatory electrostatic surface forces can appear in ionic liquids.

Screening of heterogeneous surfaces: charge renormalization of Janus particles

Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadrupolar, etc, including 'mode couplings'. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles.

Dimeric and dipolar ground state orders in colloidal molecular crystals

A two dimensional colloidal suspension subject to a periodic substrate evolves into a colloidal molecular crystal under situationsofstrongconfinement. Wefocusonthelongrangeorientationalordertherebyemerging, inthegroundstate. We study by simulations the situations where in each trap lies a pair of identical colloids, or alternatively a pair of oppositelychargedmacroions. We consider square or triangular geometries for the periodic confinement, together with less symmetric distorted lattices.

Simulations of latex particles immersed in dendrimer solutions

In this work, we present Monte Carlo simulations of mixtures containing negatively charged latex particles and positively charged dendrimers. We focus on the interaction between two latex particles as salt concentration, dendrimer dose, and generation number are varied. Interaction free energies and corresponding stability ratios are calculated. Minimal stability is found near the isoelectric point, i.e., where the amount of adsorbed dendrimer charge matches the charge of the latex particles. Away from the isoelectric point, the stability increases as the latex particles get more and more under- or overcompensated, an increase that is more steep on the overcompensated side. Increasing the dendrimer generation leads to a more "patchy" surface. This heterogeneity is particularly relevant close to the isoelectric point. Given the relative simplicity of the model, the simulation results are in surprisingly good agreement with the experimental data.

Effective shape and phase behavior of short charged rods

We explicitly calculate the orientation-dependent second virial coefficient of short charged rods in an electrolytic solvent, assuming the rod-rod interactions to be a pairwise sum of hard-core and segmental screened-Coulomb repulsions. From the parallel and isotropically averaged second virial coefficient, we calculate the effective length and diameter of the rods, for charges and screening lengths that vary over several orders of magnitude. Using these effective dimensions, we determine the phase diagram, where we distinguish a low-charge and strong-screening regime with a liquid crystalline nematic and smectic phase, and a high-charge and weak-screening regime with a plastic crystal phase in the phase diagram.

Asymmetric charge renormalization for nanoparticles in aqueous media

The effective renormalized charge of nanoparticles in an aqueous electrolyte is essential to determine their solubility. By using a molecular model for the supporting aqueous electrolyte, we find that the effective renormalized charge of the nanoparticles is strongly dependent on the sign of the bare charge. Negatively charged nanoparticles have a lower effective renormalized charge than positively charged nanoparticles. The degree of asymmetry is a nonmonotonic function of the bare charge of the nanoparticle. We show that the effect is due to the asymmetric charge distribution of the water molecules, which we model using a simple three-site molecular structure of point charges.