Molecular multivalent electrolytes: microstructure and screening lengths

Reexpansion of charged nanoparticle assemblies in concentrated electrolytes

Electrostatic forces in solutions are highly relevant to a variety of fields, ranging from electrochemical energy storage to biology. However, their manifestation in concentrated electrolytes is not fully understood, as exemplified by counterintuitive observations of colloidal stability and long-ranged repulsions in molten salts. Highly charged biomolecules, such as DNA, respond sensitively to ions in dilute solutions. Here, we use non-base-pairing DNA-coated nanoparticles (DNA-NP) to analyze electrostatic interactions in concentrated salt solutions. Despite their negative charge, these conjugates form colloidal crystals in solutions of sufficient divalent cation concentration. We utilize small-angle X-ray scattering (SAXS) to study such DNA-NP assemblies across the full accessible concentration ranges of aqueous CaCl2, MgCl2, and SrCl2 solutions. SAXS shows that the crystallinity and phases of the assembled structures vary with cation type. For all tested salts, the aggregates contract with added ions at low salinities and then begin expanding above a cation-dependent threshold salt concentration. Wide-angle X-ray scattering (WAXS) reveals enhanced positional correlations between ions in the solution at high salt concentrations. Complementary molecular dynamics simulations show that these ion-ion interactions reduce the favorability of dense ion configurations within the DNA brushes below that of the bulk solution. Measurements in solutions with lowered permittivity demonstrate a simultaneous increase in ion coupling and decrease in the concentration at which aggregate expansion begins, thus confirming the connection between these phenomena. Our work demonstrates that interactions between charged objects continue to evolve considerably into the high-concentration regime, where classical theories project electrostatics to be of negligible consequence.

The Importance of Salt-Enhanced Electrostatic Repulsion in Colloidal Crystal Engineering with DNA

Realizing functional colloidal single crystals requires precise control over nanoparticles in three dimensions across multiple size regimes. In this regard, colloidal crystallization with programmable atom equivalents (PAEs) composed of DNA-modified nanoparticles allows one to program in a sequence-specific manner crystal symmetry, lattice parameter, and, in certain cases, crystal habit. Here, we explore how salt and the electrostatic properties of DNA regulate the attachment kinetics between PAEs. Counterintuitively, simulations and theory show that at high salt concentrations (1 M NaCl), the energy barrier for crystal growth increases by over an order of magnitude compared to low concentration (0.3 M), resulting in a transition from interface-limited to diffusion-limited crystal growth at larger crystal sizes. Remarkably, at elevated salt concentrations, well-formed rhombic dodecahedron-shaped microcrystals up to 21 μm in size grow, whereas at low salt concentration, the crystal size typically does not exceed 2 μm. Simulations show an increased barrier to hybridization between complementary PAEs at elevated salt concentrations. Therefore, although one might intuitively conclude that higher salt concentration would lead to less electrostatic repulsion and faster PAE-to-PAE hybridization kinetics, the opposite is the case, especially at larger inter-PAE distances. These observations provide important insight into how solution ionic strength can be used to control the attachment kinetics of nanoparticles coated with charged polymeric materials in general and DNA in particular.

Strong attractions and repulsions mediated by monovalent salts

Controlling interactions between proteins and nanoparticles in electrolyte solutions is crucial for advancing biological sciences and biotechnology. The assembly of charged nanoparticles (NPs) and proteins in aqueous solutions can be directed by modifying the salt concentration. High concentrations of monovalent salt can induce the solubilization or crystallization of NPs and proteins. By using a multiscale coarse-grained molecular dynamics approach, we show that, due to ionic correlations in the electrolyte, NPs pairs at high monovalent salt concentrations interact via remarkably strong long-range attractions or repulsions, which can be split into three regimes depending on the surface charge densities of the NPs. NPs with zero-to-low surface charge densities interact via a long-range attraction that is stronger and has a similar range to the depletion attraction induced by polymers with radius of gyrations comparable to the NP diameter. On the other hand, moderately charged NPs with smooth surfaces as well as DNA-functionalized NPs with no possibility of hybridization between them interact via a strong repulsion of range and strength larger than the repulsion predicted by models that neglect ionic correlations, including the Derjaguin-Landau-Vervey-Overbeek (DLVO) model. Interactions between strongly charged NPs (>2 e/nm²), both types smooth and DNA-functionalized NPs, show an attractive potential well at intermediate-to-high salt concentrations, which demonstrates that electrolytes can induce aggregation of strongly charged NPs. Our work provides an improved understanding of the role of ionic correlations in NP assembly and design rules to utilize the salting-out process to crystallize NPs.

Electrostatics at the nanoscale

Electrostatic forces are amongst the most versatile interactions to mediate the assembly of nanostructured materials. Depending on experimental conditions, these forces can be long- or short-ranged, can be either attractive or repulsive, and their directionality can be controlled by the shapes of the charged nano-objects. This Review is intended to serve as a primer for experimentalists curious about the fundamentals of nanoscale electrostatics and for theorists wishing to learn about recent experimental advances in the field. Accordingly, the first portion introduces the theoretical models of electrostatic double layers and derives electrostatic interaction potentials applicable to particles of different sizes and/or shapes and under different experimental conditions. This discussion is followed by the review of the key experimental systems in which electrostatic interactions are operative. Examples include electroactive and "switchable" nanoparticles, mixtures of charged nanoparticles, nanoparticle chains, sheets, coatings, crystals, and crystals-within-crystals. Applications of these and other structures in chemical sensing and amplification are also illustrated.

Protein loop compaction and the origin of the effect of arginine and glutamic acid mixtures on solubility, stability and transient oligomerization of proteins

Addition of a 50 mM mixture of L: -arginine and L: -glutamic acid (RE) is extensively used to improve protein solubility and stability, although the origin of the effect is not well understood. We present Small Angle X-ray Scattering (SAXS) and Nuclear Magnetic Resonance (NMR) results showing that RE induces protein compaction by collapsing flexible loops on the protein core. This is suggested to be a general mechanism preventing aggregation and improving resistance to proteases and to originate from the polyelectrolyte nature of RE. Molecular polyelectrolyte mixtures are expected to display long range correlation effects according to dressed interaction site theory. We hypothesize that perturbation of the RE solution by dissolved proteins is proportional to the volume occupied by the protein. As a consequence, loop collapse, minimizing the effective protein volume, is favored in the presence of RE.

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.

A simple phenomenological fix for the dielectric constant within the reference interaction site model approach

The effective interactions among ions immersed in water are studied by means of the effective pair potentials (EPPs) [J. Chem. Phys. 2002, 117, 6133] obtained after contracting (integrating out) the degrees of freedom of the solvent molecules. The dressed interaction site theory (DIST) leads to a simple way of adjusting the effective dielectric constant of the model solvent to its experimental value at standard conditions. The molecular structure of the solvent is mirrored in the structure of the short-ranged component of the induced EPPs, with noticeable differences between the cases with trivial (ideal gas) and nontrivial (experimental) values of the dielectric constant. The shape of these EPPs remains almost invariant over the whole range of salt concentrations considered here. The asymptotic behavior of the EPP between two macroions obtained after contracting the supporting electrolyte (water molecules plus small ions) is also briefly discussed.

Effective multipoles and Yukawa electrostatics in dressed molecule theory

In this paper we derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvent. The solute and solvent molecules can have arbitrary sizes, shapes, and internal charge distributions. We use the exact statistical mechanical definition of renormalized charge distributions coming from "dressed molecule theory" to determine the effective multipoles of a molecule immersed in an electrolyte. The effects of many-body correlations are fully included in our formally exact theory. We restrict ourselves to sufficiently dilute solutions so the screened Coulomb potential decays for large distances like a Yukawa function, exp(-kappa r)/r, where r is the distance and 1/kappa is the decay length (it is normally different from the Debye length). The resulting "Yukawa electrostatics" differ in many respects from ordinary, unscreened electrostatics. The "Yukawa charge" of a molecule (the lowest order moment in the multipolar expansion) is in general not equal to its Coulombic charge and it is not the integral of the renormalized charge distribution of the molecule. Moreover, as shown in this paper, the multipolar expansion of the Yukawa potential does not correspond, contrary to the case of the Coulomb potential, to its asymptotic expansion for large r. As a consequence, the charge term in the multipolar expansion is not the leading term in the asymptotic expansion. Instead, for large r values, multipoles of all orders contribute to the leading asymptotic term. Thus, the electrostatic potential from, for example, an electroneutral solvent molecule in an electrolyte solution has generally the same range as that from an ion. The proper asymptotic expansion for electrostatic interactions in electrolytes is derived. It is briefly shown how the multipole expansion formalism can also be applied in the Poisson-Boltzmann approximation for primitive model electrolytes.