Mobility of large ions in water

Do Electrostatics Control the Diffusive Dynamics of Solitary Water? NMR and MD Studies of Water Translation and Rotation in Dipolar and Ionic Solvents

NMR-based measurements of the diffusion coefficients and rotation times of solitary water and benzene at 300 K are reported in a diverse collection of 13 conventional organic solvents and 10 imidazolium ionic liquids. Proton chemical shifts of water are found to be correlated to water OH-stretching frequencies, confirming the importance of electrostatic interactions in these shifts. However, the influence of magnetic interactions in aromatic solvents renders chemical shifts a less reliable indicator of electrostatics. Diffusion coefficients (DB) and rotational correlation times (τB) of benzene in the solvents examined are accurately described as functions of viscosity (η) by DB ∝ η-0.81 and τB ∝ η0.64. Literature values of DB and τB in alkane and normal alcohols, which were not included among the solvents studied here, are systematically faster than predicted by these correlations, indicating that factors beyond solvent viscosity play a role in determining the friction on benzene. In contrast to benzene, water diffusion and rotation are poorly described in terms of viscosity alone, even in the dipolar and ionic solvents measured here. The present data and the substantial literature data already available on dilute water diffusion show a systematic dependence of DW on solvent polarity among isoviscous solvents. The aspect of solvent polarity most relevant to water dynamics is the ability of a solvent to accept hydrogen bonds from water, as conveniently quantified by the frequency of water's OH stretching band, ΔνOH. The friction on translation, ζtr = kBT/DW, and rotation, ζrot = kBTτW, are both well correlated by functions of the form ζ(η, ΔνOH) = a1ηa2 exp (a3ΔνOH), where the ai are adjustable parameters. Molecular dynamics simulations reveal a strong coupling between electrostatic and nonelectrostatic water-solvent interactions, which makes it impossible to dissect the friction on water into additive dielectric and hydrodynamic components. Simulations also provide a tentative explanation for the unusual form of the correlating function ζ(η, ΔνOH), at least in the case of ζrot.

War and Peace between Electrostatic and van der Walls Forces Regulate Translational and Rotational Diffusion

Diffusion of a Brownian particle or a molecule in a liquid solvent is caused, in the Stokes-Einstein picture, by unbalanced fluctuations of osmotic forces on different sides of the particle. When the particle carries a charge or a higher multipolar moment, this picture is amended by fluctuations of electrostatic forces producing dielectric friction. Dielectric friction slows both the translational and rotational diffusion down. While this picture is well established and is physically sound, standard theories grossly overestimate the magnitude of dielectric friction for small dipolar solutes and larger colloidal particles, such as proteins. Motivated by recent simulation studies, this perspective discusses the interplay between osmotic (van der Waals) and electrostatic forces in promoting molecular and colloidal diffusion. Much can be learned about microscopic friction mechanisms from statistical and dynamical correlations between osmotic and electrostatic forces.

Ionic mobility driven by correlated van der Waals and electrostatic forces

Classical theories of dielectric friction make two critical assumptions: (i) friction due to van der Waals (vdW) forces is described by hydrodynamic drag and is independent of the ionic charge and (ii) vdW and electrostatic forces are statistically independent. Both assumptions turn out to be incorrect when tested against simulations of anions and cations with varying charge magnitude dissolved in water. Both the vdW and electrostatic components of the force variance scale linearly with the ionic charge squared. The two components are strongly anticorrelated producing simple relations for the total force variance in terms of self-variances. The inverse diffusion constant scales linearly with the charge squared. Solvation asymmetry between cations and anions extends to linear transport coefficients.

Effects of channel size, wall wettability, and electric field strength on ion removal from water in nanochannels

Molecular dynamics simulations are employed to estimate the effect of nanopore size, wall wettability, and the external field strength on successful ion removal from water solutions. It is demonstrated that the presence of ions, along with the additive effect of an external electric field, constitute a multivariate environment that affect fluidic interactions and facilitate, or block, ion drift to the walls. The potential energy is calculated across every channel case investigated, indicating possible ion localization, while electric field lines are presented, to reveal ion routing throughout the channel. The electric field strength is the dominant ion separation factor, while wall wettability strength, which characterizes if the walls are hydrophobic or hydrophilic has not been found to affect ion movement significantly at the scale studied here. Moreover, the diffusion coefficient values along the three dimensions are reported. Diffusion coefficients have shown a decreasing tendency as the external electric field increases, and do not seem to be affected by the degree of wall wettability at the scale investigated here.

Enhanced Molecular Diffusivity through Destructive Interference between Electrostatic and Osmotic Forces

Molecular charge asymmetrically distributed in a diffusing tagged particle causes a nonzero electrostatic force balanced by an opposing van der Waals (vdW) force. Fluctuations of electrostatic and vdW forces are highly correlated, and they destructively interfere in the force variance. This phenomenology is caused by the formation of a structurally frozen hydration layer for a particle diffusing in water and is responsible for a substantial speedup of translational diffusion compared to traditional theories of dielectric friction. Diffusion of proteins is insensitive to charge mutations, while smaller particles with asymmetric charge distribution can show a strong dependence of translational and rotational diffusion on molecular charge. Dielectric calculations of the electrostatic force require low values of ≃5 for the effective dielectric constant of interfacial water to be consistent with simulations.

Modulation of Nanoparticle Diffusion by Surface Ligand Length and Charge: Analysis with Molecular Dynamics Simulations

To help better interpret experimental measurement of nanoparticle size, it is important to understand how their diffusion depends on the physical and chemical features of surface ligands. In this study, explicit solvent molecular dynamics simulations are used to probe the effect of ligand charge and flexibility on the diffusion of small gold nanoparticles. The results suggest that despite a high bare charge (+18 e), cationic nanoparticles studied here have reduced diffusion constants compared to a hydrophobic gold nanoparticle by merely a modest amount. Increasing the ligand length by 10 CH₂ units also has a limited impact on the diffusion constant. For the three particles studied here, the difference between estimated hydrodynamic radius and radius of gyration is on the order of one solvent layer (3-5 Å), confirming that the significant discrepancies found in the size of similar nanoparticles by recent transmission electron microscopy and dynamic light scattering measurements were due to aggregation under solution conditions. The limited impact of electrostatic friction on the diffusion of highly charged nanoparticles is found to be due to the strong anticorrelation between electrostatic and van der Waals forces between nanoparticle and environment, supporting the generality of recent observation for proteins by Matyushov and co-workers. Including the first shell of solvent molecules as part of the diffusing particle has a minor impact on the total force autocorrelation function but reduces the disparity in relaxation time between the total force and its electrostatic and van der Waals components.

Driving Forces of Protein Diffusion

Diffusivity of a protein (a Brownian particle) is caused by random molecular collisions in the Stokes-Einstein picture. Alternatively, it can be viewed as driven by unbalanced stochastic forces acting from water on the protein. Molecular dynamics simulations of protein mutants carrying different charges are analyzed here in terms of the van der Waals (vdW) and electrostatic forces acting on the protein. They turn out to be remarkably strongly correlated and the total force is largely a compensation between vdW and electrostatic forces. Both vdW and electrostatic forces relax on the same time scale of 5-6 ns separated by 6 orders of magnitude from the relaxation time of the total force. Similar phenomenology applies to the dynamics and statistics of the fluctuating torque responsible for rotational diffusion. Standard linear theories of dielectric friction are grossly inapplicable to translational and rotational diffusion of proteins overestimating friction by many orders of magnitude.