Unexpectedly Large Decay Lengths of Double-Layer Forces in Solutions of Symmetric, Multivalent Electrolytes

Self-consistent electrostatic formalism of bulk electrolytes based on the asymmetric treatment of the short- and long-range ion interactions

We predict the thermodynamic behavior of bulk electrolytes from an ionic hard-core (HC) size-augmented self-consistent formalism incorporating asymmetrically the short- and long-range ion interactions via their virial and cumulant treatment, respectively. The characteristic splitting length separating these two ranges is obtained from a variational equation solved together with the Schwinger-Dyson (SD) equations. Via comparison with simulation results from the literature, we show that the asymmetric treatment of the distinct interaction ranges significantly extends the validity regime of our previously developed purely cumulant-level Debye-Hückel (DH) theory. Namely, for monovalent solutions with typical ion sizes, the present formalism can accurately predict up to molar concentrations the liquid pressure dominated by HC interactions, the internal energies driven by charge correlations, and the local ion distributions governed by the competition between HC and electrostatic interactions. We evaluate as well the screening length of the liquid and investigate the deviations of the macromolecular interaction range from the DH length. In fair agreement with simulations and experiments, our theory is shown to reproduce the overscreening and underscreening effects occurring respectively in submolar mono- and multivalent electrolytes.

A Transpiration-Driven Electrokinetic Power Generator with a Salt Pathway for Extended Service Life in Saltwater

To ensure prolonged functionality of transpiration-driven electrokinetic power generators (TEPGs) in saltwater environments, it is imperative to mitigate salt accumulation. This study presents a salt pathway transpiration-driven electrokinetic power generator (SPTEPG), incorporating MXene, graphene oxide (GO), and carbon nanotubes (CNTs) as active materials, along with cellulose nanofibers (CNF) and poly(vinyl alcohol) (PVA) as aqueous binders and nonwoven fabrics. This unique combination confers exceptional hydrophilicity and enhances the energy generation performance. When tested with deionized water, the SPTEPG achieved a maximum voltage of 0.6 V and a current of 4.2 μA. In simulated seawater conditions, the presence of conductive ions in the solution boosted these values to 0.64 V and 42 μA. The incorporation of the salt pathway mechanism facilitates the return of excess salt deposits to the bulk solution, thus extending the SPTEPG's service life in saltwater environments. This research offers a straightforward yet effective strategy for designing transpiration-driven power generators suitable for saline water applications.

Geocolloidal interactions and relaxation dynamics under nanoconfinement: Effects of salinity and particle concentration

HYPOTHESIS

Energy-related contaminants are frequently associated with geocolloids that translocate in underground fissures with dimensions comparable with geocolloids. To assess the transport and impact of energy-related contaminants in geological systems, fundamental understandings of interfacial behaviors of nanoparticles under confinement is imperative. We hypothesize that the dynamic properties of geocolloids, as well as their dependence on aqueous medium conditions would deviate from bulk behaviors under nanoconfinement.

EXPERIMENTS

Force profiles and rheological properties of 50 nm silica nanoparticles in aqueous media confined between mica surfaces as a function of surface separation, particle concentrations, and salinity were measured utilizing the surface forces apparatus.

FINDINGS

Force profiles revealed the critical surface separation for nonlinear rheological behaviors coincides with the onset of exponential repulsion between mica surfaces. When salts were absent, the normal forces and viscosity values of colloidal suspensions resembled pure water. In contrast, with salts, the force profiles and corresponding critical length scales were found to be highly sensitive to the particle concentration and the degree of confinement. A Newtonian to shear-thinning transition was captured with increasing degrees of confinement. Our results show that the interplay among confinement, particle, and ionic concentrations can alter the interparticle forces and rheological responses of true nanosized-colloidal suspensions and thus their transport behaviors under nanoconfinement for the first time.

Underscreening in concentrated electrolytes: re-entrant swelling in polyelectrolyte brushes

Hypersaline environments are ubiquitous in nature and are found in myriad technological processes. Recent empirical studies have revealed a significant discrepancy between predicted and observed screening lengths at high salt concentrations, a phenomenon referred to as underscreening. Herein we investigate underscreening using a cationic polyelectrolyte brush as an exemplar. Poly(2-(methacryloyloxy)ethyl)trimethylammonium (PMETAC) brushes were synthesised and their internal structural changes and swelling response was monitored with neutron reflectometry and spectroscopic ellipsometry. Both techniques revealed a monotonic brush collapse as the concentration of symmetric monovalent electrolyte increased. However, a non-monotonic change in brush thickness was observed in all multivalent electrolytes at higher concentrations, known as re-entrant swelling; indicative of underscreening. For all electrolytes, numerical self-consistent field theory predictions align with experimental studies in the low-to-moderate salt concentration regions. Analysis suggests that the classical theory of electrolytes is insufficient to describe the screening lengths observed at high salt concentrations and that the re-entrant polyelectrolyte brush swelling seen herein is consistent with the so-called regular underscreening phenomenon.

Anomalous Underscreening in the Restricted Primitive Model

Underscreening is a collective term for charge correlations in electrolytes decaying slower than the Debye length. Anomalous underscreening refers to phenomenology that cannot be attributed alone to steric interactions. Experiments with concentrated electrolytes and ionic fluids report anomalous underscreening, which so far has not been observed in simulation. We present Molecular Dynamics simulation results exhibiting anomalous underscreening that can be connected to cluster formation. A theory that accounts for ion pairing confirms the trend. Our results challenge the classic understanding of dense electrolytes impacting the design of technologies for energy storage and conversion.

Absence of anomalous underscreening in highly concentrated aqueous electrolytes confined between smooth silica surfaces

Recent surface forces apparatus experiments that measured the forces between two mica surfaces and a series of subsequent theoretical studies suggest the occurrence of universal underscreening in highly concentrated electrolyte solutions. We performed a set of systematic Atomic Force Spectroscopy measurements for aqueous salt solutions in a concentration range from 1 mM to 5 M using chloride salts of various alkali metals as well as mixed concentrated salt solutions (involving both mono- and divalent cations and anions), that mimic concentrated brines typically encountered in geological formations. Experiments were carried out using flat substrates and submicrometer-sized colloidal probes made of smooth oxidized silicon immersed in salt solutions at pH values of 6 and 9 and temperatures of 25 °C and 45 °C. While strong repulsive forces were observed for the smallest tip-sample separations, none of the conditions explored displayed any indication of anomalous long range electrostatic forces as reported for mica surfaces. Instead, forces are universally dominated by attractive van der Waals interactions at tip-sample separations of ≈2 nm and beyond for salt concentrations of 1 M and higher. Complementary calculations based on classical density functional theory for the primitive model support these experimental observations and display a consistent decrease in screening length with increasing ion concentration.

Colloidal Systems in Concentrated Electrolyte Solutions Exhibit Re-entrant Long-Range Electrostatic Interactions due to Underscreening

Surface force measurements have revealed that at very high electrolyte concentrations as well as in neat and diluted ionic liquids and deep eutectic solvents, the range of electrostatic interactions is far greater than the Debye length. Here, we explore the consequences of this underscreening for soft-matter and colloidal systems by investigating the stability of nanoparticle dispersions, the self-assembly of ionic surfactants, and the thickness of soap films. In each case, we find clear evidence of re-entrant properties due to underscreening at high salt concentrations. Our results show that underscreening in concentrated electrolytes is a general phenomenon and is not dependent on confinement by macroscopic surfaces. The stability of systems at very high salinity due to underscreening may be beneficially applied to processes that currently use low-salinity water.

Role of a Multivalent Ion-Solvent Interaction on Restricted Mg2+ Diffusion in Dimethoxyethane Electrolytes

The diffusion behavior of Mg²⁺ in electrolytes is not as readily accessible as that from Li⁺ or Na⁺ utilizing PFG NMR, due to the low sensitivity, poor resolution, and rapid relaxation encountered when attempting ²⁵Mg NMR. In MgTFSI₂/DME solutions, "bound" DME (coordinating to Mg²⁺) and "free" DME (bulk) are distinguishable from ¹H NMR. With the exchange rates between them obtained from 2D ¹H EXSY NMR, we can extract the self-diffusivities of free DME and bound DME (which are equal to that of Mg²⁺) before the exchange occurs using PFG diffusion NMR measurements coupled with analytical formulas describing diffusion under two-site exchange. The high activation enthalpy for exhange (65-70 kJ/mol) can be explained by the structural change of bound DME as evidenced by its reduced C-H bond length. Comparison of the diffusion behaviors of Mg²⁺, TFSI^-, DME, and Li⁺ reveals a relative restriction to Mg²⁺ diffusion that is caused by the long-range interaction between Mg²⁺ and solvent molecules, especially those with suppressed motions at high concentrations and low temperatures.

Modeling of Electron-Transfer Kinetics in Magnesium Electrolytes: Influence of the Solvent on the Battery Performance

The performance of rechargeable magnesium batteries is strongly dependent on the choice of electrolyte. The desolvation of multivalent cations usually goes along with high energy barriers, which can have a crucial impact on the plating reaction. This can lead to significantly higher overpotentials for magnesium deposition compared to magnesium dissolution. In this work we combine experimental measurements with DFT calculations and continuum modelling to analyze Mg deposition in various solvents. Jointly, these methods provide a better understanding of the electrode reactions and especially the magnesium deposition mechanism. Thereby, a kinetic model for electrochemical reactions at metal electrodes is developed, which explicitly couples desolvation to electron transfer and, furthermore, qualitatively takes into account effects of the electrochemical double layer. The influence of different solvents on the battery performance is studied for the state-of-the-art magnesium tetrakis(hexafluoroisopropyloxy)borate electrolyte salt. It becomes apparent that not necessarily a whole solvent molecule must be stripped from the solvated magnesium cation before the first reduction step can take place. For Mg reduction it seems to be sufficient to have one coordination site available, so that the magnesium cation is able to get closer to the electrode surface. Thereby, the initial desolvation of the magnesium cation determines the deposition reaction for mono-, tri- and tetraglyme, whereas the influence of the desolvation on the plating reaction is minor for diglyme and tetrahydrofuran. Overall, we can give a clear recommendation for diglyme to be applied as solvent in magnesium electrolytes.

On the modified Poisson-Boltzmann closure for primitive model electrolytes at high concentration

The modified Poisson-Boltzmann closure is applied to the Kirkwood hierarchy of integral equations to investigate high concentration primitive model electrolytes. Two approximations are considered in the two sphere fluctuation potential problem. The derived damped oscillatory mean electrostatic potentials suggest that this closure should be of use in providing a basis for understanding the large experimental decay lengths found at high electrolyte concentrations.

Untangling superposed double layer and structural forces across confined nanoparticle suspensions

The description of forces across confined complex fluids still holds many challenges due to the possible overlap of different contributions. Here, an attempt is made to untangle the interaction between charged surfaces across nanoparticle suspensions. Interaction forces are measured using colloidal-probe atomic force microscopy. The experimental force profiles are considered as a superposition of double layer and structural forces. In order to independently describe the decay of the double layer force, the ionic strength of the suspension is determined by electrolytic conductivity measurements. Jellium approximation is used to define the impact of the fluid on screening the surface potential. There, the nanoparticles are considered homogeneously distributed across the fluid and screening is only carried out via the particles counterions and added salt. The structural force follows a damped oscillatory profile due to the layer-wise expulsion of the nanoparticles upon approach of both surfaces. The description of the oscillatory structural force is extended by a depletion layer next to the confining surfaces, with no nanoparticles present. The thickness of the depletion layer is related to the electrostatic repulsion of the charged nanoparticles from the like-charged surfaces. The results show that the total force profile is a superposition of independent force contributions without any mutual effects. Using this rather simple model describes the complete experimentally determined interaction force profiles very well from surface separations of a few hundred nanometres down to the surfaces being almost in contact.

Oscillatory structural forces between charged interfaces in solutions of oppositely charged polyelectrolytes

Forces between negatively charged micron-sized silica particles were measured in aqueous solutions of cationic polyelectrolytes with an atomic force microscope (AFM). In these oppositely charged systems, damped oscillatory force profiles were systematically observed in systems at higher polyelectrolyte concentrations, typically around few g L-1. The wavelength of these oscillations is decreasing with increasing concentration. When the wavelength and concentration are normalized with the cross-over concentration, universal power-law dependence is found. Thereby, the corresponding scaling exponent changes from 1/3 in the dilute regime to 1/2 in the semi-dilute regime. This dependence is the same as in the like-charged systems, which were described in the literature earlier. This common behavior suggests that these oscillatory forces are related to the structuring of the polyelectrolyte solutions. The reason that the oppositely charged systems behave similarly to like-charged ones is that the former systems undergo a charge reversal due to the adsorption of the polyelectrolytes to the oppositely charged surface, whereby sufficiently homogeneous adsorbed layers are being formed. The main finding of the present study is that at higher polyelectrolyte concentrations such oscillatory forces are the rule, including the oppositely charged ones.

A multiple decay-length extension of the Debye-Hückel theory: to achieve high accuracy also for concentrated solutions and explain under-screening in dilute symmetric electrolytes

The Poisson-Boltzmann and Debye-Hückel approximations for the pair distributions and mean electrostatic potential in electrolytes predict that these entities have one single decay mode with a decay length equal to the Debye length 1/κD, that is, they have a characteristic contribution that decays with distance r like e-κDr/r. However, in reality, electrolytes have several decay modes e-κr/r, e-κ'r/r etc. with different decay lengths, 1/κ, 1/κ' etc., that in general are different from the Debye length. As an illustration of the significance of multiple decay modes in electrolytes, the present work uses a very simple extension of the Debye-Hückel approximation with two decay lengths, which predicts oscillatory modes when appropriate. This approach gives very accurate results for radial distribution functions and thermodynamic properties of aqueous solutions of monovalent electrolytes for all concentrations investigated, including high ones. It is designed to satisfy necessary statistical mechanical conditions for the distributions. The effective dielectric permittivity of the electrolyte plays an important role in the theory and each mode has its own value of this entity. Electrolytes with high electrostatic coupling, like those with multivalent ions and/or with solvent of low dielectric constant, have decay lengths in dilute solutions that substantially deviate from the Debye length. It is shown that this is caused by nonlinear ion-ion correlation effects and the origin of under-screening, i.e., 1/κ > 1/κD, in dilute symmetric electrolytes is analyzed. The under-screening is accompanied by an increase in the effective dielectric permittivity that is also caused by these correlations. The theoretical results for the decay length are successfully compared with recent experimental data for simple electrolytes in various solvents. The paper includes background material on electrolyte theory and screening in order to be accessible for nonexperts in the field.

Forces between solid surfaces in aqueous electrolyte solutions

This review addresses experimental findings obtained with direct force measurements between two similar or dissimilar solid surfaces in aqueous electrolyte solutions. Interpretation of these measurements is mainly put forward in terms of the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). This theory invokes a superposition of attractive van der Waals forces and repulsive double layer forces. DLVO theory is shown to be extremely reliable, even in the case of multivalent ions. However, such a description is only successful, when appropriate surface charge densities, charge regulation characteristics, and ion pairing or complexation equilibria in solution are considered. Deviations from DLVO theory only manifest themselves at distances of typically below few nm. More long-ranged non-DLVO forces can be observed in some situations, particularly, in concentrated electrolyte solutions, in the presence of strongly adsorbed layers, or for hydrophobic surfaces. The latter forces probably originate from patch-charge surface heterogeneities, which can be induced by ion-ion correlation effects, charge fluctuations, or other types of surface heterogeneities.

Dynamic Transport Control of Colloidal Particles by Repeatable Active Switching of Solute Gradients

Diffusiophoresis (DP) is described as typically being divided into chemiphoresis (CP) and electrophoresis (EP), and the related theory is well-established. However, not only the individual effect of CP and EP but also the size dependency on the resulting DP of colloidal particles has not yet been comprehensively demonstrated in an experimental manner. In this paper, we present a dynamic transport control mechanism for colloidal particles by developing a micro-/nanofluidic DP platform (MNDP). We demonstrate that the MNDP can generate transient and/or steady-state concentration gradients, making it possible to control the direction and rate of transport of colloidal particles through the individual manipulation of CP and EP by simply and rapidly switching solutions. In addition, the MNDP allows the size-dependent separation as well as fractionation of submicron particles through the individual manipulation of CP and EP, thus empirically validating the classic theoretical model for DP under the influence of electrical double layer (EDL) thickness. Furthermore, we provide theoretical analysis and simulation results that will enable the development of a versatile separation and/or fractionation technique for various colloidal particles, including biosamples, according to their size or electrical feature.

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.