Article

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

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## Abstract

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.

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... In recent years unexpectedly long decay lengths of electrostatic forces have been observed in concentrated electrolytes [1][2][3][4][5][6][7][8] subsumed under the term "underscreening". A lot of effort has been committed to explaining underscreening [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. We distinguish regular underscreening which can be attributed to steric interactions, from anomalous underscreening characterized by much longer decay lengths compared to its regular counterpart. ...
... Numerous studies have concluded that one of the most fundamental models for electrolytes and ionic liquids, the restricted primitive model (RPM), does not exhibit anomalous underscreening. As even some experimental studies could not find these large decay lengths [25,26], the phenomenon itself has been questioned. In this work we demonstrate that there is anomalous underscreening in the RPM using Molecular Dynamics simulations. ...
... In contrast to that, the long-ranged decay was found exclusively in a few experimental studies. Recent works concluded that the RPM which accurately explains the structural decay is incapable of predicting the longranged decay [18,21,24,25] which we refer to as anomalous underscreening. Thus, either the RPM is missing a crucial ingredient or the long-ranged decay is an artifact of the experiment. ...
Preprint
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 which 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.
... Surface force apparatus (SFA), atomic force microscopy (AFM) or the colloidal probe technique based on AFM have recently demonstrated their value in probing the balance of forces and their interdependence between short range hydration structural oscillatory forces and longer ranged Derjaguin-Landau-Verwey-Overbeek forces at solid-liquid interfaces [52][53][54][55][56]. However, the measured interaction contains many unrelated as well as related effects, stemming in general from non-electrostatic couplings in the system 1 such as the chemical nature of ions, their size and charge, as well as polarizability, and solvent structuring hydrogen bonds, to invoke just a few [55]. ...
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We use high resolution Atomic Force Microscopy to study the surface charge of the basal plane of gibbsite nanoparticles, with a lateral resolution of approximately 5 nm, in ambient electrolyte of variable pH and salt content. Our measurements reveal surface charge variations on the basal planes that correlate with the presence of topographic defects such as atomic steps. This surface charge heterogeneity, which increases with increasing pH, suggests that for a pH between 6 and 9 the defect sites display a stronger chemical activity than adjacent, apparently atomically smooth regions of the basal plane. Smooth regions display a slight positive surface charge of ≈0.05e per nm(2) that hardly varies within this pH range. In contrast, near the topographic defects we observe a much lower charge. Considering the size of the interaction area under the probing tip, this implies that at the defect sites the charge density must be negative, ≈-0.1e per nm(2). These measurements demonstrate that surface defects have a large influence on the average surface charge of the gibbsite basal plane. These findings will contribute to understand why surface defects play an important role in various applications, such as fuel cells, chemical synthesis, self-assembly, catalysis and surface treatments.
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Screening of a surface charge by electrolyte and the resulting interaction energy between charged objects is of fundamental importance in scenarios from bio-molecular interactions to energy storage. The conventional wisdom is that the interaction energy decays exponentially with object separation and the decay length is a decreasing function of ion concentration; the interaction is thus negligible in a concentrated electrolyte. Contrary to this conventional wisdom, we have shown by surface force measurements that the decay length is an increasing function of ion concentration and Bjerrum length for concentrated electrolytes. In this paper we report surface force measurements to test directly the scaling of the screening length with Bjerrum length. Furthermore, we identify a relationship between the concentration dependence of this screening length and empirical measurements of activity coefficient and differential capacitance. The dependence of the screening length on the ion concentration and the Bjerrum length can be explained by a simple scaling conjecture based on the physical intuition that solvent molecules, rather than ions, are charge carriers in a concentrated electrolyte.
Article
A repulsive double layer force has been measured for ethylammonium nitrate (EAN) at 373 K and 393 K, which is absent at lower temperatures. This temperature-tuneable change in behaviour is the opposite of recent observations which challenge traditional views of ionicity. This finding thus widens the debate about the very nature of ionic liquids.
Article
According to classical electrolyte theories interactions in dilute (low ion density) electrolytes decay exponentially with distance with the Debye screening length the characteristic length-scale. This decay length decreases monotonically with increasing ion concentration, due to effective screening of charges over short distances. Thus within the Debye model no long-range forces are expected in concentrated electrolytes. Here we reveal, using experimental detection of the interaction between two planar charged surfaces across a wide range of electrolytes, that beyond the dilute (Debye-Hückel) regime the screening length increases with increasing concentration. The screening lengths for all electrolytes studied – including aqueous NaCl solutions, ionic liquids diluted with propylene carbonate, and pure ionic liquids – collapse onto a single curve when scaled by the dielectric constant. This non-monotonic variation of the screening length with concentration, and its generality across ionic liquids and aqueous salt solutions, demonstrates an important characteristic of concentrated electrolytes of substantial relevance from biology to energy storage.
Article
Forces between negatively charged silica particles in aqueous electrolyte solutions were measured with the colloidal probe technique based on the atomic force microscope (AFM). The present study focuses on the comparison of monovalent and multivalent counterions, namely K(+), Mg(2+), and La(3+). The force profiles can be well described with the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) down to distances of about 4nm. At smaller distances, the forces become strongly repulsive due to additional non-DLVO repulsion. In the presence of La(3+), one observes an additional attractive force with a range of about 1nm at intermediate salt concentrations. This force is probably related to ion-ion correlations, but could also be influenced by surface charge heterogeneities or charge fluctuation forces.
Article
Significance Liquid solutions with high concentrations of electrically charged ions are key elements of many energy storage technologies and are prevalent in biology. Nevertheless, they remain poorly understood. We study ionic liquids—liquids composed solely of ions—with the goal of providing a general picture of concentrated ionic solutions. Using molecular-scale experiments, we show that, surprisingly, less than 0.1% of the ions in ionic liquids are “free” to contribute to electrostatic screening, with the remainder “stuck” as neutral aggregates. Our temperature-dependent results provide fundamental guidance for designing high-performance ionic liquids for numerous applications. More broadly, we provide a novel way of envisioning concentrated ionic solutions with wide-ranging implications, such as elucidating the nanoscale properties of underwater bioadhesives and other self-assembled biomolecules.
Article
Isothermal compressibility data of 23 aqueous electrolyte solutions at 25 ºC from the literature are used to calculate their hydration numbers, which diminish as the concentration increases. Their limit at very high concentration is near the 'number of adsorption sites' of water molecules on the ions, obtained by the BET method. On the contrary, hydration numbers obtained from ultrasound speed measurements yielding isentropic compressibilities cannot be valid, being much too large at infinite dilution.
Article
Calculations of Hamaker constants using Lifshitz theory require the availability of accurate dielectric data, especially in the ultraviolet spectral region, and the use of a convenient and appropriate mathematical representation. In this review, a multiple oscillator model — the so-called Ninham-Parsegian (N-P) representation — has been used and spectral parameters for 31 different inorganic materials (including diamond) have been generated from critically evaluated optical data or collected from the literature. For most materials, a two-oscillator model (one UV and one IR term) was used but more detailed representations were included when available. The spectral parameters presented here can be combined with previous data, mainly focused on hydrocarbon and organic systems, to yield an extensive spectral data base for both solids and liquids enabling Lifshitz calculations of Hamaker constants for many materials combinations.
Article
Ions and water structuring at charged-solid/electrolyte interfaces and forces arising from interfacial structuring in solutions above 100 mM concentrations dominate structure and functionality in many physiological, geological and technological systems. In these concentrations electrolyte structuring occurs within the range of molecular dimensions. Here, we quantitatively measure and describe electric double layer (EDL) and adhesive interactions at mica-interfaces in aqueous CsCl and LiCl solutions with concentrations ranging from 50 mM to 3M. Complementary, using atomic force microscopy and surface forces apparatus experiments we characterize concentration-dependent stark differences in the inner and outer EDL force profiles, and discuss differences between the used methods. From 50 mM to 1 M concentrations, interactions forces measured in CsCl-solutions exhibit strong hydration repulsions, but no diffuse EDL-repulsions beyond the Stern layer. In confinement the weakly hydrated Cs+ ions condensate into the mica-lattice screening the entire surface charge within the Stern layer. In contrast, strongly hydrated Li+ ions only partially compensate the surface charge within the Stern layer, leading to the formation of a diffuse outer double layer with DLVO behaviour. Both, LiCl and CsCl solutions exhibit oscillatory ion-hydration forces at surface separations from 2.2 nm to 4-8 Å. Below 4-8 Å the force profiles are dominated in both cases by forces originating from water and/or ion confinement at the solid/electrolyte/solid interface. Adhesive minima and their location vary strongly with the electrolyte and its concentration due to specific ion-correlations across the interface, while dispersion forces between the surfaces are overpowered. Highly concentrated 3 M solutions exhibit solidification of the inner EDL structure and an unexpected formation of additional diffuse EDL forces with an increasing range, as recently measured in ionic liquids. Our results may have important implications for understanding and modelling of interaction forces present in static and dynamic systems under physiological and high salt conditions.
Article
Van der Waals dispersive forces produce attractive interactions between bodies, playing an important role in many material systems influencing colloidal and emulsion stability, wetting behavior, and intergranular forces in glass–ceramic systems. It is of technological importance to accurately quantify these interactions, conveniently represented by the Hamaker constant,A. To set the current level of accuracy for determiningA, they were calculated from Lifshitz theory using full spectral data for muscovite mica, Al2O3, SiO2, Si3N4, and rutile TiO2, separated by vacuum or water. These were compared to Hamaker constants calculated from physical properties using the Tabor–Winterton approximation, a single oscillator model, a multiple oscillator model, andA’s calculated using force vs separation data from surface force apparatus and atomic force microscope studies. For materials with refractive indices between 1.4 and 1.8 separated by vacuum, all methods produce similar values, but for indices larger than 1.8 separated by vacuum, and any of these materials separated by water, results span a broader range. The present level of accuracy for the determination of Hamaker constants, here taken to be represented by the level of agreement between various methods, ranges from about 10% for the case of SiO2/vacuum/SiO2and TiO2/water/TiO2to a factor of approximately 7 for mica/water/mica.
Article
The linearized Poisson-Boltzmann theory is used to calculate the electrical double layer interaction free energy between two parallel charged plates for the case in which charge regulation due to the dissociation of surface groups may be modelled by the linearized regulation model that specifies a linear relationship between the surface charge and the surface potential. This charge regulation model is characterized by a constant—termed the regulation capacitance of the surface. Analytic expressions for the force per unit area, the interaction free energy per unit area as well as the interaction free energy between two nonidentical spheres in the Deryaguin limit are given for the general case of nonidentical surfaces. An expression for the interaction free energy, applicable to any geometry, is obtained by thermodynamic arguments. Numerical comparisons for the case of identical amphoteric surfaces show that linearizing the charge regulation boundary conditions produces little error in the resultant interaction free energy.
Article
A force microscope has been used to measure surface forces between a colloidal sphere (3.5-mu-m radius) and a flat surface in aqueous solution. The force between silica surfaces was measured as a function of surface separation, salt concentration, and pH, and the results agree well both with earlier measurements between macroscopic surfaces and, at separations greater than 3 nm, with the force predicted by DLVO theory. The technique is simple and reproducible and could be used to measure the forces acting on other colloid particles and fibers of a variety of compositions. This is demonstrated by measurement of the force on a gold-coated sphere.
Article
Force measurements between two pyrogenic silica sheets immersed in a series of monovalent electrolytes (CsCl, KCl, NaCl, LiCl) were performed using a surface force apparatus (SFA). For each species, a shortrange repulsive hydration force prevented any adhesion of the surfaces. The data were fitted using a charge regulation model of the double-layer repulsion by solving the nonlinear Poisson-Boltzmann equation numerically, together with the full Lifshitz calculation of the van der Waals attraction. The hydration force was obtained by subtracting these calculated forces from the data. The results showed that the strength and the range of the hydration force decrease with increasing the degree of hydration of the counterion. This is opposite to the behavior of mica for which adsorbed counterions have been reported to generate a hydration repulsion. The effects of counterions on hydration forces, weakening for silica and enhancing for mica, show that the origin of the short-range interaction is not unique.
Article
The charge density of the particles in the commercial silica sol "Ludox" was determined as a function of the pH. A new technique was developed for this purpose, which allows the continuous measurement of the adsorption isotherm of the potential determining ion, without interference of a suspension effect. It was shown that the results obtained by means of this technique are consistent with certain theoretical expectations.
Article
Self-potential electric and magnetic anomalies are increasingly being observed associated with hydrothermal fields, volcanic activity, and subsurface water flow. Until now a formal theoretical basis for predicting streaming potential of porous materials has not been available. We develop here a model giving both the macroscopic constitutive equations and the material properties entering these equations. The material properties, like the streaming potential coupling coefficient, depend on pore fluid salinity, temperature, water and gas saturations, mean grain diameter, and porosity. Some aspects of the model are directly tested with success against laboratory data. The streaming potential increases with temperature, grain size, and gas saturation, and decreases with salinity. At the scale of geological structures the model provides an explanation for the presence of kilometer-scale dipolar self-potential anomalies in geothermal systems and volcanoes. Positive self-potential anomalies are associated with fluid discharge areas, whereas negative self-potential anomalies are associated with fluid recharge areas. Self-potential anomaly maps determined at the surface of active hydrothermal fields appear to be a powerful way of mapping the fluid recharge and discharge areas. In the case of free convection the vorticities of the convection pattern generate a magnetic field. The greater these vorticities, the greater the associated magnetic field. It follows that hydrothermal systems act as natural geobatteries because of the now of pore fluids in the subsurface of these systems.