Mapping the Binding Energy of Layered Crystals to Macroscopic Observables.

Van der Waals (vdW) integration of two dimensional (2D) crystals into functional heterostructures emerges as a powerful tool to design new materials with fine-tuned physical properties at an unprecedented precision. The intermolecular forces governing the assembly of vdW heterostructures are investigated by first-principles models, yet translating the outcome of these models to macroscopic observables in layered crystals is missing. Establishing this connection is, therefore, crucial for ultimately designing advanced materials of choice-tailoring the composition to functional device properties. Herein, components from both vdW and non-vdW forces are integrated to build a comprehensive framework that can quantitatively describe the dynamics of these forces in action. Specifically, it is shown that the optical band gap of layered crystals possesses a peculiar ionic character that works as a quantitative indicator of non-vdW forces. Using these two components, it is then described why only a narrow range of exfoliation energies for this class of materials is observed. These findings unlock the microscopic origin of universal binding energy in layered crystals and provide a general protocol to identify and synthesize new crystals to regulate vdW coupling in the next generation of heterostructures.

Self-consistent dielectric functions of materials: Toward accurate computation of Casimir-van der Waals forces.

Research on theoretical calculation of Casimir-van der Waals (vdW) forces is characterized by a great number of inconsistencies and conflicting reports with widely differing results for many known materials, including water, contradicting experimental measurements. Despite its importance for conceptual advances in both fundamental aspects and practical applications, a universal framework for the accurate determination of Casimir-vdW forces is lacking. Here, we propose a universal theoretical platform for computing Casimir-vdW forces, accounting for the electronic dielectric constant, optical bandgap, density, and chemical composition. Using this methodology, we determine the dielectric function for 55 materials, over a wide range of photon energies, covering an extensive list of common metals, organic and inorganic semiconductors, and insulators. Internal consistency of the compiled data is validated using optical sum rules and Kramers-Kronig relations. We demonstrate that the calculated vdW forces based on these data match remarkably well with the experimentally measured vdW forces.

Interactions between similar and dissimilar charged interfaces in the presence of multivalent anions.

Direct force measurements involving amidine latex (AL) and sulfate latex (SL) particles in aqueous solutions containing multivalent ferrocyanide anions are presented. These measurements feature three different pairs of particles, namely SL-SL, AL-SL, and AL-AL. The force profiles are quantitatively interpreted in terms of the theory by Derjaguin, Landau, Verwey, and Overbeek (DLVO) that is combined with a short-ranged exponential attraction. In monovalent salt solutions, the AL particles are positively charged, while the SL particles are negatively charged. In solutions containing ferrocyanide, the charge of the AL particles is reversed as the concentration is increased. The longer-ranged component of all force profiles is fully compatible with DLVO theory, provided effects of charge regulation are included. At shorter distances, an additional exponential attraction must be introduced, whereby the respective decay length is about 2 nm for the AL-AL pair, and below 1 nm for the SL-SL pair. This non-DLVO force is intermediate for the asymmetric AL-SL pair. These additional forces are probably related to charge fluctuations, patch-charged interactions, or hydrophobic forces.

Depletion and double layer forces acting between charged particles in solutions of like-charged polyelectrolytes and monovalent salts.

Interaction forces between silica particles were measured in aqueous solutions of the sodium salt of poly(styrene sulphonate) (PSS) and NaCl using the colloidal probe technique based on an atomic force microscope (AFM). The observed forces can be rationalized through a superposition of damped oscillatory forces and double layer forces quantitatively. The double layer forces are modeled using Poisson-Boltzmann (PB) theory for a mixture of a monovalent symmetric electrolyte and a highly asymmetric electrolyte, whereby the multivalent coions represent the polyelectrolyte chains. The effective charge of the polyelectrolyte is found to be smaller than the bare number of charged groups residing on one polyelectrolyte molecule. This effect can be explained by counterion condensation. The interplay between depletion and double layer forces can be further used to predict the phase of the depletion force oscillations. However, this picture holds only at not too elevated concentrations of the polyelectrolyte and salt. At higher salt concentrations, attractive van der Waals forces become important, while at higher polyelectrolyte concentrations, the macromolecules adsorb onto the like-charged silica interface.

Interactions between charged particles with bathing multivalent counterions: experiments vs. dressed ion theory.

We compare the recent experimentally measured forces between charged colloidal particles, as well as their effective surface potentials (surface charge) in the presence of multivalent counterions in a bathing monovalent salt solution, with the predictions of the dressed ion theory of strongly charged colloidal systems. The benchmark for comparison is provided by the DLVO theory and the deviations from its predictions at small separations are taken as an indication of the additional non-DLVO attractions that can be fitted by an additional phenomenological exponential term. The parameters characterizing this non-DLVO exponential term as well as the dependencies of the effective potential on the counterion concentration and valency predicted by the dressed ion theory are well within the experimental values. This suggests that the deviations from the DLVO theory are probably caused by ion correlations as formalized within the dressed ion theory.

Forces between different latex particles in aqueous electrolyte solutions measured with the colloidal probe technique.

In this article, a compilation of results on direct force measurements between colloidal particles in monovalent salts carried out with the colloidal probe technique based on Atomic Force Microscopy was presented. The interaction forces between similar and dissimilar particles was studied and it was concluded that, in general, these force profiles may be satisfactorily quantified by the DLVO theory down to distances of few nanometers. However, in the specific case where the charge of one of the involved particle is close to neutral, it was found that the surface potential of this particle may change its sign depending on the sign of charge of the opposite particle. In this respect, the assumption that the surface potential of a particle is a property only related to the particle surface features and the bulk properties is called into question. Microsc. Res. Tech. 80:144-152, 2017. © 2016 Wiley Periodicals, Inc.

Interplay between Depletion and Double-Layer Forces Acting between Charged Particles in Solutions of Like-Charged Polyelectrolytes.

Direct force measurements between negatively charged silica particles in the presence of a like-charged strong polyelectrolyte were carried out with an atomic force microscope. The force profiles can be quantitatively interpreted as a superposition of depletion and double-layer forces. The depletion forces are modeled with a damped oscillatory profile, while the double-layer forces with the mean-field Poisson-Boltzmann theory for a strongly asymmetric electrolyte, whereby an effective valence must be assigned to the polyelectrolyte. This effective valence is substantially smaller than the bare valence due to ion condensation effects. The unusual aspect of the electrical double layer in these systems is the exclusion of the like-charged polyelectrolyte from the vicinity of the surface, leading to a strongly nonexponential diffuse ionic layer that is dominated by counterions and has a well-defined thickness. As the oscillatory depletion force sets in right after this layer, this condition can be used to predict the phase of the oscillatory depletion force.

Nanometer-ranged attraction induced by multivalent ions between similar and dissimilar surfaces probed using an atomic force microscope (AFM).

Direct force measurements between positively charged amidine latex (AL) and negatively charged sulfate latex (SL) particles are carried out using an atomic force microscope (AFM). Forces between three different pairs, namely AL-AL, AL-SL, and SL-SL, are measured in solutions containing multivalent cationic aliphatic hexamines (N6) and in simple monovalent KCl solutions. The classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) can rationalize the observed force profiles very well, provided the PB equation is solved for the appropriate asymmetric electrolyte and charge regulation effects are included in the analysis. However, the DLVO description is typically valid only at distances beyond several nanometers. At shorter distances, a short-ranged non-DLVO attraction is present, which can be modeled with an exponential force profile. In KCl solutions, the range of this attraction is around 0.3 nm. In N6 solutions, the range of this attraction is about 1.0 nm in the SL-SL system, 0.6 nm in the AL-SL system, and 0.3 nm in the AL-AL system.

Long-ranged and soft interactions between charged colloidal particles induced by multivalent coions.

Forces between charged particles in aqueous solutions containing multivalent coions and monovalent counterions are studied by the colloidal probe technique. Here, the multivalent ions have the same charge as the particles, which must be contrasted to the frequently studied case where multivalent ions have the opposite sign as the substrate. In the present case, the forces remain repulsive and are dominated by the interactions of the double layers. The valence of the multivalent coion is found to have a profound influence on the shape of the force curve. While for monovalent coions the force profile is exponential down to separations of a few nanometers, the interaction is much softer and longer-ranged in the presence of multivalent coions. The force profiles in the presence of multivalent coions and in the mixtures of monovalent and multivalent coions can be accurately described by Poisson-Boltzmann theory. These results are accurate for different surfaces and even in the case of highly charged particles. This behavior can be explained by the fact that the force profile follows the near-field limit to much larger distances for multivalent coions than for monovalent ones. This limit corresponds to the conditions with no salt, where the coions are expelled between the two surfaces.