Double Layer Theory Research Articles

Reply to the 'Comment on "Can bulk nanobubbles be stabilized by electrostatic interaction?"' by S. Koshoridze and Y. Levin, Phys. Chem. Chem. Phys., 2022, 24, DOI: 10.1039/D1CP04406K.

We investigated the effect of the adsorbed ions on the stability of nanobubbles suspended in the liquid in a recent article published in Physical Chemistry Chemical Physics. We calculated the electrostatic pressure using the classical electrical double layer (EDL) theory and pointed out that the electrostatic pressure is overestimated in previous theories due to the overlook of the stress in the diffusive double layer. Recently, S. I. Koshoridze and Yu. K. Levin questioned our calculations and results based on their intuition that diffusive ions in the EDL will drift and, therefore, not contribute to hydrostatic pressure. In this reply, we explain why mobile ions can also produce hydrostatic pressure from a hydrodynamic perspective.

Topology analysis of Lanzhou public transport network based on double-layer complex network theory

The network topology is the basis of studying the overall performance and dynamic evolution mechanism of network. In regards to the study on the topology of multi-layer complex networks, the current studies fail to consider the heterogeneity of edges and nodes in multi-layer complex networks, and such methods are insufficient when they are used to analyze the static characteristics of topology. Therefore, this paper based on the theoretical basis of the multi-layer complex network, establishes a two-layer public transit complex network model where urban rail transit and bus transit cooperate with each other, and by optimizing this two-layer public transit complex network model, further proposes an integrated public transit network model. According to the method of analyzing the static statistical characteristics of complex networks, and considering the heterogeneity of nodes and edges in multi-layer network, this​ paper gives the evaluation indicators of static statistical characteristics of multi-layer public transit complex networks. Taking the two-layer public transit complex network structure in Lanzhou as an example, this paper finds out the main factors affecting its network stability and efficiency by analyzing the physical structure characteristics of this two-layer public transit complex network in Lanzhou where urban rail transit and bus transit cooperate with each other, and then puts forward the network optimization suggestions from the point of view of optimizing key nodes by using the method of identifying key nodes with centrality. In this study, the coupling among heterogeneous public transit network layers and the static structure characteristics of multi-layer public transit complex network are studied from the perspective of network structure, to assist the traffic management department in finding out the problems of the road network for the management and improvement of the performance and efficiency of the network. This has a profound influence on the development planning of urban public transit system.

Overlapping double layers in electrokinetics of concentrated dispersions

The traditional model of the Isolated Double Layer (DL) becomes inadequate in concentrated dispersions when the distance between particles becomes comparable to the Debye length and DLs overlap. The notion of “overlapping DLs” was introduced to Electrophoretic theory 60 years ago by Prof. T. Overbeek’s group. The theory posed in that paper and a subsequent publication by Long and Ross predicts a decline of electrophoretic mobility due to DLs overlap. There is also more recent theory that describes electrokinetics at the extreme case of complete DLs overlap. We call it “quasi-homogeneous DL theory”. It predicts an increase of electrophoretic mobility. We conducted an experimental study to verify which theoretical prediction is correct. We used an equilibrium dilution protocol, which allowed us to maintain the same interface-bulk electrochemical equilibrium at all volume fractions, ranging from 1 %vl up to 36 %vl (56 %wt). Electroacoustics were applied for measuring electrophoretic mobility and zeta potential. They remain constant up to 15% vl. At the higher volume fraction, where DLs become overlapping, they increase. This confirms prediction of “quasi-homogeneous DL theory” at least on qualitative level.

Revealing Electrical Double-Layer Potential of Substrates by Hysteresis Ion Transport in Scanning Ion Conductance Microscopy.

The electrical double layer (EDL) at solid-liquid interfaces is key to interfacial transport and reaction processes and numerous emerging applications exploiting such processes. Herein, by studying hysteresis ion-transport processes in nanopipettes near charged substrates, we found the resulting cross-point potential (Vcp) to represent the surface potential of both nanopipettes and substrates. After the subtraction of Vcp in bulk solution, the remaining ΔVcp shows excellent exponential decay with respect to the separation distance from the substrates and agrees very well with the classical double-layer theory. The revealed new hysteresis ion transport in nanopipettes would provide a new way for the simple and direct EDL imaging of various interfaces of interest with nanoscale resolution in scanning ion conductance microscopy.

Insight into Debye H\xfcckel length (\u03ba\u22121): smart gravimetric and swelling techniques reveals discrepancy of diffuse double layer theory at high ionic concentrations

Smart gravimetric and swelling techniques were utilized in this work to examine the validity of the Debye Hückel length (κ−1) equation when shale interacts with highly concentrated salt solutions. The swelling and shrinkage behavior of two different shales, when exposed to monovalent and divalent ionic solutions (NaCl, KCl and CaCl2) at concentrations ranging from 2 to 22%w/w was observed and measured. Shale swelling and shrinkage results show that Debye Hückel length (κ−1) equation seems to work adequately at low ionic concentrations where osmotic water flow out of shale plays a major role in decreasing the diffuse double layer thickness by withdrawing water out and thereby shrinking κ−1. At high ionic concentration levels, the flow of associated water into the diffuse double layer negates the withdrawal of osmotic water out of the diffuse double layer which could maintain κ−1 or possibly increase it. Data on measured ionic uptake into shale suggests that excessive ionic diffusion into shale, especially at high concentrations, leads to higher electrical repulsion between alike ions in the diffuse layer which could lead to the expansion of the diffuse double layer thickness. Furthermore, swelling and shrinkage data analysis for shale suggests the existence of a ‘critical concentration’ below which the Debye Hückel length equation works. Above the critical concentration, the validity of the Debye Hückel length equation might be in question. The critical concentration is different for all ions and depends on ionic valence, hydrated ion diameter, and clay type.

Heterogeneity in Lateral Distribution of Polycations at the Surface of Lipid Membrane: From the Experimental Data to the Theoretical Model.

Natural and synthetic polycations of different kinds attract substantial attention due to an increasing number of their applications in the biomedical industry and in pharmacology. The key characteristic determining the effectiveness of the majority of these applications is the number of macromolecules adsorbed on the surface of biological cells or their lipid models. Their study is complicated by a possible heterogeneity of polymer layer adsorbed on the membrane. Experimental methods reflecting the structure of the layer include the electrokinetic measurements in liposome suspension and the boundary potential of planar bilayer lipid membranes (BLM) and lipid monolayers with a mixed composition of lipids and the ionic media. In the review, we systematically analyze the methods of experimental registration and theoretical description of the laterally heterogeneous structures in the polymer layer published in the literature and in our previous studies. In particular, we consider a model based on classical theory of the electrical double layer, used to analyze the available data of the electrokinetic measurements in liposome suspension with polylysines of varying molecular mass. This model suggests a few parameters related to the heterogeneity of the polymer layer and allows determining the conditions for its appearance at the membrane surface. A further development of this theoretical approach is discussed.

Kinetic theory of double layers driven by temperature anisotropy in a non-homogeneous magnetic field

A double layer (DL) is created in a plasma when the plasma is perturbed in the presence of a temperature anisotropy. We derive a new simple theory for the existence of an unstable, non-oscillatory electrostatic DL-like structure in the presence of a magnetic field gradient in a collisionless plasma with a temperature anisotropy in the direction perpendicular to the magnetic field. The DL is treated as a wave perturbation in the plasma using kinetic theory with a gyro-kinetic approximation to obtain a dispersion relation. The presence of an electron temperature anisotropy is the necessary condition to obtain an exponentially growing instability, and the corresponding growth rate is found to be the ratio of the electron kinetic energy and the electric field energy across the DL region. The theoretical predictions are then validated against a one-dimensional electrostatic particle simulation carried out in a traveling magnetic field thruster environment. An anisotropy ratio parameter was introduced, and the theoretical growth rates were found to be in good agreement with the simulation for different anisotropy ratios. An ion beam, associated with the DL dynamics, is observed within the simulation domain. A parametric study revealed that the DL-like structure loses its ambipolar shape for temperature ratios less than 10. It has been found that a stronger anisotropy is required to obtain the DL-like structure.

The role of reversible and polarizable surface charge in the electro-sorption of NaCl electrolyte onto activated carbon-graphite electrode

An electrode made of activated carbon that had high-specific-surface area and low pHzpc supported on graphite sheet was fabricated. The electrode, NSA/G, was used to study the effect of reversible surface charge on the adsorption of simple electrolyte, i.e., NaCl, on polarizable electrode. Polarizable surface charge is originated from externally applied potential whereas reversible surface charge is derived from change of activity of potential-determining ions, i.e., H+ or OH– owning to hydrous surface, which undergoes protonation and deprotonation of surface hydroxyl groups. Ion adsorption density was obtained from direct analytical measurement of corresponding ion studied instead of conductivity measurement. Langmuir adsorption isotherm was applied to estimate the monolayer ion adsorption density. Electrosorption/desorption kinetics was fitted well by the first-order rate law. In the applied potential range of −0.3 to −1.0 V (vs. SCE) and pH of 3 to 10, the pH-determining surface, i.e., reversible charge, accounted for Na+ sorption intensity was estimated based on the Gouy-Chapman version of electrical double layer theory. Results revealed that the two major surface charges, i.e., polarizable (σE) and reversible (σpH), contributed equally to the total charge density (σT). At high pH (pH 10) and low applied voltage (-0.3 V vs. SCE), the fraction of pH-determining contribution to total surface charge with respect to Na+ sorption, i.e., σpH/σT, was around 0.50. Results reaffirmed the importance of reversible surface charge together with polarizable surface charge on the design and operation of CDI system for electrosorption of ions from water.

Predicting the electrokinetic properties on an outcrop and reservoir composite carbonate surfaces in modified salinity brines using extended surface complexation models

Surface complexation models (SCM), based mainly on the diffuse double layer (DDL) theory, have been used to predict zeta potential at the crude oil-brine-rock (COBR) interface with limited success. However, DDL is inherently limited in accurately predicting zeta potential by the assumptions that all the brine ions interact with the rock surface at the same plane and by the double layer collapse at higher brine ionic strength (>1M). In this work, a TLM-based SCM captured zeta potential trends at the calcite-brine interface with ionic strength up to 3 M. An extended DDL and TLM-based SCMs were used to predict the electrokinetic properties of a composite carbonate rock showing a different mineralogical composition. The extended TLM-based SCM captured the zeta potential prediction trends and magnitude, highlighting the contribution of the inorganic minerals and organic impurities on the composite carbonate surface. In contrast, the extended DDL-based SCM captured the zeta potential trends but failed to capture the magnitude of the measured zeta potential. Interestingly, the TLM-based SCM predicted a positive SP for the rock-brine interface, which could explain the oil-wet nature of composite carbonate rocks due to electrostatic adsorption of negatively charged carboxylic acids. Conversely, the DDL-based SCM predicted a negative SP, leading to an inaccurate interpretation of the electrokinetic properties at the rock-brine interface. Thus, the use of extended TLM-based SCM was required to accurately predict the zeta potential and account for the adsorption of carboxylic acids on the reservoir composite carbonate surface.

ПОЛУАНАЛИТИЧЕСКИЙ МЕТОД В ЗАДАЧЕ ОБТЕКАНИЯ КРЫЛОВОГО ПРОФИЛЯ С ОСТРОЙ ЗАДНЕЙ КРОМКОЙ ПОТОКОМ ИДЕАЛЬНОЙ ЖИДКОСТИ

In the present work we propose a method to study a two-dimensional flow of non-viscous fluid around an airfoil with a sharp trailing edge, by the double-layer potential theory. The circulation of velocity vector is modeled by the potential of a point vortex whose center is located inside the boundary contour. The magnitude of the circulation is defined on the basis of the Joukowski-Chaplygin postulate. There are presented some results for a Joukowski rudde, as well as for the airfoil in the form of a pair of interacting circles. It is performed a comparison of the circulation with its theoretical value.

Theory of Ionic Liquids with Polarizable Ions on a Charged Electrode

We formulate a general mean-field theory of a flat electric double layer in ionic liquids and electrolyte solutions with ions possessing static polarizability and a permanent dipole moment on a charged electrode. We establish a new analytical expression for electric double layer differential capacitance determining it as an absolute value of the ratio of the local ionic charge density to the local electric field on an electrode surface. We demonstrate that this expression generalizes the analytical expressions previously reported by Kornyshev and Maggs and Podgornik. Using the obtained analytical expression, we explore new features of the differential capacitance behavior with an increase in the static polarizability and permanent dipole moment of cations. We relate these features to the behavior of ionic concentrations on the electrode. In particular, we elucidate the role of the competition between the dielectrophoretic attraction and Coulomb repulsion forces acting on polarizable or polar cations in the electric double layer in the behavior of the differential capacitance. The developed theoretical model and obtained theoretical findings could be relevant for different electrochemical applications, e.g. batteries, supercapacitors, catalysis, electrodeposition, etc.

Observation of specific ion effects in humus aggregation process

Specific ion effects play a vital role in a variety of colloidal and interfacial processes. However, few studies have reported the specific ion effects in the humus aggregation process, which strongly influence the transport and fate of environmental pollutants. In this study, soil humus colloids were prepared and characterized, and the specific ion effects on humus aggregation in electrolyte solutions were investigated at a variety of concentrations and pH values using dynamic light scattering methods. Activation energy (ΔE), which is known to reflect the dynamics and stability of a colloidal system, was used to quantitatively characterize the specific ion effects. The results showed that given ΔE value of 2.48 × 103 J mol−1 at pH 3.0, the electrolyte concentrations were 91.6, 58.2, 3.8, and 0.8 mmol L−1 for Na+, K+, Mg2+, and Ca2+, respectively, thus indicating significant specific ion effects in the humus aggregation process. Most importantly, decreasing the electrolyte concentrations increased the differences in the ΔE value between two cation species with the same valence (i.e., ΔENa – ΔEK and ΔEMg – ΔECa), while increasing the pH increased the magnitude of ΔEMg – ΔECa. However, the classic Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory and the double layer theory, as well as the currently widely used ionic hydration and dispersion effects, failed to predict the experimentally observed increase in the specific ion effects with decreasing electrolyte concentrations in a quantitative sense. These results have implications for the necessity of involving specific ion effects for a better understanding of humus aggregation and interactions in aqueous and soil systems.

A theoretical model for the hydraulic conductivity of montmorillonite in relation to the concentration and valence of electrolyte cations in solution

This study is among the first to report on a theoretical relationship linking the hydraulic conductivity of soil and aquifer with environmental solution conditions. A mathematical model is developed for predicting the hydraulic conductivity of montmorillonite from the concentration and valence of electrolyte cations in solution. The model relies on the diffuse double layer and DLVO theories, the aggregation kinetics, and the Hazen equation, with a few plausible assumptions, for establishing three individual relationships, with each corresponding to one of three steps in the cation-to-particle-to-grain-to-hydraulic conductivity pathway. It is based on a mechanistic understanding that the concentration and valence of electrolyte cations controls the size of montmorillonite primary particles by influencing the electrical double layer, subsequently regulates the grain-size distribution of montmorillonite via inter-particle collision, and finally determines the hydraulic conductivity of montmorillonite. The model is validated by direct measurements of the surface charge density, the grain-size distribution and the hydraulic conductivity of montmorillonite in NaCl and CaCl2 solutions of various concentrations. The theoretical model of predicting hydraulic conductivity developed here is novel for implementing more accurate modeling of contaminant transport in the environment with advantage of cost-savings.

Diffusion of tritiated water, 137Cs+, and 125I− in compacted Ca-montmorillonite: Experimental and modeling approaches

Mechanistic understanding and predictive modeling of radionuclide diffusion in Na- and Ca-montmorillonite are essential to evaluate the long-term evolution of the bentonite barrier and their impact on radionuclide migration during geological disposal of radioactive wastes. Thus, the diffusion behavior of 137Cs+, 125I−, and tritiated water (HTO) in compacted Ca-montmorillonite was investigated as a function of porewater salinity and dry density via both experiments and models. The effective diffusion coefficient (De) followed in the order of 137Cs+ > HTO > 125I−. The De of 137Cs+ decreased with increasing salinity, whereas the dependence of De of 125I− on salinity was uncertain. The cation excess and anion exclusion effects for Ca-montmorillonite were lower than those for Na-montmorillonite. The integrated sorption and diffusion (ISD) model, assuming the homogeneous pore structure and the electrical double layer (EDL) theory for 2:1 electrolyte (CaCl2), could account for the observed trends for De in Ca-montmorillonite. The lower dependence of De on the porewater salinity in Ca-montmorillonite was caused by the reduction of the EDL thickness for divalent cations (Ca2+) in comparison with that for monovalent cations (Na+). The multipore model could improve the fit for De of 125I− at low salinity due to the reduction of interlayer pore volumes and anion exclusion effect, however, the disparity at higher densities was considerably larger. From these results, cation diffusion for compacted Ca-montmorillonite could be mainly explained by the electrostatic interactions in the homogeneous pore model; in contrast, anion diffusion was sensitive to both electrostatic interactions and heterogeneous pore structures. The proposed ISD model is an effective tool to evaluate the radionuclide diffusion and sorption behavior in both compacted Ca-montmorillonite and Na-montmorillonite.

Hybrid density-potential functional theory of electric double layers

We present a field theoretic derivation for the free energy of the electrolyte solution. A reference system is introduced to describe non-electrostatic interactions, notably hard-sphere interactions, between charged particles in the electrolyte solution. The reference system is described by the Bikerman theory — a local density approximation, and the fundamental measure theory (FMT) — a nonlocal density approximation. Combining the classical part for charged particles in electrolyte solution and a quantum mechanical part for interacting electrons, we obtain a hybrid density-potential functional for the grand canonical potential of the electric double layer (EDL). Variation analysis of the hybrid density-potential functional leads to two controlling equations in terms of the electron density and the electric potential, respectively. Numerical implementation of the developed model is demonstrated for a simple EDL without specific adsorption. Particularly, oscillating density of counterions occurs near the metal surface when the FMT is used for the reference system.

Surface adsorption and foam performance of sodium perfluoroalkyl polyoxyethylene ether sulfate in ethanol-water mixed system

In this study, we synthesized a new fluorocarbon surfactant, viz. sodium perfluoroalkyl polyoxyethylene ether sulfate (FES-Na), and studied its interface adsorption behavior and foam performance in 50 vol% ethanol. The mechanism of foam stability conforms to the classic double-layer film theory. The results show that FES-Na can produce stable foam in 50 vol% ethanol, and is thus an alternative foaming agent in ethanol-water system.

Investigation of Electrochemical and Chemical Processes Occurring at Positive Potentials in “Water-in-Salt” Electrolytes

Lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) based water-in-salt electrolytes (WiSEs) has recently emerged as a new promising class of electrolytes, primarily owing to their wide electrochemical stability windows (∼3–4 V), that by far exceed the thermodynamic stability window of water (1.23 V). Upon increasing the salt concentration towards superconcentration the onset of the oxygen evolution reaction (OER) shifts more significantly than the hydrogen evolution reaction (HER) does. The OER shift has been explained by the accumulation of hydrophobic anions blocking water access to the electrode surface, hence by double layer theory. Here we demonstrate that the processes during oxidation are much more complex, involving OER, carbon and salt decomposition by OER intermediates, and salt precipitation upon local oversaturation. The positive shift in the onset potential of oxidation currents was elucidated by combining several advanced analysis techniques: rotating ring-disk electrode voltammetry, online electrochemical mass spectrometry, and X-ray photoelectron spectroscopy, using both dilute and superconcentrated electrolytes. The results demonstrate the importance of reactive OER intermediates and surface films for electrolyte and electrode stability and motivate further studies of the nature of the electrode.

Influence of dielectric constant of pore fluids on double-layer swelling: a validation study

The clay platelets are negatively charged, and hence, the behavior of clays is physicochemical in nature. The clay–pore liquid interaction depends upon pore medium chemistry, which is a function of many factors. Dielectric constant of the pore medium is one such important factor. The clay swelling is considered to be explained by the Gouy–Chapman theory of diffuse double layer. This paper intends to study the effect of dielectric constant of the pore fluid on the equilibrium sediment volume in light of diffuse double-layer equation of the Gouy–Chapman theory. It has been illustrated that the Gouy–Chapman theory cannot explain the equilibrium sediment volume behavior of montmorillonite and kaolinite clay minerals satisfactorily. It is also brought out that the equilibrium sediment volume behavior of these two clay minerals is quite opposite to each other.

Investigating the selectivity and interference behavior for detoxification of Cr(VI) using lanthanum phosphate polyaniline nanocomposite via adsorption-reduction mechanism

A novel Lanthanum phosphate polyaniline (LaPO4-PANI) nanocomposite was synthesized by the simple sol-gel technique. The nanocomposite prepared at 1:1 ratio provided the highest ion exchange capacity and selective adsorption of Cr(VI). The phase composition and particle morphology of the as-prepared material was evaluated by XRD, FESEM and TEM analyses. The FTIR, Raman, and TGA data inferred the definite chemical interaction between the organic and inorganic counterparts in the formation of LaPO4-PANI. The selective adsorption of Cr(VI) was estimated by evaluating the distribution coefficient, electrical double layer theory as well as valency and Pauling’s ionic radii of interfering ions (phosphate, iodide, sulfate, chloride, sulfide). The high tolerance capability of LaPO4-PANI against the interfering ions made it appropriate for selective and efficient removal of Cr(VI) ions from solutions. The nanocomposite showed the highest removal percentage of 98.6% towards Cr(VI) in a wide pH range of 2–6 at room temperature, as compared to sole lanthanum phosphate (56%) and polyaniline (75%). The XPS analysis revealed the adsorption mechanism due to the combined effect of both adsorption and reduction. Cr(VI) is adsorbed through electrostatic interactions while the = N−/−NH- group facilitated the in situ chemical reduction. The procured results make the LaPO4-PANI nanocomposite a promising adsorbent for the removal of Cr(VI).

Design of facile technology for the efficient removal of hydroxypropyl guar gum from fracturing fluid.

With the increasing demand for energy, fracturing technology is widely used in oilfield operations over the last decades. Typically, fracturing fluids contain various additives such as cross linkers, thickeners and proppants, and so forth, which makes it possess the properties of considerably complicated components and difficult processing procedure. There are still some difficult points needing to be explored and resolved in the hydroxypropyl guar gum (HPG) removal process, e.g., high viscosity and removal of macromolecular organic compounds. Our works provided a facile and economical HPG removal technology for fracturing fluids by designing a series of processes including gel-breaking, coagulation and precipitation according to the diffusion double layer theory. After this treatment process, the fracturing fluid can meet the requirements of reinjection, and the whole process was environment friendly without secondary pollution characteristics. In this work, the fracturing fluid were characterized by scanning electron microscopy (SEM), Energy dispersive X-ray (EDX), X-ray diffraction (XRD) and Fourier transformed infrared (FTIR) spectroscopy technologies, etc. Further, the micro-stabilization and destabilization mechanisms of HPG in fracturing fluid were carefully investigated. This study maybe opens up new perspective for HPG removal technologies, exhibiting a low cost and strong applicability in both fundamental research and practical applications.