Gouy-Chapman Theory Research Articles

Zeta Potentials of Cotton Membranes in Acetonitrile Solutions.

Solid surfaces in contact with nonaqueous solvents play a key role in electrochemistry, analytical chemistry, and industrial chemistry. In this work, the zeta potentials of cotton membranes in acetonitrile solutions were determined by streaming potential and bulk conductivity measurements. By applying the Gouy-Chapman theory and the Langmuir adsorption isotherm of ions to the experimental data, the mechanism of the electrification at the cotton/acetonitrile interface is revealed for the first time to be solely due to ion adsorption on the surface, rather than proton dissociation at the interface. Different salts were found to produce opposite signs of the zeta potentials. This behavior can be attributed to ion solvation effects and the strong ordering of acetonitrile molecules at the interface. Furthermore, a trend of the electroviscous effect was observed, in agreement with the standard electrokinetic theory. These findings demonstrate that electrokinetics in acetonitrile, a polar aprotic solvent, can be treated in the same manner as in water.

A colloidal model for the equilibrium assembly and liquid-liquid phase separation of the reflectin A1 protein

Reflectin is an intrinsically disordered protein known for its ability to modulate the biophotonic camouflage of cephalopods based on its assembly-induced osmotic properties. Its reversible self-assembly into discrete, size-controlled clusters and condensed droplets are known to depend sensitively on the net protein charge, making reflectin stimuli-responsive to pH, phosphorylation, and electric fields. Despite considerable efforts to characterize this behavior, the detailed physical mechanisms of reflectin’s assembly are not yet fully understood. Here, we pursue a coarse-grained molecular understanding of reflectin assembly using a combination of experiments and simulations. We hypothesize that reflectin assembly and phase behavior can be explained from a remarkably simple colloidal model whereby individual protein monomers effectively interact via a short-range attractive and long-range repulsive (SA-LR) pair potential. We parameterize a coarse-grained SA-LR interaction potential for reflectin A1 from small-angle x-ray scattering measurements, and then extend it to a range of pH values using Gouy-Chapman theory to model monomer-monomer electrostatic interactions. The pH-dependent SA-LR interaction is then used in molecular dynamics simulations of reflectin assembly, which successfully capture a number of qualitative features of reflectin, including pH-dependent formation of discrete-sized nanoclusters and liquid-liquid phase separation at high pH, resulting in a putative phase diagram for reflectin. Importantly, we find that at low pH size-controlled reflectin clusters are equilibrium assemblies, which dynamically exchange protein monomers to maintain an equilibrium size distribution. These findings provide a mechanistic understanding of the equilibrium assembly of reflectin, and suggest that colloidal-scale models capture key driving forces and interactions to explain thermodynamic aspects of native reflectin behavior. Furthermore, the success of SA-LR interactions presented in this study demonstrates the potential of a colloidal interpretation of interactions and phenomena in a range of intrinsically disordered proteins.

Anisotropic swelling pressures of compacted GMZ bentonite infiltrated with salt solutions

In the high-level radioactive waste (HLW) deep geological repository, bentonite is compacted uniaxially, and then arranged vertically in engineered barriers. The assembly scheme induces the initial anisotropy, and with hydration, it develops more evidently under chemical conditions. To investigate the anisotropic swelling of compacted Gaomiaozi (GMZ) bentonite and the further response to saline effects, a series of constant-volume swelling pressure tests were performed. Results showed that dry density enhanced the bentonite swelling and raised the final anisotropy, whereas saline inhibited the bentonite swelling but still promoted the final anisotropy. The final anisotropy coefficient (ratio of radial to axial pressure) obeyed the Boltzmann sigmoid attenuation function, decreasing with concentration and dry density, converging to a minimum value of 0.76. The staged evolution of anisotropy coefficient was discovered, that saline inhibited the rise of the anisotropy coefficient (Δδ) in the isotropic process greater than the valley (δ1) in the anisotropic process, leading to the final anisotropy increasing. The isotropic stage amplified the impact of soil structure rearrangement on the macro-swelling pressure values. Thus, a new method for predicting swelling pressures of compacted bentonite was proposed, by expanding the equations of Gouy-Chapman theory with a dissipative wedge term. An evolutionary function was constructed, revealing the correlation between the occurrence time and the pressure value due to the structure rearrangement and the former crystalline swelling. Accordingly, a design reference for dry density was given, based on the chemical conditions around the pre-site in Beishan, China. The anisotropy promoted by saline would cause a greater drop of radial pressure, making the previous threshold on axial swelling fail.

Measurement of the double-layer capacitance of Pt(111) in acidic conditions near the potential of zero charge

Quantifying the charge density stored at the Pt(111)/aqueous interface using the double-layer capacitance close to the potential of zero charge (Cdl,PZC) at 0.30 VNHE is of critical importance to elucidating the structure of the electrical double layer (EDL) in the absence of any competing adsorption processes. Marked discrepancies in the values of Cdl for this interface exist in the literature, which we show are likely attributable to the measurement technique used. To directly observe the predicted Gouy-Chapman capacitance minimum at the PZC in the double-layer window between 0.40-0.55 VRHE, anomalously low electrolyte concentrations (0.1 mM HClO4) are needed. The measurement of accurate values of Cdl,PZC is made highly non-trivial by the extremely large solution resistances (∼80-100 kΩ) measured in this required dilute electrolyte as well as the non-negligible deviations from ideal capacitive behaviour (i.e., constant phase element behaviour) displayed even by this well-ordered model electrochemical system. We provide here a comparison between using cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), and alternating current-cyclic voltammetry (AC-CV) in determining Cdl,PZC for the Pt(111)/HClO4 interface, for different concentrations of the electrolyte. In particular, even when using optimized experimental parameters, we show that the estimated values of Cdl,PZC at 0.1 mM HClO4 still display a marked discrepancy depending on the technique used, ranging from 27-41 μF cm−2. At higher HClO4 concentrations, the discrepancies are much less pronounced. Importantly, however, the measured deviation from Gouy-Chapman theory, as quantified by the Parsons-Zobel plot slope, remains consistent across these techniques, implying that the EDL structure of the Pt(111)/aqueous interface continues to prove anomalous and enigmatic.

Non-equilibrium steady states of electrolyte interfaces

The non-equilibrium steady states of a semi-infinite quasi-one-dimensional univalent binary electrolyte solution, characterised by non-vanishing electric currents, are investigated by means of Poisson-Nernst-Planck (PNP) theory. Exact analytical expressions of the electric field, the charge density and the number density are derived, which depend on the electric current density as a parameter. From a non-equilibrium version of the Grahame equation, which relates the total space charge per cross-sectional area and the corresponding contribution of the electric potential drop, the current-dependent differential capacitance of the diffuse layer is derived. In the limit of vanishing electric current these results reduce to those within Gouy-Chapman theory. It is shown that improperly chosen boundary conditions lead to non-equilibrium steady state solutions of the PNP equations with negative ion number densities. A necessary and sufficient criterion on surface conductivity constitutive relations is formulated which allows one to detect such unphysical solutions.

Biological lipid hydration: distinct mechanisms of interfacial water alignment and charge screening for model lipid membranes.

Studying lipid monolayers as model biological membranes, we demonstrate that water molecules interfacing with different model membranes can display preferential orientation for two distinct reasons: due to charges on the membrane, and due to large dipole fields resulting from zwitterionic headgroups. This preferential water orientation caused by the charge or the dipolar field can be effectively neutralized to net-zero water orientation by introducing monolayer counter-charges (i.e. lipids with oppositely charged headgroups). Following the Gouy-Chapman model, the effect of monolayer surface charge on water orientation is furthermore strongly dependent on the electrolyte concentration and thus on the counterions in solution. In contrast, the effect of ions in the subphase on the dipolar alignment of water is zero. As a result, the capability of monolayer counter-charges to null the effect of dipolar orientation is strongly electrolyte-dependent. Notably, the different effects are additive for mixed charged/zwitterionic lipid systems occurring in nature. Specifically, for an E. coli lipid membrane extract consisting of both zwitterionic and negatively charged lipids, the water orientation can be explained by the sum of the constituents. Our results can be quantitatively reproduced using Gouy-Chapman theory, revealing the relatively straightforward electrostatic effects on the hydration of complex membrane interfaces.

A new method for estimating zeta potential of carboxylic acids’ functionalised particles

Zeta potential is an important colloid parameter that dictates many intriguing phenomena such as colloid stability/aggregation, electrophoretic deposition and particle separation technology. Zeta potential is commonly used to characterise colloid particles’ electrostatic interactions coupled with other forces such as van der Waals attraction, hydration and steric forces. However, the measurement of zeta potential involves complicated sample preparation and instrument/theory selection, often resulting in inaccurate measurement. Here, we developed a simple method that combines Stern–Grahame and Gouy–Chapman theories, for estimating zeta potential using parameters such as acid site pKa, acid site density and particle size. The method is applied to a wide range of carboxylic acids’ functionalised colloid particles with various pKa. Results show that the new method is capable of capturing zeta potential dependence on pKa and pH. The new method can be applied to particles with complicated or multiple acid/base sites. Without the need for sample preparation/instrument, this new method is believed to save efforts for estimating zeta potential with good accuracy.

A new formulation of the surface charge/surface potential relationship in electrolytes with valence less than three

AbstractSurface complexation models (SCMs) based on Gouy-Chapman theory are often used to describe adsorption of ions onto mineral surfaces. To compensate for the buildup of charge at a solid surface, the composition of the electric diffuse layer next to the surface must balance the surface charge. To calculate the diffuse layer composition, several nonlinear equations and integrals must be solved, usually with an iterative approach. Before convergence, charge balance is typically not fulfilled. One numerical difficulty is that, because of these charge balance errors, the iterative solver may attempt to take the square root of a negative number. Herein, we show that for electrolytes containing only monovalent or divalent ions (i.e., most electrolytes encountered in practice), we can greatly simplify the integrals and eliminate the appearance of complex-valued integrands; it is even possible to derive explicit analytical formulas. Furthermore, using the new method prevents converging to non-physical roots of the Grahame equation, which links surface potential to surface charge. To the best of our knowledge, the presented formulation has not been implemented in geochemical modelling software before, although similar mathematical expressions have been presented in the literature. In Gouy-Chapman theory, ions can only be distinguished by their charges, but this is not consistent with all experimental findings. We present a model that allows for the preferential accumulation of ions in the diffuse layer. The model, which is implemented mathematically by including ion exchange sites with a variable exchange capacity, is flexible and more numerically tractable than the standard models for the diffuse layer.

Polarization effects at the surface of aqueous alkali halide solutions

The polarizability of ions, with its strong influence on their surface affinity, is one of the crucial pieces of the complex puzzle that determines the surface properties of electrolyte solutions. Here, we investigate the electrical and structural properties of alkali halide solutions at a concentration of about 1.3 M using molecular dynamics simulations of polarizable water and ions models. We show that capillary fluctuations have a dramatic impact on the sampled quantities and that without removing their smearing effect, it would be impossible to resolve the local structure of the interfacial region. This procedure allows us to investigate in detail the dependence of the permanent and induced dipoles on the distance from the interface. The enhanced resolution gives us access to the surface charges, estimated using the Gouy-Chapman theory, despite the Debye length being shorter than the amplitude of capillary fluctuations.

Electric double layer of Pt(111): Known unknowns and unknown knowns

The electric double layer is one of the most fundamental concepts in electrochemistry. Nevertheless, its exact structure is still often unresolved. In this contribution, we discuss what we, at present, believe to know and what we believe not to know about the structure of the Pt(111) double layer close to the potential of zero charge. To this end, we discuss and compare several models put forward in the last few years in order to explain recent (and less recent) experimental observations. Through a discussion of several models, we conclude that water adsorption at the interface likely plays an important role in correctly interpreting capacitance features observed close to the potential of zero charge (pzc). The capacitance features at low electrolyte concentration, which show important deviations from Gouy-Chapman diffuse layer theory, are, to date, not yet resolved beyond doubt, but we critically analyze and compare the various models that have been put forward to model the interface. We thereby point out weaknesses in the models as well as similarities and differences between the models.

Elucidation of the pH-Dependent Electric Double Layer Structure at the Silica/Water Interface Using Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy

The silica/water interface is one of the most abundant charged interfaces in natural environments, and the elucidation of the water structure at the silica/water interface is essential. In the present study, we measured the interface-selective vibrational (χ(2)) spectra in the OH stretch region of the silica/water interface in a wide pH range of pH 2.0-12.0 while changing the salt concentration by heterodyne-detected vibrational sum-frequency generation spectroscopy. With the help of singular value decomposition analysis, it is shown that the imaginary part of the χ(2) (Imχ(2)) spectra can be decomposed into the spectra of the diffuse Gouy-Chapman layer (DL) and the compact Stern layer (SL), which enables us to quantitatively analyze the spectra of DL and SL separately. The salt-concentration dependence of the DL spectra at different pH values is analyzed using the modified Gouy-Chapman theory, and the pH-dependent surface charge density and the pKa value (4.8 ± 0.2) of the silica/water interface are evaluated. Furthermore, it is found that the pH-dependent change of the SL spectra is quantitatively explained by three spectral components that represent the three characteristic water species appearing in different pH regions in SL. The quantitative understanding obtained from the analysis of each spectral component in the Imχ(2) spectra provides a clear molecular-level picture of the electric double layer at the silica/water interface.

Concentration dependence of yield stress of bentonite suspension and corresponding particle interactions

The prediction of the concentration dependence of the yield stress of bentonite suspension is important for both practical use and fundamental study. Whilst a great amount of research work has been undertaken concerning the theoretical prediction based on the Face-Face repulsive interactions alone, the effect of inclination angle α and separation distance D between clay particles has seemingly received little attention in the research literature. This article presents the prediction model of yield stress developed using the strength of interparticle interactions between two non-parallel platy particles of finite dimensions, aimed at providing insights into the evolution of interparticle interaction with increasing the mass fraction. The repulsive force between the particles for a range of values of geometrical parameters computed using the Gouy-Chapman theory of electrical double layer, along with the calculation presented on van der Waals force, provide a more quantitative means of evaluating the interparticle force in bentonite suspension. It was found that as α and D between particles increase, the magnitude of interparticle force including repulsive and attractive force decreases quickly. The ultimate comprehensive investigation indicated that as the mass fraction of bentonite suspension increases, interparticle interaction propagates from attractive interaction to repulsive attraction, and finally shifts to attractive interaction. In this process, inter-particle separation distance decreases, accompanied by a transition process from a larger inclination angle to a nearly parallel orientation between the particles. The prediction model of yield stress considering the influence of concentration variation on α and D yields a good prediction of experimental data. The results of the present study should help interpret test results in cases where it may not be entirely possible to maintain a parallel particle orientation.

Molecular Dynamics Simulation of the Interfacial Structure and Differential Capacitance of [BMI+][PF6−] Ionic Liquids on MoS2 Electrode

MoS2 nanomaterials and ionic liquids (ILs) have attracted tremendous interest as the prime electrodes and electrolytes of supercapacitors. However, the corresponding charge storage mechanisms have not yet been clearly understood. Herein, we study the molecular-level energy storage mechanisms of the MoS2 electrode in imidazolium ionic liquid ([BMI+][PF6−]) using molecular dynamics (MD) simulation. The electric double-layer (EDL) structures of MoS2 electrodes in [BMI+][PF6−] electrolytes are comprehensively studied in terms of number density, MD snapshots, separation coefficient, and ion-electrode interaction energy. Based on this, the electric potential and electric field distributions are calculated by integrating Poisson equations. Importantly, a bell-shaped differential capacitance profile is proposed, different from the U-shaped curve from the conventional Gouy–Chapman theory. Especially, it can be well reproduced by the differential charge density curve in the Helmholtz layer. This indicates that the capacitive behaviors of the MoS2 electrode are primarily determined by the counterion population/structure in the EDL region 5.0 Å from the electrode surface. In the end, ion diffusion coefficients within different interfacial EDL regions are evaluated, revealing that dynamics are significantly suppressed by ~50% in the Helmholtz region. However, the dynamics can be recovered to a bulk state with the ion position 10 Å away from the electrode surface. The as-obtained insights reveal the charge storage mechanisms of MoS2 in ILs, which can provide useful guidance on improving the energy density of MoS2 supercapacitors.

Compressibility Behavior of Bentonites by Stern Theory based on Constant Surface Charge Conditions

AbstractThe compressibility behavior of clays is governed by the electrical double layer formed around the clay particles. The Gouy-Chapman diffuse double layer theory is often utilized to predict the compressibility behavior of clay minerals. The theory does not consider the effect of the size of the cations, however, and thus predicts unrealistically small void ratios for compacted bentonites under large mechanical pressures expected in high-level nuclear waste-repository applications. In this study, the Stern layer was introduced to incorporate the cation size effect in the prediction of the compressibility behavior of bentonites. The overall diffuse double-layer thickness at large pressures was much smaller than the initially assumed Stern layer thickness based on the exchangeable cation size for all the bentonites studied. A compressible Stern layer was, therefore, considered for the first time in the prediction of the compressibility behavior of bentonites. The compression behavior of the Stern layer under the applied loading is influenced by the ratio of the mid-plane to the Stern potential, which is dependent on the type and composition of the exchangeable cations on the clay surface. Stern layer compression was initiated when the potential ratio was in the range 0.65–0.75 for bentonites with various surface cation characteristics. The incorporation of cation size and a compressible Stern layer provided significant improvements over the existing models in predicting the compressibility behavior of bentonites over a wide pressure range. The compressibility data predicted by the proposed model showed very good agreement with the data measured for five bentonites from the literature in the pressure range 0.1–42 MPa.

Effect of Dielectric Saturation on Ion Activity Coefficients in Ion Exchange Membranes.

Polymeric ion exchange membranes are used in water purification processes to separate ions from water. The distribution and transport of ionic species through these membranes depend on a variety of factors, including membrane charge density, morphology, chemical structure, and the specific ionic species present in the fluid. The electrical potential distribution between membranes and solutions is typically described using models based on Donnan theory. An extension of the original theory is proposed to account for the nonideal behavior of ions both in the fluid and in the membrane as well to provide a more robust description of interactions of solutes with fixed charge groups on the polymer backbone. In this study, the variation in dielectric permittivity in the membrane medium with electric field strength is taken into account in a model based on Gouy–Chapman double-layer theory to provide a more accurate description of ion activity coefficients in an ion exchange membrane. A semianalytical model is presented that accounts for the variation in dielectric permittivity of water in a charged polymer membrane. A comparison of this model with Manning’s counterion condensation model clearly demonstrates that by incorporating changes in water dielectric permittivity with electric field strength, much better agreement with experiments can be obtained over a range of salt concentrations for different ions.

Mechanism of oscillation of aqueous electrical double layer capacitance: Role of solvent

The present classical density functional theory (CDFT) study is focused on role of solvent in differential capacitance (Cd) behavior of aqueous electrolyte electric double-layer capacitor (EDLC). In the CDFT, water molecule is described by a solvent primitive model, which is constructed to give two experimentally measured aandb parameters in the van der Waals equation of state of water; Lennard-Jones parameters of both cation and anion are chosen to be reminiscent of properties of K+ andCl-1; a structureless and soft wall comprised of carbon atoms is considered to represent a graphene electrode. Main findings are summarized as follows. (i) The CdH (H is separation between two graphene electrodes) curve is always shifted up (at lower electrode voltage) or down (at higher electrode voltage) by increasing the electrolyte bulk concentrationc. The anomalous negative correlation between c and Cd at high voltage originates from the so-called charge inversion and one additional weak co-ion peak located closer to the electrode surface at higher voltage. (ii) Oscillation periods of CdH curves are basically fixed at 3 Å regardless of molecular characteristics of counter- and co-ions, c value, and electrode voltage; explicit consideration of the solvent granularity and polarity greatly reduces the attenuation rate of the oscillation with pore size. Increase of CdH with pore size reducing towards the ion size, does occur but only with moderate magnitude; a main CdH extreme value occurs approximately around H being two times ion diameter, which can be either a maximum or a minimum, depending on electrolyte bulk concentration, polarity and strength of the electrode. These oscillation features differ greatly from those observed in solvent-free ionic liquids and continuum solvent model. (iii) Potential of zero charge ψpzc for the case of small size of cation and weaker LJ interaction of the cation with solvent molecule in large number, is necessarily positive and its value is positively correlated with the c value; minimum point ψMin of the Cdψs curve is always larger than theψpzc, not consistent with the Gouy-Chapman theory, and both the ψpzcH curve and ψMinH curve change quasi periodically with the pore size H also in 3 Å cycle. (iv) Theoretical analysis shows that the capacitance behavior is mainly controlled by the number and position of solvent peaks and their changes with pore size, while distribution of ions is largely controlled by their LJ interaction with solvent. This shows the importance of the solvent in modulating the capacitance behavior.

Gibbs Free Energy Implications of Electric Double Layer for Wettability Trend in Geologic Carbon Storage

In this paper, we demonstrated the theoretical relationship between Gibbs free energy of the electric double layer and aqueous solution pH. The basis for our theoretical derivation is the fundamental electrochemical equation of Nernst and the Gouy Chapman theory of the electric double layer. In the thermodynamic sense, the partial derivative of Gibbs free energy with regard to interface/surface area is shown to directly linked to interfacial or surface energy, where the former is pH dependent. Accordingly, our theoretical derivation has permitted the interpretation of wettability trends in saline aquifers under geological carbon storage.

Capacitance of the interface between two immiscible electrolyte solutions – A controversial issue

Electrochemical impedance spectroscopy is used to evaluate the capacitance of the polarizable interface between a solution of LiCl + HCl in water and a solution of bis(triphenylphospho-ranylidene)ammonium tetrakis(pentafluorophenyl)borate in 1,2-dichloroethane (DCE).A significant effect of both the interfacial potential difference and the electrolyte concentration on the capacitance is observed using two different experimental arrangements. The former effect is supported by an independent evaluation of the capacitance as the second derivative of the interfacial tension vs. the potential difference plot. It is shown that the experimental data can be reproduced relatively well by means of the Gouy-Chapman theory and the modified Verwey-Niessen model of the electric double layer consisting of two back-to-back space charge regions separated by an inner layer of the solvent molecules. However, the effect of the electrolyte concentration points to an easy penetration of ions into the inner layer leading to its negative contribution to the inverse capacitance. These conclusions are at variance with those made recently on the basis of the impedance measurements at the micro-hole supported water/DCE interface. A tentative explanation is proposed, which refers to the possible absence of the direct control of the active area of the liquid/liquid interface shape and position in the micro-hole over a broad range of the potential differences.

Modulatory Effects of Acidic pH and Membrane Potential on the Adsorption of pH-Sensitive Peptides to Anionic Lipid Membrane.

Anionic lipid membrane electrostatic potential and solution pH can influence cationic peptide adsorption to these bilayers, especially those containing simultaneously acid and basic residues. Here, we investigate the effects of the pH solution on MP1 (IDWKKLLDAAKQIL-NH2) adsorption to anionic (7POPC:3POPG) lipid vesicles in comparison to its analog H-MP1, with histidines substituting lysines. We used the association of adsorption isotherms and constant pH molecular dynamic simulations (CpHMD) to explore the effects of membrane potential and pH on peptides’ adsorption on this lipid membrane. We analyzed the fluorescence and zeta potential adsorption isotherms using the Gouy–Chapman theory. In CpHMD simulations for the peptides in solution and adsorbed on the lipid bilayer, we used the conformations obtained by conventional MD simulations at a μs timescale. Non-equilibrium Monte Carlo simulations provided the protonation states of acidic and basic residues. CpHMD showed average pKa shifts of two to three units, resulting in a higher net charge for the analog than for MP1, strongly modulating the peptide adsorption. The fractions of the protonation of acidic and basic residues and the peptides’ net charges obtained from the analysis of the adsorption isotherms were in reasonable agreement with those from CpHMD. MP1 adsorption was almost insensitive to solution pH. H-MP1 was much more sensitive to partitioning, at acidic pH, with an affinity ten times higher than in neutral ones.

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.