Gouy Chapman Stern Research Articles

Combining electrochemistry and direct force measurements: from the control of surface properties towards applications

Direct force measurements contributed in the last years much to our understanding of the diffuse double layer of charged interfaces in electrolyte solutions. Such measurements have been performed with the atomic force microscope or the surface force apparatus. This review gives an overview over the recent studies based on force measurements with electrode surfaces. Not only bare metal electrodes but also electrodes modified by different organic layers, including electroactive films, have been studied by these techniques. Direct force measurements indicate that further effects besides classical Gouy–Chapman–Stern theory have to be taken into consideration in order to describe the force profiles. In addition to the long-range forces also the adhesion between surfaces can be tuned by potentiostatic control. New single-molecule techniques based on the atomic force microscope allow to probe the extension of polymer strands or their desorption from solid interfaces. In combination with electrochemistry, it became now possible to tune the desorption behavior of polymer strands or to measure the electromechanical coupling of motors from single strands of electroactive polymers.

Nonlinear dynamics of capacitive charging and desalination by porous electrodes

The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by supercapacitors, water desalination and purification by capacitive deionization, and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) valid in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory for the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) in the "supercapacitor regime" of small voltages and/or early times, the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore, and (ii) in the "desalination regime" of large voltages and long times, the porous electrode slowly absorbs counterions, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration.

A mean spherical approximation study of the capacitance of an electric double layer formed by a high density electrolyte

In a recent grand canonical Monte Carlo simulation and modified Poisson–Boltzmann (MPB) theoretical study of the differential capacitance of a restricted primitive model double layer at high electrolyte densities, Lamperski, Outhwaite and Bhuiyan (J. Phys. Chem. B 2009, 113, 8925) have reported a maximum in the differential capacitance as a function of electrode charge, in contrast to that seen in double layers at lower ionic densities. The venerable Gouy–Chapman–Stern (GCS) theory always yields a minimum and gives values for the capacitance that tend to be too small at these higher densities. In contrast, the mean spherical approximation (MSA) leads to better agreement with the simulation results than does the GCS approximation at higher densities but the agreement is not quite as good as for the MPB approximation. Since the MSA is a linear response theory, it gives predictions only for small electrode charge. Nonetheless, the MSA is of value since it leads to analytic results. A simple extension of the MSA to higher electrode charges would be valuable.

Membrane capacitive deionization

Membrane capacitive deionization (MCDI) is an ion-removal process based on applying an electrical potential difference across an aqueous solution which flows in between oppositely placed porous electrodes, in front of which ion-exchange membranes are positioned. Due to the applied potential, ions are adsorbed in the electrodes and a product stream with a reduced salt concentration is obtained. Including the membranes in the process has two advantages: first, they block co-ions from leaving the electrodes, thereby increasing the salt removal efficiency of the process, and second, when during ion release a reversed voltage is used, counterions can be more fully flushed from the electrode region, thereby increasing the driving force for ion removal in the next cycle. Here we present pilot-plant experimental data for salt removal in MCDI as function of inlet ionic strength and flow rate. In the subsequent stage of ion release the flow rate is temporarily reduced to zero and the voltage sign reversed. This “stop-flow” operation mode results in a small and concentrated product stream. We present a theoretical process model for MCDI which describes the time-dependent electric current and effluent ion concentration, both during the deionization stage and during the subsequent stage of ion release. The process model describes the MCDI cell as a number of stirred volumes placed in-series, and includes the transport resistance of the ion-exchange membrane and of the stagnant diffusion layer in front of the membrane. Ion storage in the electrodes is described according to the equilibrium Gouy–Chapman–Stern model for the electrostatic double layer.

Dynamic Adsorption/Desorption Process Model for Capacitive Deionization

In capacitive deionization (CDI), an electrical potential difference is applied across oppositely placed electrodes, resulting in the adsorption of ions from aqueous solution and a partially ion-depleted product stream. CDI is a dynamic process which operates in a sequential mode; i.e., after a certain ion adsorption capacity has been reached, the applied voltage is reduced, and ions are released back into solution, resulting in a solution concentrated in ions. The energetic input of CDI is very small, while there are no ion-exchange materials involved that need to be replaced regularly. Here we present a dynamic process model for CDI which includes the storage and release of ions in/from the polarization layers of the electrodes. The charge and ion adsorption capacity of the polarization layers is described using the equilibrium Gouy−Chapman−Stern (GCS) model, while the charge transfer rate from bulk solution into the polarization layer is modeled according to Ohm’s law, i.e., depends solely on an electric field term across a mass-transfer layer. An important element in the model is the differential charge efficiency: the effective salt removal rate relative to the electronic current, for which an analytical expression is derived based on the GCS model. We present results for the effluent salt concentration and electron current, both as function of time, based on a process model that assumes ideal mixing in the CDI unit cell. The theoretical results are in very good agreement with an example data set.

Thermodynamic cycle analysis for capacitive deionization

Capacitive deionization (CDI) is an ion removal technology based on temporarily storing ions in the polarization layers of two oppositely positioned electrodes. Here we present a thermodynamic model for the minimum work required for ion separation in the fully reversible case by describing the ionic solution as an ideal gas of pointlike particles. The work input is fully utilized to decrease the entropy of the outflowing streams compared to that of the inflow. Based on the Gouy–Chapman–Stern (GCS) model for planar diffuse polarization layers—with and without including additional ion volume constraints in the diffuse part of the double layer—we analyze the electric work input during charging and the work output during discharging, for a reversible charging–discharging cycle. We present a graphical thermodynamic cycle analysis for the reversible net work input during one full cycle of batchwise operation of CDI based on the charge–voltage relations for different ionic strengths. For the GCS model, an analytical solution is derived for the charge efficiency Λ, which is the number of salt molecules removed per electron transferred from one electrode to the other. Only in the high voltage limit and for an infinite Stern layer capacity does Λ approach unity.

Molecular dynamics simulation of ion transport in a nanochannel

A molecular dynamics (MD) model of the fluidic electrokinetic transport in a nano-scale channel with two bulk sinks was presented, and the process of ion transport in the nanochannel was simulated in this paper. The model consists of two water sinks at the two ends and a pump in the middle, which is different from a single pump model in previous MD simulations. Simulation results show that the charged surfaces of the nanochannel result in the depletion of co-ions and the enrichment of counterions in the nanochannel. A stable current is induced because of the motion of ions when an external electric field is applied across the nanochannel, and the current in the pump region is mainly induced by the motion of counterions. In addition, the ion number in the pump region rapidly decreases as the external electric field is applied. In the equilibrated system, the electrically neutral character in the pump region is destroyed and this region displays a certain electrical character, which depends on the surface charge. The ion distribution is greatly different from the results predicted by the continuum theory, e.g. a smaller peak value of Na+ concentration appears near the wall. The transport efficiency of counterions (coions) can be effectively increased (decreased) by increasing the surface charge density. The simulation results demonstrate that the ion distribution in the electric double layer (EDL) of a nanochannel cannot be exactly described by the classical Gouy-Chapman-Stern (GCS) theory model. The mechanism of some special experimental phenomena in a nanochannel and the effect of the surface charge density on the ion-transport efficiency were also explored to provide some theoretical insights for the design and application of nano-scale fluidic pumps.

A discussion on ion conductivity at cation exchange membrane/solution interface

Abstract By Gouy–Chapman–Stern–Grahame (CGSG) model, the electric double layer at ion exchange membrane/solution interface consists of two parts: the Stern layer and the diffusion layer. The ions in Stern layer are compacted and considered to be immobile. The relation of diffusion layer mean conductivity K with outer Stern layer potential φ 0 , the boundary potential φ δ and the electrolyte concentration C 0 is educed for symmetric electrolyte system. The results show that K is higher than that of the bulk solution and is greatly influenced by φ 0 , φ δ and C 0 . The examination of PE01 cation exchange membrane/solution interface resistance R e measured by ac impedance technique, shows that R e value decreases quickly as the KCl electrolyte concentration rises. The effect of electrolyte concentration on the resistance of EDL can be explained by the electrical interactions between ions and charged groups of the membrane. Since the membrane/solution interface resistance is much higher than that of bulk solution, therefore, a further analysis based on the theory developed in this study proves that the ion transfer resistance R e of membrane–solution interface predominantly occurs at Stern layer as a result of static electrical interaction.

A Gouy–Chapman–Stern model of the double layer at a (metal)/(ionic liquid) interface

Abstract Kornyshev [A.A. Kornyshev, J. Phys. Chem. B 111 (2007) 5545] has recently modelled the (metal)/(ionic liquid) junction and predicted therefrom the capacitance of that interface as a function of the applied potential. One of the purposes of the present article is to demonstrate that, at least in one particular case, the same prediction can be made more simply by applying the principles that Gouy, Chapman and Stern adopted in their classic treatments of the double layer at a (metal)/(electrolyte solution) interface. The analysis predicts the distributions of potential, charge and ionic concentration, leading to support of Kornyshev’s finding of a capacitance that displays a maximum value at the point of zero charge, whereas a minimum is expected for a double layer at an electrode in electrolyte solution. The two systems are compared and contrasted in respect to capacitance and the distribution of ions.

Identification of the electroelastic coupling from full multi-physical fields measured at the micrometre scale

Metal coated microcantilevers are used as transducers of their electrochemical environment. Using the metallic layer of these cantilevers as a working electrode allows one to modify the electrochemical state of the cantilever surface. Since the mechanical behaviour of micrometre scale objects is significantly surface-driven, this environment modification induces bending of the cantilever. Using a full-field interferometric measurement set-up to monitor the objects then provides an optical phase map, which is found to originate from both electrochemical and mechanical effects. The scaling of the electrochemically-induced phase with respect to the surface charge density is modelled according to Gouy–Chapman–Stern theory, whereas the relationship between the mechanical effect and the surface charge density is analysed. An identification technique is described to determine a modelling of the electroelastic coupling and to identify the spatial charge density distribution from full-field phase measurements. Minimizing the least-squares gap between the measured phase and a statically admissible phase field, the mechanical effect is found to be charge-driven. The charge density field is also found to be singular on the cantilever edge, and the shear stress versus charge density is found to be non-linear.

Effects of temperature reduction on monolayer-protected gold nanoparticle capacitance

The electrochemistry of monolayer-protected gold nanoparticle (MPC) solutions at reduced temperatures was studied using differential pulse voltammetry. Different tetrabutylammonium electrolytes in CH2Cl2 were compared in the analysis of the hexanethiolate-protected gold nanoparticles (C6-MPCs). In agreement with Gouy–Chapman–Stern (GCS) theory, the double-layer capacitance (CMPC )o f the C6-MPCs increased with decreasing solution temperature. Separate electron transfers in redox-modified MPCs were observed in this work. Electron transfer to and from the MPC gold core was observed simultaneously with the electron transfer of the attached anthraquinone molecules. The resulting double-layer capacitance of the anthraquinone-modified nanoparticles (AQ-MPCs) was determined at various temperatures. There was less correlation between temperature and capacitance in the AQ-MPCs. AQ-MPCs were synthesized with the anthraquinone molecule at two different chain lengths from the gold core surface. The shorter-chain AQ-MPC exhibited better resolved electron transfer peaks from the gold core, while the voltammetry of the longer-chain AQ-MPC had better resolved anthraquinone peaks. Additionally, this was the first observation of quantized double-layer (QDL) charging events from a non-ethanol-soluble (NES) fraction of MPCs that have been functionalized. � 2007 Elsevier B.V. All rights reserved.

Label-free detection of biomolecules on microarrays using surface–colloid interaction

Binding of charged nanoparticles to nonmodified DNA and RNA target molecules on microarrays allows detection of these nucleic acids by locating bound nanoparticles on microarray surface. Two computational models have been developed to study the ionic interaction of colloidal particles and biopolymer molecules on a microarray surface. One model represents a basic approach based on mass action law for simulation charge effects versus the chemical composition of the interacting array surface and nanoparticle. The second model is implementation of the advanced Gouy–Chapman–Stern–Graham model for describing effects on liquid–solid interface. We found that both models predict selective binding of colloidal particles to large target molecules on the surface with no binding to smaller capture molecules. This binding regime is considered to be very beneficial for application of charged nanoparticles for detection of nonmodified DNA and RNA target molecules on microarrays. The theoretical considerations are in qualitative agreement with the experimental results for detecting large target DNA and a 50-base long synthetic oligonucleotide on the amino-modified microarray substrate. The experimental and theoretical results of this study allow further development of the label-free microarray technology demonstrated previously for gene expression analysis that is free of reverse transcription and dye labeling.

Electrical double layer interactions between dissimilar oxide surfaces with charge regulation and Stern–Grahame layers

Models of surfaces with intrinsic ionisable amphoteric surface sites governed by the dissociation of acid–base potential determining ion species together with the capacity for the adsorption of anion and cations of the supporting electrolyte are required to describe both the results of electrokinetic and titration measurements of inorganic oxides. The Gouy–Chapman–Stern–Grahame (CGSG) model is one such model that has been widely used in the literature. The electrical double layer interaction between two dissimilar CGSG surfaces has been studied by Usui recently [S. Usui, J. Colloid Interface Sci. 280 (2004) 113] where erroneous discontinuities in the slope of the pressure–separation relation were observed. We revisit this calculation and provide a simple general methodology to analyse the electrical double layer interaction between dissimilar ionisable surfaces with ion adsorption.

Zn 2+ and Sr 2+ adsorption at the TiO 2 (110)–electrolyte interface: Influence of ionic strength, coverage, and anions

The X-ray standing wave technique was used to probe the sensitivity of Zn 2+ and Sr 2+ ion adsorption to changes in both the adsorbed ion coverage and the background electrolyte species and concentrations at the rutile ( α-TiO 2) (110)–aqueous interface. Measurements were made with various background electrolytes (NaCl, NaTr, RbCl, NaBr) at concentrations as high as 1 m. The results demonstrate that Zn 2+ and Sr 2+ reside primarily in the condensed layer and that the ion heights above the Ti–O surface plane are insensitive to ionic strength and the choice of background electrolyte (with <0.1 Å changes over the full compositional range). The lack of any specific anion coadsorption upon probing with Br −, coupled with the insensitivity of Zn 2+ and Sr 2+ cation heights to changes in the background electrolyte, implies that anions do not play a significant role in the adsorption of these divalent metal ions to the rutile (110) surface. Absolute ion coverage measurements for Zn 2+ and Sr 2+ show a maximum Stern-layer coverage of ∼0.5 monolayer, with no significant variation in height as a function of Stern-layer coverage. These observations are discussed in the context of Gouy–Chapman–Stern models of the electrical double layer developed from macroscopic sorption and pH-titration studies of rutile powder suspensions. Direct comparison between these experimental observations and the MUltiSIte Complexation (MUSIC) model predictions of cation surface coverage as a function of ionic strength revealed good agreement between measured and predicted surface coverages with no adjustable parameters.

Interaction between dissimilar double layers with like signs under charge regulation on the basis of the Gouy–Chapman–Stern–Grahame model

The force of interaction between two flat double layers with dissimilar surface potentials but of the same signs, in contact with 1-1 electrolyte solutions (0.001, 0.01, and 0.1 M), was calculated as a function of the surface separation. The calculation was carried out on the basis of the Gouy-Chapman-Stern-Grahame double-layer model, incorporating the site-dissociation and site-binding model used previously for many oxide studies. The results demonstrated that the interaction force under surface charge regulation was always repulsive, increasing progressively with decreasing surface separation. This result is in contrast to the predictions of previous theories that are based on the Gouy-Chapman (GC) double-layer model. Dependence of surface potentials and surface charge densities on the surface separation is also presented.

Specific counterion effect on the adsorption of alkali decyl sulfate surfactants at air/solution interface

Experimental results are presented on the counterion dependence of the adsorption of alkali (Li+, Na+, K+, Rb+ and Cs+) decyl sulfates at the air/solution interface. The adsorption isotherms calculated from equilibrium surface tension vs. concentration data by means of the Gibbs equation show significant counterion dependence. We propose a theoretical model based on the Gouy–Chapman–Stern theory for the description of the ionic surfactant adsorption at the air/solution interface. The model is based on the physical picture that the counterions can enter among the surfactant headgroups if the hydrated counterion size is smaller than that of the headgroups. In this case, the diffuse part of the double layer starts from the plane of the headgroups. If the size of the counterions is larger than the size of the headgroups then the closest approach of the counterions in the diffuse layer is assumed to be equal to the difference between the size of the hydrated surfactant headgroup and that of the counterion. The model correctly describes the counterion dependence of the adsorption isotherms measured for the alkali alkyl sulfates using the electrical capacity of the Stern-layer and the hydrophobic driving force as fitting parameters. The results indicate that the fine structure of the double layer can play an important role on the counterion specificity of ionic surfactant adsorption. Beyond the description of the Stern-layer the description of the hydrophobic driving force was also modified in order to reflect recent experimental and theoretical results about the structure of the monolayer.

Applying a Gouy–Chapman–Stern model for adsorption of organic cations to soils

An effective adsorption model was developed by S. Nir in 1978 for predicting adsorption to synthetic membranes and was also adapted by him afterwards to clay minerals. The main principles of the model are the solution of the electrostatic Gouy–Chapman equations while calculating the adsorbed amounts of the cations as the sum of those residing in the double-layer region and the cations that are chemically bound in a closed system. Thus, the equilibrium concentration in solution is influenced by the adsorption as the function of the amounts bound. The model was later developed and adapted for the adsorption of organic cations, and, in most cases, the fit of calculated results to measured adsorbed amounts of cations was very good, after calibrating the model for the chemical tested, with only two adjustable parameters for each chemical. In the current work, we tested the applicability of this model for the adsorption of a monovalent and a divalent organic cation by several soils, by considering the cation exchange capacities (CEC) and the specific surface areas (SSA) of the soils. For three out of four soils, a very good fit was obtained by using the required parameters for the calculations from previous studies of cation adsorption on clay minerals. The main advantage of the presented model over Langmuir and Freundlich adsorption isotherms is that no additional changes in the parameters were needed when the background concentration of salts in the suspensions was increased from 10 to 50 or 500 mM.

Specific Features of the Structure of the Electrical Double Layer on Intermetallic Compound Ag3Sn in Aqueous Surface-Inactive Electrolytes

The behavior of a polycrystalline electrode of intermetallic compound Ag3Sn in aqueous NaF solutions is studied using an impedance method. At potentials of –1.3 to –0.6 V (SCE), the electrode may be viewed as ideally polarizable. The Gouy–Chapman–Stern–Grahame model quite satisfactorily describes capacitance curves obtained at various electrolyte concentrations. Experimental capacitance curves for an Ag3Sn electrode are compared with those for polycrystalline Ag and Sn electrodes renewed by cutting. Characteristics of an Ag3Sn electrode are unique and its capacitance curves cannot be simulated from the data for Ag and Sn electrodes within the known phenomenological approaches.

Protons and calcium alter gating of the hyperpolarization-activated cation current (Ih) in rod photoreceptors

We investigated the effects of protons and calcium ions on the voltage-dependent gating of the hyperpolarization-activated, nonselective cation channel current, Ih, in rod photoreceptors. Ih is a cesium-sensitive current responsible for the peak-plateau sag during the rod response to bright light. The voltage dependence of Ih activation shifted about 5 mV per pH unit, with external acidification producing positive shifts and alkalinization producing negative shifts. Increasing external [Ca2+] from 3 to 20 mM resulted in a large (∼17 mV) positive shift in Ih activation. External [Ca2+] (20 mM) blocked pH-induced shifts in activation. Cytoplasmic acidification produced by 25 mM sodium acetate led to a negative shift in inactivation (−9 mV) and internal alkalinization produced with 20 mM ammonium chloride resulted in a positive shift (+6 mV). Surface charge binding and screening theory (Gouy–Chapman–Stern) accounted for the observed shifts in Ih activation, with the best fit achieved when protons and calcium ions were assumed to bind to distinct sites on the membrane. Since light induces changes in the retinal ionic environment, these results permit us to gauge the degree to which rod light responses could be modified via alterations in Ih activation.

Acidity and Alkali Metal Adsorption on the SiO 2–Aqueous Solution Interface

The intrinsic deprotonation constant (p K int a 2 ) and the intrinsic ion exchange constants (p K int Me + ) of Li +, Na +, and K + on SiO 2 were uniquely determined at 30°C by using the potentiometric titration data, the Gouy–Chapman–Stern–Grahame (GSCG) model for the structure of the electrical double-layer (edl) and the double-extrapolation method. The values of these constants were p K int a 2 =6.57, p K int Li + =p K int Na + =p K int K + =5.61. The chemical meaning of intrinsic equilibrium constants and the equality in the values of p K int Li + , p K int Na + and p K int K + were discussed.