Charge Density Profiles Research Articles

On the contact conditions for the density and charge profiles in the theory of electrical double layer: From planar to spherical and cylindrical geometry

In this paper, starting from the Bogoliubov-Born–Green–Yvon equations of the liquid-state theory, we formulate two equivalent approaches for the calculation of the total density profile and of the charge density profile of ionic fluids near nonplanar charged surfaces. In the framework of these approaches, we establish exact conditions, that a particular point of these profiles should satisfy, in the form of contact theorems. These contact theorems for the total density profile and the charge density profile are obtained by direct integration of a system of equations derived from the Bogoliubov-Born–Green–Yvon equations. The contact theorems for both profiles have nonlocal character. It is shown that the contact value of the total density profile for uncharged surfaces is characterized by the bulk pressure and the surface tension. The contact theorems are applied to the cases of spherical and cylindrical surfaces. It is shown that the contact theorem for the total density profile coincides with the recent results obtained by W. Silvester-Alcantara, D. Henderson and L.B. Bhuiyan (Mol. Phys., 113, 3403, 2015).

Real-Space Charge Density Profiling of Electrode-Electrolyte Interfaces with Angstrom Depth Resolution.

The accumulation and depletion of charges at electrode-electrolyte interfaces is crucial for all types of electrochemical processes. However, the spatial profile of such interfacial charges remains largely elusive. Here we develop charge profiling three-dimensional (3D) atomic force microscopy (CP-3D-AFM) to experimentally quantify the real-space charge distribution of the electrode surface and electric double layers (EDLs) with angstrom depth resolution. We first measure the 3D force maps at different electrode potentials using our recently developed electrochemical 3D-AFM. Through statistical analysis, peak deconvolution, and electrostatic calculations, we derive the depth profile of the local charge density. We perform such charge profiling for two types of emergent electrolytes, ionic liquids, and highly concentrated aqueous solutions, observe pronounced sub-nanometer charge variations, and find the integrated charge densities to agree with those derived from macroscopic electrochemical measurements.

Finite amplitude electro-thermo convection in a cubic box

Three-dimensional electro-thermo-hydrodynamic (ETHD) flows of dielectric fluids driven by simultaneous Coulomb and buoyancy forces in a cubic box is numerically studied. The set of coupled equations associated with the ETHD phenomena are solved with the finite volume method. The code is first validated by comparing the numerically obtained linear critical values of the pure electro-convection and thermal convection with the previous studies. Then the neutral stability curve of the system is given and the finite amplitude instability thresholds with different Rayleigh numbers () are presented. It is found that along the neutral stability curve, the flow strength becomes weaker with the increase of and the decrease of electric Rayleigh number (T). Besides, the gap between the linear and nonlinear critical values expressed in terms of T decreases with the increase of . Primarily, the distributions of charge density, temperature and velocity fields with different governing parameters near neutral stability curve are presented. The temperature and charge density profiles near the linear and nonlinear critical values are given, showing that higher T results in wider charge void region and shorter distance between the charge void region’s lower boundary and injection electrode. Finally, the symmetries of the flow patterns along the neutral stability curve are also discussed briefly.

Molecular dynamics of preferential adsorption in mixed alkali-halide electrolytes at graphene electrodes.

Understanding the microscopic behavior of aqueous electrolyte solutions in contact with graphene and related carbon surfaces is important in electrochemical technologies, such as capacitive deionization or supercapacitors. In this work, we focus on preferential adsorption of ions in mixed alkali-halide electrolytes containing different fractions of Li+/Na+ or Li+/K+ and/or Na+/K+ cations with Cl- anions dissolved in water. We performed molecular dynamics simulations of the solutions in contact with both neutral and positively and negatively charged graphene surfaces under ambient conditions, using the effectively polarizable force field. The simulations show that large ions are often intuitively attracted to oppositely charged electrodes. In contrast, the adsorption behavior of small ions tends to be counterintuitive. In mixed-cation solutions, one of the cations always supports the adsorption of the other cation, while the other cation weakens the adsorption of the first cation. In mixed-cation solutions containing large and small cations simultaneously, adsorption of the larger cations varies dramatically with the electrode charge in an intuitive way, while adsorption of the smaller cations changes oppositely, i.e., in a counterintuitive way. For (Li/K)Cl mixed-cation solutions, these effects allow the control of Li+ adsorption by varying the electrode charge, whereas, for LiCl single-salt solutions, Li+ adsorption is nearly independent of the electrode charge. We rationalize this cation-cation lever effect as a result of a competition between three driving forces: (i) direct graphene-ion interactions, (ii) the strong tendency of the solutions to saturate the network of non-covalent intermolecular bonds, and (iii) the tendency to suppress local charge accumulation in any region larger than typical interparticle distances. We analyze the driving forces in detail using a general method for intermolecular bonding based on spatial distribution functions and different contributions to the total charge density profiles. The analysis helps to predict whether an ion is more affected by each of the three driving forces, depending on the strength of the ion solvation shells and the compatibility between the contributions of the charge density profiles due to the ion and water molecules. This approach is general and can also be applied to other solutions under different thermodynamic conditions.

Drivers of Low Salinity Effect in Carbonate Reservoirs Using Molecular Dynamic Simulation

• Molecular dynamic simulation of calcite-oil-brine system reveals that monovalent ions are settled at calcite-brine interface. • The time-dependent evolution of the mass density profile demonstrates oil detachment from the calcite mineral. • The extension of the charge density profile coincides to the detachment of oil from the calcite surface. • The MD results show that an electrical double layer (EDL) is formed at calcite-brine interface. • The extension of the charge density profile occure ofter the settling of the monovalent ions at calcite-brine interface. Low salinity water (LSW) flooding has yielded promising results in improving the enhanced oil recovery (EOR) techniques in sandstone and carbonate reservoirs. Despite various studies and advances, the main mechanism behind the oil displacement in the rock-brine-oil system is unclear. To get a better understanding of the governing mechanisms, we used the molecular dynamic (MD) method to simulate a system including calcite-brine-oil under two different scenarios. At T=300 K and T=360 K each scenario is completed during 40 ns using a canonical ensemble. The results show that all mono/divalent ions are hydrated initially. Furthermore, Na + , Cl − and H 2 O molecules reside close to the calcite surface and their positions show little change at different time steps. However, the position of divalent ions is dynamic depending on the simulation time steps. Ca 2+ , which is initially detected at 2.35 Å above the solid surface at T=300 K and T=360 K, migrates away by time. On the other hand, Mg 2+ and SO 4 2− which are invisible up to t = 16 ns even at the radius of 10 Å, move gradually toward the surface with time and consolidate their position after oil displacement. Namely, prior to oil displacement, a shift in Na + , Cl − and Ca 2+ locations is noticed, and the trend of double electric layer (EDL) is extended, which might be the cause of oil displacement. The findings of this study are applicable in the improvement of EOR technology, water resource treatment and contaminant transfer from geological systems, dealing with solid solutions such as ocean-soil systems.

Simulation of Space Charge Dynamics in Low-Density Polyethylene Using the Gaussian Disorder Model

Space charge dynamics in a low-density polyethylene (LDPE) film is calculated using mobility based on the Gaussian disorder model (GDM), which is commonly used to describe hopping conduction in disordered materials. The GDM exhibits a negative differential mobility under a strong positional disorder. In simulations, injected charges do not form packet-like space charges when using a constant mobility model, whereas packet-like space charges appear when using the mobility based on the GDM. The simulation using the GDM mobility can reproduce the time and voltage dependences of space charge behavior in LDPE. The calculated space charge, electric field, and current density profiles show good agreement with experimental results.

Message-passing neural network based multi-task deep-learning framework for COSMO-SAC based σ-profile and VCOSMO prediction

• A message-passing neural network based feedforward neural network (MPNN-FNN) is developed for σ-profile and V COSMO prediction. • Hybrid molecular representations are utilized to extract the molecular features. • The proposed model can well discriminate the cis/trans and structural isomers. • The IDAC calculated by predicted σ -profile and V COSMO is very close to the QM derived ones. The correct implementation of the quantum mechanics (QM) calculation for COSMO-SAC based surface charge density profiles ( σ -profile) and cavity volumes ( V COSMO ) is tricky and time-consuming. As a shortcut, the GC approaches (GC-COSMO) were proposed to predict the required σ -profile and V COSMO for COSMO based methods. However, the GC-COSMO model cannot discriminate the isomers and cannot predict the complex molecules due to a lack of diverse functional groups. In this context, a message-passing neural network based feedforward neural network (MPNN-FNN) is proposed for rapid and accurate predicting COSMO-SAC based σ -profile and V COSMO . The hybrid molecular representation integrated the message-passing neural network (MPNN) learned representations and 200 additional molecule-level RDKit features, which can capture both local and global features of the overall molecule, is utilized to develop a better molecular feature extraction model. Based on the hybrid molecular representations, a feedforward neural network (FNN) model for the σ -profile and V COSMO prediction is trained and tested on the VT-2005 database. The developed MPNN-FNN model demonstrates significantly better performance than the GC-COSMO method and can well discriminate the cis/trans and structural isomers. In addition, the calculation speed based on the proposed model for COSMO-SAC based infinite dilution activity coefficient (IDAC) reaches about 100 compounds per second, which are the prerequisite to performing a high throughput green solvent screening.

Characteristics of plasma sheath in multi-component plasmas with three-ion species

The plasma sheath of a three ion species plasma is studied numerically, relying on the results of the experiment by Yip et al. (Phys. Plasmas 23:050703 (2016) to measure the positive ion velocities at the sheath edge. The positive ion species (Ar^+, Kr^+, and Xe^+) are assumed to be singly charged and to be characterized by the same temperature. It is shown that the sheath characteristics, viz. the particle number densities, the electrostatic potential and the space charge density profile in the sheath all depend on the Kr^+ concentration that is gradually added to the argon-xenon plasma as the third positive ion species. Also, the effect of ion-neutral collisions on the sheath properties is investigated numerically. Our results may be extended to a multi-ion plasma with more than two species of positive ions.

Molecular dynamics of the interfacial solution structure of alkali-halide electrolytes at graphene electrodes

The interactions of graphene electrodes with aqueous solutions of electrolytes play important roles in many technologies such as capacitive deionisation. Particularly important is the surface adsorption of ions due to the electric potential of the electrode. In this paper, we have studied structural changes in several prototypical aqueous solutions of electrolytes (NaCl, KCl, and LiCl) in contact with graphene induced by its either positive or negative electric charge, under ambient conditions. We have carried out molecular-dynamics simulations using the most accurate interaction models available. We have analysed the solution structure using an advanced analysis of the intermolecular bonding, and also standard properties such as density and charge density profiles, electrostatic potential, and screening functions. Our results show that the graphene charge has nearly no translational effect on water molecules, whereas it significantly changes their orientations, and the effect on ions’ distributions differ from solution to solution. Larger ions, whose hydration shells are weaker, are affected directly in an intuitive fashion, i.e., cations are attracted by negatively charged graphene and vice versa, whereas effects on smaller ions may vary and may be even counterintuitive, e.g., the number of chlorine anions in aqueous KCl in contact with negatively charged graphene is greater when compared to neutral graphene. The surplus of chlorine anions adsorbed on a positively charged electrode strengthens the structure of water and counterintuitively rotates the water molecules in the second layer pointing their electric dipoles preferentially to the electrode. The surplus of cations due to a negatively charged electrode is accompanied by a weakening of the water structure in the case of larger ions, whereas in the case of the lithium cation the structure is stronger due to the direct effects of the graphene charge on water molecules. Regardless of the graphene charge, the total number of intermolecular bonds connected with a single water molecule is nearly independent of the distance from the graphene surface and the same applies to the number of intermolecular bonds connected with a single ion, which means that whenever a particle loses an intermolecular bond it nearly always forms a new bond as a compensation.

Coupling between Ion Drift and Kinetics of Electronic Current Transients in MAPbBr3 Single Crystals.

The optoelectronic properties of halide perovskite materials have fostered their utilization in many applications. Unravelling their working mechanisms remains challenging because of their mixed ionic–electronic conductive nature. By registering, with high reproducibility, the long-time current transients of a set of single-crystal methylammonium lead tribromide samples, the ion migration process was proved. Sample biasing experiments (ionic drift), with characteristic times exhibiting voltage dependence as ∝ V–3/2, is interpreted with an ionic migration model obeying a ballistic-like voltage-dependent mobility (BVM) regime of space-charge-limited current. Ionic kinetics effectively modify the long-time electronic current, while the steady-state electronic currents’ behavior is nearly ohmic. Using the ionic dynamic doping model (IDD) for the recovering current at zero bias (ion diffusion), the ionic mobility is estimated to be ∼10–6 cm2 V–1 s–1. Our findings suggest that ionic currents are negligible in comparison to the electronic currents; however, they influence them via changes in the charge density profile.

Interactions between conducting surfaces in salt solutions.

In this work, we simulate interactions between two perfectly conducting surfaces, immersed in a salt solution. We demonstrate that these forces are quantitatively different from those between (equally charged) non-conducting surfaces. There is, for instance, a significant repulsion between net neutral surfaces. On the other hand, there are also qualitative similarities, with behaviours found with non-conducting surfaces. For instance, there is a non-monotonic dependence of the free energy barrier height, on the salt concentration, and the minimum essentially coincides with a flat profile of the apparent surface charge density (i.e. the effective net surface charge density, some distance away from the surface, when accounting for ion neutralization), outside the so-called Stern layer. These conditions can be described as "perfect surface charge neutralization". Despite observed quantitative differences, we demonstrate that it might be possible to mimic a dispersion containing charged colloidal metal particles by a simpler model system with charged non-conducting particles, using modified particle-ion interactions.

Formation of an inverted sheath in a one-dimensional bounded plasma system studied by particle-in-cell simulation

Formation of an “inverted sheath” is studied by particle-in-cell (PIC) simulation using the code XPDP1 [Verboncoeur et al., J. Comp. Phys. 104, 321–328 (1993)]. Examples of current carrying and floating sheaths are presented. It is shown that the results of the PIC simulation are in excellent agreement with the model developed recently [Gyergyek et al., Phys Plasmas 27, 023520 (2020)]. In this work, it is shown how to normalize the results from the simulations, which are given in SI units, to the dimensionless variables of the model. The procedure can also be reversed. From a given solution of the model, the input parameters of the simulation can be determined. Excellent matching between the results of the model and of the simulations is obtained in both cases. The length of the system is an eigenvalue of the model, while for the simulations, it has to be selected in advance and it is fixed. The appropriate selection of the length of the system is briefly discussed, and so it is the role of the external circuit in the XPDP1 code. Injection of particles into the system is such that monotonically decreasing potential profiles are enforced. A monotonic space charge density profile with surplus of negative charge at the left (collector) electrode and surplus of positive charge at the right (source) electrode must be created. As a consequence, a neutrality point must exist somewhere between the electrodes. The “inverted sheath” is the region between the neutrality point and the collector. By appropriate injection of the particles, the location of the neutrality point can be enforced to any position between the electrodes including the electrodes themselves.

Electrostatic Potential Analysis in Polyelectrolyte Brush-Grafted Microchannels Filled with Polyelectrolyte Dispersion

In this study, the model framework that includes almost all relevant parameters of interest has been developed to quantify the electrostatic potential and charge density occurring in microchannels grafted with polyelectrolyte brushes and simultaneously filled with polyelectrolyte dispersion. The brush layer is described by the Alexander-de Gennes model incorporated with the monomer distribution function accompanying the quadratic decay. Each ion concentration due to mobile charges in the bulk and fixed charges in the brush layer can be determined by multi-species ion balance. We solved 2-dimensional Poisson–Nernst–Planck equations adopted for simulating electric field with ion transport in the soft channel, by considering anionic polyelectrolyte of polyacrylic acid (PAA). Remarkable results were obtained regarding the brush height, ionization, electrostatic potential, and charge density profiles with conditions of brush, dispersion, and solution pH. The Donnan potential in the brush channel shows several times higher than the surface potential in the bare channel, whereas it becomes lower with increasing PAA concentration. Our framework is fruitful to provide comparative information regarding electrostatic interaction properties, serving as an important bridge between modeling and experiments, and is possible to couple with governing equations for flow field.

Control of plasmons in topological insulators via local perturbations

We use a fully quantum mechanical approach to demonstrate control of plasmonic excitations in prototype models of topological insulators by molecule-scale perturbations. Strongly localized surface plasmons are present in the host systems, arising from the topologically nontrivial single-particle edge states. A numerical evaluation of the random phase approximation equations for the perturbed systems reveals how the positions and the internal electronic structure of the added molecules affect the degeneracy of the locally confined collective excitations, i.e., shifting the plasmonic energies of the host system and changing their spatial charge density profile. In particular, we identify conditions under which significant charge transfer from the host system to the added molecules occurs. Furthermore, the induced field energy density in the perturbed topological systems due to external electric fields is determined.

Transformer-convolutional neural network for surface charge density profile prediction: Enabling high-throughput solvent screening with COSMO-SAC

A deep learning (DL) method for quickly predicting surface charge density profiles (σ-profile) and cavity volumes (VCOSMO) of molecules for the COSMO-SAC model is developed. The molecular fingerprints are derived from the encoder state of a Transformer model pre-trained on the ChEMBL database, which allows transfer learning from large-scale unlabeled data and improve generalization performance by developing better molecular fingerprints for building models with significantly smaller datasets. Employing the pre-trained molecular fingerprints, a convolutional neural network (CNN) model for the σ-profile and VCOSMO prediction is trained and tested on the VT-2005 database. The obtained Transformer-CNN model presents superior performance to the GC-COSMO approach and enables the prediction of σ-profile and VCOSMO of millions of molecules in only a few minutes. Taking advantages of the model, a high-throughput solvent screening framework based on COSMO-SAC is further proposed and exemplified by searching sustainable solvent for the deterpenation process of citrus essential oils.

Odor prediction and aroma mixture design using machine learning model and molecular surface charge density profiles

Structure-Odor Relationship (SOR) is the key to the understanding of the mechanism of odors, which further facilitates the odor prediction and aroma design. However, the modeling of SOR is still a challenge since the understanding of odor mechanism is unresolved. In this paper, an Artificial Neural Network (ANN) model is developed to generate the SOR model for aroma mixtures, in which the molecular surface charge density profiles (σ-profiles) are used as the descriptors. In this ANN model, the aroma mixture properties are the input, and the σ-profiles of the mixtures are the output, which can directly predict the σ-profiles of the aroma mixtures under certain odor requirements. Then, Euclidean distance-based ingredient screening method is applied to search the aroma mixture that fits the predicted σ-profiles from the ANN model. Finally, a Computer-Aided Aroma Design (CAAD) framework is formulated for the design of aroma mixtures. Two case studies of aroma mixture design are presented. The results are verified by the electronic nose, which highlight the effect of the developed SOR model as well as the CAAD framework.

Multicomponent extraction of aromatics and heteroaromatics from diesel using acidic eutectic solvents: Experimental and COSMO-RS predictions

Eutectic solvents (ESs) have been extensively studied in the literature for the purification of fuels. Nevertheless, most studies investigated the extraction of a single type of aromatic from n-alkanes. In this work, aiming to provide insights about the performance of ESs in a process that mimics the multicomponent dearomatization used industrially, a salt-acid-based ES, comprised of methyltriphenyl-phosphonium bromide and acetic acid, was applied in simultaneously extracting toluene, thiophene, quinoline, and pyrrole from n-decane. First, the DES was characterized for its eutectic composition, physicochemical, and critical properties. Then, an initial screening to determine the molecular-level interactions and extraction mechanism were studied experimentally and using COSMO-RS screening charge density profiles and potentials. A physical mechanism was confirmed for the extraction of pyrrole, thiophene, and toluene while for quinoline, an acid-base reaction was the predominant extraction mechanism. The phase diagrams of each impurity were also experimentally determined, predicted using the COSMO-RS model, and correlated using the NRTL model in Aspen Plus. Lastly, a parametric investigation studying the impact of key parameters including stirring time, initial concentration, mixing effects, solvent-to-feed ratio, multi-stage extraction, and repetitive usage of solvent was conducted. On multi-stage extraction, full recovery of pyrrole and quinoline (≈99.9%) was achieved in only 2-stages, whereas for thiophene and toluene efficiencies of 82.2% and 58.4% were reached after the 5th stage, respectively.

Structure of cholinium glycinate biocompatible ionic liquid at graphite electrode interface.

We use constant potential molecular dynamics simulations to investigate the interfacial structure of the cholinium glycinate biocompatible ionic liquid (bio-IL) sandwiched between graphite electrodes with varying potential differences. Through number density profiles, we observe that the cation and anion densities oscillate up to ∼1.5 nm from the nearest electrode. The range of these oscillations does not change significantly with increasing electrode potential. However, the amplitudes of the cation (anion) density oscillations show a notable increase with increasing potential at the negative (positive) electrode. At higher potential differences, the bulkier N(CH3)3CH2 group of cholinium cations ([Ch]+) overcomes the steric barrier and comes closer to the negative electrode as compared to oxygen atom (O[Ch]+ ). We observe an increase in the interaction between O[Ch]+ and the positive electrode with a decrease in the distance between them on increasing the potential difference. We also observe hydrogen bonding between the hydroxyl group of [Ch]+ cations and oxygens of glycinate anions through the simulated tangential radial distribution function. Orientational order parameter analysis shows that the cation (anion) prefers to align parallel to the negative (positive) electrode at higher applied potential differences. Charge density profiles show a positive charge density peak near the positive electrode at all the potential differences because of the presence of partially positive charged hydrogen atoms of cations and anions. The differential capacitance (Cd) of the bio-IL shows two constant regimes, one for each electrode. The magnitude of these Cd values clearly suggests potential application of such bio-ILs as promising battery electrolytes.

Nonlocal self-organization of a dissipative system

We study the self-organization process induced by a nonlocal critical field, in analogy with the electric field that is derived from the global spatial profile of electric charge density during a discharge. In this nontrivial extension of standard sandpilelike models of intermittent dissipation, the charges move in a similar manner to grains of sand when the threshold condition on the field is achieved. Here we focus our attention on the long term statistics of events, so that we consider an extremely simplified model in close similarity with sandpiles, avoiding some of the extremely interesting complexities that occur in three-dimensional electric discharges. For the observed avalanches (discharges in this case) we analyze four characteristic quantities: current, charge discharged, energy discharged, and duration of the discharge. We have run several simulations to explore the parameter space and found in general that they exhibit well defined power law event statistics spanning for one to three decades in general. For some parameter values we observe the existence of large or global events, in addition to the power law statistics, some of which may be related to finite size effects due to the size of the simulation box. This is the first step in understanding the long term statistics of systems with avalanches or discharges, when the criticality is controlled by nonlocality, as there are a number systems, such as lightning discharges or heat transport in tokamaks, where this type of dynamics is expected to occur.

Mathematical model of electromigration allowing the deviation from electroneutrality.

The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern-Gouy-Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigrationconsidering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G-function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.