Effect of the surface charge discretization on electric double layers: A Monte Carlo simulation study

Effect of Mixed Morphology (Simple Cubic, Face-Centered Cubic, and Body-Centered Cubic)-Based Electrodes on the Electric Double Layer Capacitance of Supercapacitors

Supercapacitors store energy due to the formation of an electric double layer (EDL) at the interface of the electrodes and electrolyte. The present article deals with the finite element study of equilibrium electric double layer capacitance (EDLC) in the mixed morphology electrodes comprising all three fundamental crystal structures, simple cubic (SC), body-centered cubic (BCC), and face-centered cubic morphologies (FCC). Mesoporous-activated carbon forms the electrode in the supercapacitor with (C2H5)4NBF4/propylene carbonate organic electrolyte. Electrochemical interference is clearly demonstrated in the supercapacitors with the formation of the potential bands, as in the case of interference theory due to the increasing packing factor. The effects of electrode thickness varying from a wide range of 50 nm to 0.04 mm on specific EDLC have been discussed in detail. The interfacial geometry of the unit cell in contact with the electrolyte is the most important parameter determining the properties of the EDL. The critical thickness of the electrodes is 1.71 μm in all the morphologies. Polarization increases the interfacial potential and leads to EDL formation. The Stern layer specific capacitance is 167.6 μF cm-2 in all the morphologies. The maximum capacitance is in the decreasing order of interfacial geometry, as FCC > BCC > SC, dependent on the packing factor. The minimum transmittance in all the morphologies is 98.35%, with the constant figure of merit at higher electrode thickness having applications in the chip interconnects. The transient analysis shows that the interfacial current decreases with increasing polarization in the EDL. The capacitance also decreases with the increase of the scan rate.

Thermodynamics of Charge Regulation near Surface Neutrality

The interaction between two adjacent charged surfaces immersed in aqueous solution is known to be affected by charge regulation─the modulation of surface charge as two charged surfaces approach each other. This phenomenon is particularly important near surface neutrality where the stability of objects such as colloids or biomolecules is jeopardized. Focusing on this ubiquitous case, we elucidate the underlying thermodynamics and show that charge regulation is governed in this case by surface entropy. We derive explicit expressions for charge regulation and formulate a new universal limiting law for the free energy of ion adsorption to the surfaces. The latter turns out to be proportional to k_BT, and independent of the association energy of ions to surface groups. These new results are applied to the analysis of unipolar as well as amphoteric surfaces such as oxides near their point of zero charge or proteins near their isoelectric point.

Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface

Poisson-Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson-Boltzmann theory, we calculate the surface potential inside a Wigner-Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law.

Influence of macromolecular crowding on the charge regulation of intrinsically disordered proteins

In this work we study the coupling between ionization and conformational properties of two IDPs, histatin-5 and β-amyloid 42, in the presence of neutral and charged crowders. The latter is modeled to resemble bovine serum albumin (BSA). With this aim, semi-grand canonical Monte Carlo simulations are performed, so that the IDP charge is a dynamic property, undergoing protonation/deprotonation processes. Both ionization properties (global and specific amino acid charge and binding capacitance) and radius of gyration are analyzed in a large range of pH values and salt concentrations. Without crowder agents, the titration curve of histatin-5, a polycation, is salt-dependent while that of β-amyloid 42, a polyampholyte, is almost unaffected. The salt concentration is found to be particularly relevant at pH values where the protein binding capacitance (directly linked with charge fluctuation) is larger. Upon addition of neutral crowders, charge regulation is observed in histatin-5, while for β-amyloid 42 this effect is very small. The main mechanism for charge regulation is found to be the effective increase in the ionic strength due to the excluded volume. In the presence of charged crowders, a significant increase in the charge of both IDPs is observed in almost all the pH range. In this case, the IDP charge is altered not only by the increase in the effective ionic strength but also by its direct electrostatic interaction with the charged crowders.

On the reasons for α-lactalbumin adsorption on a charged surface: a study by Monte Carlo simulation

This work studies α-lactalbumin adsorption on a charged substrate using Monte Carlo simulation. The protein is represented by a coarse-grained model with enough components as to reproduce the complex behavior of α-lactalbumin on electrically-charged substrates. The simulation results in particular can reproduce protein adsorption when both the protein and the substrate are negatively charged. The energetic and entropic contributions to the free energy of the adsorption process are estimated and analyzed. The effects of the charge regulation mechanism, the localization of titratable groups in α-lactalbumin as well as the distribution of small ions around the interface are studied in detail. Both the asymmetrical distribution of the charged groups of the protein and the counterion distribution play predominant roles in α-lactalbumin adsorption on a substrate with the same sign of electrical charge.

Surface charging behavior of nanoparticles by considering site distribution and density, dielectric constant and pH changes – a Monte Carlo approach

Monte Carlo simulations are used to describe the charging behavior of metal oxide nanoparticles thus enabling a novel and original approach to predict nanoparticle reactivity and the possible interactions with biological and environmental molecules.

Electric double layer force between charged surfaces: effect of solvent polarization

In this paper, we develop a theory to delineate the consequences of finite solvent polarization in electric double layer interaction or the osmotic pressure between two similar or oppositely charged surfaces. We use previously published Langevin-Bikerman equations to calculate this electric double layer interaction force or the osmotic pressure between the charged surfaces. The osmotic pressure between oppositely charged surfaces is found to be much larger than that between similarly charged surfaces, and for either case, the influence of solvent polarization ensures a larger pressure than that predicted by the Poisson-Boltzmann (PB) model. We derive distinct scaling relationships to explain the increase of the pressure as a function of the separation between the surfaces, the solvent polarizability, and the number density of water molecules. Most importantly, we demonstrate that our theory can successfully reproduce the experimental results of interaction force between similar and oppositely charged surfaces, by accounting for the large under-prediction made by the corresponding PB model.

Electrophoretic mobility and charge inversion of a colloidal particle studied by single-colloid electrophoresis and molecular dynamics simulations

Optical Tweezers are employed to study the electrophoretic and the electroosmotic motion of a single colloid immersed in electrolyte solutions of ion concentrations between 10(-5) and 1 mol/l and of different valencies (KCl, CaCl(2), LaCl(3)). The measured particle mobility in monovalent salt is found to be in agreement with computations combining primitive model molecular dynamics simulations of the ionic double layer with the standard electrokinetic model. Mobility reversal of a single colloid-for the first time-is observed in the presence of trivalent ions (LaCl(3)) at ionic strengths larger than 10(-2) mol/l. In this case, our numerical model is in a quantitative agreement with the experiment only when ion specific attractive forces are added to the primitive model, demonstrating that at low colloidal charge densities, ion correlation effects alone do not suffice to produce mobility reversal.

Effects of mixed discrete surface charges on the electrical double layer

Adsorption of surface coions and charge reversal are induced at the electrical double layer of a wall charged with positive and negative surface sites next to an electrolyte solution. While for the considered surface charge density these effects are found over a wide range of conditions, they are not observed for the typically employed surface models in equivalent conditions. Important consequences in electrophoresis experiments for different colloids with equal effective surface charge density are foreseen. This study is carried out by means of molecular dynamics simulations.

The weighted correlation approach for density functional theory: a study on the structure of the electric double layer

Within the framework of density functional theory, a weighted correlation approach is developed in order to obtain the density distributions of an inhomogeneous fluid. It results in a formally exact expression, by means of the concept of a weighted pair correlation function, used to evaluate the change of the single-particle direct correlation function of the system relative to that of a reference state. When applying the approach for practical use, however, an approximation of the pair correlation function has to be made, along with an appropriate definition of a weight function. Noticeably, combining this approach with fundamental measure theory gives rise to a new method, which we call the FMT/WCA-k(2) approach, for studying the structural and thermodynamic properties of a charged hard-sphere fluid subjected to a spatially varying external potential. Application of the FMT/WCA-k(2) approach in a range of electrolyte concentrations and surface charge densities, against the Monte Carlo simulations, shows that it is superior to the typical approaches of density functional theory in predicting the ionic density profiles of both counter-ions and co-ions near a highly charged surface. It is capable of capturing the fine features of the structural properties of the electric double layers, to well reproduce the layering effect and the charge inversion phenomenon, also in strongly coupled cases where divalent counter-ions are involved. In addition, it is found that the FMT/WCA-k(2) approach even has an advantage over the anisotropic, hyper-netted chain approaches in giving better agreement with the Monte Carlo results.

The interaction between electrolyte and surfaces decorated with charged groups: A molecular dynamics simulation study

In this paper, we perform molecular dynamics simulations of an interface containing charged functional groups of different valences in contact with 2:1 ionic solution. We take into account both the finite sizes of the ions in solution and the functional groups but we neglect the structural details of the solvent (primitive model). We show that the distribution of ions and the electrostatic properties of the system depend strongly on the valence of the interfacial charged groups. In the case of surfaces containing well-separated charged interfacial groups, we observe counterion binding at these groups induced by electrostatic interactions. A detailed analysis of the potential of mean force between interfacial charged groups and ions reveals significant features not anticipated by present theories of electrolytes near interfaces. Overall, our results show that, in primitive models of the ion-interface interaction, not only the ionic size and valence are important but the size and valence of the interfacial charged groups also have a significant impact.

Monte Carlo determination of mixed electrolytes next to a planar dielectric interface with different surface charge distributions

Employing canonical ensemble Monte Carlo simulations, we report a calculation of the distribution of small ions next to a planar negatively charged surface in the presence of mixed electrolytes of monovalent and trivalent salt ions within the framework of the primitive model under more realistic hydrated ion size conditions. The effects of surface charge discreteness and dielectric breakdown on charge inversion are discussed based on increasing concentration of both monovalent and trivalent salt. Moreover, a comparison of the simulation results for different discretization models is made along with the case of uniformly distributed charge in terms of the ionic density profiles as well as the integrated charge distribution function. For finite size charged groups located inside the lower dielectric region, a complete equivalence with the case of uniform distribution is observed if the quantities of interest are exclusively analyzed as a function of the distance to the charged interface. With protruding head groups into the aqueous solution, the excluded volume dominates over the correlation effect, therefore the ions are less accumulated in the vicinity of the charged surface, inducing that the onset position of charge inversion experiences an evident shift toward the aqueous environment. Overall, the effect of repulsive image forces on the diffuse double layer structure can be significant at low surface charge density irrespectively of surface charge distributions.

Additional considerations about the role of ion size in charge reversal

The effect of the ion size on the charge reversal process is studied via canonical Monte Carlo simulation. To this end, a primitive model of electrolyte is used to analyze the electric double layer formed by an asymmetric electrolyte in the presence of a charged planar wall. Different values of ion diameters and surface charge densities are used so as to determine the conditions at which the charge reversal first occurs. For each case, the apparent surface charge density is calculated as a function of the distance from the charged wall for the different electrolyte concentrations in order to establish the minimal salt concentration required for the charge reversal. We will refer to this electrolyte concentration as the reversal concentration and will show how it depends on the surface charge density and on the ion size. From the apparent surface charge density profiles, the distance from the wall at which the charge reversal arises as well as its intensity can be also inferred.

Enhancement of charge inversion by multivalent interfacial groups

In this Brief Report, we perform molecular-dynamics simulations of an interface containing charged functional groups of different valences in contact with 2:1 ionic solution. We take into account both the finite sizes of the ions in solution and the functional groups but we neglect the structural details of the solvent (primitive model). We show that the interaction between a charged interface (of given surface charge density) and electrolyte depends strongly on the individual charges of the interfacial groups originating the surface charge. In particular, we show that charge inversion (i.e., interfacial charges attracting counterions in excess of their own nominal charge) is enhanced by the presence of multivalent interfacial groups (such as certain phospholipids). Overall, our results reveal that in primitive models of the ion-interface interaction not only the ionic size and valence are important but also the size and valence of the interfacial charged groups have a significant impact.

Effect of surface charge on colloidal charge reversal

The objective of this research work is to understand the effect of the surface charge density on the charge reversal phenomenon. To this end, we use experimental results and computer simulations. In particular, we measure the electrophoretic mobility of latex particles (macroions) in the presence of a multivalent electrolyte. We have focused on the electrolyte concentration range at which a reversal in the electrophoretic mobility is expected to happen. In particular, the role of the surface charge on the charge reversal process is looked into from several latexes with the same functional group but different surface charge densities. Although the mechanism responsible for the colloidal charge reversal is still a controversial issue, it is proved that ionic correlations are behind the appearance of such phenomenon (especially near the macroion surface). This conclusion can be inferred from a great variety of theoretical models. According to them, one of the factors that determine the charge reversal is the surface charge density of the macroions. However, this feature has been rarely analyzed in experiments. Our results appear therefore as a demanded survey to test the validity of the theoretical predictions. Moreover, we have also performed Monte Carlo simulations that take the ion size into account. The correlation found between experiments and simulations is fairly good. The combination of these techniques provides new insight into the colloidal charge reversal phenomena showing the effect of surface charge.

Effect of ion dispersion forces on the electric double layer of colloids: a Monte Carlo simulation study

In this work, the effect of ionic dispersion forces on the electric double layer of colloids is evaluated through Monte Carlo simulations. Particularly, the influence of these forces on the zeta-potential (as a representative electrokinetic property) is assessed. Ion polarizability is included in the primitive model with the help of the Lifshitz theory. In this way, ion specificity is not considered by means of phenomenological (and unknown a priori) parameters. Our results reveal that the ionic van der Waals forces are responsible (to some extent) for the specificity of the zeta-potential. In any case, the specific ion effects due to ion polarizability are strongly influenced by ion size. Furthermore, a preliminary study on the effect of ionic dehydration shows how this phenomenon improves the qualitative agreement between experimental data and simulations achieved in considering ionic dispersion forces.

Electrostatics in soft matter

Recent progress in understanding the effect of electrostatics in soft matter is presented. A vast number of materials contain ions, ranging from the molecular scale (e.g. electrolyte) to the meso/macroscopic one (e.g. charged colloidal particles or polyelectrolytes). Their (micro)structure and physico-chemical properties are especially dictated by the famous and redoubtable long-ranged Coulomb interaction. In particular, theoretical and simulational aspects, including the experimental motivations, will be discussed.