Modified Poisson-Boltzmann Theory Research Articles

Higher-order lattice Boltzmann simulation of energy conversion of electrokinetic nanobatteries

As a novel green technology to harvest electric power, electrokinetic batteries appeal to more theoretical investigation in order to optimize their physical parameters, and hence to achieve higher energy conversion efficiency at nanoscales as expected. Generally, transport phenomena at nanoscales are out of the scope of continuum fluid mechanics theories. In addition, the electric double layer (EDL) requires a more comprehensive description incorporating image effect and ion size effect. In this study, the higher-order Lattice Boltzmann method (LBM) and the modified Poisson-Boltzmann theory (MPB) are used to investigate electrokinetic phenomena in nanochannels. Energy conversion is studied in terms of ion size, and dielectric properties of liquid and solid. 24.95% mechanical-electrical energy conversion efficiency may be achieved in a 16 nm electrokinetic battery. And hence about 6% mechanical energy can be utilized by the external load of the electrokinetic nanobattery.

Grand canonical Monte Carlo investigations of electrical double layer in molten salts

Results of the Monte Carlo simulation of the electrode/molten salt interface are reported. The system investigated was modeled by the restricted primitive model of electrolyte being in contact with the charged hard wall (hard spheres of diameter d=400 pm and relative permittivity epsilon(r)=10). The temperature analysis of the mean activity coefficient gamma(+/-), heat capacity C(v) and radial distribution function, g, indicated the range of temperatures of the study. Calculations for the electrode/electrolyte interface were carried out for temperatures 1300, 1400, and 1500 K and in the range of the electrode charge densities sigma from 0.025 to 0.5 C m(-2). Singlet distribution functions showed a multilayer structure of the electrolyte in the vicinity of the electrode surface. The structure depended on the electrode charge, but not much on temperature. The capacitance curves had a parabolalike shape with the maximum located at sigma=0. This result is not consistent with the Gouy-Chapman theory, but has been confirmed by the modified Poisson-Boltzmann theory, which includes the correlation and exclusion volume effects.

Electronic structure calculations of liquid-solid interfaces: Combination of density functional theory and modified Poisson-Boltzmann theory

A robust and efficient computational method for electronic structure calculations of liquid-solid interfaces is presented. The theory employs the density functional theory and a modified Poisson-Boltzmann theory, combining them through a smooth dielectric model function. The free energy, including electrostatic and nonelectrostatic interactions between solutes and the solvation medium, is formulated, and its first derivatives with atomic positions are presented. This methodology is applied to two different topics; one is the potential of zero charge (PZC) of Pt(111), and the other is a poisoning of active sites for the oxygen-reduction reaction (ORR) by interfacial water molecules on Pt(111). The results of the first topic show that induced charge redistributions caused by the adsorption of water molecules form a surface dipole moment that dominates the experimentally observed negative shift in the PZC when platinum is immersed in an aqueous electrolyte. The results of the second topic show the possibility of a decrease in the surface coverage of the first reaction precursor to the ORR due to site blocking by the adsorbed water molecules.

Where there is a valley, there is a peak: Study of ion size and image effects on nanoelectroosmotic pumping

With the advent of nanotechnology, nano-electro-osmosis flow (nano-EOF) has shown great promise in the next generation of lab-on-a-chip systems such as attoliter or picoliter syringes or pipettors. In order to optimize the design of such systems and to precisely control analysis processes, it is important to obtain better fundamental understanding of EOF at nanoscales. Therefore, a more comprehensive electric double layer (EDL) theory is in need to improve upon the conventional EDL theory based on the Poisson-Boltzmann (PB) equation. In this paper, the modified PB theory is utilized to investigate the flow behavior of EOF at micro- and nanoscales. The effect of ion size and the image effect are particularly emphasized. Both effects remarkably influence nano-EOF. More importantly, this study predicts a new phenomenon: two "peaks" may appear in the velocity profile of nano-EOF for some specific solid-electrolyte systems.

The effect of dielectric polarization of the electrode on anomalous temperature effects in the electrical double layer

Monte Carlo simulations and a modified Poisson–Boltzmann (MPB) theory are used to investigate the temperature dependence of the capacitance (around the potential of zero charge) of an electric double layer in the presence of surface polarization due to a dielectric boundary. Within the context of the restricted primitive model planar double layer, whose solvent dielectric constant is ε2, the cases when the electrode is an insulator (ε1 = 1), when the electrode and the electrolyte have the same permittivity (ε1 = ε2, no polarization), and when the electrode is a conductor (ε1 → ∞) are studied for the case where the electrolyte concentration is 0.1 M. The simulations reveal a capacitance anomaly, that is, a positive temperature dependence of the capacitance at low temperatures for the former two situations. The MPB theory also shows this effect for these two situations and is in qualitative or better agreement with the simulation data. In these two cases, both the simulations and theory show a dramatic increase of the diffuse layer potential in the temperature regime where capacitance anomaly occurs. However, in the latter situation, where the electrode is metallic, the capacitance always has a negative temperature derivative for the MPB theory and probably also for the simulation data.

Charged Colloidal Particles and Small Mobile Ions near the Oil-Water Interface: Destruction of Colloidal Double Layer and Ionic Charge Separation

We study suspensions of hydrophobic charged colloids in a demixed oil-water solvent with salt by means of a modified Poisson-Boltzmann theory, taking into account image-charge effects and partitioning of the monovalent ions. We find that the ion's aversion for oil can deform the double layers of the oil-dispersed colloids, which qualitatively affects the colloidal density profiles. The same theory also predicts crystallization of colloid-free micron-sized water-in-oil droplets at water volume fractions as small as approximately 10(-3) in a narrow range of the oil-dielectric constant. These findings explain recent observations by M. E. Leunissen et al. [Proc. Natl. Acad. Sci. U.S.A. 104, 2585 (2007)10.1073/pnas.0610589104].

The modified Poisson–Boltzmann electric double layer capacitance for point ions at low temperatures

Abstract The electric double layer capacitance due to the modified Poisson–Boltzmann theory is evaluated for point ions at low temperatures. An anomalous capacitance behaviour is found for 1:1 and 2:2 electrolytes for no imaging and for an insulating wall. No anomalous behaviour was found for 1:2 electrolytes.

A modified Poisson–Boltzmann theory and Monte Carlo simulation study of surface polarization effects in the planar diffuse double layer

The equilibrium structural properties of an electric double layer in the presence of a dielectric discontinuity at a plane charged interface are studied through a modified Poisson–Boltzmann equation and some Monte Carlo simulations. The diffuse double layer is modelled by a symmetric valency restricted primitive model electrolyte next to a uniformly charged planar wall whose relative permittivity () is, in general, different from that of the electrolyte () leading to polarization or image forces. The situations when the wall is a conductor (, ), or when the wall is an insulator (1, ) are treated and contrasted with the case , that is, no imaging. The results show that the influence of image forces on the diffuse double layer structure can be substantial, especially at or near zero surface charge density. The theoretical predictions are in nearly quantitative agreement for 1:1 salts or in semi-quantitative or better agreement for 2:2 salts with existing Monte Carlo simulations in the literature and some new simulations presented here.

Ion partitioning at the oil–water interface as a source of tunable electrostatic effects in emulsions with colloids

We present a combined experimental and theoretical investigation of the surprisingly strong electrostatic effects that can occur in mixtures of low- and high-polar liquids (e.g. oil-water emulsions), here in the presence of colloidal particles. For our experiments, we used confocal microscopy imaging, supplemented with electrophoresis and conductivity measurements. Theoretically, we studied our systems by means of a modified Poisson-Boltzmann theory, which takes into account image charge effects and the electrostatic self-energies of the micro-ions in the different dielectric media. Our results show that the unequal partitioning of micro-ions between the two liquid phases is the common driving force behind most of the observed electrostatic effects. The structural signatures of these effects typically develop on a time scale of hours to days and are qualitatively well-described by our theory. We demonstrate how the partitioning process and its associated phenomena can be controlled by shifting the balance of the interlocked ionic dissociation and partitioning equilibria. Moreover, we present strong experimental proof that the two-dimensional colloidal crystals at the oil-water interface are due to long-ranged Coulombic repulsion through the oil phase. The acquired insight in the role of electrostatics in oil-water emulsions is important for understanding the interactions in particle-stabilized ('Pickering') and charge-stabilized emulsions, emulsion production, encapsulation and self-assembly.

Some simulation and modified Poisson–Boltzmann theory results for the contact values of an electrolyte near a charged electrode

Abstract Since the development of a contact value theorem by Henderson et al. it has been known that the prediction of the venerable Gouy–Chapman (GC) theory for the contact value of the density profile of an electrolyte near an electrode is incorrect. The more recent semi-empirical work of Fawcett and Henderson and the simulations of Boda and Henderson have shown that the contact value of the charge profile at low electrode charge is also given incorrectly by the GC theory, at least for a binary symmetric restricted primitive model electrolyte. In the present study we examine the contact values of the profiles of the double layer formed by the electrolyte species in a binary symmetric restricted primitive model electrolyte as a function of the electrode charge by means of simulation. It is difficult to extract detailed information from simulation values of the density and charge profiles at large electrode charge because the contact values of these profiles are dominated by the large quadratic term in the electrode charge. However, we find from our simulations for a fairly wide range of concentrations and electrode charges, that the product of the counterion and coion profiles is a sensitive probe with which to study the double layer because it is a direct test of the basis of the GC approximation that the counterion and coion profiles are exponentials of ± zeψ ( x )/ kT and so have a product that is identically one. We find that this product is not one or even a constant as the electrode charge is varied and, thus, the GC contact values do not agree even qualitatively with the simulation results. In contrast, the modified Poisson–Boltzmann theory is quite successful in accounting for the behavior of this product.

The capacitance of the electrical double layer of valence-asymmetric salts at low reduced temperatures

The low temperature anomalies in the double layer properties of electrolytes have been observed in recent simulations and reproduced by a number of theoretical methods. This anomaly means that the capacitance of the electrical double layer increases with increasing reduced temperature when the reduced temperature is small, while the behaviour is the reversed at high reduced temperatures. In this paper, we give a concise overview of Monte Carlo simulation results for a 1:1 electrolyte together with the results of various theories such as the Gouy–Chapman theory, various versions of the mean spherical approximation, density functional theories, the modified Poisson–Boltzmann theory, and a field theoretical approach. We report our simulation results for the reduced temperature dependence of the capacitance of 2:1 and 3:1 electrolytes. Finally, we investigate the effect of a concentration dependent dielectric constant by means of a Parsons–Zobel plot.

Planar Electric Double Layer for a Restricted Primitive Model Electrolyte at Low Temperatures

Monte Carlo simulation and the modified Poisson-Boltzmann theory are used to investigate the planar electric double layer for a restricted primitive model electrolyte at low temperatures. Capacitance as a function of temperature at low surface charge is determined for 1:1, 2:2, 2:1, and 3:1 electrolytes. Negative adsorption can occur for 1:1 electrolytes at low surface charge with low electrolyte concentration. The 1:1 electrolyte diffuse layer potential as a function of surface charge displays a maximum at low densities. At high densities, the diffuse layer potential is negative with a negative slope. The Gouy-Chapman-Stern theory fails in this low-temperature regime, whereas the modified Poisson-Boltzmann theory is fairly successful in this regard.

A modified Poisson–Boltzmann analysis of the capacitance behavior of the electric double layer at low temperatures

The modified Poisson-Boltzmann theory is used to analyze the anomalous behavior of the electric double layer capacitance for small surface charge at low temperatures and densities. Good agreement is found with simulation and recent density-functional theory results. Negative adsorption is also found in line with theory and simulation. An unsatisfactory feature is the relatively poor structure in this region due to the inherent approximations in the theory. This feature is unimportant in relation to the capacitance results but has implications when calculating adsorption properties.

Theoretical Study of Catalytic Effects in Micellar Solutions

The catalytic effect of charged micelles as manifested through the increased collision frequency between the counterions of an electrolyte in the presence of such micelles is explored by the Monte Carlo simulation technique and various theoretical approaches. The micelles and ions are pictured as charged hard spheres embedded in a dielectric continuum with the properties of water at 298 K with the charge on micelles varying from zero to z(m) = 50 negative elementary charges. Analytical theories such as (i) the symmetric Poisson-Boltzmann theory, (ii) the modified Poisson-Boltzmann theory, and (iii) the hypernetted-chain integral equation are applied and tested against the Monte Carlo data for micellar ions (m) with up to 50 negative charges in aqueous solution with monovalent counterions (c; z(c) = +1) and co-ions (co; z(co) = -1). The results for the counterion-counterion pair correlation function at contact, g(cc)(sigma(cc)), are calculated in a micellar concentration range from c(m) = 5 x 10(-)(6) to 0.1 mol/dm(3) with an added +1:-1 electrolyte concentration of 0.005 mol/dm(3) (for most cases), and for various model parameters. Our computations indicate that even a small concentration of a highly charged polyelectrolyte added to a +1:-1 electrolyte solution strongly increases the probability of finding two counterions in contact. This result is in agreement with experimental data. For low charge on the micelles (z(m) below -8), all the theories are in qualitative agreement with the new computer simulations. For highly charged micelles, the theories either fail to converge (the hypernetted-chain theory) or, alternatively, yield poor agreement with computer data (the symmetric Poisson-Boltzmann and modified Poisson-Boltzmann theories). The nonlinear Poisson-Boltzmann cell model results yield reasonably good agreement with computer simulations for this system.

Comparison of the modified Poisson–Boltzmann theory with recent density functional theory and simulation results in the planar electric double layer

A comparative study is made of the modified Poisson–Boltzmann results with those of some recent density functional theory and Monte-Carlo results, for the structure and thermodynamics of the planar electric double layer. The results for the diffuse layer potential drop, the wall–ion distribution functions, and the mean electrostatic potential indicate a remarkable degree of consistency in the predictive properties of the two theories. These predictions are also in very close agreement with a new generation of corresponding machine simulation results. Some modified Poisson–Boltzmann results for imaging are also presented.

A modified Poisson-Boltzmann approach to homogeneous ionic solutions

The mean electrostatic potential approach to ionic solutions was initiatedby the mean field work of Gouy and Chapman for inhomogeneous systems,and Debye and Huckel for bulk solutions. Any successful extension of the¨mean field theories requires an adequate treatment of both the exclusionvolume and fluctuation terms. One such development has been the modi-fied Poisson-Boltzmann approach. Although the bulk modified Poisson-Boltzmann theory was introduced 35 years ago, only a limited amount ofwork has been put into its development due to the successful applicationof liquid state theories to ionic systems. We outline here the bulk modifi-ed Poisson-Boltzmann equation, comment on some of its successes, andmention some outstanding problems.Key words: Poisson-Boltzmann, modified Poisson-Boltzmann, ionicsolutions, primitive model electrolytesPACS: 05.20Jj, 61.20.Qg, 82.45.Gj

Theory and simulation of electrolyte mixtures

Monte Carlo simulation and theoretical results on some aspects of thermodynamics of mixtures of electrolytes with a common species are presented. Both charge symmetric mixtures, where ions differ only in size, and charge asymmetric but size symmetric mixtures at ionic strength ranging generally from I = 10−4 to 1.0 M, and in a few cases up to I = 2 M, are examined. The theoretical methods explored are: (i) the symmetric Poisson-Boltzmann theory, (ii) the modified Poisson-Boltzmann theory and (iii) the hypernetted-chain integral equation. The first two electrolyte mixing coefficients w 0 and w 1 of the various mixtures are calculated from an accurate determination of their osmotic pressure data. The theories are seen to be consistent among themselves, and with certain limiting laws in the literature, in predicting the trends of the mixing coefficients with respect to ionic strength. Some selected relevant experimental data have been analysed and compared with the theoretical and simulation trends. In addition the mean activity coefficients for a model mimicking the mixture of KC1 and KF electrolytes are calculated and hence the Harned coefficients obtained for this system. These calculations are compared with the experimental data and Monte Carlo results available in the literature. The theoretically predicted Harned coefficients are in good agreement with the simulation results for the model KC1-KF mixture.

Long-range electrostatic interactions between like-charged colloids: Steric and confinement effects

Within the framework of a modified Poisson-Boltzmann theory accounting for steric effects of microions, we prove analytically that the effective pair interactions between like-charge colloids immersed in a confined electrolyte are repulsive. Our approach encompasses and extends previously known results to the case of complete confinement, and further incorporates the finite size of the microions which is absent in the standard Poisson-Boltzmann theory.

Polyelectrolyte solutions containing mixed valency ions in the cell model: A simulation and modified Poisson–Boltzmann study

Monte Carlo simulations of linear polyelectrolyte solutions containing mixed valency simple ions in the cylindrical cell model are reported. The equilibrium distributions of the simple ions and the osmotic pressure of the solution are calculated at various concentrations of the monomer units of the polyelectrolyte. Specifically, the following systems are studied—monovalent counterions with added 2:2 salt, divalent counterions with added 1:1 salt, and systems containing mono- and divalent counterions only, and mono- and trivalent counterions only. The simulation results are compared with the corresponding predictions from the Poisson–Boltzmann and modified Poisson–Boltzmann theories applied to the cell model. It is seen that upto moderate concentrations of the polyion, the modified Poisson–Boltzmann theory provides a very good description of the systems with deviations occurring at higher concentrations. The theory also reproduces the charge reversal observed in the simulations when strongly correlated counterions overscreen the charge of the polyion. On the other hand, the classical Poisson–Boltzmann results begin to show discrepencies from the Monte Carlo results at relatively lower concentrations. Comparisons of the simulated osmotic pressures with available experimental results confirm the validity of the cell model in a spectrum of practical situations of interest.

Structure functions of rod-like DNA fragment and polystyrenesulfonate solutions in the modified Poisson-Boltzmann theory

The partial structure functions of aqueous solutions of rod-like DNA fragments and polystyrenesulfonic acid are calculated in the modified Poisson-Boltzmann theory. The cylindrical cell model appropriate for linear polyelectrolyte solutions with monovalent counterions and without any added salt is utilized. The predicted results are compared with the corresponding results from the classical Poisson-Boltzmann theory, and experimental small angle neutron scattering data obtained in the monomer concentration range 0.05-0.2 mol/dm 3. It is seen that both the modified Poisson-Boltzmann and the Poisson-Boltzmann results lead to a very good fit to the experimental structure functions.