Modified Poisson-Boltzmann Model Research Articles

Ionic surface propensity controls pH in nanopores

<h2>Summary</h2> To predict many proton-involved reactions in natural and engineered systems, a better understanding of the difference between the solution pH in nanopores and the pH in the bulk solution is critical. However, how the pH in nanopores changes in response to changes in the bulk solution composition remains elusive. Here, the capability of surface-enhanced Raman scattering spectroscopy to measure both pH and ion concentrations enables us to discover a new mechanism: opposite ionic surface propensities induce differences in aqueous concentration and control the pH in nanopores. As further confirmed by our modified Poisson-Boltzmann model, in negatively charged nanopores, anion concentrations are still enhanced, whereas cation concentrations are suppressed. These effects can change the buffer's conjugated acid and base ratio and attract protons to compensate for the excess negative charge in nanopores. Collectively, compared with the bulk solution pH, these factors cause an unexpectedly low pH in nanopores.

Theoretical investigation of electroviscous flows in hydrophilic slit nanopores: Effects of ion concentration and pore size

Nanopores with various shapes are well developed in unconventional reservoirs, and the transport phenomena of solutions in these reservoir rocks are ubiquitous but have not yet been fully understood. This article investigates the flow characteristics of solutions in hydrophilic slit nanopores through the combination of a modified Poisson–Boltzmann (MPB) model and the modified Navier–Stokes (NS) equation. To account for the nanoconfinement effects on ion concentration and fluid viscosity, an electrochemical potential term is used in the MPB model and a varying viscosity model (VVM) is introduced in the NS equation. The model rationality is first confirmed, and then the influences of ion concentration and pore size on the transport capacities of solutions in nanopores are illuminated. In addition, the hydrodynamic features of liquids in nanopores and the limitations of this coupled model are discussed as well. The results show that the dimensionless apparent permeability of the slit increases with an increase in ion concentration and pore size. The relative contributions of the electroviscous effect (EVE) and VVM to the total flow resistance reveal different varying trends as ion concentration or pore size increases, which is greatly related to the surface charge density and the sign of the charged wall. Additionally, although the effects of EVE and VVM resulting from the nanoconfinement are considered, average velocities of fluids in nanopores exhibit a linear correlation with the pressure gradient, which cannot be used to explain the nonlinear flow mechanism occurring in tight reservoirs. Furthermore, we also compare the velocity difference between the classical PB and MPB models. We hope that the findings in this work can help improve our understanding of the characteristics of liquid flow in tight reservoirs and provide vital practical implications for diverse engineering applications.

The impact of the modified Poisson–Boltzmann model on protein bound to a lipid coated silicon nanowire field effect transistor biosensor in an electrolyte environment

ABSTRACTThe aim of this work was to analyse the electrostatic potential profile, various effects of electrolyte concentrations, and the influences of surface charge on a protein bound to a lipid coated Silicon nanowire field effect transistor (Si-NW FET) biosensor by implementing the modified Poisson–Boltzmann (MPB) model. In this work, we modelled a lipid monolayer-coated Si-NW FET for the sensing of proteins, which consisted of variable amounts of aspartic acid. The electrostatic potential profile, protein charge distributions, the response to various electrolyte concentration, and the impacts of various surface charge were studied by implementing the MPB model with the Si-NW FET biosensor. Additionally, a comparison between the use of the MPB and the Poisson–Boltzmann model in studying the effects of various surface charges was carried out. Taken together, it was found that the MPB model showed a higher resolution in studying the Si-NW FET biosensor model when higher concentrations and surface charges were administered.

Investigation of the effect of finite-sized ions on the nanowire field-effect transistor in electrolyte concentration using a modified Poisson–Boltzmann model

ABSTRACTOne-dimensional (1D) nanowire field-effect transistors (FETs) have recently played a major role in sensing applications. Due to charging of the surface functional chemical groups with protonation and deprotonation, the transport properties of these nanowire transistors affect the aqueous environment, altering the electrical double layer (EDL) potential drops and charge distributions in the electrolyte concentration. In this work, we have implemented the simple modified Poisson–Boltzmann (MPB) theory in a 1D silicon nanowire FET, and the effect of the various finite sizes of ions in z:z symmetric electrolyte concentration was investigated. For a given ionic concentration and surface charge, the EDL potential drop, accumulation of charges and the charge distributions of NaCl and CsCl ions were studied. From the MPB model results with the nanowire FET, it was observed that the potential drop of the EDL depends on the size of the ions in the electrolyte. The study of various electrostatic investigations of finite-sized ions was successfully done by implementing the MPB model on a silicon nanowire FET. It can be used in both chemical and biological sensors.

Numerical Analysis of Electric Double Layer Capacitors with Mesoporous Electrodes: Effects of Electrode and Electrolyte Properties

A theoretical study is presented of the behavior of electric double layer (EDL) supercapacitors constructed from mesoporous activated carbon electrodes. A three-dimensional (3D) computational model is developed to predict the equilibrium charge distribution within the supercapacitor as a function of key electrode and electrolyte properties. The model is based on the modified Poisson–Boltzmann (MPB) equation and takes into account the impact of critical device parameters, including the size of the ions, the bulk ion concentration, the field-dependent permittivity of the electrolyte, the specific surface area of the electrodes, and the applied voltage. A key feature of the MPB model is that it limits the accumulation of ionic charge at the electrode–electrolyte interface by accounting for the finite size of the ions. This provides more accurate predictions of capacitance than models based on a point charge approximation. The model is used to perform a systematic parametric analysis of device performance and...

Ionic effects on the transport characteristics of nanowire-based FETs in a liquid environment

For the development of ultra-sensitive electrical bio/chemical sensors based on nanowire field effect transistors (FETs), the influence of the ions in the solution on the electron transport has to be understood. For this purpose we establish a simulation platform for nanowire FETs in the liquid environment by implementing the modified Poisson-Boltzmann model into Landauer transport theory. We investigate the changes of the electric potential and the transport characteristics due to the ions. The reduction of sensitivity of the sensors due to the screening effect from the electrolyte could be successfully reproduced. We also fabricated silicon nanowire Schottky-barrier FETs and our model could capture the observed reduction of the current with increasing ionic concentration. This shows that our simulation platform can be used to interpret ongoing experiments, to design nanowire FETs, and it also gives insight into controversial issues such as whether ions in the buffer solution affect the transport characteristics or not. Open image in new window

Scaling laws for carbon-based electric double layer capacitors

This paper presents scaling laws for the integral capacitance of electric double layer capacitors (EDLCs) supported by rigorous analysis and experimental data for porous carbon-based electrodes. First, dimensionless similarity parameters were identified based on dimensional analysis of the modified Poisson–Boltzmann model for binary and symmetric electrolytes. Then, a correlation for the equilibrium potential at the Stern/diffuse layer interface near planar electrodes and near cylindrical and spherical pores was obtained as a function of previously identified dimensionless numbers for a wide range of parameters. Similarly, an analytical expression was proposed for the dimensionless double layer integral capacitance of planar electrodes. Finally, scaling analysis was applied to experimentally measured integral capacitance of mesoporous carbon electrodes with a wide range of morphology and different electrolytes. To maximize the integral areal capacitance, the electrolyte should have small ion effective diameter and large dielectric constant. The electrode pore diameter should be tailored to match the ion diameter.

Ions near the air/water interface. II: Is the water/air interface acidic or basic? Predictions of a simple model

A simple modified Poisson–Boltzmann model, compatible with zeta potential experiments, is used to calculate the concentrations of ions on the interface. It is shown that, for most pH values and salt concentrations, both H+ and OH− accumulate on the interface, making their interfacial concentrations larger than in the bulk. However, at extreme pH values, the interfacial concentrations of both H+ and OH− have been found to be lower than in bulk, which might explain some contradictory results from literature. The ratio between H+ and OH− concentrations is smaller at the interface than in bulk for most (but not all) pH values and salt concentrations. Recent experimental results, which show that H+ is present on the interface only at very low pH values, are explained on the basis of this model. It is shown that, when the adsorption of Cl− on the interface is sufficiently large compared to that of OH−, the number of H+ ions adsorbed on the interface passes through a maximum with salt concentration, also in agreement with experiment. The concentration at which the maximum occurs is of the order of the adsorption equilibrium constant of Cl− on the interface.

Simulating Electric Double Layer Capacitance of Mesoporous Electrodes with Cylindrical Pores

This paper aims to numerically assess the effects of electrolyte properties and electrode morphology on the capacitance of electric double layer capacitors (EDLCs) made of mesoporous electrodes consisting of ordered cylindrical pores in non-aqueous electrolytes. Simulations solved a three-dimensional modified Poisson-Boltzmann model. They accounted for the finite size of ions and field-dependent electrolyte permittivity while the pores were perpendicular to the current collector. The effects of pore radius, porosity, effective ion diameter, and electrolyte field-dependent permittivity on the diffuse layer gravimetric capacitance were investigated systematically in order to determine key parameters affecting EDLCs’ performance. The simulations showed that reducing the ion effective diameter and the pore radius resulted in the strongest increase in diffuse layer gravimetric capacitance up to a critical radius below which the capacitance reaches a plateau. Increasing the electrode porosity also increased the diffuse layer gravimetric capacitance. Accounting for more realistic field-dependent permittivity was found to significantly reduce the predicted diffuse layer gravimetric capacitance. Finally, accounting for the contribution of the Stern layer to the total capacitance was essential in predicting experimental data for a wide range of porous activated carbon electrodes and non-aqueous electrolytes.

The effect of ion size on the pressure between two surfaces in liquid

The pressure between two parallel planar surfaces at equal electric potentials is calculated using both the classical Poisson–Boltzmann (PB) equation and the modified PB (MPB) equation of Borukhov et al. (2000) to account for finite ion size. Results are presented for a z:z symmetric electrolyte. The pressures predicted by the two models differ more as the bulk ion concentration, surface potential, and ion size increase. For a bulk ion concentration of 0.001 M and a surface potential of 25 mV, the two models predict almost identical pressures. However, for a bulk ion concentration of 1 M and a surface potential of 100 mV, the MPB model predicted a pressure that is 60 and 400 percent higher than the PB model for an ion size of 0.6 nm and 0.9 nm, respectively. The ratio of the pressures predicted by the two models is relatively independent of the distance of separation between the two plates.

Screening of strongly charged macroparticles in liquid electrolyte solutions

A modified Poisson-Boltzmann model has been proposed which makes it possible to describe the screening of strongly charged macroparticles in liquid electrolyte Z: Z solutions in the case when parameter B= ZeQ 0/eRT≫1(Q 0 is the surface electric charge, T is the temperature, e is the solution permittivity, and Z is the valence of ions) provided that the solution is dilute: κR ≡ (8πZ 2 e 2 n i0/eT)1/2 R≪1 (n i0 is the equilibrium number density of ions). It is assumed that the charge Q 0 of a macroparticle appears as a result of adsorption of ions of a certain polarity on its surface. Quantitative criteria of division of dissolved ions into capable and incapable of adsorption are formulated. For aqueous solutions, the adsorption mechanism always leads to values of B ≫ 1. It is shown that the charge inversion effect predicted by other authors on the basis of different models must be observed for such solutions for all Z ≥ 1. The effect of Brownian movement of macroparticles on their screening is considered. It is shown that viscous forces emerging during such movement lead to peripheral destruction (“washing out”) of the screening ionic shell of macroparticles and, as a result, to violation of their electroneutrality. This results in the emergence of two types of oppositely charged compound particles with small radii close to R and with radii much larger than R, the charge polarity of the latter being opposite to the polarity of Q 0. It is found that both types of ions of compound particles obey the “law of distribution” of the mean energy of their electric field, expressed by formula (29). The problem of ionic screening of gas bubbles accompanied by the formation of bubstons (bubbles stabilized by ions) is considered separately. It is shown that the bubston radius R in pure water and in aqueous solutions of electrolytes is equal to 14 nm irrespective of the ion number density n i0. The value of n i0 determines the number density n b of bubstons themselves, which are formed spontaneously under equilibrium conditions.