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

Bhuiyan, L. B.; Outhwaite, C.W.

doi:10.1039/b316098j

Cited by 82 publications

(109 citation statements)

References 34 publications

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“…(The macroion radius has been kept at R = 15 · 10 −10 m.) A motivation for these calculations is the fact that in their DFT and MC work on the PDL at these diameters, Boda et al [7,8] had noted an increasing discrepancy between the classical PB and DFT (or MC) diffuse layer potentials with decreasing ion size. The behaviour was confirmed by the MPB calculations in the PDL [17], and by the DFT and MPB calculations in the CDL [18]. In the present case the trend is clearly visible at the higher absolute values of the surface charge for each of the 1:1, 2:1/1:2, and 2:2 situations with the deviation between the PB and the MPB ζ increasing as the ion size decreases from 3 · 10 −10 m to 2 · 10 −10 m. For divalent counterions the MPB ζ continues to show a maximum (or a minimum), while the PB ζ remains monotonic as in the planar or cylindrical geometries [17,18].…”

Section: Resultsmentioning

confidence: 54%

“…The behaviour was confirmed by the MPB calculations in the PDL [17], and by the DFT and MPB calculations in the CDL [18]. In the present case the trend is clearly visible at the higher absolute values of the surface charge for each of the 1:1, 2:1/1:2, and 2:2 situations with the deviation between the PB and the MPB ζ increasing as the ion size decreases from 3 · 10 −10 m to 2 · 10 −10 m. For divalent counterions the MPB ζ continues to show a maximum (or a minimum), while the PB ζ remains monotonic as in the planar or cylindrical geometries [17,18]. …”

Section: Resultsmentioning

confidence: 54%

“…The DFT and MPB approaches to the electric double layer have now been compared for planar [17], cylindrical [18], and spherical geometries. The accumulated evidence clearly suggests that the aforementioned consistency is global, extending to all the three symmetries, and that under ordinary laboratory conditions, viz., σ 0.3 C/m 2 and electrolyte solution regimes, the two theories are comparable in their predictive properties.…”

Section: Discussionmentioning

confidence: 99%

“…To this end some work has already been reported. In an earlier paper [17] we have compared the DFT results of Boda et al [7,8] for a RPM planar double layer at ionic diameter of a = 4.25 · 10 −10 m with the corresponding modified Poisson-Boltzmann (MPB) results. With few exceptions the two theories were seen to be on par with each other in reproducing the MC simulation data of Boda et al [7,8] for the model systems.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of density functional and modified Poisson-Boltzmann structural properties for a spherical double layer

Bhuiyan¹,

Outhwaite²

2005

Condens. Matter Phys.

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The density functional and modified Poisson-Boltzmann descriptions of a spherical (electric) double layer are compared and contrasted vis-a-vis existing Monte Carlo simulation data (for small ion diameter 4.25 · 10 −10 m) from the literature for a range of physical parameters such as macroion surface charge, macroion radius, valencies of the small ions, and electrolyte concentration. Overall, the theoretical predictions are seen to be remarkably consistent between themselves, being also in very good agreement with the simulations. Some modified Poisson-Boltzmann results for the zeta potential at small ion diameters of 3 and 2 · 10 −10 m are also reported.

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Section: Resultsmentioning

confidence: 54%

Section: Resultsmentioning

confidence: 54%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparison of density functional and modified Poisson-Boltzmann structural properties for a spherical double layer

Bhuiyan¹,

Outhwaite²

2005

Condens. Matter Phys.

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“…Some of them concerns microscopic descriptions of ion-ion correlations and the finite size of the ions [19][20][21][22][23]. Others are based on macroscopic descriptions considering average interactions by mean-field approximations, that include entropic contributions related with the excluded volume effect when the ions have a finite size [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. While the former ones are physically more robust to describe real systems, they are basically restricted to equilibrium conditions.…”

Section: Introductionmentioning

confidence: 99%

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

Roa

Carrique

2011

Phys. Chem. Chem. Phys.

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The equilibrium electric double layer (EDL) that surrounds the colloidal particles is determinant for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed by the charged colloidal particles and the ionic countercharge released by the charging mechanism. The existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterions concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the large importance of such corrections for moderate to high particle charges at every particle volume fraction, specially, when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study nonequilibrium properties in concentrated colloidal suspensions, particularly the salt-free ones with small and highly charged particles.

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Principles and Applications of Liquid‐Environment Atomic Force Microscopy

Chen

Liao

et al. 2022

Adv Materials Inter

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has been devoted to these areas due to the appearance of divergent phenomena at different scales, such as macroscopic fluid dynamics, mesoscopic hydrogen bond network, and nanoscopic hydration layer. Especially, as the basis of numerous important but complex physicochemical processes, such as dissolution, crystallization, corrosion, catalysis, protein folding, and so on, [10][11][12][13][14][15] the research of the underlying mechanism and atomic dynamics at the solid-liquid interface call for characterization technology of both high spatial and temporal resolution in liquid. Furthermore, forces between solid objects in liquid are very different from those in vacuum or air due to the emergence of the solid-liquid interface, and the measurement of these forces could provide a unique pathway to understanding the system dynamics in liquid. As a whole, an in-depth understanding of a solid-liquid system calls for efficient characterization techniques of high spatial and temporal resolution, as well as force measurement of high sensitivity. For various widely adopted characterization methods including Fourier transform infrared spectroscopy, [16] sum-frequency vibrational spectroscopy, [17] X-ray photoelectron spectroscopy, [18] environment scanning electron microscope, [19] surface force apparatus, [20] and so on, only one or two of these goals could be achieved. By contrast, the fast-developing atomic force microscopy (AFM) provides a feasible strategy for the investigation of solid-liquid interfaces.AFM was invented in 1986 for obtaining the high-resolution surface topography of materials [21] regardless of their electrical conductivity, which utilizes a cantilever as the force sensor to raster scan the interaction between a sample and a tip at the cantilever's free end and obtains the sample topography through a feedback control system. Three years later, Hansma's group [22] applied AFM in the liquid environment for the first time and obtained atomic-scale images of a mica surface, which unveiled the prelude to the application of LE-AFM. However, the static mode used by early LE-AFM was invasive to the sample during raster scanning. When LE-AFM was applied to susceptible samples such as biological materials, the static scanning mode is no longer adequate. To overcome this issue, various dynamic modes were proposed, including amplitude modulation (AM) mode, frequency modulation (FM) mode, and so on. In 1994, Putman et al. [23,24] applied AM mode LE-AFM to image monkey Liquid environment is essential for the occurrence of various vital processes in fields of chemistry, biology, mechanics, and so on, underscoring the importance of understanding the solid-liquid interfaces. In the past decades, liquid-environment atomic force microscopy (LE-AFM) has played a nonsubstitutable role in studying solid-liquid interfaces because of its sub-nanometer spatial resolution, video-level imaging rates as well as piconewton-level force measuring capabilities. Various state-of-the-art developments and exciting applications are made r...

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

Cited by 82 publications

References 34 publications

Comparison of density functional and modified Poisson-Boltzmann structural properties for a spherical double layer

Comparison of density functional and modified Poisson-Boltzmann structural properties for a spherical double layer

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

Principles and Applications of Liquid‐Environment Atomic Force Microscopy

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