Fundamentals and Modeling of Electrokinetic Transport in Nanochannels

Yeh, Hung Chun; Wang, Moran; Chang, Chia Chin; Yang, Ruey-Jen

doi:10.1002/ijch.201400079

Cited by 18 publications

(11 citation statements)

References 100 publications

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“…22 The Dukhin number (and a characteristic length called Dukhin length, l Du = Du R) was used in several modeling studies describing nanopores, more specifically, when volume and surface transport processes competed inside the pore. [17][18][19][23][24][25][26][27][28][29][30][31][32][33] The definition in Eq. 7 is in agreement with the traditional definition of Bikerman because it can be computed from the ratio of the surface excess of the cations, |σ|2πRH assuming perfect exclusion of the anions, and the number of charge carriers assuming a bulk electrolyte in the pore, 2cR 2 πH (the factor 2 is needed because both cations and anions carry current).…”

Section: B Axial Dimension: the Effect Of Pore Entrances Inside The Porementioning

confidence: 99%

From nanotubes to nanoholes: scaling of selectivity in uniformly charged nanopores through the Dukhin number for 1:1 electrolytes

Sarkadi,

Fertig,

Ható

et al. 2021

Preprint

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Scaling of the behavior of a nanodevice means that the device function (selectivity) is a unique smooth and monotonic function of a scaling parameter that is an appropriate combination of the system's parameters. For the uniformly charged cylindrical nanopore studied here these parameters are the electrolyte concentration, c, voltage, U , the radius and the length of the nanopore, R and H, and the surface charge density on the nanopore's surface, σ. Due to the non-linear dependence of selectivites on these parameters, scaling can only be applied in certain limits. We show that the Dukhin number, Du = |σ|/eRc ∼ |σ|λ 2 D /eR (λ D is the Debye length), is an appropriate scaling parameter in the nanotube limit (H → ∞). Decreasing the length of the nanopore, namely, approaching the nanohole limit (H → 0), an alternative scaling parameter has been obtained that contains the pore length and is called the modified Dukhin number: mDu ∼ Du H/λ D ∼ |σ|λ D H/eR. We found that the reason of non-linearity is that the double layers accumulating at the pore wall in the radial dimension correlate with the double layers accumulating at the entrances of the pore near the membrane on the two sides. Our modeling study using the Local Equilibrium Monte Carlo method and the Poisson-Nernst-Planck theory provides concentration, flux, and selectivity profiles, that show whether the surface or the volume conduction dominates in a given region of the nanopore for a given combination of the variables. We propose that the inflection point of the scaling curve may be used to characterize the transition point between the surface and volume conductions.

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Section: B Axial Dimension: the Effect Of Pore Entrances Inside The Porementioning

confidence: 99%

From nanotubes to nanoholes: scaling of selectivity in uniformly charged nanopores through the Dukhin number for 1:1 electrolytes

Sarkadi,

Fertig,

Ható

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…11 The Dukhin number (and a characteristic length called Dukhin length, l Du = Du R) was used in several modeling studies describing nanopores, more specifically, when volume and surface transport processes competed inside the pore. [6][7][8][12][13][14][15][16][17][18][19][20][21][22] The definition in Eq. 4 is in agreement with the traditional definition of Bikerman, because it can be computed from the ratio of the surface excess of the cations, |σ|2πRH (H is the length of the pore) assuming perfect exclusion of the anions, and the number of charge carriers assuming a bulk electrolyte in the pore, 2cR 2 πH (the factor 2 is needed because both cations and anions carry current).…”

Section: Modified Dukhin Number As Scaling Parametermentioning

confidence: 99%

Scaling of selectivity in uniformly charged nanopores through a modified Dukhin number for 1:1 electrolytes

Sarkadi¹,

Fertig²,

Valiskó³

et al. 2020

Preprint

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We show that a modified version of the Dukhin number is an appropriate scaling parameter for the ionic selectivity of uniformly charged nanopores. The modified Dukhin number is an unambiguous function of the variables σ (surface charge), R (pore radius), and c (salt concentration), and defined as mDu = |σ|/e(R/λ), where λ is the screening length of the electrolyte carrying the c dependence (λ ∼ c −1/2 ). Scaling means that the device function (selectivity) is a smooth and (in this case) monotonic function of mDu. The original Dukhin number defined as Du = |σ|/eRc (c −1 dependence) was introduced to indicate whether the surface or the volume conduction is dominant in the pore. The modified version satisfies scaling and characterizes selectivity in the intermediate regime, where both surface and bulk conductions are present and the pore is neither perfectly selective, nor perfectly non-selective. Our modeling study using the Local Equilibrium Monte Carlo method and the Poisson-Nernst-Planck theory provides the radial flux profiles from which the radial selectivity profile can be computed. These profiles show in which region of the nanopore the surface or the volume conduction dominates for a given combination of the variables σ, R, and c. We show that the inflection point of the scaling curve may be used to characterize the transition point between the surface and volume conductions.

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“…In accordance with our concept of scaling the need to develop a simple parameter depending on the input device parameters and, in the meantime, characterizing the device's behavior also arose. A parameter called Bikerman-Dukhin number, Bi, [8,9] or just Dukhin number, Du, [10][11][12][13][14][15][16][17][18][19][20][21] was proposed as the ratio of the excess counterion quantity in the double layer and the quantity of ions in the bulk. For a 1:1 electrolyte, if we assume perfect exclusion of coions, the excess counterion quantity is proportional to |σ|2πRH, while the quantity of charge carriers in the bulk electrolyte is proportional to 2cR 2 πH.…”

Section: Introductionmentioning

confidence: 99%

The Dukhin number as a scaling parameter for selectivity in the infinitely long nanopore limit: extension to multivalent electrolytes

Sarkadi¹,

Fertig²,

Valiskó³

et al. 2022

Preprint

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Scaling of the behavior of a nanodevice means that the device function (selectivity, in this work) is a unique function of a scaling parameter that is an appropriate combination of the device parameters. Although nanopores facilitate the transport of ions through a membrane of finite length if the pore is long compared to the pore radius, we deal with an important limiting case, the infinitely long nanopore (nanotube). In this case, device parameters are the pore radius, the electrolyte concentration, the surface charge density on the nanopore's wall, and ionic valences. While in our previous study (Sarkadi et al., J. Chem. Phys. 154 (2021) 154704.) we showed that the Dukhin number is an appropriate scaling parameter in the nanotube limit for 1:1 electrolytes, in this work we obtain the Dukhin number from first principles on the basis of the Poisson-Boltzmann (PB) theory and generalize it to electrolytes containing multivalent ions as well. We show that grand canonical Monte Carlo simulations for charged hard spheres in an implicit solvent give results that are similar to those obtained from the PB theory with deviations that are the consequences of ionic correlations (including finite size of ions) beyond the mean-field level of the PB theory. Such a deviation occurs when charge inversion is present, in 2:2 and 3:1 electrolytes, for example.

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Fundamentals and Modeling of Electrokinetic Transport in Nanochannels

Cited by 18 publications

References 100 publications

From nanotubes to nanoholes: scaling of selectivity in uniformly charged nanopores through the Dukhin number for 1:1 electrolytes

From nanotubes to nanoholes: scaling of selectivity in uniformly charged nanopores through the Dukhin number for 1:1 electrolytes

Scaling of selectivity in uniformly charged nanopores through a modified Dukhin number for 1:1 electrolytes

The Dukhin number as a scaling parameter for selectivity in the infinitely long nanopore limit: extension to multivalent electrolytes

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