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Screening and separation of charges in microscale devices: complete planar solution of the Poisson-Boltzmann equation

(2008) JOURNAL OF PHYSICAL CHEMISTRY B. 112(41). p.13038-13050
Author
Organization
Abstract
The Poisson-Boltzmann (PB) equation is widely used to calculate the interaction between electric potential and the distribution of charged species. In the case of a symmetrical electrolyte in planar geometry, the Gouy-Chapman (GC) solution is generally presented as the analytical solution of the PB equation. However, we demonstrate here that this GC solution assumes the presence of a bulk region with zero electric field, which is not justified in microdevices. In order to extend the range of validity, we obtain here the complete numerical solution of the planar PB equation, supported with analytical approximations. For low applied voltages, it agrees with the GC solution. Here, the electric double layers fully absorb the applied voltage such that a region appears where the electric field is screened. For higher voltages (of order I V in microdevices), the solution of the PB equation shows a dramatically different behavior, in that the double layers can no longer absorb the complete applied voltage. Instead, a finite field remains throughout the device that leads to complete separation of the charged species. In this higher voltage regime, the double layer characteristics are no longer described by the usual Debye parameter kappa, and the ion concentration at the electrodes is intrinsically bound (even without assuming steric interactions). In addition, we have performed measurements of the electrode polarization current on a nonaqueous model electrolyte inside a microdevice. The experimental results are fully consistent with our calculations, for the complete concentration and voltage range of interest.
Keywords
NUMERICAL-ANALYSIS, ELECTRICAL DOUBLE-LAYER, ELECTROLYTE, ELECTROSTATICS, DIFFUSION, DYNAMICS, SURFACES, LIQUIDS, BIOLOGY, SYSTEM

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Chicago
Verschueren, Alwin RM, Peter HL Notten, Luc JM Schlangen, Filip Strubbe, Filip Beunis, and Kristiaan Neyts. 2008. “Screening and Separation of Charges in Microscale Devices: Complete Planar Solution of the Poisson-Boltzmann Equation.” Journal of Physical Chemistry B 112 (41): 13038–13050.
APA
Verschueren, A. R., Notten, P. H., Schlangen, L. J., Strubbe, F., Beunis, F., & Neyts, K. (2008). Screening and separation of charges in microscale devices: complete planar solution of the Poisson-Boltzmann equation. JOURNAL OF PHYSICAL CHEMISTRY B, 112(41), 13038–13050.
Vancouver
1.
Verschueren AR, Notten PH, Schlangen LJ, Strubbe F, Beunis F, Neyts K. Screening and separation of charges in microscale devices: complete planar solution of the Poisson-Boltzmann equation. JOURNAL OF PHYSICAL CHEMISTRY B. 2008;112(41):13038–50.
MLA
Verschueren, Alwin RM, Peter HL Notten, Luc JM Schlangen, et al. “Screening and Separation of Charges in Microscale Devices: Complete Planar Solution of the Poisson-Boltzmann Equation.” JOURNAL OF PHYSICAL CHEMISTRY B 112.41 (2008): 13038–13050. Print.
@article{674675,
  abstract     = {The Poisson-Boltzmann (PB) equation is widely used to calculate the interaction between electric potential and the distribution of charged species. In the case of a symmetrical electrolyte in planar geometry, the Gouy-Chapman (GC) solution is generally presented as the analytical solution of the PB equation. However, we demonstrate here that this GC solution assumes the presence of a bulk region with zero electric field, which is not justified in microdevices. In order to extend the range of validity, we obtain here the complete numerical solution of the planar PB equation, supported with analytical approximations. For low applied voltages, it agrees with the GC solution. Here, the electric double layers fully absorb the applied voltage such that a region appears where the electric field is screened. For higher voltages (of order I V in microdevices), the solution of the PB equation shows a dramatically different behavior, in that the double layers can no longer absorb the complete applied voltage. Instead, a finite field remains throughout the device that leads to complete separation of the charged species. In this higher voltage regime, the double layer characteristics are no longer described by the usual Debye parameter kappa, and the ion concentration at the electrodes is intrinsically bound (even without assuming steric interactions). In addition, we have performed measurements of the electrode polarization current on a nonaqueous model electrolyte inside a microdevice. The experimental results are fully consistent with our calculations, for the complete concentration and voltage range of interest.},
  author       = {Verschueren, Alwin RM and Notten, Peter HL and Schlangen, Luc JM and Strubbe, Filip and Beunis, Filip and Neyts, Kristiaan},
  issn         = {1520-6106},
  journal      = {JOURNAL OF PHYSICAL CHEMISTRY B},
  language     = {eng},
  number       = {41},
  pages        = {13038--13050},
  title        = {Screening and separation of charges in microscale devices: complete planar solution of the Poisson-Boltzmann equation},
  url          = {http://dx.doi.org/10.1021/jp800675w},
  volume       = {112},
  year         = {2008},
}

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