Skip to main content Accessibility help
×
Home
Hostname: page-component-684899dbb8-662rr Total loading time: 0.595 Render date: 2022-05-19T00:27:12.843Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

On the structure of generalized Poisson–Boltzmann equations

Published online by Cambridge University Press:  20 November 2015

N. GAVISH
Affiliation:
Department of Mathematics, Technion–Israel Institute of Technology, Haifa, Israel email: ngavish@tx.technion.ac.il
K. PROMISLOW
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI, USA email: kpromisl@math.msu.edu

Abstract

In this work, we analyse a broad class of generalized Poisson–Boltzmann equations and reveal a common mathematical structure. In the limit of a wide electrode, we show that a broad class of generalized Poisson–Boltzmann equations admits a reduction that affords an explicit connection between the functional form of the corresponding free energy and the associated differential capacitance data. We exploit the relation to we show that differential capacitance curves generically undergo an inflection transition with increasing salt concentration, shifting from a local minimum near the point of zero charge for dilute solutions to a local maximum point near the point of zero charge for concentrated solutions. In addition, we develop a robust numerical method for solving generalized Poisson–Boltzmann equations which is easily applicable to the broad class of generalized Poisson–Boltzmann equations with very few code adjustments required for each model

Type
Papers
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bazant, M. Z., Sabri, Kilic M., Storey, B. D. & Ajdari, A. (2009) Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions. Adv. Colloid Interface Sci. 152 (1–2), 4888.CrossRefGoogle Scholar
[2] Ben-Yaakov, D., Andelman, D., Harries, D. & Podgornik, R. (2009) Beyond standard Poisson–Boltzmann theory: Ion-specific interactions in aqueous solutions. J. Phys.: Condens. Matter 21 (42), 424106.Google ScholarPubMed
[3] Ben-Yaakov, D., Andelman, D. & Podgornik, R. (2011) Dielectric decrement as a source of ion-specific effects. J. Chem. Phys. 134 (7), 074705.CrossRefGoogle ScholarPubMed
[4] Ben-Yaakov, D., Andelman, D., Podgornik, R. & Harries, D. (2011) Ion-specific hydration effects: Extending the Poisson-Boltzmann theory. Curr. Opin. Colloid Interface Sci. 16 (6), 542550.CrossRefGoogle Scholar
[5] Bikerman, J. J. (1942) Xxxix. structure and capacity of electrical double layer. Phil. Mag. 33 (220), 384397.CrossRefGoogle Scholar
[6] Booth, F. (1951) The dielectric constant of water and the saturation effect. J. Chem. Phys. 19 (4), 391394.CrossRefGoogle Scholar
[7] Boublík, T. (1970) Hard-sphere equation of state. J. Chem. Phys. 53 (1), 471472.CrossRefGoogle Scholar
[8] Di Caprio, D., Borkowska, Z. & Stafiej, J. (2003) Simple extension of the Gouy–Chapman theory including hard sphere effects: Diffuse layer contribution to the differential capacity curves for the electrode? electrolyte interface. J. Electroanalytical Chem. 540 (1), 1723.CrossRefGoogle Scholar
[9] di Caprio, D., Borkowska, Z. & Stafiej, J. (2004) Specific ionic interactions within a simple extension of the Gouy–Chapman theory including hard sphere effects. J. Electroanal. Chem. 572 (1), 5159.CrossRefGoogle Scholar
[10] Eisenberg, B. (2013) Interacting ions in biophysics: Real is not ideal. Biophys. J. 104 (9), 18491866.CrossRefGoogle Scholar
[11] Fedorov, M. V. & Kornyshev, A. A. (2014) Ionic liquids at electrified interfaces. Chem. Rev. 114 (5), 29783036.CrossRefGoogle ScholarPubMed
[12] Hatlo, M. M., van Roij, R. & Lue, L. (2012) The electric double layer at high surface potentials: The influence of excess ion polarizability. EPL (Europhys. Lett.) 97 (2), 28010.CrossRefGoogle Scholar
[13] Horng, T.-L., Lin, T.-C., Liu, C. & Eisenberg, B. S. (2012) PNP equations with steric effects: A model of ion flow through channels. J. Phys. Chem. B 116 (37), 1142211441.CrossRefGoogle ScholarPubMed
[14] Islam, M. M., Alam, M. T. & Ohsaka, T. (2008) Electrical double-layer structure in ionic liquids: A corroboration of the theoretical model by experimental results. J. Phys. Chem. C 112 (42), 1656816574.CrossRefGoogle Scholar
[15] Kilic, M., Bazant, M. Z. & Ajdari, A. (2007) Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging. Phys. Rev. E 75 (2), 021502.CrossRefGoogle ScholarPubMed
[16] Kornyshev, A. A. (2007) Double-Layer in ionic liquids: Paradigm change? J. Phys. Chem. B 111 (20), 55455557.CrossRefGoogle ScholarPubMed
[17] López-García, J. J., Horno, J. & Grosse, C. (2011) Poisson–Boltzmann description of the electrical double layer including ion size effects. Langmuir 27 (23), 1397013974.CrossRefGoogle ScholarPubMed
[18] Mansoori, G. A., Carnahan, N. F., Starling, K. E. & Leland, T. W. Jr (1971) Equilibrium thermodynamic properties of the mixture of hard spheres. J. Chem. Phys. 54 (4), 15231525.CrossRefGoogle Scholar
[19] Stern-Hamburg, H. O. (1924) Zur theorie c⋅ der elektrolytischen doppelschicht, Z. Elektrochem. S. f. Electrochemie 30, 508.Google Scholar
[20] Valette, G. (1981) Double layer on silver single crystal electrodes in contact with electrolytes having anions which are slightly specifically adsorbed: Part I. J. Electroanal. Chem. 122, 285297.CrossRefGoogle Scholar
[21] Wei, G.-W., Zheng, Q., Chen, Z. & Xia, K. (2012) Variational multiscale models for charge transport. SIAM Rev. 54 (4), 699754.CrossRefGoogle ScholarPubMed
14
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

On the structure of generalized Poisson–Boltzmann equations
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

On the structure of generalized Poisson–Boltzmann equations
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

On the structure of generalized Poisson–Boltzmann equations
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *