Skip to main content Accessibility help
×
Home
Hostname: page-component-5cfd469876-9knjr Total loading time: 0.231 Render date: 2021-06-25T11:14:35.547Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

Investigation of Dielectric Decrement and Correlation Effects on Electric Double-Layer Capacitance by Self-Consistent Field Model

Published online by Cambridge University Press:  21 July 2016

Manman Ma
Affiliation:
Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Shuangliang Zhao
Affiliation:
State Key laboratory of Chemical Engineering, East China University of Science and Technology, 200237, Shanghai, China
Zhenli Xu
Affiliation:
Institute of Natural Sciences, Department of Mathematics, and MoE Key Lab of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China
Corresponding
Get access

Abstract

The differential capacitance of electric double-layer capacitors is studied by developing a generalized model of the self-consistent Gaussian field theory. This model includes many-body effects of particles near the interface such as ionic sizes, the order of water alignment and electrostatic correlations, and thus can present more accurate predictions of the electric double-layer structure and hence the capacitance than traditional continuum theories. Analytical simplification of the model and efficient numerical method are introduced, in particular, the approximation of the self-Green's function which describes the self energy of a mobile ion. We show that, when the applied voltage on interfaces is small the dielectric effect of the electrode materials plays an important role. For large voltage, this effect is screened, but the dielectric saturation due to the alignment of the nearby water is shown to be essential. For 2:1 electrolytes, abnormal enhancement on the capacitance due to the dielectric electrode is observed, which is due to the interplay of the image charge effect and Born solvation energy in the self energy of ions.

Type
Research Article
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below.

References

[1] Huang, J., Sumpter, B. G., Meunier, V., Theoretical model for nanoporous carbon supercapacitors, Angew. Chem. Int. Ed. 47 (3) (2008) 520524.CrossRefGoogle ScholarPubMed
[2] Fedorov, M. V., Kornyshev, A. A., Ionic liquids at electrified interfaces, Chem. Rev. 114 (2014) 29783036.CrossRefGoogle ScholarPubMed
[3] Rica, R. A., Ziano, R., Salerno, D., Mantegazza, F., van Roij, R., Brogioli, D., Capacitive mixing for harvesting the free energy of solutions at different concentrations, Entropy 15 (4) (2013) 13881407.CrossRefGoogle Scholar
[4] Fernández, M. M., Ahualli, S., Iglesias, G. R., González-Caballero, F., Delgado, Á. V., Jiménez, M., Multi-ionic effects on energy production based on double layer expansion by salinity exchange, J. Colloid Interf. Sci. 446 (2015) 307316.CrossRefGoogle ScholarPubMed
[5] Iglesias, G. R., Fernández, M.M., Ahualli, S., Jiménez, M. L., Kozynchenko, O. P., Delgado, Á. V., Materials selection for optimum energy production by double layer expansion methods, J. Power Sources 261 (2014) 371377.CrossRefGoogle Scholar
[6] Gouy, G., Constitution of the electric charge at the surface of an electrolyte, J. Phys. 9 (1910) 457468.Google Scholar
[7] Chapman, D. L., A contribution to the theory of electrocapillarity, Phil. Mag. 25 (1913) 475481.CrossRefGoogle Scholar
[8] Stern, O., The theory of the electrolytic double-layer, Zeit. Elektrochem 30 (1924) 508516.Google Scholar
[9] Borukhov, I., Andelman, D., Orland, H., Steric effects in electrolytes: A modified Poisson-Boltzmann equation, Phys. Rev. Lett. 79 (1997) 435438.CrossRefGoogle Scholar
[10] Ben-Yaakov, D., Andelman, D., Harries, D., Podgornik, R., Beyond standard Poisson–Boltzmann theory: Ion-specific interactions in aqueous solutions, J. Phys.: Condens. Matter 21 (2009) 424106.Google ScholarPubMed
[11] Li, B., Continuum electrostatics for ionic solutions with nonuniform ionic sizes, Nonlinearity 22 (2009) 811833.CrossRefGoogle Scholar
[12] Kornyshev, A. A., Double-layer in ionic liquids: paradigm change?, J. Phys. Chem. B 111 (2007) 55455557.CrossRefGoogle ScholarPubMed
[13] Rosenfeld, Y., Free-energy model for the inhomogeneous hard-sphere fluid mixture and density-functional theory of freezing, Phys. Rev. Lett. 63 (9) (1989) 980983.CrossRefGoogle ScholarPubMed
[14] Wu, J., Density functional theory for liquid structure and thermodynamics, in: Molecular Thermodynamics of Complex Systems, Vol. 131 of Structure and Bonding, Springer Berlin Heidelberg, 2009, pp. 173.Google Scholar
[15] Zhao, S., Liu, Y., Chen, X., Lu, Y., Liu, H., Hu, Y., Unified framework of multiscale density functional theories and its recent applications, in: Mesoscale Modeling in Chemical Engineering Part II, Vol. 47 of Advances in Chemical Engineering, Academic Press, 2015, pp. 183.Google Scholar
[16] Jiang, D.-e., Jin, Z., Wu, J., Oscillation of capacitance inside nanopores, Nano letters 11 (12) (2011) 53735377.CrossRefGoogle ScholarPubMed
[17] Hasted, J., Ritson, D., Collie, C., Dielectric properties of aqueous ionic solutions. Parts I and II, J. Chem. Phys. 16 (1) (1948) 121.CrossRefGoogle Scholar
[18] Lyashchenko, A., Zasetsky, A. Y., Complex dielectric permittivity and relaxation parameters of concentrated aqueous electrolyte solutions in millimeter and centimeter wavelength ranges, J. Molecular Liquids 77 (1) (1998) 6175.CrossRefGoogle Scholar
[19] Booth, F., The dielectric constant of water and the saturation effect, J. Chem. Phys. 19 (4) (1951) 391394.CrossRefGoogle Scholar
[20] Booth, F., Dielectric constant of polar liquids at high field strengths, J. Chem. Phys. 23 (3) (1955) 453457.CrossRefGoogle Scholar
[21] Paunov, V., Dimova, R., Kralchevsky, P., Broze, G., Mehreteab, A., The hydration repulsion between charged surfaces as an interplay of volume exclusion and dielectric saturation effects, J. Colloid Interf. Sci. 182 (1) (1996) 239248.CrossRefGoogle Scholar
[22] Abrashkin, A., Andelman, D., Orland, H., Dipolar Poisson-Boltzmann equation: ions and dipoles close to charge interfaces, Phys. Rev. Lett. 99 (7) (2007) 077801.CrossRefGoogle ScholarPubMed
[23] Frydel, D., Oettel, M., Charged particles at fluid interfaces as a probe into structural details of a double layer, Phys. Chem. Chem. Phys. 13 (9) (2011) 41094118.CrossRefGoogle ScholarPubMed
[24] Gur, Y., Ravina, I., Babchin, A. J., On the electrical double layer theory. II. the Poisson-Boltzmann equation including hydration forces, J. Colloid Interf. Sci. 64 (2) (1978) 333341.CrossRefGoogle Scholar
[25] Macdonald, J. R., Theory of the differential capacitance of the double layer in unadsorbed electrolytes, J. Chem. Phys. 22 (11) (1954) 18571866.CrossRefGoogle Scholar
[26] Wang, H., Varghese, J., Pilon, L., Simulation of electric double layer capacitors with mesoporous electrodes: Effects of morphology and electrolyte permittivity, Electrochimica Acta 56 (17) (2011) 61896197.CrossRefGoogle Scholar
[27] Glueckauf, E., Bulk dielectric constant of aqueous electrolyte solutions, Trans. Faraday Soc. 60 (1964) 16371645.CrossRefGoogle Scholar
[28] Ben-Yaakov, D., Andelman, D., Podgornik, R., Dielectric decrement as a source of ion-specific effects, J. Chem. Phys. 134 (7) (2011) 074705.CrossRefGoogle ScholarPubMed
[29] Levy, A., Andelman, D., Orland, H., Dielectric constant of ionic solutions: A field-theory approach, Phys. Rev. Lett. 108 (2012) 227801.CrossRefGoogle ScholarPubMed
[30] Levy, A., Andelman, D., Orland, H., Dipolar Poisson-Boltzmann approach to ionic solutions: A mean field and loop expansion analysis, J. Chem. Phys. 139 (16) (2013) 164909.CrossRefGoogle ScholarPubMed
[31] Li, B., Wen, J., Zhou, S., Mean-field theory and computation of electrostatics with ionic concentration dependent dielectrics, Commun. Math. Sci. 14 (1) (2016) 249271.CrossRefGoogle ScholarPubMed
[32] Bikerman, J., Structure and capacity of electrical double layer, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 33 (220) (1942) 384397.Google Scholar
[33] Hatlo, M., Van Roij, R., Lue, L., The electric double layer at high surface potentials: The influence of excess ion polarizability, EPL (Europhysics Letters) 97 (2) (2012) 28010.CrossRefGoogle Scholar
[34] Nakayama, Y., Andelman, D., Differential capacitance of the electric double layer: The interplay between ion finite size and dielectric decrement, J. Chem. Phys. 142 (4) (2015) 044706.CrossRefGoogle ScholarPubMed
[35] Bonthuis, D. J., Gekle, S., Netz, R. R., Dielectric profile of interfacial water and its effect on double-layer capacitance, Phys. Rev. Lett. 107 (2011) 166102.CrossRefGoogle ScholarPubMed
[36] Bonthuis, D. J., Gekle, S., Netz, R. R., Profile of the static permittivity tensor of water at interfaces: Consequences for capacitance, hydration interaction and ion adsorption, Langmuir 28 (20) (2012) 76797694.CrossRefGoogle Scholar
[37] Bonthuis, D. J., Netz, R. R., Beyond the continuum: How molecular solvent structure affects electrostatics and hydrodynamics at solid-electrolyte interfaces, J. Phys. Chem. B 117 (39) (2013) 1139711413.CrossRefGoogle ScholarPubMed
[38] Fahrenberger, F., Xu, Z., Holm, C., Simulation of electric double layers around charged colloids in aqueous solution of variable permittivity, J. Chem. Phys. 141 (6) (2014) 064902.CrossRefGoogle ScholarPubMed
[39] Netz, R. R., Orland, H., Beyond Poisson-Boltzmann: Fluctuation effects and correlation functions, Eur. Phys. J. E 1 (2000) 203214.CrossRefGoogle Scholar
[40] Netz, R. R., Orland, H., Variational charge renormalization in charged systems, Eur. Phys. J. E 11 (2003) 301311.CrossRefGoogle ScholarPubMed
[41] Wang, Z. G., Fluctuation in electrolyte solutions: The self energy, Phys. Rev. E 81 (2010) 021501.CrossRefGoogle ScholarPubMed
[42] Wang, R., Wang, Z.-G., Effects of image charges on double layer structure and forces, J. Chem. Phys. 139 (2013) 124702.CrossRefGoogle ScholarPubMed
[43] Xu, Z., Ma, M., Liu, P., Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches, Phys. Rev. E 90 (1) (2014) 013307.CrossRefGoogle ScholarPubMed
[44] Xu, Z., Maggs, A., Solving fluctuation-enhanced Poisson-Boltzmann equations, J. Comput. Phys. 275 (2014) 310322.CrossRefGoogle Scholar
[45] Lu, B.-S., Xing, X., Correlation potential of a test ion near a strongly charged plate, Phys. Rev. E 89 (2014) 032305.Google Scholar
[46] Ma, M., Xu, Z., Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media, J. Chem. Phys. 141 (24) (2014) 244903.CrossRefGoogle ScholarPubMed
[47] Wang, R., Wang, Z.-G., On the theoretical description of weakly charged surfaces, J. Chem. Phys. 142 (10) (2015) 104705.CrossRefGoogle ScholarPubMed
[48] Gillespie, D., Valiskó, M., Boda, D., Density functional theory of the electrical double layer: the RFD functional, J. Phys. Condens. Matter 17 (42) (2005) 66096626.CrossRefGoogle Scholar
[49] Jiang, J., Cao, D., Henderson, D., Wu, J., Revisiting density functionals for the primitive model of electric double layers, J. Chem. Phys. 140 (4) (2014) 044714.CrossRefGoogle ScholarPubMed
[50] Butt, H.-J., Graf, K., Kappl, M., Physics and Chemistry of Interfaces, Wiley/VCH, Berlin, 2003.CrossRefGoogle Scholar
[51] Paunovic, M., Schlesinger, M., Fundamentals of Electrochemical Deposition, Vol. 45, John Wiley & Sons, Hoboken, 2006.CrossRefGoogle Scholar
[52] Frydel, D., Mean-field electrostatics beyond the point-charge description, Adv. Chem. Phys. 160 (2016) 209260.Google Scholar
[53] Lin, L., Yang, C., Lu, J., Ying, L., W. E, , A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations, SIAM J. Sci. Comput. 33 (3) (2011) 13291351.CrossRefGoogle Scholar
[54] Lin, L., Yang, C., Meza, J. C., Lu, J., Ying, L., W. E, , Selinv—An algorithm for selected inversion of a sparse symmetric matrix, ACM Trans. Math. Softw. 37 (2011) 40:140:19.CrossRefGoogle Scholar
[55] Grahame, D. C., Differential capacity of mercury in aqueous sodium fluoride solutions. I. effect of concentration at 25°, J. Am. Chem. Soc. 76 (19) (1954) 48194823.CrossRefGoogle Scholar
[56] Onsager, L., Samaras, N. N. T., The surface tension of Debye-Hückel electrolytes, J. Chem. Phys. 2 (1934) 528536.CrossRefGoogle Scholar
[57] Levin, Y., Dos Santos, A. P., Diehl, A., Ions at the air-water interface: an end to a hundred-year-old mystery?, Phys. Rev. Lett. 103 (25) (2009) 257802.CrossRefGoogle ScholarPubMed
[58] Wang, R., Wang, Z.-G., Continuous self-energy of ions at the dielectric interface, Phys. Rev. Lett. 112 (13) (2014) 136101.CrossRefGoogle ScholarPubMed
[59] Jungwirth, P., Tobias, D. J., Specific ion effects at the air/water interface, Chem. Rev. 106 (4) (2006) 12591281.CrossRefGoogle ScholarPubMed
[60] Grahame, D. C., The electrical double layer and the theory of electrocapillarity, Chem. Rev. 32 (1947) 441501.CrossRefGoogle Scholar
10
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@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 sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent 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.

Investigation of Dielectric Decrement and Correlation Effects on Electric Double-Layer Capacitance by Self-Consistent Field Model
Available formats
×

Send article to Dropbox

To send 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 use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Investigation of Dielectric Decrement and Correlation Effects on Electric Double-Layer Capacitance by Self-Consistent Field Model
Available formats
×

Send article to Google Drive

To send 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 use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Investigation of Dielectric Decrement and Correlation Effects on Electric Double-Layer Capacitance by Self-Consistent Field Model
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? *