Modeling the camel-to-bell shape transition of the differential capacitance using mean-field theory and Monte Carlo simulations

Autor(es)

Bossa, V, Guilherme ; Caetano, Daniel L. Z. ^[1] ; de Carvalho, Sidney J. ^[1] ; Bohinc, Klemen ^[2] ; May, Sylvio ^[3]

Afiliação do(s) autor(es)

^[1] Bossa, Guilherme, V, Sao Paulo State Univ UNESP, Dept Phys, Inst Biosci Humanities & Exact Sci, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Ljubljana, Fac Hlth Sci, Poljanska 26a, Ljubljana 1000 - Slovenia

^[3] Bossa, Guilherme, V, North Dakota State Univ, Dept Phys, Fargo, ND 58108 - USA

• Tipo de documento: Artigo Científico
• Fonte: EUROPEAN PHYSICAL JOURNAL E; v. 41, n. 9 SEP 27 2018.
• Citações Web of Science: 4

Resumo

Mean-field electrostatics is used to calculate the differential capacitance of an electric double layer formed at a planar electrode in a symmetric 1:1 electrolyte. Assuming the electrolyte is also ion-size symmetric, we derive analytic expressions for the differential capacitance valid up to fourth order in the surface charge density or surface potential. Our mean-field model accounts exclusively for electrostatic interactions but includes an arbitrary non-ideality in the mixing entropy of the mobile ions. The ensuing criterion for the camel-to-bell shape transition of the differential capacitance is analyzed using commonly used mixing models (one based on a lattice gas and the other based on the Carnahan-Starling equation of state) and compared with Monte Carlo simulations. We observe a reasonable agreement between all our mean-field models and the simulation data for the camel-to-bell shape transition. The absolute value of the differential capacitance for an uncharged (or weakly charged) electrode is, however, not reproduced by our mean-field approaches, not even upon introducing a Stern layer with a thickness equal of the ion radius. We show that, if a Stern layer is introduced, its thickness dependence on the ion size is non-monotonic or, depending on the salt concentration, even inversely proportional. (AU)

• Processo FAPESP: 17/21772-2 - Extensões da Teoria de Poisson-Boltzmann para o estudo da capacitância diferencial de uma dupla camada elétrica
• Beneficiário: Guilherme Volpe Bossa
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 18/01841-2 - Estudo por Simulação Computacional da Interação entre Polieletrólitos e Macromoléculas
• Beneficiário: Sidney Jurado de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Regular