A simple model for charge storage in a nanotube

Schmickler, Wolfgang

doi:10.1016/j.electacta.2015.04.177

Cited by 17 publications

(21 citation statements)

References 13 publications

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“…Such quasi-1D systems have been studied by mapping them on the corresponding models of statistical mechanics [23][24][25][26][27][28][29][30][31]. The simplest appropriate model is a classical two-state anti-ferromagnetic Ising model with nearest neighbor interactions in external field [28].…”

Section: Introductionmentioning

confidence: 99%

Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior

Dudka

Kondrat

Bénichou

et al. 2019

The Journal of Chemical Physics

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South Kensington Campus, London SW7 2AZ, United Kingdom ‡ 7 Interdisciplinary Scientific Center J-V Poncelet, UMI CNRS 2615, 11 Bol. Vlassievsky per., Moscow, Russia §We develop a theory of charge storage in ultra-narrow slit-like pores of nanostructured electrodes. Our analysis is based on the Blume-Capel model in external field, which we solve analytically on a Bethe lattice. The obtained solutions allow us to explore the complete phase diagram of confined ionic liquids in terms of the key parameters characterising the system, such as pore ionophilicity, interionic interaction energy and voltage. The phase diagram includes the lines of first and second-order, direct and re-entrant, phase transitions, which are manifested by singularities in the corresponding capacitance-voltage plots. To test our predictions experimentally requires mono-disperse, conducting, ultra-narrow slit pores, permitting only one layer of ions, and thick pore walls, preventing interionic interactions across the pore walls. However, some qualitative features, which distinguish the behavior of ionophilic and arXiv:1909.13089v1 [cond-mat.soft] 28 Sep 2019 ionophobic pores, and its underlying physics, may emerge in future experimental studies of more complex electrode structures.

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Section: Introductionmentioning

confidence: 99%

Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior

Dudka

Kondrat

Bénichou

et al. 2019

The Journal of Chemical Physics

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“…In a recent communication one of us [19] has considered the capacity of a nanotube permeable to only one kind of ion. In this context, he also considered the phonon spectrum of the vibrations along the axis of the tube.…”

Section: Phonon Spectrummentioning

confidence: 99%

Interactions of anions and cations in carbon nanotubes

2016

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We consider the insertion of alkali-halide ion pairs into a narrow (5,5) carbon nanotube. In all cases considered, the insertion of a dimer is only slightly exothermic. While the image charge induced on the surface of the tube favors insertion, it simultaneously weakens the Coulomb attraction between the two ions. In addition, the anion experiences a sizable Pauli repulsion. For a one dimensional chain of NaCl embedded in the tube the most favorable position for the anion is at the center, and for the cation near the wall. The phonon spectrum of such chains shows both an acoustic and an optical branch.

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“…While such pores are kinetically advantageous over single-file pores, the exact solutions of two-dimensional models are much more challenging to obtain and approximations are necessary [25,[34][35][36][37]. Due to the possibility of analytical solutions and lower computational costs of simulations, therefore, one-dimensional models have been a convenient testbed for gaining new physical insights into the supercapacitor charging [27,31,32,[38][39][40][41][42][43][44]. With some exceptions [39,45], however, 1D analytical approaches have been limited to lattice models [27,31,32,44,[46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Capacitive energy storage in single-file pores: Exactly-solvable models and simulations

Verkholyak,

Kuzmak,

Kondrat

2021

Preprint

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Understanding charge storage in low-dimensional electrodes is crucial for developing novel ecologically friendly devices for capacitive energy storage and conversion, water desalination, etc. Exactly-solvable models allow in-depth analyses and essential physical insights into the charging mechanisms. So far, however, such analytical approaches have been mainly limited to lattice models. Herein, we develop a versatile, exactly-solvable, one-dimensional off-lattice model for charging single-file pores.Unlike the lattice model, this model shows an excellent quantitative agreement with three-dimensional Monte Carlo simulations. With analytical calculations and simulations, we show that the differential capacitance can be bell-shaped (one peak), camel-shaped (two peaks), or have four peaks. Transformations between these capacitance shapes can be induced by changing pore ionophilicity, cation-anion size asymmetry, or by adding solvent. We find that the camel-shaped capacitance, characteristic of dilute electrolytes, appears for strongly ionophilic pores with high ion densities, which we relate to charging mechanisms specific to narrow pores. We also derive a large-voltage asymptotic expression for the capacitance, showing that the capacitance decays to zero as the inverse square of the voltage, C ∼ u −2 . This

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A simple model for charge storage in a nanotube

Cited by 17 publications

References 13 publications

Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior

Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior

Interactions of anions and cations in carbon nanotubes

Capacitive energy storage in single-file pores: Exactly-solvable models and simulations

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