One-Dimensional Systems: Exact Solution for Nearest-Neighbor Interactions

Santos, Andrés

doi:10.1007/978-3-319-29668-5_5

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…These solutions have been further generalized to binary [59] and multicomponent [50][51][52][53][54] systems. Here, we present a derivation for an M -component system in the grand canonical ensemble, based on ref.…”

Section: Exact Solution Of the 1d Off-lattice Modelmentioning

confidence: 99%

“…Motivated by 1D lattice models of refs. [27,31,32], we map the charging of ultranarrow cylindrical pores onto a 1D multi-component system of hard rods with nearest-neighbour interactions, which has an exact solution [50][51][52][53][54]. In our work, we perform this mapping analytically and derive relations between the chemical potentials of 3D single-file and 1D lattice and off-lattice models, which allows a direct comparison among all models.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Exact Solution Of the 1d Off-lattice Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Verkholyak,

Kuzmak,

Kondrat

2021

Preprint

View full text Add to dashboard Cite

show abstract

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

Verkholyak

Kuzmak

Kondrat

2021

The Journal of Chemical Physics

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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 and water desalination. 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, by changing 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 dependence follows from hard-core interactions and is not captured by the lattice model.

show abstract

One-Dimensional Systems: Exact Solution for Nearest-Neighbor Interactions

Cited by 2 publications

References 15 publications

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

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

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

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