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The one-dimensional Coulomb lattice fluid capacitor
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10.1063/1.4740233
/content/aip/journal/jcp/137/6/10.1063/1.4740233
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/6/10.1063/1.4740233
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Lattice Coulomb fluid model. Dark balls stand for cations and light balls for anions. Boundary charges are at sites −1 and M.

Image of FIG. 2.
FIG. 2.

Dimensionless grand potential as a function of the system size for γ = 1 and μ = 100.

Image of FIG. 3.
FIG. 3.

Dimensionless free enthalpy as a function of the system size for γ = 1 and μ = 100.

Image of FIG. 4.
FIG. 4.

Average potential drop as a function of the imposed charge for γ = 1 and μ = 1 and system size 104.

Image of FIG. 5.
FIG. 5.

Left: Average surface charge as a function of the imposed voltage, for γ = 1 and μ = 1 with system size 104. Right: Average surface charge as a function of the imposed voltage, for γ = 1 and μ = 0.5 with system size 104.

Image of FIG. 6.
FIG. 6.

Difference of the bulk pressure as a function of the parameters γ and μ. Contour line where λ0(Q = 0) = λ0(Q = 0.5) (blue solid line) compared with the approximate transition line (65) (red dashed line).

Image of FIG. 7.
FIG. 7.

Left: Capacitance as a function of the voltage drop for μ = 1: appearance of the peaks as γ increases for a bell shaped capacitance. Right: Capacitance as a function of the voltage drop for μ = 0.03: appearance of the peaks as γ increases for a camel shaped capacitance. The system size is 104.

Image of FIG. 8.
FIG. 8.

Left: Capacitance as a function of the voltage drop for μ = 1 and γ = 1. Right: Capacitance as a function of the voltage drop for μ = 0.03 and γ = 0.3. The system size is 104.

Image of FIG. 9.
FIG. 9.

Capacitance as a function of the voltage drop for γ = 1 and different values of the fugacity. The system size is 104.

Image of FIG. 10.
FIG. 10.

PZC capacitance as a function of μ for different values of γ, for an infinite system.

Image of FIG. 11.
FIG. 11.

Left: Charge density close to the left electrode (located at x = −1) as a function of the position for γ = 1, μ = 1, and Q = 1. Right: Charge density close to the left electrode (located at x = −1) as a function of the position for γ = 1, μ = 1, and Q = 4.25. The system size is 80.

Image of FIG. 12.
FIG. 12.

Left: Exact result for the mean charge density close to the left electrode (located at x = −1) as a function of the position for γ = 1, μ = 1, and Q = 0.5, for different values of the fugacity. Right: Exact result for the mean charge density as a function of the position for γ = 1, μ = 1, and Q = 0.5, for different values of the fugacity. The system size is 80.

Image of FIG. 13.
FIG. 13.

Exact result for the mean charge density as a function of the position for γ = 1 and μ = 100, for different values of the boundary charge. The system size is 80.

Image of FIG. 14.
FIG. 14.

Exact result for the mean charge density as a function of the position for μ = 1000 and Q = 0.5, for an odd number of sites (M = 81).

Image of FIG. 15.
FIG. 15.

Mean charge density ρ0 of the first layer as a function of the surface charge Q for γ = 1 and μ ∈ {3, 10, 100} (the two big arrows indicate the change when μ increases). The system size is 500.

Image of FIG. 16.
FIG. 16.

Left: Theory and simulation for mean charge ⟨Q⟩ versus Δv for γ = 1, μ = 1 on a lattice with M = 128. Right: Theory and simulation for mean voltage difference ⟨Δv⟩ versus Q for γ = 1, μ = 1 on a lattice with M = 1024.

Image of FIG. 17.
FIG. 17.

Theory and simulation in the fixed Q ensemble for the mean charge density ρ versus distance x from the left-hand plate located at x = −1 for γ = 1, μ = 10, Q = −0.5 on a lattice with M = 1024. Note that there is mild over-screening at x = 0.

Image of FIG. 18.
FIG. 18.

Left: Theory and simulation for capacitance c Δv versus Δv in the fixed Δv ensemble for γ = 1, μ = 1 on lattice with M = 128. Right: Theory and simulation for capacitance c Δv versus Δv in the fixed Δv ensemble for γ = 0.3, μ = 0.03 on lattice with M = 128.

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/content/aip/journal/jcp/137/6/10.1063/1.4740233
2012-08-08
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The one-dimensional Coulomb lattice fluid capacitor
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/6/10.1063/1.4740233
10.1063/1.4740233
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