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Electrostatic interactions mediated by polarizable counterions: Weak and strong coupling limits
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10.1063/1.4763986
/content/aip/journal/jcp/137/17/10.1063/1.4763986
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/17/10.1063/1.4763986
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Polarizable counter-ions of excess polarizability α between two charged plates. The solvent in between has a permittivity εw, while the two semi-infinite regions 0 > z > L have permittivity εext. The two surfaces at z = 0, L bear a surface charge of surface charge density σ. R is the radius of the ions, or more precisely of their cavity.

Image of FIG. 2.
FIG. 2.

Pressure P (1)(L) from Eq. (34) as a function of the plate separation L for εext = 0.05, Ξ = 1, and R = 1. The dashed lines are the mean field result, the solid lines include the fluctuations. (Left) For α = −0.1 and large plate separation, the difference is barely distinguishable. (Right) For small plate separation L and various values of the polarizability α. The effect of fluctuations can be quite important for large counterion polarizabilities.

Image of FIG. 3.
FIG. 3.

Counterions density profile within the slab—dependence on the coupling constant Ξ. (Left) Weak coupling density close to the left electrode taking into account the fluctuations around the mean field as a function of the position within the slab (), for R = 0.3, α = −0.3, εext = 0.05, and Ξ = 0.3 (dashed line) or Ξ = 1 (solid line). The mean-field density itself is presented by the dotted line. (Right) Strong coupling density as a function of the position for R = 2, α = −0.01, εext = 0.05, and Ξ = 10 (solid line) or Ξ = 50 (dashed line).

Image of FIG. 4.
FIG. 4.

Counterions density profile within the slab—dependence on the polarizability α. (Left) Weak coupling density close to the left electrode taking into account the fluctuations around the mean field as a function of the position within the slab (), for R = 0.3, εext = 0.05, Ξ = 0.3, and α = −0.3 (solid line), α = −0.1 (dashed line), or α = −10−6 (dotted line). (Inset) Deviation from the mean-field density. (Right) Strong coupling density as a function of the position within the dielectric slab for R = 1, εext = 0.05, Ξ = 10, and α = −0.05 (solid line), α = −0.01 (dashed line), or α = −10−6 (dotted line).

Image of FIG. 5.
FIG. 5.

Strong coupling pressure as a function of the plate separation L. (Left) R = 2, εext = 0.05, and Ξ = 10 for different values of α. (Right) α = −0.01, εext = 0.05, and Ξ = 10 for different values of R.

Image of FIG. 6.
FIG. 6.

Effect of the outer permittivity on the counterion density distribution. (Left) Weak coupling density with α = −0.3, R = 0.3, Ξ = 0.3, and εext = 0.05 (solid line) or εext = 1 (dashed line). (Right) Strong coupling density with α = −0.01, R = 2, Ξ = 10, and εext = 0.05 (solid line) or εext = 1 (dashed line).

Image of FIG. 7.
FIG. 7.

Effect of the outer permittivity on the interaction pressure. (Left) Weak coupling pressure with α = −0.1, R = 1, Ξ = 0.3, and εext = 0.05 (solid line) or εext = 1 (dashed line). (Right) Strong coupling pressure with α = −0.01, R = 2, Ξ = 10, and εext = 0.05 (solid line) or εext = 1 (dashed line).

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/content/aip/journal/jcp/137/17/10.1063/1.4763986
2012-11-06
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Electrostatic interactions mediated by polarizable counterions: Weak and strong coupling limits
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/17/10.1063/1.4763986
10.1063/1.4763986
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