Transport in one-dimensional Coulomb gases: From ion channels to nanopores

Physica A: Statistical Mechanics and its Applications

Volumn 359, Issue 1-4, 2006, Pages 129-161

  Kamenev, A ^a   Zhang, J ^b   Larkin, A I ^a,b   Shklovskii, B I ^a,b  

^a University of Minnesota   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Activation barrier; Charge transport; Ion channel; Nanopore; One dimensional Coulomb gas

Indexed keywords

CHARGE TRANSFER; ELECTROSTATICS; LIPIDS; PERMITTIVITY; SILICON;

ACTIVATION BARRIER; ION CHANNELING; ONE-DIMENSIONAL COULOMB GAS;

STATISTICAL MECHANICS;

EID: 27344435607     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2005.05.097     Document Type: Article

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27. To carry out this averaging one parameterizes the ions coordinates as x i (t ) = σ i (q (t ) - 1 / 2 ) / (2 n ) + δ x i (t ), where the constraint (84) is reduced to ∑ i σ i δ x i (t ) = 0. The second term on the r.h.s. of Eq. (87) may be written now as: ∂ U ∂q| δ x i | = ∂U ∂q | x i | + ∑ i ∂ U ∂ x i q ∂ x i ∂ q | δ x i | = 1 2 n ∑ i σ i ∂ U ∂ x i q, where we employed that ∂ U / ∂ q | |xi| = 0. Averaging over the equilibrium distribution function Z - 1 exp | - U (| δ x i |, q (t ) ) / (k B T ) |, one finds: (2 n ) - 1 〈 ∑ i σ i ∂ U / ∂ x i | q 〉 = 〈 ∂ U / ∂ q| |δ xi| 〉 = ∂ F L * (q ) / ∂ q.
28. Another possible application of our theory is the transport in single-crystal silicon nanowires [7] suspended in air between two conductors. They have a ∼ 1 nm and lengths up to several microns. In this case, κ 1 = 11 and κ 2 = 1 so that the ratio κ 1 / κ 2 is relatively large. We will address this application in a future publication.