The one-dimensional Coulomb lattice fluid capacitor.
The one-dimensional Coulomb lattice fluid in a capacitor configuration is studied. The model is formally exactly soluble via a transfer operator method within a field theoretic representation of the model. The only interactions present in the model are the one-dimensional Coulomb interaction between cations and anions and the steric interaction imposed by restricting the maximal occupancy at any lattice site to one particle. Despite the simplicity of the model, a wide range of intriguing physical phenomena arise, some of which are strongly reminiscent of those seen in experiments and numerical simulations of three-dimensional ionic liquid based capacitors. Notably, we find regimes where over-screening and density oscillations are seen near the capacitor plates. The capacitance is also shown to exhibit strong oscillations as a function of applied voltage. It is also shown that the corresponding mean-field theory misses most of these effects. The analytical results are confirmed by extensive numerical simulations.
Laboratoire de Physique Théorique (IRSAMC), Université de Toulouse, UPS and CNRS, F-31062 Toulouse, France.
Vincent
V
Démery
David S
DS
Dean
Thomas C
TC
Hammant
Ronald R
RR
Horgan
Rudolf
R
Podgornik
D000838:Anions / Q000737:chemistry*; D002412:Cations / Q000737:chemistry*; D003198:Computer Simulation; D052578:Ionic Liquids / Q000737:chemistry*; D013816:Thermodynamics
D000838:Anions; D002412:Cations; D052578:Ionic Liquids