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Updated: Mar 30, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
Published on: May 18, 2021
Screening like charges in one-dimensional Coulomb systems: Exact results
Gabriel Téllez1, Emmanuel Trizac2
1Departamento de Física, Universidad de los Andes, Bogotá, Colombia.
Abstract:
The possibility that like charges can attract each other under the mediation of mobile counterions is by now well documented experimentally, numerically, and analytically. Yet, obtaining exact results is in general impossible, or restricted to some limiting cases. We work out here in detail a one-dimensional model that retains the essence of the phenomena present in higher-dimensional systems. The partition function is obtained explicitly, from which a wealth of relevant quantities follow, such as the effective force between the charges or the counterion profile in their vicinity. Isobaric and canonical ensembles are distinguished. The case of two equal charges screened by an arbitrary number N of counterions is first studied, before the more general asymmetric situation is addressed. It is shown that the parity of N plays a key role in the long-range physics.
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