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Conductance of Polyelectrolyte Solutions: A One—Dimensional Model
Author(s) -
Lifson Shneior
Publication year - 1973
Publication title -
israel journal of chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.908
H-Index - 54
eISSN - 1869-5868
pISSN - 0021-2148
DOI - 10.1002/ijch.197300023
Subject(s) - polyelectrolyte , chemistry , conductance , counterion , square (algebra) , limit (mathematics) , charge (physics) , chemical physics , superposition principle , charge density , electrostatics , statistical physics , condensed matter physics , ion , physics , quantum mechanics , polymer , mathematical analysis , mathematics , organic chemistry , geometry
An exact derivation of the conductance of parallel double‐layers as a one‐dimensional model of polyelectrolyte solutions is presented. The conductance tends to a finite limit, inversely proportional to the square of the (one‐dimensional) polyelectrolyte concentration, as the polyelectrolyte charge density increases indefinitely. In other words, the conductance tends to zero with the square of the inverse polyelectrolyte concentration in a way independent of the polyelectrolyte charge density. Approaching these limits, the ionic mobility of the counterions predominates over that of the fixed charges. The assumption of superposition of the external and internal electrostatic fields is shown to be inexact even at the limit of very small external fields.