Open AccessTheory of Ionic Conductivity with Morphological Control in Polymers
Author(s) -
Murugappan Muthukumar
Publication year - 2021
Publication title -
acs macro letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.966
H-Index - 92
ISSN - 2161-1653
DOI - 10.1021/acsmacrolett.1c00245
Subject(s) - ionic conductivity , ionic bonding , conductivity , thermal conduction , arrhenius equation , materials science , permeation , ion , electrical conductor , chemical physics , activation energy , conductive polymer , polymer , thermodynamics , membrane , chemistry , physics , electrode , composite material , organic chemistry , electrolyte , biochemistry
We present a general theory of ionic conductivity in polymeric materials consisting of percolated ionic pathways. Identifying two key length scales corresponding to inter-path permeation distance ξ and one-dimensional hopping conduction path length mλ , we have derived closed-form formulas in terms of the energy U required to unbind a conductive ion from its bound state and the partition ratio ξ/mλ between the three-dimensional permeation and one-dimensional hopping pathways. The results provide design strategies to significantly enhance ionic conductivity in single-ion conductors. For large barriers to dissociate an ion, corrections to the Arrhenius law are presented. The predicted dependence of ionic conductivity on the unbinding time is in agreement with results in the literature based on simulations and experiments. This theory is generally applicable to conductive systems where the two mechanisms of permeation and hopping occur concurrently.