Theory of ionic conductivity with morphological control in polymers.

Area of Science:

• Materials Science
• Physical Chemistry
• Polymer Science

Background:

• Ionic conductivity in polymers is crucial for applications like batteries and sensors.
• Understanding ion transport mechanisms, such as permeation and hopping, is essential for material design.

Purpose of the Study:

• To present a general theory for ionic conductivity in polymeric materials with percolated ionic pathways.
• To derive closed-form formulas for ionic conductivity based on key physical parameters.

Main Methods:

• Developed a theoretical framework identifying two critical length scales: inter-path permeation distance (ξ) and 1D hopping path length (mλ).
• Derived formulas relating ionic conductivity to ion unbinding energy (U) and the partition ratio (ξ/mλ).

Main Results:

• The theory provides design strategies to significantly enhance ionic conductivity in single-ion conductors.
• Derived corrections to the Arrhenius law for cases with large ion dissociation energy barriers.
• Predicted dependence of ionic conductivity on unbinding time aligns with experimental and simulation data.

Conclusions:

• The presented theory offers a general framework applicable to concurrent permeation and hopping conduction systems.
• The findings facilitate the rational design of advanced polymeric electrolytes with improved ionic conductivity.