# Conductivity of Filled Diblock Copolymer Systems: Identifying the Main Influencing Factors

## TL;DR

This paper identifies key factors influencing the conductivity of composites made from diblock copolymers and conductive particles using a multi-scale theoretical approach.

## Contribution

The study introduces a multi-scale theoretical framework combining phase-field, Monte-Carlo, and resistor network models to analyze conductivity in DBC composites.

## Key findings

- Filler affinities for copolymer blocks significantly affect composite conductivity.
- The order-disorder transition in symmetric DBC causes a conductor-insulator transition in the filler network.
- The order-order transition in asymmetric DBC leads to a spike in composite conductivity.

## Abstract

By developing and making use of the multi-scale theoretical approach, we identify the main factors that affect the conductivity of a composite composed of a diblock copolymer (DBC) system and conductive particles. This approach relies on the consistent phase-field model of DBC, Monte-Carlo simulations of the filler localization in DBC, and the resistor network model that mimics the conductive filler network formed in DBC. Based on the described approach, we thoroughly explore the relation among the morphological state of the microphase-separated DBC, localization of fillers in DBC, and the electrical response of the composite. Good agreement with experimental results confirms the accuracy of our theoretical predictions regarding the localization of fillers in the DBC microphases. The main factors affecting the composite conductivity are found to be: (i) affinities of fillers for copolymer blocks; (ii) degree of the segregation of a host DBC system, driven by external stimuli; (iii) geometry of the microphases formed in the microphase-separated DBC; and (iv) interactions between fillers. The conductor-insulator transition in the filler network is found to be caused by the order-disorder transition in the symmetric DBC. The order-order transition between the ordered lamellae and cylindrical microphases of asymmetric DBC causes a spike in the composite conductivity.