Conductivity of Insulating Diblock Copolymer System Filled with Conductive Particles Having Different Affinities for Dissimilar Copolymer Blocks

Abstract

We investigate the electrical response of the insulating diblock copolymer system (DBC) filled with conductive spherical fillers depending on the affinities of these fillers for copolymer blocks and the interaction between fillers. We demonstrate that the contrast (difference) between the affinities of the fillers for dissimilar copolymer blocks is a decisive factor that determines the distribution of these fillers in the DBC system. The distribution of filler particles, in turn, is found to be directly related to the electrical response of the DBC-particle composite. In particular, increasing the affinity contrast above a certain threshold value results in the insulator-conductor transition. This transition is found to be caused by the preferential localization of the fillers in the microphases of the DBC system having larger affinity for these fillers. The effect of the interaction between fillers is found to be secondary to the described effect of the affinity contrast that dominates in determining the distribution of fillers in the composite. This effect of the inter-particle interactions is shown to be significant only when the affinity contrast and filler volume fraction are sufficiently large.

Effect of the Interplay between Polymer–Filler and Filler–Filler Interactions on the Conductivity of a Filled Diblock Copolymer System

“…Yet another superior feature of the developed approach is its ability to properly describe the effect of the volume excluded by the fillers to copolymers, overlooked in the above previous work. As is demonstrated in our present and previous work in [16,17], this osmotic effect, along with the interaction between fillers, is critical for predicting the localization of fillers in the DBC. In particular, the mentioned excluded volume effect explains the interfacial localization of neutral fillers observed in experiments [1].…”

“…The present work extends the method, previously developed [9,16,17] by the author, over the study of the relative roles of the filler affinity for copolymer blocks and the interaction between fillers in promoting the conductivity of a filled DBC system. Specifically, we focused on the study of the effect of the above two factors on the localization of fillers in the DBC-based composite that assumes cylindrical (hexagonal) morphology.…”

“…Following our previous work in [9,16,17], we describe the compositional structure of the DBC system by a singe order parameter η. η varies between two limiting values 1 and −1 that correspond to the pure polymer phases A and B, respectively. The thermodynamic state of this system is described by the grand potential Ω, which is written as a functional of η, and reduced external fields ϕ A,B = β(µ A,B − w A,B ).…”

“…This effect depends, in particular, on the relative affinity of fillers for dissimilar copolymer blocks and the interaction between fillers. Previously, we have separately studied these two effects on the formation of the conductive filler network in the simplest lamellar morphology of the DBC [ 16 , 17 ]. In the present work, we essentially extend this study by investigating the complicated interplay between the effects caused by the filler–filler and filler–polymer interactions in a filled DBC system.…”

Conductivity of diblock copolymer system filled with conducting nano‐particles: Effect of copolymer morphology

“…In the present section, we extend our previously developed theory 34,35 describing the distribution of fillers in the symmetric DBC over the case of arbitrary DBC compositions. Each DBC is comprised of two chemically uniform blocks containing fN and (1 À f )N of A-and Bmonomers, respectively, N being the polymerization degree.…”