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

Abstract

We investigate the relative roles of the involved interactions and micro-phase morphology in the formation of the conductive filler network in an insulating diblock copolymer (DBC) system. By incorporating the filler immersion energy obtained by means of the phase-field model of the DBC into the Monte Carlo simulation of the filler system, we determined the equilibrium distribution of fillers in the DBC that assumes the lamellar or cylindrical (hexagonal) morphology. Furthermore, we used the resistor network model to calculate the conductivity of the simulated filler system. The obtained results essentially depend on the complicated interplay of the following three factors: (i) Geometry of the DBC micro-phase, in which fillers are preferentially localized; (ii) difference between the affinities of fillers for dissimilar copolymer blocks; (iii) interaction between fillers. The localization of fillers in the cylindrical DBC micro-phase has been found to most effectively promote the conductivity of the composite. The effect of the repulsive and attractive interactions between fillers on the conductivity of the filled DBC has been studied in detail. It is quantitatively demonstrated that this effect has different significance in the cases when the fillers are preferentially localized in the majority and minority micro-phases of the cylindrical DBC morphology.

Keywords: conductivity; diblock copolymers; filler.

Figure 1

Conductivity of the micro-phase-separated asymmetric DBC system ($f=0.45$) as a function of segregation parameter $\lambda$ for selected volume fractions of fillers $\phi$.

Figure 2

Dependence of the conductivity of the micro-phase-separated asymmetric DBC system ($f=0.45$) that assumes the cylindrical morphology for different localizations of fillers in DBC micro-phases. Segregation $\lambda$, volume fraction of fillers $\phi$ and reduced inter-filler interaction energy $\beta U$ are set equal to $0.2$, $0.1$ and $-1.0$, respectively. (a) Conductivity as a function of the filler affinity contrast for dissimilar copolymer blocks $ϵ$. (b–d) Localization of fillers for selected values of $ϵ$: (b) $ϵ$ = −40 mJ/m², (c) $ϵ$ = −4 mJ/m², (d) $ϵ$ = 8 mJ/m². See explanation in the text.

Figure 3

Conductivity of the micro-phase-separated asymmetric DBC system ($f=0.45$) that assumes cylindrical morphology as a function of the filler affinity contrast for dissimilar copolymer blocks $ϵ$ for selected inter-filler interaction energies $\beta U$. Segregation $\lambda$ and volume fraction of fillers $\phi$ are set equal to $0.2$ and $0.15$, respectively. (a) $\beta U=-5.0$. (b) $\beta U=1.0$. (c) $\beta U=5.0$. See explanation in the text.