Directing Colloidal Assembly and a Metal-Insulator Transition Using a Quench-Disordered Porous Rod Template

Replica and effective-medium theory methods are employed to elucidate how to massively reconfigure a colloidal assembly to achieve globally homogeneous, strongly clustered, and percolated equilibrium states of high electrical conductivity at low physical volume fractions. A key idea is to employ a quench-disordered, large-mesh rigid-rod network as a templating internal field. By exploiting bulk phase separation frustration and the tunable competing processes of colloid adsorption on the low-dimensional network and fluctuation-driven colloid clustering in the pore spaces, two distinct spatial organizations of greatly enhanced particle contacts can be achieved. As a result, a continuous, but very abrupt, transition from an insulating to metallic-like state can be realized via a small change of either the colloid-template or colloid-colloid attraction strength. The approach is generalizable to more complicated template or colloidal architectures.

Figure 1

(a) From bottom to top, the dimensionless compressibility as a function of $\beta {ϵ}_{T,F}$ for $\beta {ϵ}_{F,F}=0$ (dashed black), 4 (magenta), 4.5 (orange), and 4.75 (blue), respectively, at ${\eta }_T=0.00001$. (b) Corresponding quantity based on varying $\beta {ϵ}_{F,F}$. Solid and long-dashed curves correspond to ${\eta }_T=0.00001$ and ${\eta }_T=0.00008$ (mean pore radius of $\approx 40d_T$), respectively, and bottom to top are for fixed $\beta {ϵ}_{T,F}=1.2$ (magenta), 1.175 (orange), and 1.15 (blue), respectively. The thin dashed black curve corresponds to $\beta {ϵ}_{T,F}=0$.

Figure 2

(a) and (b) Radial distribution functions at $\beta {ϵ}_{F,F}=4.75$ for $\beta {ϵ}_{T,F}=1.10$, 1.14, 1.16, and 1.20 in order of increasing darkness and arrows. (c) and (d) From left to right, the coordination number for $\beta {ϵ}_{F,F}=4.75$ (blue), 4.5 (orange), 4 (magenta), and zero (dashed black). (e) From left to right, the dimensionless conductivity for $\beta {ϵ}_{F,F}=4.75$ (blue), 4.5 (orange), 4 (magenta), and zero (dashed black).

Figure 3

(a) and (b) Radial distribution functions at $\beta {ϵ}_{T,F}=1.15$ for $\beta {ϵ}_{F,F}=2$, 4, 5, and 7 in order of increasing darkness and arrows. (c) From top to bottom and (d) bottom to top on rightmost side, the coordination number for $\beta {ϵ}_{T,F}=1.2$ (magenta), 1.175 (orange), and 1.15 (blue). (e) From left to right, the dimensionless conductivity for $\beta {ϵ}_{T,F}=1.2$ (magenta), 1.175 (orange), and 1.15 (blue).