Depletion-Induced Percolation in Networks of Nanorods

Abstract

Above a certain density threshold, suspensions of rodlike colloidal particles form system-spanning networks. Using Monte Carlo simulations, we investigate how the depletion forces caused by spherical particles affect these networks in isotropic suspensions of rods. Although the depletion forces are strongly anisotropic and favor alignment of the rods, the percolation threshold of the rods decreases significantly. The relative size of the effect increases with the aspect ratio of the rods. The structural changes induced in the suspension by the depletant are characterized in detail and the system is compared to an ideal fluid of freely interpenetrable rods. DOI: 10.1103/PhysRevLett.98.108303 PACS numbers: 82.70.Dd, 61.20.Ja, 64.60.Ak Networks of electrically conducting carbon nanotubes (CNTs) have important applications in the development of lightweight conducting composites and films [1][2][3][4][5]. At equilibrium, colloidal suspensions of CNTs contain clusters with a distribution of sizes. Contiguous conducting paths first appear on a macroscopic scale when the CNT density crosses the percolation threshold, at which the average cluster size diverges. The sample's conductivity rises sharply by several orders of magnitude at this point [1][2][3][4][5]. The large aspect ratio of CNTs means that, for a disordered distribution of positions and orientations, a single particle provides connectivity over a longer distance than several more spherical particles with the same total volume. Hence, an insulating matrix can be loaded with a smaller volume fraction of conducting filler, leading to a lighter material.The percolation threshold of the CNTs depends both on their aspect ratio, and on the interactions between them. Recent studies show that the addition of surfactant to a suspension of CNT bundles (CNTBs) substantially lowers the percolation threshold [6]. At sufficiently high concentrations, the surfactant self-assembles into micelles, which induce depletion attraction between the bundles [7]. Since the attraction is weak, percolation is reversible and the system remains at thermodynamic equilibrium, in contrast to strongly interacting particles, which may form structurally arrested gels [8].The depletion forces arise from competition between the translational and orientational entropy of the CNTBs on the one hand, and the translational entropy of the micelles on the other. If two bundles approach closely, the volume available to micelles increases, inducing an effective attraction between bundles. The effect is highly anisotropic, since the volume excluded to the depletant depends on the relative orientations of the bundles [9,10]. The excluded volume is minimized in parallel arrangements of neighboring rods, but alignment also reduces the spatial extent of a cluster, and should therefore suppress rather than enhance the formation of percolating networks [11]. Even in systems of spheres, it is possible for attraction to raise the percolation threshold [12]. Nevertheless, recent analytic work on mixtures of ro...

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