Connectedness percolation in monodisperse rod systems: clustering effects

Continuum percolation in colloidal dispersions of hard nanorods in external axial and planar fields

We present a theoretical study on continuum percolation of rod-like colloidal particles in the presence of axial and planar quadrupole fields. Our work is based on a self-consistent numerical treatment of the connectedness Ornstein-Zernike equation, in conjunction with the Onsager equation that describes the orientational distribution function of particles interacting via a hard-core repulsive potential. Our results show that axial and planar quadrupole fields both in principle increase the percolation threshold. By how much depends on a combination of the field strength, the concentration, the aspect ratio of the particles, and percolation criterion. We find that the percolated state can form and break down multiple times with increasing concentration, i.e., it exhibits re-entrance behaviour. Finally, we show that planar fields may induce a high degree of triaxiality in the shape of particle clusters that in actual materials may give rise to highly anisotropic conductivity properties.

Percolation of rigid fractal carbon black aggregates

We examine network formation and percolation of carbon black by means of Monte Carlo simulations and experiments. In the simulation, we model carbon black by rigid aggregates of impenetrable spheres, which we obtain by diffusion-limited aggregation. To determine the input parameters for the simulation, we experimentally characterize the micro-structure and size distribution of carbon black aggregates. We then simulate suspensions of aggregates and determine the percolation threshold as a function of the aggregate size distribution. We observe a quasi-universal relation between the percolation threshold and a weighted average radius of gyration of the aggregate ensemble. Higher order moments of the size distribution do not have an effect on the percolation threshold. We conclude further that the concentration of large carbon black aggregates has a stronger influence on the percolation threshold than the concentration of small aggregates. In the experiment, we disperse the carbon black in a polymer matrix and measure the conductivity of the composite. We successfully test the hypotheses drawn from simulation by comparing composites prepared with the same type of carbon black before and after ball milling, i.e., on changing only the distribution of aggregate sizes in the composites.

Percolation probability in a system of cylindrical particles

A broad variety of materials, ranging from composites and heat transfer nano-fluids to electrochemical energy storage electrodes, widely employ cylindrical particles of various aspect ratios, such as carbon nanotubes. These particles are generally excellent conductors of heat and electricity and when dispersed in a continuous medium influence dramatically the transport properties of the heterogeneous material by forming a percolating network. Numerous theories exist to predict key parameters such as particle concentration at the percolation threshold and transport properties at concentrations beyond the threshold. The microstructure formed by connecting particles in the material is an important determinant toward such parameters but often requires complex numerical models to resolve. In this paper, we present an analytical, probabilistic model capturing the microstructure of a system of randomly positioned, soft-core, cylindrical particles with a finite aspect ratio, valid at arbitrary particle concentration. Our analytical framework allows for the calculation of the particle contact number distribution and percolation probability of the particle system. We show that our analytical model is more accurate than excluded volume theory for predicting the percolation threshold for spherocylinders of finite aspect ratios, and agrees well with the corresponding numerical results. Our theory describes the percolating network topology above the percolation threshold and can serve as the foundation for analytical composition-structure-property relationships for heterogeneous materials with conducting cylindrical particles.

Graphene liquid crystal retarded percolation for new high-k materials

Graphene flakes with giant shape anisotropy are extensively used to establish connectedness electrical percolation in various heterogeneous systems. However, the percolation behaviour of graphene flakes has been recently predicted to be far more complicated than generally anticipated on the basis of excluded volume arguments. Here we confirm experimentally that graphene flakes self-assemble into nematic liquid crystals below the onset of percolation. The competition of percolation and liquid crystal transition provides a new route towards high-k materials. Indeed, near-percolated liquid-crystalline graphene-based composites display unprecedented dielectric properties with a dielectric constant improved by 260-fold increase as compared with the polymer matrix, while maintaining the loss tangent as low as 0.4. This performance is shown to depend on the structure of monodomains of graphene liquid-crystalline phases. Insights into how the liquid crystal phase transition interferes with percolation transition and thus alters the dielectric constant are discussed.

It is commonly believed that graphene flakes form electrical percolation networks at low concentration, and thus can be used as conductive materials. Here, Yuan et al. show in graphene polymer composites that the transition to liquid crystals hinders the formation of percolated networks, resulting in high-k materials.

Rheology of polymer carbon nanotubes composites

In this review paper the rheology of polymer nanocomposites with dispersed carbon nanotubes is presented. The major factors controlling the rheology of these nanocomposites are the overall concentration of the nanotubes and their state of dispersion. Percolation of anisotropic nanotubes and the transition from isotropic to nematic structures bound the range of concentrations over which the rheological properties of these nanocomposites is dominated by the meso-scale structure and dispersion and are of significance to the processing of nanotube based polymer nanocomposites. The percolation threshold and the concentration for the isotropic to nematic transition are strong functions of the inverse of the effective aspect ratio of the dispersed nanotubes and therefore restrict the range of concentrations over which such nanocomposites can be deployed. In this review we briefly describe the rheology in the dilute regime, where especially for the case of polymer nanocomposites the rheology is dominated by that of the polymer. Subsequently, the percolation phenomenon and rheological significances are presented. Finally, both linear and non-linear rheologies of semi-dilute dispersions with random orientation of nanotubes are discussed in detail. Where possible, the rheological responses are contextualized through the underlying structure of the nanocomposites and interplay of different forces.