Isotropic–nematic phase separation and demixing in mixtures of spherical nanoparticles with length‐polydisperse nanorods
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An extension of Onsager theory is developed to simulate isotropic-nematic phase separation in a mixture of spheres with length-polydisperse system of rods. This work is motivated by recent experimental data on nanorod liquid crystals. Prior theoretical investigations indicate that both polydispersity and the presence of spheres should increase the biphasic-nematic phase transition, that is, the nematic cloud point. Results indicate that the phase diagrams undergo drastic changes depending upon both particle geometry and rod length polydispersity. The key geometric factor is the ratio between the sphere diameter and the rod diameter. In general, length fractionation is enhanced by the addition of spheres, which may be experimentally advantageous for separating short nanorods from a polydisperse population. Simulation results also indicate that the nematic cloud and shadow curves may cross one another because of the scarcity of spheres in the shadow phase. In general, these results do indicate that the nematic cloud point increases as a function of sphere loading; however, in certain areas of phase space, this relationship is nonmonotonic such that the nematic cloud point may actually decrease with the addition of spheres. This work has application to a wide range of nanoparticle systems, including mixtures of spherical nanoparticles with nanorods or nanotubes. Additionally, a number of nonspherical particles and structures may behave as spheres, including crumpled graphene and tightly coiled polymers. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012 Although liquid-crystalline phase formation has been observed for rod-like polymers for many years, anisotropic nanomaterials are driving novel developments in the theoretical descriptions of these systems. This work addresses the important issue of the addition of spherical nanoparticles to length-polydisperse systems of nanorods. A new formulation of Onsager theory has been developed for mixtures of length-polydisperse rods and spheres. The effects of nanorod and nanoparticle geometry on phase diagram shape are investigated. Copyright © 2011 Wiley Periodicals, Inc.
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