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Self-organisation of anisometric particles : statistical theory of shape, confinement and external-field effects

By R.H.J. Otten

Abstract

Colloidal particles dispersed in a uid exhibit rich and unusual behaviour, in par- ticular if the particles are strongly anisometric, i.e., highly elongated or very at. Fluid dispersions containing anisometric colloids are, apart from being interesting in their own right, relevant to the industrial production and processing of nanocompos- ites, high-performance ??bers, gels and so on. Their unusual properties result from strongly anisotropic interactions that, amongst others, give rise to the buildup of temporal, system-spanning networks of particles as well as various liquid-crystalline states even at quite low concentrations below one volume per cent. By invoking microscopic and mesoscopic statistical theories, we investigate in this thesis aspects of both network formation and liquid crystallinity as they present themselves on a macroscopic scale. We ??nd that both are strongly a??ected by the particle shape. Our work on network formation focuses on the critical concentration where the in??nite network forms, and the properties of the clusters at concentrations just below and above this. We investigate how particle shape, variation in the dimensions, externally applied ??elds, and so on impact upon them. Our calculations, based on so-called connectedness-percolation theory, are inspired by observations of strong variations in the emergence of electrical conduction in composites containing carbon nanotubes and graphene. We make plausible that this is caused by the formulation of the nanocomposite on the one hand and the processing conditions on the other. Our predictions agree favourably with experimental data on polymeric composites containing graphene of known size distribution, and con??rm that the presence of very few, very elongated or very at particles dictate the critical loading. Our calculations also predict that at higher particle concentrations, the particle network breaks down due to a competition with a transition to the uniaxial, ne- matic liquid-crystalline phase. This phase presents itself initially in the form of droplets that eventually coalesce to become a macroscopic uid. Properties of both we investigate at the level of Frank-Oseen-Rapini-Papoular theory to describe the competition between elastic and surfaces forces. These determine the interfacial shape and spatial structure of the uniaxial symmetry axis. We predict that under conditions of isotropic-nematic phase co-existence, the capillary rise of a macroscopic nematic uid up a vertical solid wall produces a non-monotonic isotropic-nematic uid interface. Our theory allows us to extract from capillary-rise experiments on dispersions of plate-like clay particles estimates for the surface tension and the an- choring strength of the nematic symmetry axis to the interface. Observations on droplets of the same (gibbsite) clay particles, which have a nega- tive diamagnetic susceptibility and prefer perpendicular anchoring of the symmetry axis to the isotropic-nematic uid interface, have shown that their internal structure and shape depend strongly on their size and on the strength of an externally applied magnetic ??eld that aligns them. Our calculations show that the transitions between spherical and elongated droplets, and between di??erent kinds of internal organisation of the symmetry axis, are sharp, i.e., resemble phase transitions. By comparing our theory to shape and internal-structure measurements, we have been able to extract values for an elastic constant, the surface tension and anchoring strength. We ??nd that whether or not the droplets elongate under the presence of a magnetic ??eld, depends only on the ratio of the anchoring strength and surface tension

Publisher: Technische Universiteit Eindhoven
Year: 2011
DOI identifier: 10.6100/ir716778
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Provided by: NARCIS
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