Floating nematic phase in colloidal platelet-sphere mixtures

The analysis of the effect of gravity on colloidal dispersions dates back to Perrin1 and is used in computer simulations2,3 and experiment with e.g. depolarized light scattering4,5,6 to obtain the osmotic equation of state over a wide range of densities from a single sample. Added depletion agents, e.g. non-adsorbing polymers7, modify the effective interactions between particles of the primary component, but are typically gravity-neutral. However, in colloidal mixtures all components are subject to gravity, and hence compete to minimize their gravitational energy. The strength of gravity can be quantified by the gravitational lengths ξi = kBT/(mig), where kB is the Boltzmann constant, T is absolute temperature, mi is the buoyant mass of species i (obtained by subtracting the solvent background), and g is the acceleration due to gravity. Colloidal liquid crystals8,9,10,11 constitute ideal candidates for the investigation of gravitational effects due to their rich phase behaviour. We used electro-sterically stabilized mixtures of gibbsite platelets and alumina-coated silica spheres (Klebosol 30CAL25 and 30CAL50). Particle dimensions were obtained from transmission electron microscopy and atomic force microscopy (AFM). The average bare diameter of the spheres was σS = 30 nm and 74 nm for Klebosol 30CAL25 and 30CAL50, respectively, with polydispersity of ca. 15% and 21% (3 volume % of the particles are below 60 nm in the case of 30CAL50). The average diameter of the platelets was 186 nm with 29% polydispersity. AFM measurements of a diluted platelet sample deposited on a mica substrate gave a bare platelet thickness of d ≈ 5 nm. As such results can easily be affected by differences in chemistry between substrate and platelets, we rather treat d as an adjustable parameter, with d = 3.7 nm giving the best agreement of the isotropic-nematic (IN) coexistence densities obtained in theory12 and experiment13. The value of d enters the conversion from packing fraction, ηi, to number density, ρi, via ρi = ηi/vi, where vi is the bare particle volume of species i = S (spheres), P (platelets). Both species were purified by dialysis against deionised water containing 5 mM NaCl in order to screen electrostatic interactions. Both species had a stabilizer (Solsperse 41000) adsorbed onto them. As a result, small-angle neutron scattering showed effective particle diameters that were larger by ≈ 10 nm than the bare sizes, hence . The sample preparation follows that in a closely related system13. The (bare) packing fraction of spheres was ηS = 0.05 throughout, and we considered (bare) platelet packing fractions ηP = 0.01, 0.025 and 0.05. The gravitational lengths were ξP = 2.92 mm for the platelets, ξS = 22.4 mm for the small spheres, and ξS = 1.49 mm for the large spheres. These were obtained by considering the mass density for silica 2.30 g/cm3, for gibbsite 2.42 g/cm3, and for the aqueous solvent 1.00 g/cm3. The density of the adsorbed layer of stabilizer is 1.02 g/cm3. As the latter value is very close to the solvent density, we neglected its effect on the buoyant masses and hence the gravitational lengths of both species. Experiments were carried out at room temperature, T = 293 K. The value of the temperature is irrelevant for the slope of the sedimentation path, as this depends only the ratio of the gravitational lengths, such that the temperature dependence of the ξi cancels out.