Orientation dependent Stokes drag in a colloidal liquid crystal

Abstract

Stokes drag on the (sub)micrometre scale plays a key role in phenomena ranging from Brownian motion to the rheology of particulate suspensions. We report the first measurement of the direction dependent Stokes drag in a nematic liquid crystal of colloidal rods, where the viscous forces are of equal importance to the elastic forces. By tracking a sedimenting sphere with combined fluorescence confocal microscopy and polarization microscopy we find that the Stokes drag for motion along the director is two times larger than for motion perpendicular to the director. This brings the unique viscoelastic properties of a colloidal liquid crystal into focus.The Stokes drag force F s ¼ 6phav, experienced by a sphere with radius a moving at velocity v in a viscous medium with viscosity h, plays an important role in phenomena such as Brownian motion 1 and hydrodynamic interactions between moving particles.2 In anisotropic media like liquid crystals, theory predicts a Stokes drag which depends on the direction of motion relative to the director.3,4 This has been confirmed experimentally for thermotropic nematic liquid crystals, from diffusion coefficients of tracer droplets determined by video microscopy 5 and optical trapping of tracer spheres.6 Here we report the first measurement of the orientation dependent Stokes drag in a colloidal nematic liquid crystal. We achieve this by studying a sedimenting fluorescent glass bead with simultaneous fluorescence confocal microscopy and polarization microscopy. This application of the falling sphere method 7 on the micrometre scale enables the measurement of local Stokes drag as a function of director orientation.Laser scanning confocal microscopy, with its high contrast and the elimination of out-of-focus light by the use of a pinhole, enables accurate tracking of the tracer sphere position.8 At the same time the orientation of the local director field is visualized by polarization microscopy, combined with the laser scanning confocal microscope in a single setup [see Fig 1(a)]. A Nikon C1 confocal scanhead was mounted on a Nikon Eclipse E400 polarization microscope, with the focal plane along gravity. Two light sources were used: the white light of the polarization microscope and the 488 nm laser of the confocal unit. The light coming out of the sample is transported through an optical fibre to the three confocal detector channels. The complete detector unit consists of two dichroic mirrors and three sets of high and low band pass filters, which guide the light to one of three photo multiplier tubes. The green light confocal detector channel (wavelengths 515-530 nm) was used for tracking of the fluorescent tracer sphere. The blue (wavelengths 435-450 nm) and red (wavelengths 605-675 nm) light confocal detector channels were used to determine the director orientation of the nematic phase from the optical path difference (OPD) of the transmitted polarized light. The OPD of a birefringent nematic phase is given by Dnd with Dn the birefringence of the nematic phase and d the sample pat...

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“…It was found that the ratio between the viscosities becomes much smaller in this case, and the defect structure changes, e.g. from a Saturn ring to a dipole [5,6].…”

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