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Understanding and controlling the director field configuration, shape, andorientation in nematic and cholesteric liquid crystals is of fundamentalimportance in several branches of science. Liquid crystalline droplets, alsoknown as tactoids, which spontaneously form by nucleation and growth within thebiphasic region of the phase diagram where isotropic and nematic phasescoexist, challenge our current understanding of liquid crystals underconfinement, due to the influence of anisotropic surface boundaries atvanishingly small interfacial tension and are mostly studied under quiescent,quasi-equilibrium conditions. Here, we show that different classes of amyloidfibril nematic and cholesteric tactoids undergo out-of-equilibrium order-ordertransitions by flow-induced deformations of their shape. The tactoids alignunder extensional flow and undergo extreme deformation into highly elongatedoblate shapes, allowing the cholesteric pitch to decrease as an inverse powerlaw of the tactoids aspect ratio. Energy functional theory and experimentalmeasurements are combined to rationalize the critical elongation ratio abovewhich the director-field configuration of tactoids transforms from bipolar anduniaxial cholesteric to homogenous and to debate on the thermodynamic nature ofthese transitions. Our findings suggest new opportunities in designingself-assembled liquid crystalline materials where structural and dynamicalproperties may be tuned by non-equilibrium phase transitions.

Flow-induced order-order transitions in amyloid fibril liquid crystalline tactoids