Layered mesophases, such as smectic and cholesteric liquid crystals or lyotropic lamellar phases are fascinating materials with a complex and unique variety of mechanical properties. These properties depend crucially on the presence of defects in the lamellar ordering, which are usually delicate to control and characterize. We have invented a new system, in which the defects are stabilized in a controlled fashion, allowing the number of defects to be controlled and their properties to be precisely measured and described. The system we study on both theoretical and experimental levels consists in a cholesteric liquid crystal doped with colloidal particles. When inclusions of size exceeding the cholesteric pitch are dispersed in a well-aligned cholesteric sample, a long-lived network of linear defects is obtained, with colloidal inclusions located at the nodes of the network. The presence of the defect network transforms the cholesteric liquid into a new type of material exhibiting gel-like rheological properties (see figure). The size of the pitch is of the order of a few microns and allows a direct characterization of the properties of the defect network in well-aligned thin samples using light microscopy and a subsequent comparison with the rheological properties probed in bulk samples.
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The study of the coarsening of the defects enables us to understand the mechanisms for the formation and stabilization of the network. For a pure cholesteric sample, the dense network of defects that emerges after a temperature quench coarsens quickly with time: after two minutes no defects are left in the sample, which thus achieves a lowest energy state. The mechanisms for this coarsening are the disconnection of a streak from a node and the subsequent shrinking of this streak with a constant velocity. Dramatically different behavior is observed in the presence of colloidal inclusions. The early stages of the coarsening are identical as in the case of as pure cholesteric but, after about one minute, there is a considerably slowing down of the coarsening and subsequently, a network with a characteristic mesh size smaller than 100 microns persists during several hours. The stabilization occurs due to high energy barriers for disconnection from nodes with inclusions. The energy barrier is estimated theoretically to exceed the thermal energy by 4 orders of magnitude.
An aligned sample is obtained by strongly preshearing the system. After this preshear, the pure cholesteric sample displays at frequencies higher than 10 rad/s a typical Maxwell-fluid behavior: G''(w) = w eta and G’(w) = w^2 eta tau. (eta is the viscosity and tau is a relaxation time.)
A dramatic change in the measured moduli occurred when the same experiment is performed with particles added to the cholesteric. At high frequencies, the fluid-like behavior persists but at lower frequencies, G’ exhibits a pronounced increase compared to the pure cholesteric case, while G'' is not changed. This behavior reflects the elasticity of the oily streak defects present in the sample. Below w=1 rad/s, we observe a plateau in the storage modulus of magnitude 0.03 Pa, and furthermore the value of G’(w) exceeds that of the loss modulus G''(w) for w below 0.5 rad/s. This provides a clear signature of gel-like behavior.
Theoretical models have been developed which account for the elastic shear modulus at low frequencies and the crossover between the gel-like and the fluid-like behaviors and which are consistent with the rheological data. The theoretical part of this work is done in collaboration with Martin Zapotocky and Tom Lubensky.
Laurence Ramos completed
this work during her
postdoc with the Weitz group.
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