THE ERICKSEN NUMBER AND DEBORAH NUMBER CASCADES IN SHEARED POLYMERIC NEMATICS

Samples of liquid crystalline poly(gamma-benzyl-glutamate) solutions are sheared between glass surfaces with gaps, d=10-500 mu, and shearing velocities, V=0.05-10000 mus-1 so that the Ericksen number E= Vdgamma1/K is varied over a large range, E almost-equal-to 1-10(7). Here gamma1 is the rotational viscosity and K1 is the Frank splay constant, with gamma1/K1 estimated to be approximately 1 s mu-2 for our samples. We observe by polarizing microscopy a sequence of transitions with increasing Ericksen number analogous to that observed in small molecule tumbling nematics: namely rotation of the director out of the shearing plane and into the vorticity direction at V(d) almost-equal-to 25 mu2 s-1, and formation of roll cells at Vd almost-equal-to 50 mu2 s-1. The roll cells become finer with increased Vd in accord with predictions of linear stability theory using the Leslie-Ericksen equations, and at Vd greater than or similar to 500 mu2 s-1, the cells become very irregular, producing director turbulence. The turbulence becomes finer in scale as Vd increases, reaching sub-micron, and possibly molecular scales when Vd greater-than-or-equal-to 10(5) mu2s-1. At the highest velocities, transitions in orientation and texture are controlled by the Deborah number De=lambdaV/d, where lambda is the molecular relaxation time, and uniform texture-free samples are obtained when De greater than or similar to 5.