Dynamics of kink bands in layered liquids: Theory and in situ SAXS experiments on a block copolymer melt

We consider the dynamics of an isolated kink band within an otherwise well- aligned lamellar block copolymer (or other smectic A liquid crystal) subjec ted to a macroscopic shear flow. We find on geometrical grounds that normal relative motion of the tilt boundaries that delineate such a band, relativ e to the normal velocity of the fluid, can occur only if there is jump in t he tangential component of the fluid velocity across the boundary. We show that such tangential slippage should be negligible for well-developed bands with narrow boundaries. These observations lead to a simple description of the evolution of an idealized kink band, in which the kink bandwidth remai ns constant after the formation of narrow tilt boundaries, and the tilt bou ndaries rotate as material surfaces in a shear flow. The resulting predicti on for the rate of rotation of the layers within such a band is confirmed b y in situ small-angle X-ray scattering (SAXS)-steady shear experiments, whi ch measure the evolution of the distribution of lamellar orientations withi n kink bands in a predominantly parallel poly(styrene-co-ethylenepropylene) diblock copolymer.