A Study of Flow Alignment Instability During Rectilinear Oscillatory Shear of Nematics

Rectilinear oscillatory shearing of nematic liquid crystals in thin large-area (10 cm × 8 cm × 10 μm) cells has been studied in the range 20 to 100 Hz for two uniform initial alignments, one planar and parallel to the direction of oscillation and the other homeotropic. In the former case, for certain positive values of the viscosity coefficient α₃ a flow-alignment instability occurs above a critical amplitude A_c for the displacement of the movable upper plate, leading to formation of regular cm-wide bands of alternating 2 π and -2 π twist, running parallel to the alignment direction. The width of the bands decreases with decreasing temperature and increasing frequency, the total number present depending on the size of the cell. In homeotropic alignment, similar bands of lower twist form at an angle to the direction of oscillation, in this case both for certain positive values of α₃ and, in addition, for α₃ slightly negative. A theoretical expression for A _c in the cases with α₃ > O has been derived and substantially confirmed experimentally. The theory further predicts the existence of a remarkable “stability gap” where, although the expression for A_c is a minimum, there is no instability and formation of bands should not occur. By exploiting the divergence of α₃ at a smectic A phase, theory and experiment have been compared over a wide range of α₃ values, and the stability gap confirmed experimentally for several materials. In the case of “weak” smectic phases (i. e., showing actual or incipient re-entrant behavior) the expected divergence of A_c does not occur until significantly inside the smectic phase range. Extrapolation of 1/A² _c against temperature can be used to locate accurately in the temperature at which α₃ is zero. A variety of materials has been studied, revealing that α₃ may be positive in a rather wider range of materials than had previously been realized, and that when α₃ is positive it usually remains so over most or all of the nematic range.