Liquid crystal quenched orientational disorder at an AFM-scribed alignment surface.

A polyimide substrate was scribed using the stylus of an atomic force microscope, then covered with a nematic liquid crystal. The fiber from a near field scanning optical microscope was immersed into the liquid crystal and rastered approximately 80 nm above the surface, thereby obviating smearing effects that occur in thicker samples. By appropriate averaging of multiple data sets, a histogram of the "frozen-in" director deviation Δφ from the average easy axis was obtained, having a full-width-half-maximum of ∼0.02 rad. Additionally, the spatial autocorrelation function of Δφ was extracted, where the primary correlation length was found to be comparable to, but larger than, the liquid crystal's extrapolation length. A secondary characteristic length scale of a few µm was observed, and is thought to be an artifact due to material ejection during the scribing process. Our results demonstrate the utility of nanoscale imaging of the interface behavior inside the liquid crystal.

Independent control of polar and azimuthal anchoring.

Monte Carlo simulation, experiment, and continuum theory are used to examine the anchoring exhibited by a nematic liquid crystal at a patterned substrate comprising a periodic array of rectangles that, respectively, promote vertical and planar alignment. It is shown that the easy axis and effective anchoring energy promoted by such surfaces can be readily controlled by adjusting the design of the pattern. The calculations reveal rich behavior: for strong anchoring, as exhibited by the simulated system, for rectangle ratios ≥2 the nematic aligns in the direction of the long edge of the rectangles, the azimuthal anchoring coefficient changing with pattern shape. In weak anchoring scenarios, however, including our experimental systems, preferential anchoring is degenerate between the two rectangle diagonals. Bistability between diagonally aligned and edge-aligned arrangement is predicted for intermediate combinations of anchoring coefficient and system length scale.

Competition of elasticity and flexoelectricity for bistable alignment of nematic liquid crystals on patterned substrates.

We show that patterned surfaces can promote bistable configurations of nematics for reasons other than the symmetry of the surface. Numerical and analytical calculations reveal that a nematic liquid crystal in contact with a striped surface is subject to the competing aligning influences of elastic anisotropy, differing energy cost of various types of deformation, and flexoelectricity, curvature-induced spontaneous polarization. These effects favor opposing ground states where the azimuthal alignment is, respectively, parallel or perpendicular to the stripes. Material parameters for which the effect might be observed lie within the range measured for bent-core nematogens.

Competing alignments of nematic liquid crystals on square-patterned substrates.

A theoretical analysis is presented of a nematic liquid crystal confined between substrates patterned with squares that promote vertical and planar alignment. Two approaches are used to elucidate the behavior across a wide range of length scales: Monte Carlo simulation of hard particles and Frank-Oseen continuum theory. Both approaches predict bistable degenerate azimuthal alignment in the bulk along the edges of the squares; the continuum calculation additionally reveals the possibility of an anchoring transition to diagonal alignment if the polar anchoring energy associated with the pattern is sufficiently weak. Unlike the striped systems previously analyzed, the Monte Carlo simulations suggest that there is no "bridging" transition for sufficiently thin cells. The extent to which these geometrically patterned systems resemble topographically patterned substrates, such as square wells, is also discussed.

Orientational transition in a nematic liquid crystal at a patterned surface.

We consider a semi-infinite nematic in contact with a periodic patterned surface with alternate planar and homeotropic stripes. Extending the work of Barbero, we find the free energy (assuming K1 = K3) for the situations where the easy direction on the planar stripe is either perpendicular or parallel to the length of the stripes. We find the bulk free energy difference between the structures to be proportional to square root(K2/K1) and so we consider the possibility of a spontaneous transition between the two states if the azimuthal anchoring energy is sufficiently weak and K1 not equal K2. We compute the critical azimuthal anchoring energy for such a transition in terms of the relative width of the stripes and the period of the pattern and find it to be approximately 10(-6) J m(-2), comparable to experimental values.

Energy and phase orientation mechanisms: a computational model.

A computational model is proposed for spatial orientation processing beyond the initial stage of linear filtering in visual cortex. The model accounts for orientation pop-out, edge location and orientation, and bar location and orientation. It naturally extends to higher order orientation symmetries. The model is consistent with much of the current understanding of early processing in mammalian visual cortex. It builds on the notions of orientation and spatial frequency specific simple cells, any subsequent non-linearity, and orientation 'pooling'. The processing treats simple cell energy, real, and imaginary responses in a unified way to generate 'feature maps'. The 'pooling' operation in each case is a discrete Fourier transform of the simple cell responses over orientation. The suggested processing has implications for psychophysics (e.g. providing an explanation of why orientation discrimination thresholds are more than an order of magnitude less than simple cell orientation bandwidths), provides some understanding of the variety of 'complex-cell' properties found in visual cortex, and provides a plausible starting point for subsequent processing.