the nematic phase

The nematic is the simplest liquid crystal, the one closest to an ordinary liquid while still holding a whisper of crystalline order. Picture a great school of fish all facing the same way but swimming in a scattered, ever-shifting crowd, or logs floating down a river all pointing downstream yet drifting freely past one another. The molecules — usually rod-shaped — keep a shared average direction of pointing, but their centres of mass are as disordered and mobile as in any liquid. Orientation is ordered; position is not.

That average pointing direction is a single axis called the director, written n. It is headless, meaning n and minus n describe the same state, because a typical rod looks the same end for end. How tightly the rods hug the director is measured by the order parameter S = the average of (3 cos^2 theta minus 1) divided by 2, where theta is the angle each molecule makes with the director; S is 0 in a disordered liquid and would be 1 for perfect alignment, and a real nematic runs about 0.3 to 0.8, loosening toward 0 as you heat it to the clearing point. Because there is no positional order and no layering, the molecules diffuse and flow freely — a nematic pours like a slightly viscous liquid. The name comes from the Greek nema, thread: under the microscope nematics are laced with thread-like defect lines (disclinations) where the director direction becomes undefined.

The nematic is the liquid crystal that runs the world's flat-panel displays. In a twisted-nematic cell the director is anchored to twist a quarter-turn between two glass plates, guiding polarized light through so the pixel looks bright; apply a small voltage and the rods swing to line up with the field, the twist unwinds, the light is blocked, and the pixel goes dark. Because the nematic flows so readily, this switching is fast and needs very little energy — which is exactly why nematics, not more ordered smectics, became the basis of nearly every LCD.