Why are the two polarizers in a twisted-nematic display placed at right angles to each other?
In nematic arrangements the crystals are randomly positioned with all their long axes pointing in essentially the same direction, given by a vector known as the director. In smectic arrangements the crystals are further constrained to parallel planes; in smectic A the director is perpendicular to these planes, while in smectic C the director is at some other angle to the planes.
In a twisted-nematic (TN) display, the two polarizers are placed at right angles to each other to control the transmission of light through the cell.12
When no voltage is applied, the liquid crystal molecules adopt a 90-degree twisted configuration that matches the orientation of the crossed polarizers. As light passes through the first polarizer, the twisted liquid crystal layer acts as an optical guide, rotating the polarization of the light by 90 degrees. This rotation aligns the light with the axis of the second polarizer, allowing it to pass through and making the cell appear transparent.12
When an electric field is applied, the liquid crystal molecules reorient perpendicular to the substrate plates, destroying the twisted state. In this condition, the liquid crystal can no longer rotate the light's polarization, causing the light to be blocked by the second polarizer and resulting in a dark appearance. By toggling this field, the display can create images by switching individual pixels between transparent and opaque states.12