Why does a twisted-nematic LCD appear transparent when no voltage is applied?
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.
A twisted-nematic (TN) liquid crystal display appears transparent when no voltage is applied because of the specific way the liquid crystal molecules interact with light and the display's polarizers.
In a TN cell, the top and bottom substrate plates are aligned so that their rubbing directions are perpendicular to each other. This forces the liquid crystal molecules to adopt a twisted configuration across the gap between the plates.1
The display is placed between two polarizers that are also oriented perpendicularly (crossed polarizers). Normally, crossed polarizers would block all light, making the cell appear dark. However, the twisted structure of the liquid crystal acts as an optical guide; as light passes through the cell, the twisted molecules rotate the polarization of the light to match the orientation of the second polarizer. This allows the light to pass through the exit polarizer, rendering the display transparent.1
When voltage is applied, this twisted state is destroyed, causing the molecules to align perpendicular to the plates, which prevents the rotation of light and results in a dark appearance.1