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Why are the alignment directions of the two glass plates perpendicular in a twisted-nematic cell?

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Diagram comparing three liquid crystal phases: nematic with parallel rods aligned vertically, smectic A with rods arranged in horizontal layers, and smectic C with rods in tilted layers. — liquid crystal display Liquid crystal arrangements
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 cell, the alignment directions of the two glass plates are arranged perpendicularly to force the liquid crystal molecules into a 90-degree twisted configuration.12

This specific orientation is essential for the display's optical function when paired with crossed polarizers:

Light Transmission: In the absence of an electric field, the twisted structure of the liquid crystal molecules rotates the polarization of incoming light by 90 degrees. This rotation aligns the light with the axis of the top polarizer, allowing it to pass through and making the cell appear transparent.12
Light Blocking: When a voltage is applied, the liquid crystal molecules reorient perpendicular to the substrate plates, destroying the twisted state. Because the molecules no longer rotate the light's polarization, the light is blocked by the crossed top polarizer, causing the cell to appear dark.12

By setting the alignment layers at a 90-degree angle, the cell effectively acts as a light valve that can be switched between transparent and opaque states to create images.12