= Solution
Long anisometric molecules cannot pack independently. In the <Onsager excluded-volume mechanism>, two slender rods of length $L$ and diameter $D$ exclude a relative-position volume approximately $2L^2D|\sin\gamma|$, where $\gamma$ is their mutual angle. Aligning rods reduces this <excluded volume>, increasing the translational entropy available at a fixed <number density>. It simultaneously reduces orientational <entropy>. At sufficiently high concentration the positional gain wins, producing a <nematic liquid crystal> even for purely repulsive rods.
The <nematic director> is apolar: $\mathbf n$ and $-\mathbf n$ describe the same orientation. The molecules retain liquid-like positional disorder, in contrast to a <smectic phase> with layered order. A typical dimensionless concentration controlling the slender-rod competition is $cL^2D$, although finite aspect ratio, flexibility and attractions change the transition. The mechanism illustrates that ordering can increase total <entropy>: the lost orientational freedom is compensated by less mutual obstruction.
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