  We show that the relative stability of the nematic tetratic phase with
respect to the usual uniaxial nematic phase can be greatly enhanced by
clustering effects. Two--dimensional rectangles of aspect ratio $\kappa$
interacting via hard interactions are considered, and the stability of the two
nematic phases (uniaxial and tetratic) is examined using an extended
scaled--particle theory applied to a polydispersed fluid mixture of $n$
species. Here the $i$--th species is associated with clusters of $i$
rectangles, with clusters defined as stacks of rectangles containing
approximately parallel rectangles, with frozen internal degrees of freedom. The
theory assumes an exponential cluster size distribution (an assumption fully
supported by Monte Carlo simulations and by a simple chemical--reaction model),
with fixed value of the second moment. The corresponding area distribution
presents a shoulder, and sometimes even a well-defined peak, at cluster sizes
approximately corresponding to square shape (i.e. $i\simeq\kappa$), meaning
that square clusters have a dominant contribution to the free energy of the
hard--rectangle fluid. The theory predicts an enhanced region of stability of
the tetratic phase with respect to the standard scaled--particle theory, much
closer to simulation and to experimental results, demonstrating the importance
of clustering in this fluid.
