Structural crossovers of quasi-one-dimensional patchy hard superellipses

We study a quasi-one-dimensional associating fluid composed of hard superellipses carrying two patches interacting through a directional Kern--Frenkel potential. Using the Transfer Operator Method, we show that the selective patch--patch association promotes horizontal alignment and chain formation at low-to-intermediate densities, whereas hard-core interaction favours vertical alignment without bonds at high densities. The competition between these two mechanisms drives a structural crossover upon compression from a horizontally aligned bonded chain structure to a completely unbonded, vertically aligned structure. While patchy ellipses undergo a tilted-to-vertical realignment, patchy rectangle-like superellipses exhibit a horizontal-to-vertical change. These structural changes manifest as a plateau in the equation of state. To capture these properties, we generalise Wertheim's first-order thermodynamic perturbation theory by introducing an orientation-dependent fraction of sites not in a bond. When combined with the Parsons--Lee hard-body theory, the orientationally resolved perturbation theory provides quantitatively reliable results for the structural properties and phase behaviour. Therefore, the generalised Wertheim theory together with Parsons-Lee theory can be suitable in higher dimensions, too.