Theory of Uniaxial-Biaxial Nematic Phase Transition in Ribbon-Like Conjugated Polymers

The ribbon-like structure of conjugated and ladder-type polymers gives rise to orientational ordering phenomena beyond standard chain models. In this work, we study the uniaxial-biaxial nematic transition of infinitely stiff, rodlike chains that are twistable but not bendable, using a Maier-Saupe approach. We show that this transition is continuous (second-order), with mean-field exponent β = 1/2 for the biaxial order parameter. We consider two different torsional regimes: one with continuous twist along the backbone and one with localized twist at hinges. We predict a shift of the critical interaction parameter by a factor of π²/3 between the two cases. Beyond the onset, we provide interpolation formulas for the biaxial order parameter across interaction strengths and uncover distinct strong-ordering asymptotes: the hinged case approaches full biaxiality faster than the continuous-twist case.