Potential Barrier Heights and Phase Transition in Polyphenyls and Poly(p-Phenylene)

Abstract

The analysis from X-ray or neutron diffraction data, of the unusually high librational motion around the long molecular axis of the p-terphenyl central ring, reveals a doubly-peaked probability density function (p.d.f.), associated with a double-well potential function between two twisted conformations (φ = ± 13.3° on either side of the average molecular plane). This p.d.f. is the pretransitional effect of an order-disorder transition which takes place at low-temperature. With a simple model averaging the intermolecular interactions, it is possible to separate in the overall libration on each site, at the bottoms of the double well, the contribution of the torsional g mode (θ²) = 35 deg², responsible for the jumps above the barrier, from the contribution of the other modes (θ²) = 17.5 deg². Thus it becomes possible to determine the parameters of the model describing the intermolecular, as well as the intramolecular interactions and to specify the non-sinusoidal shape of the intramolecular potential between two adjacent phenyl rings. It is straightforward to extend the model to any p-polyphenyl molecule with any number of phenyl rings, by considering that the molecular packings are the same in all the family. The model gives an estimate of the reorientational potential barrier heights V = 4.57 kJ mol⁻¹ in p-terphenyl, V = 7.91 kJ mol⁻¹ in p-quaterphenyl, in good agreement with NMR results; the calculated p.d.f. are doubly peaked and V < kT at room temperature, which characterizes order-disorder transitions. On the other hand, the model gives a singly peaked p.d.f. and V = 1.25 kJ mol⁻¹ < kT in crystalline biphenyl, which agrees with the displacive nature of the phase transition. Combined with the features of the incommensurate phase of biphenyl at T = 20K, it gives an estimate of the interactions involved in the modulated phase, predicting a large increase of intermolecular interactions in biphenyl at low-temperature. Finally it is applied to poly(p-phenylene), predicting a twisted conformation in agreement with recent diffraction results and high reorientational barrier potentials.

Key Words:

• Polyphenyls
• biphenyl
• p-terphenyl
• p-quaterphenyl
• poly(p-phenylene)
• potential barrier
• structural phase transition.