The incommensurate phase transition of biphenyl

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Abstract
The authors extend the model of phase III biphenyl (introduced by Heine and Price in 1985), based on enmeshed rotation of phenyl rings of neighbouring molecules, by including an intramolecular potential in the form of a double well: Vintra=1/2AQ2+1/4BQ4 where Q is the twist of one ring. Within this model, they study both the transition to the incommensurate phase and the possibility that this may be biphenyl's ground state as some experiments have indicated. They build up a coherent picture of biphenyl which includes the following physical properties: (i) the possibility of lack of lock-in as T to O; (ii) squaring up of the modulation as T drops below Tc; (iii) an optimal twist angle for the molecule in the solid (5.1 degrees ) that is lower than that in the vapour phase (21 degrees ); and (iv) the temperature of a notional I-III transition (which should be very close to the temperature of the actual I-II transition). This picture agrees both qualitatively and quantitatively with experimental results.