STRUCTURAL PHASE-TRANSITION IN POLYPHENYLS .10. POTENTIAL BARRIER HEIGHTS IN CRYSTALLINE POLYPHENYLS AND IN GASEOUS BIPHENYL DETERMINED UNIQUELY FROM DIFFRACTION DATA

The analysis from X-ray or neutron diffraction data, of the librational motion around the long molecular axis of the p-terphenyl central ring permits resolution of its disorder: the phenyl rotation angle on either side of the average molecular plane is phi = +/- 13.3-degrees. This disorder is associated with a double-well potential between two twisted conformations, and the overall libration on each site, at the bottoms of the double well, has the mean-square amplitude <theta-2> = 52.5 deg2 at room temperature. The analysis also permits separation in <theta-2> of the mean-square amplitude of the torsional g mode <theta-i2> = 35 deg2 from that of the external mode <theta-e2> = 17.5 deg2. Thus it becomes possible to scale the parameters of a simple model describing inter- and intramolecular interactions in the whole family of polyphenyls. It is shown that the intramolecular potential between two adjacent phenyl rings cannot be described by a simple sinusoidal function but exhibits a steeper gradient near the planar conformation. This double potential well model accounts for disorder and libration in crystalline p-terphenyl and p-quaterphenyl. It gives an estimation of potential barrier heights: V = 4.57 kJ mol-1 in p-terphenyl and 7.91 kJ mol-1 in p-quaterphenyl in good agreement with NMR results. It agrees with the displacive nature of the biphenyl transition by giving in this case a barrier height, V = 1.25 kJ mol-1, significantly less than the thermal energy kT and a singly peaked probability density function associated with a large libration amplitude as observed experimentally. Combined with the estimation of librational amplitude from diffraction data it predicts a large increase of intermolecular interactions in biphenyl at low temperature and gives an estimation of the interactions involved in the low-temperature incommensurate phase of biphenyl. Indirectly it is one of the very few experimental determinations of the potential-energy curve for gaseous biphenyl, giving V0 = 10.82 kJ mol-1 for the planar conformation in agreement with the results of gas-phase electron diffraction for deuterated biphenyl.