Relaxation modes of the fluctuations of the order parameter in the vicinity of the uniaxial-to-biaxial nematic phase transition

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Abstract
A classical analysis of the relaxation modes of the fluctuations of the order parameter is developed in the vicinity of the uniaxial to biaxial nematic phase transition. Using polar coordinates, the 5 relaxation modes of the order parameter are followed across the uniaxial to biaxial nematic phase transition : 2 out of these modes are amplitude modes, and the 3 others are orientational modes. It is shown that the amplitude modes in the biaxial phase mix the components of biaxiality and birefringence of the order parameter, the critical (quasi-biaxial) mode presenting temperature variations twice larger than in the uniaxial phase, according to classical theory. The backflow effets on the pretransitional behaviour of the orientational modes are also studied in the uniaxial and biaxial nematic phases