Thermodynamic scaling and the characteristic relaxation time at the phase transition of liquid crystals

The longitudinal relaxation time tau of a series of alkyl-isothiocyanato-biphenyls (nBT) liquid crystals in the smectic E phase was measured as a function of temperature T and pressure P using dielectric spectroscopy. This relaxation time was found to become essentially constant, independent of T and P, at both the clearing point and the lower temperature crystalline transition. tau(T,P) could also be superposed as a function of the product TV(gamma), where V is the specific volume and gamma is a material constant. It then follows from the invariance of the relaxation time at the transition that the exponent gamma superposing tau(T,V) can be identified with the thermodynamic ratio Gamma=- partial differential log(T(c)) partial differential log(V(c)), where the subscript c denotes the value at the phase transition. Analysis of literature data on other liquid crystals shows that they likewise exhibit a constant tau at their phase transitions. Thus, there is a surprising relationship between the thermodynamic conditions defining the stability limits of a liquid crystalline phase and the dynamic properties reflected in the magnitude of the longitudinal relaxation time.