The Orientational order in So-Called de Vries Materials

There is a great interest in smectic materials that show no layer shrinkage (NLS) in the transition from smectic A to smectic C. Such materials are often discussed in terms of ode Vries materialso or ode Vries behavioro after A. de Vries, who proposed different mechanisms for this NLS behavior, involving a significant tilt of the individual molecules in the smectic A phase. According to the original proposition of de Vries, the molecules are already tilted in this kind of smectic A phase, with a large constant tilt and the same tilt direction in each layer but random tilt direction between different layers. Despite the individual molecular tilt the smectic A phase remains uniaxial and the transition to the biaxial smectic C state is seen as a global ordering in the tilt directions. The model thus ad hoc predicts that there is zero layer shrinkage at the A - C transition. We refer to this model as the ohollow cone distributiono. As later pointed out by de Vries there are, however, other possible models for describing a tilt disorder (thermodynamically unavoidable) in the A phase. Nevertheless, the hollow cone has been a widely accepted model in the literature and is repeatedly referred to in discussing de Vries behavior or even taken as a basis for theories describing it. We discuss different smectic A orientational distribution functions that could be related to de Vries behavior or de Vries transitions. We find that two opposite models have comparable predictive power but only one gives a consistent picture together with existing data. Our conclusion is that the smectic A - smectic C transition can have a continuously changing character from a opure tilto to a opure de Vrieso, and we illustrate the orientational distribution functions in the A and C phases for these two limiting cases. We find that de Vries behavior is not related to any exotic distribution of hollow cone or similar kind in the A phase, but instead to an unusual combination of low nematic order and high smectic order in the de Vries smectic A. As the technical interest in such materials is considerable, a directed effort toward the synthesis of new optimized materials would be important