WEAK CRYSTALLIZATION THEORY

We discuss the weak crystallization of a liquid or a liquid crystal which is a first-order phase transition close to a continuous one. Such a phase transition is accompanied by the softening of the order parameter, describing the short-wavelength density modulation. The softening occurring in the vicinity of certain lines or surfaces in the reciprocal space induces a number of characteristic peculiarities of the transition. Quantitatively the softening may be characterized by the value of the gap, figuring in the expression for the pair correlator of fluctuations of the order parameter. The value of the gap is small near the phase transition temperature and possesses a complex behaviour. A peculiarity of the weak crystallization is the important role of fluctuations of the order parameter accounted for by a large phase volume of the fluctuations. We investigate the behaviour of the gap both in the framework of mean field approximation and with the effects of fluctuations taken into account. The theory enables us to construct the phase diagram of the system which appears to be rather reach for all the considered cases. In this diagram there arise (depending on the strength of the anisotropy and fluctuations) both crystalline phases of different symmetry and smectic, columnar and quasicrystalline phases. The dynamics of the order parameter is pure relaxational and the respective kinetic coefficient proves to be insensitive to the phase transition, therefore the relaxation time is inversely proportional to the gap. All physical characteristics of the system in some degree depend on the proximity to the transition point. For example the heat capacity and the compressibility of the system have singular contributions which may be expressed explicitly through the value of the gap. The most singular behaviour near the phase transition is inherent in the bulk viscosity coefficients determining the sound attenuation.