Liquid Instability and Freezing –Reductive Perturbation Approach–

Dynamical behaviour of a (metastable) liquid near the instability point is studied based on a Vlasov-Fokker-Planck equation (VFP eq.) or equivalently on a nonlinear diffusion equation (ND eq.) derivable from the VFP eq. on coarse-graining in space and time. Near the instability point the ND eq. is reduced, with the use of a reductive perturbation method, to a time-dependent Ginzburg-Landau (TDGL) equation for the order parameter W ( R , T ) for freezing. The TDGL equation shows that the second maximum of the structure factor S ( k ) at k =2 k 0 plays a crucial role in determining whether the TDGL equation is of a continuous type or of a discontinuous type, where k 0 is the wave-number at which S ( k ) takes its maximum.