During the ice formation in the Arctic Ocean, small liquid-saline channels remain, which are colonised by various small microorganisms. The size of the ice domains separating regions of concentrated sea water depends on salinity and temperature and corresponds to the size of sea ice platelets obtained from a morphological stability theory for the solidification of salt water. We consider a pattern formation on the bases of the theory of phase transitions using the Landau-Ginzburg free energy. Instead of a reaction-diffusion kinetics with the formation of morphological Turing structures or the BCM-model modified thermodynamic approaches are considered. These are characterised by a total differential according to Schwarz’s theorem. We modify the original Kobayashi’s phase field model by including freezing point depression due to salt in order to describe the phase boundary of the fine network and cavities filled with brine which are formed during the freezing process in sea ice. A modified Cahn-Hilliard like model allows deeper supercooling temperatures than the modified Kobayashi approach and is therefore better suited for coupling to larger scales which can be realised by the extend Theory of Porous Media (eTPM). A linear stability analysis selects the parameter range that enables formation of structures. Initially, the diffusion parameter is time-dependent because of the changing porosity and tends towards a constant value at equilibrium.