Pair correlation function and freezing transitions in a two-dimensional system of model ultrasoft colloids

Density functional theory (DFT) of freezing has been used to investigate the freezing transitions in a system of colloidal particles confined to a two-dimensional plane. The particles interact via a model Hertzian type potential of varying softness. The pair-correlation functions (PCFs) needed as input structural information in DFT are calculated by solving hypernetted chain (HNC) integral equation theory. The PCFs thus obtained have been compared with those obtained through experiment and simulations and are found to be in good qualitative agreement. We found that the PCFs are sensitive to the softness of the potential: showing splitting of pair-correlation peak in the harder case and anomalous non-monotonic density dependence in the softer case. Using the common tangent construction method, we have also proposed the fluid-triangular solid phase diagrams in the temperature-density plane. We found that the phase diagram exhibit solid-fluid coexistence region whose thickness decreases with the increasing temperature as well as with increasing softness of the potential. In the temperature and density range of our calculation, DFT fails to produce any reentrance in the phase diagram.