Density functional theory of freezing for soft interactions in two dimensions

PACS. 64.10.+h – General theory of equations of state and phase equilibria. Abstract. – A density functional theory of two-dimensional freezing is presented for a soft interaction potential that scales as inverse cube of particle distance. This repulsive potential between parallel, induced dipoles is realized for paramagnetic colloids on an interface, which are additionally exposed to an external magnetic field. An extended modified weighted density approximation which includes correct triplet correlations in the liquid state is used. The theoretical prediction of the freezing transition is in good agreement with experimental and simulation data. A microscopic theory of freezing and melting is a great challenge in statistical physics. There are two complementary approaches to the liquid-to-solid transition: first, classical density functional theory [1–3] starts from liquid state and views the solid as a condensation of liquid density modes, hence it is a liquid-based approach. Second, crystal elasticity theory [4] is a solid-based theory where the liquid is viewed as a solid with an accumulation of defects. In three dimensions, the freezing transition is first order and it is known that it is not defect mediated. Here, density functional theory provides a molecular theory for the freezing transition. Crystal elasticity theory is appropriate to two dimensions and predicts a possible scenario of two-stage melting via an intermediate hexatic phase [5–8]. The advantage of density functional theory is that it can be used to calculate the structure of the solid, whereas it is not possible to extract the structure of the fluid out of crystal elasticity theory. An excellent realization of a two-dimensional system is provided by paramagnetic colloidal particles in a pendant water droplet, which are confined to the air-water interface [9]. If an external magnetic field is applied perpendicular to the interface, a magnetic moment is induced in the particles resulting into a tunable, mutual dipolar repulsion between them. The corresponding interaction pair potential u(r) is repulsive and soft, being proportional to 1/r 3 , with r denoting the distance between the particles. The prefactor can easily be tuned by varying the external magnetic field strength. In real-space experiments [10, 11], the two-stage melting process was confirmed with an intermediate hexatic phase which had a tiny stability range bracketed between the fluid and crystalline phase. There are also computer