(440h) Phase Diagram for a 2-D Colloidal System With An Isotropic Potential

We demonstrate how a two-dimensional paramagnetic colloidal system under the influence of a rotational magnetic field (PURM) can be used to induce an isotropic potential between the particles. The interaction potential well depth can be precisely tuned from 5kT to 40kT. We make use of this experimental system and complement our experiments with a Monte Carlo simulation to show how this system can be used to probe the phase behavior of systems that exhibit long-range attractive potentials, such as a monoatomic system.

A highly tunable long-range attractive interaction is induced by a rotating magnetic field generated by two pairs of coaxial air-core solenoids connecting with multi-frequency AC power supply. The solenoids are calibrated to be orthogonal to each other. The repulsive component to the interaction potential is the short-range electrostatic interactions. The potential well formed by summing the two interaction potentials and is tuned by changing the input voltage of power supply. The phase diagram can be mapped out by using samples of different particle concentration and different field strength.

In the Monte Carlo simulation, a density-dependent pair potential is used due to the many body effect shown by our previous study. We start from solving the Laplace equation that describes the magnetic field distribution of paramagnetic colloid system under external field. Then Maxwell stress tensor is used to calculate the magnetic force experienced on each particle and compare with superposed force from pair interaction. The density-dependent pair potential is obtained by the comparison above.

A grand canonical ensemble is used in the Monte Carlo simulation. A fixed chemical potential allows us to simulate phase transition from one phase to another without coexistence. Pressures and pair distribution function near transition have been plotted out to locate the phase point for transition for different densities. The temperature-density phase diagram is thus scanned, mapped out, and is in good agreement with that obtained from experiments. This phase diagram shows good qualitative agreement with the one obtained from experiment as well as the one of a typical atomic system.